Post-processing Routes for Design of Giant Magnetoimpedance Response and Domain Wall Dynamics Control in Glass-coated Magnetic Microwires

Pos -p ocessing Rou es o Design o
Gian Magne oimpedance Response
and Domain Wall Dynamics Con ol
in Glass-coa ed Magne ic Mic owi es
by
Paula Co e-León
Supe iso s
P o . D . A kady Zhuko Ego o a
P o . D . Julián Ma ía González Es é ez
Depa amen o de Políme os y Ma e iales A anzados: Física, Química y Tecnología
Facul ad de Ciencias Químicas
San Sebas ián, 2022
(cc) 2022 Paula Co e-León (cc by-nc 4.0)
Abs ac
The p incipal objec i e o his hesis is o in es iga e he pos -p ocessing ou es
o he op imiza ion o he magne ic p ope ies o cobal and i on based glass-coa ed
mic owi es acco ding o hei applica ions. Fo his pu pose se e al se ies o
mic owi es we e p epa ed and cha ac e ized paying a en ion on he e ec o pos -
p ocessing condi ions allowing maximizing magne ic so ness, Gian
Magne oimpedance (GMI) e ec and/o as domain wall (DW) dynamics con ol.
The wo k a emp s o gi e an o e iew o he uning possibili ies o glass-
coa ed mic owi es, which is one o he cha ac e is ics, in addi ion o hei simple
ab ica ion me hod and inexpensi eness ha make hem qui e a ac i e and sui able
o an eno mous ange o applica ions.
We ha e wo ked wi h nea ly-ze o magne os ic ion amo phous Co- ich glass-
coa ed mic owi es, o CoFeBSiC composi ion wi h small addi ions o Ni, Mo and C o C
and di e en diame e s, which p esen magne ic so ness in as-p epa ed s a e. The
esul s show ha app op ia e pos -p ocessing allows u he imp o emen o magne ic
so ness and GMI e ec . I is no ewo hy he ema kable GMI a io enhancemen (up
o 650%) achie ed by Joule hea ing a op imal condi ions o CoFeNiBSiMoC amo phous
glass-coa ed mic owi es.
Fo Fe and Fe-Ni based glass-coa ed mic owi es, wi h ec angula hys e esis
loops and hence, single DW p opaga ion in as-p epa ed s a e, DW dynamics is u he
imp o ed by u nace annealing owing o he in e nal s esses elaxa ion. On he o he
hand, low GMI a io is enhanced mo e han an o de o magni ude a e s ess-
annealing, Joule hea ing o combined s ess-annealed ollowed by con en ional
u nace annealing. Induced aniso opy depends on he pos -p ocessing condi ions.
Annealing was demons a ed as an e ec i e ool o op imizing magne ic
so ness and GMI e ec o FeSiBNbCu de i i ied mic owi es, bu de e io a ion and
poo mechanical p ope ies lead o ocus on pos -p ocessing ha allows main aining
he amo phous s uc u e.
Unique combina ion o GMI e ec and as single DW p opaga ion is ob ained
o FeBSiC amo phous glass-coa ed mic owi es wi h mode a e s ess-annealing
induced aniso opy. Such s ess-annealing induced aniso opy is ound o possess a
pa ially e e sible cha ac e . Subsequen annealing o s ess-annealed samples
allowed e e sing pa o he aniso opy induced by he s ess-annealing.
As a ule, Co- & Fe-based mic owi es p esen amo phous s uc u e i hei
diame e s a e below 30 µm. Fu he mo e, Fe- ich glass coa ed mic owi es o
FeBSiNbNi composi ion o abou 100

m o me allic nucleus, conside ed as “ hick”
mic owi es, a e success ully ob ained by modi ied Taylo Uli o sky echnique. “Thick”
mic owi es a e highly demanded o ce ain applica ions and ew documen ed. A e
p ope annealing desi able combina ion o high GMI e ec and single DW p opaga ion
is exhibi ed.
Likewise, o samples o bo h g oups o mic owi es a simple ou e o achie e
g aded magne ic aniso opy along he sample leng h is p oposed. G aded magne ic
aniso opy is sa is ac o ily achie ed a e s ess-annealing unde empe a u e g adien .
Finally, among he many possibili ies, a no el sensing echnology is p oposed
and explo ed in o de o illus a e he possibili y o implemen ing he use o glass-
coa ing mic owi es in sensing echnologies. Wi h his aim, as-p epa ed Co-based
mic owi es and s ess-annealed Fe-based mic owi es we e used o non-des uc i e
and non-con ac moni o ing o a composi e ma e ial wi h mic owi e inclusions.
Sensi i i y o such mic owi es o ensile s ess and empe a u e allows moni o ing
ma ix polyme iza ion p ocess o he composi e h ough he changes in he hys e esis
loops o he mic owi es. The sensi i i y o Fe- ich mic owi es o ensile s ess can be
imp o ed by he s ess-annealing induced aniso opy. Composi e polyme iza ion e ec
is obse ed o be opposi e o he e ec o applied ensile s ess on he hys e esis loops
o he mic owi e inclusions. The e o e, allows assuming comp essi e cha ac e o
s esses ac ing upon he mic owi es du ing he polyme iza ion p ocess. Addi ionally,
upon polyme iza ion conside able a ia ion o he ansmission and e lec ion
pa ame e s (in he ange o 4-7 GHz) o he composi e wi h mic owi e inclusions is also
obse ed by means o ee space echnique.
Resumen (Spanish)
El p incipal obje i o de es a esis es in es iga las u as de posp ocesamien o
pa a la op imización de las p opiedades magné icas de mic ohilos ecubie os de id io
basados en cobal o y hie o de acue do con sus aplicaciones. Pa a ello, se p epa a on y
ca ac e iza on a ias se ies de mic ohilos p es ando a ención al e ec o de las
condiciones de posp ocesado que pe mi ie an maximiza el compo amien o
magné ico blando, el e ec o de magne oimpedancia gigan e (GMI) y/o el con ol de la
dinámica de pa edes de dominio.
El abajo in en a da una isión gene al de las posibilidades de ajus e de las
p opiedades de los mic ohilos ecubie os de id io, que es una de las ca ac e ís icas,
además de su sencillo mé odo de ab icación y bajo cos o, que los hacen bas an e
a ac i os y ap os pa a una eno me gama de aplicaciones.
Se ha abajado con mic ohilos amo os ecubie os de id io icos en Co de
magne os icción casi nula, de composición CoFeBSiC con pequeñas adiciones de Ni,
Mo y C ó C y de di e en es diáme os, que p esen an compo amien o magné ico
blando sin necesidad de posp ocesado. Los esul ados mues an que el p ocesamien o
pos e io adecuado pe mi e una mejo a de la sua idad magné ica y el e ec o GMI.
Cabe des aca la no able mejo a del e ec o GMI (has a un 650 %) log ada op imizando
las condiciones de calen amien o po e ec o Joule en mic ohilos amo os ecubie os
de id io de composición CoFeNiBSiMoC.
Pa a los mic ohilos ecubie os de id io basados en Fe y Fe-Ni, con ciclos de
his é esis ec angula es y, que po lo an o, p esen an p opagación de una única pa ed
de dominio sin necesidad de a amien o de posp ocesado, la dinámica de pa edes de
dominio se mejo a aún más median e el ecocido en ho no debido a la elajación de
las ensiones in e nas. Po o o lado, el bajo a io GMI mejo a más de un o den de
magni ud después del ecocido bajo ensión, el calen amien o Joule o el ecocido bajo
ensión combinado seguidamen e de ecocido en ho no con encional. La aniso opía
inducida depende de las condiciones de posp ocesamien o.
Se demos ó que el ecocido es una he amien a e icaz pa a op imiza la
sua idad magné ica y el e ec o GMI en mic ohilos des i i icados de FeSiBNbCu, pe o
el de e io o de las p opiedades mecánicas lle an a cen a se en posp ocesado que
pe mi a man ene la es uc u a amo a.
Se ob iene una combinación única de e ec o GMI y p opagación ápida de una
única pa ed de dominio pa a mic ohilos amo os ecubie os de id io FeBSiC con
aniso opía inducida po ecocido bajo ensión mode ada aplicada. Se encuen a que
al aniso opía inducida po ecocido bajo ensión posee un ca ác e pa cialmen e
e e sible. El ecocido pos e io de mues as ecocidas bajo ensión pe mi ió e e i
pa e de la aniso opía inducida po el ecocido bajo ensión.
Gene almen e, los mic ohilos basados en Fe y Co p esen an es uc u a amo a
cuando sus diáme os es án po debajo de 30 µm. Se han ob enido con éxi o median e
la écnica modi icada de Taylo Uli o sky mic ohilos ecubie os de id io icos en Fe
de composición FeBSiNbNi de ap oximadamen e 100

m de núcleo me álico,
conside ados como mic ohilos "g uesos". Los mic ohilos “g uesos” son muy
demandados pa a cie as aplicaciones y es án poco documen ados. Después de un
ecocido adecuado, exhiben una combinación deseable de al o e ec o GMI y
p opagación de una única pa ed de dominio.
Asimismo, pa a mues as de ambos g upos de mic ohilos se p opone una u a
sencilla pa a log a una aniso opía magné ica g aduada a lo la go de la longi ud de la
mues a. La aniso opía magné ica g aduada se log a sa is ac o iamen e después del
ecocido bajo ensión bajo un g adien e de empe a u a.
Finalmen e, en e las muchas posibilidades, se p opone y explo a una nue a
ecnología de de ección pa a ilus a la posibilidad de implemen a el uso de
mic ohilos ecubie os de id io en ecnologías de de ección. Con es e obje i o, se
u iliza on mic ohilos a base de Co sin posp ocesa y mic ohilos a base de Fe ecocidos
bajo ensión pa a el con ol no des uc i o y sin con ac o de un ma e ial compues o
con inclusiones de mic ohilos. La sensibilidad de ales mic ohilos a la ensión de
acción y la empe a u a pe mi e moni o ea el p oceso de polime ización de la
ma iz del ma e ial compues o a a és de los cambios en los ciclos de his é esis de los

mic ohilos. La sensibilidad de los mic ohilos icos en Fe a la ensión de acción puede
mejo a se median e la aniso opía inducida po ecocido de ensión. A a és de los
ciclos de his é esis, se obse a que la polime ización de la ma iz del ma e ial
compues o iene un e ec o sob e las inclusiones de mic ohilo de ca ác e opues o a la
aplicación de ensión de acción sob e los mic ohilos. Po lo an o, pe mi e asumi el
ca ác e comp esi o de las ensiones que ac úan sob e los mic ohilos du an e el
p oceso de polime ización. Además, as la polime ización ambién se obse a una
a iación conside able de los pa áme os de ansmisión y e lexión (en el ango de 4-7
GHz) del compues o con inclusiones de mic ohilos.
Acknowledgmen s
Fi s o all, I wan o men ion P o . Ignacio Gue a, o being so much mo e han a
iend o e he yea s and ou i s guide in he esea ch wo ld.
I would be g a e ul o li e o P o . Blanca He nando o gi ing me he oppo uni y and
he encou agemen o ake his pa h, how no o do i keeping in mind he en husiasm. Also
P o . Víc o de la P ida and all he Magne ic Ma e ials and Nanoma e ials esea ch g oup a
he Uni e si y o O iedo.
All my g a i ude o my Supe iso s P o . Julián González Es é ez and P o . A kady
Zhuko o he suppo , guidance and con inuous help ecei ed om hem and especially om
P o . Valen ina Zhuko a, I admi e he in many aspec s, he mos impo an he human quali y,
and I will be always g a e ul o hei i eless help, also she in oduce me o he use o he
equipmen s needed and made me amilia in wo king on mic owi es. I deeply app ecia e he
ime and e o s hey made o me. This wo k has been accomplished hanks o hem.
Many since e hanks o ou en i e g oup, Juan Ma ía Blanco, Alexande Chizhik and
especially Mihail Ipa o o helping me in uncoun able occasions, I hones ly app ecia e hem,
hei iendship and he hings hey made o me. Wo king wi h hem was g a i ying and a
g ea pleasu e. I am e y glad o he place hey ga e me in hei g oup making me eel pa o
i since he i s day, and making easy my day o day, I am e y hank ul o hem o hei help
in all aspec s ha could con inue saying so much mo e. I wan o gi e a huge hank you o all
o hem.
I wan o gi e special hanks o P o . Ca los Ga cía, o he accep ance o my s ay a his
labo a o y in he Depa men o Physics o he Uni e sidad Técnica Fede ico San a Ma ía in
Valpa aíso, Chile, o his kind welcome, his help, iendship and suppo and he es o he
g oup, especially D a. Ma ián Abellán, o making he ime spen he e a aluable and
un o ge able expe ience.
I g ea ly hank P o . I an Ško ánek, Head o Depa men o Applied Magne ism and
Nanoma e ials a he Ins i u e o Expe imen al Physics o he Slo ak Academy o Sciences in
Košice, Slo akia o he accep ance o my i ual s ay, he ui ul collabo a ion ca ied ou , his
in aluable discussions and his kindness and e iciency and D . F an išek And ejka o his c ucial
and ex emely use ul assis ance and help.
Special hanks o Alexande To cuno and Vic o Muho o o le ing me in oduce in
he mic owi es ab ica ion p ocedu e, sha ing hei p iceless expe ience and also
un o ge able anecdo es.
I would also like o gi e special hanks o D a. Lo ena González-Lega e a and D a.
And ea Džubinská, co-wo ke s o sho ime, bu hei g ea help and iendship has been
essen ial, and Ahmed Talaa , doing he same pa h be o e me, o his kindness and suppo .
Many hanks o PhD colleagues Al onso Ga cía and Ál a o González who came o b ing
eshness o he g oup and also D . Mohamed Salaheldeen o his signi ican help and suppo
in he inal s ech.
I would like o hank D . Koldo Gond a and D a. Sand a Allue, ou collabo a ion
es ablished in he amewo k o ELKARTEK p ojec , allowed me in oduce mysel in he ield o
sma composi e ma e ials wi h he help o hei expe ise.
I am uly g a e ul o my iends, especially Co al, Alba, C is ina and Bea, o always
being he e o me.
I mus exp ess my g a i ude o Tousee , my husband, o been by my side, I wan o
p omise him ha all ou e o s will be wo h i . My child en, Hakim and Ay a, bo n a he
same ime ha his hesis b inging he bigges joy o my li e, o hem e e y hing makes sense.
Fo my pa en s I will ne e ha e enough wo ds o g a i ude o hei e o s in helping
me, o hem belongs he g ea es me i o his wo k. To my b o he o been always he bes
companion and counselo .
I would like o acknowledge o he echnical and human suppo p o ided by SGike
o UPV/EHU (Medidas Magné icas Gipúzcoa) and he Go e nmen o he Basque Coun y in
he amewo k o HAZITEK and ELKARTEK p ojec s and unde he scheme o “Ayuda a G upos
Consolidados” and Spanish MINECO o he inancial suppo o he g oup.
Finally, I hank he ollowing g an o inancial suppo : NEOHIRE-NEOdymium-I on-
Bo on base ma e ials, ab ica ion echniques and ecycling solu ions o HIghly REduce he
consump ion o Ra e Ea hs in Pe manen Magne s o Wind Ene gy Applica ion, H2020-
NMBP-720838, Eu opean Comission (Ho izon 2020).
This hesis is also de o ed o hose who a e no longe bu made us being he e.
Thanks o e e yone who has con ibu ed o his wo k.
Con en s
Pa I: Fundamen als ………………….……………………….………………………………………………………………………….
1-52
1. In oduc ion ……….…………………………………………………….……………………………………………………..……..
1
1.1. Me allic glasses ……..……………………………………….……………………………………………………..…………..
2
1.2. So magne ic ma e ials …………………………………………………………………….………………………..……..
3
1.3. Amo phous glass coa ed mic owi es ……………………………………………………………………….....……..
4
1.3.1. Fab ica ion me hod …………………………………………………………………….……………................
4
1.3.2. E ec o composi ion on magne ic p ope ies ………….…………………………..……..............
6
1.3.3. Hys e esis loops and domain s uc u e ………………………………………………..….……............
7
1.3.4. Induced aniso opies ………………………………………………….………………………..……..………….
9
1.3.5. Nanoc ys alline glass-coa ed mic owi es ……………………………………………..…………….……
11
1.4. Gian magne oimpedance (GMI) e ec …………………………………………………..…………..…………….
11
1.5. Magne ic bis abili y and Fas domain wall (DW) p opaga ion ………….…………………………………
13
1.6. Technological applica ions o magne ic glass-coa ed mic owi es …………………………..…………..
15
1.7. Resea ch s uc u e ………………………………..…………………………………………………………….…………….
18
1.8. Re e ences …………………………………………………………………………………………………………………………
19
2. Expe imen al echniques …………………………………………………………………………………………….………….
25
2.1. Glass-coa ed mic owi es ab ica ion: Taylo Uli o sky me hod ………….…………..…….….………..
25
2.2. Pos -p ocessing echniques: Annealing p ocedu es ……………………..…………....………….………….
27
2.2.1. Con en ional u nace annealing ……………………………………………………………………………..
27
2.2.2. S ess annealing ………………………………………………………………………………………………………
27
2.2.3. Cu en annealing ……………………………………………………………………………………………………
28
2.3. Magne ic cha ac e iza ion echniques …………………………………………………………..…………………..
29
2.3.1. Hys e esis in e omagne ic ma e ials ……..……………………….………………………….………….
29
2.3.2. Flux-me ic me hod o hys e esis loops measu emen s ……...……………….………………...
30
2.3.3. PPMS Magne ome e ……………………………..………………………….……….…………….……………..
33
2.3.4. Gian Magne o-Impedance (GMI) e ec measu emen s …………………..………..…………..
34
2.3.5. F ee space elec omagne ic pa ame e s measu emen sys em ……..…………….………….
37
2.3.6. Domain wall (DW) p opaga ion measu emen s ……………….…..……………..…………………..
39
2.3.7. Small angle magne iza ion o a ion (SAMR) echnique o magne os ic ion
measu emen s …………………………………………………………………………………………………………
40
2.4. Mic os uc u al cha ac e iza ion echniques …………………………………………………..….……….….…
43
2.4.1. Powde X- ay di ac ion (XRD) …………………………………….…………………………………….…..
43
2.4.2. Op ical mic oscopy (OM) ………………………………………..…………….………………………………..
45
2.4.3. Scanning Elec on Mic oscopy (SEM) ……………………………………….……………………………….
46
2.4.4. Di e en ial Scanning Calo ime y (DSC) ………….………………………….………………………….
47
2.5. Re e ences ………………………..…………………………………….………………………………..……………...……...
51
Pa II: Resul s and discussion …….…………..………………………………..……………………..…………………………..54-187
3. Enginee ing o magne ic p ope ies o Co- ich mic owi es ………………….…………………………....
54
3.1. As-p epa ed Co- ich mic owi es …….………………….…………………………..…………..….…….……………
55
In oduc ion 5
mechanical p ope ies a o emen ioned wi e p ope ies, he glass coa ing adds
an ico osi e p ope ies and biocompa ibili y [18].
Figu e 1.1. Glass-coa ed mic owi es cas ing a TAMAG Ibe ica, S.L., Spain (a).
SEM (b) and op ical (c) images o glass-coa ed mic owi e samples
( he glass coa ing has been cu and he me allic co e is exposed)
and sample o a mic owi e bobbin p oduced (d).
Among he apid mel quenching me hods o p oduce glass-coa ed
mic owi es, he p ocess used in his hesis consis s on he modi ied Taylo -
Uli o sky echnique, based on apid cooling o he mol en alloy. The main
easons a e: because o he dimensionali y educ ion ha i allows, wi h he
p oduc ion o he hinnes amo phous glass-coa ed me al mic owi es ( ypically
wi h 1 - 30 µm in diame e ) [19,20]; I is well known, being known since he ‘60s
[18], and including magne ic ma e ials since he ‘70s [21]; because i allows a
con olled manu ac u e o con inuous and homogeneous me allic mic owi es

Fundamen als: Chap e I 6
(Figu e 1d) (up o a ew kilome es) [22]; and i is sui able o ab ica ion o
magne ic mic owi es wi h ei he amo phous o nanoc ys alline s uc u e [22-
23].
As compa ed wi h c ys alline mic owi es, amo phous mic owi es
p esen high ensile s eng h alues ha a e obse ed o dec ease wi h he
inc ease in he me allic co e diame e s. This endency is explained by highe
cooling a es wi h dec easing me allic co e diame e s [24,25]. Now, while he
ensile s eng h in amo phous s a e seems o be due o he me allic co e o he
mic owi e, he addi ion o he glass coa ing does no seem o con ibu e
signi ican ly in he ac u e oughness. The glass a ound he ac u e poin
b eaks, no because o he s ess, bu because o he sound wa e p oduced by
he up u e o he me allic co e [26].
1.3.2. E ec o composi ion on magne ic p ope ies
The ene gy balance be ween long and sho - ange in e ac ions
de e mines he magne ic p ope ies o a ma e ial. In he case o amo phous
ma e ials, he absence o magne oc ys alline aniso opy, gi es a main ole o
he magne oelas ic aniso opy, Kme, gi en as [27,28]:
𝐾𝑚𝑒 = 3/2λ𝑆
σ
(1.1)
whe e λs is he magne os ic ion coe icien , σ = σi + σapp he o al s esses and
σi and σapp he in e nal and applied s esses, espec i ely. The e o e, in
amo phous mic owi es, s ess and magne iza ion a e linked and s ess can
ei he be sensed, o used as a mean o une he magne ic p ope ies.
The λs sign and alue o amo phous ma e ials p ima y depends on he
chemical composi ion. Acco dingly, he easies way o une he λs sign and
alue in amo phous alloys is o modi y hei chemical composi ion [27,28].
Thus, Fe- ich composi ions possess high and posi i e λs - alues (up o λs ≈ 40 x
10-6), while o he Co- ich alloys he magne os ic ion is low (up o λs ≈ -5 x 10-
In oduc ion 7
6) [28]. E en lowe λs alues can be ob ained by doping o Co- ich alloy wi h Fe
o Mn: λs can ake anishing alues in Co1-xFex o Co1-xMnx amo phous alloys a
0.05 ≤ x ≤ 0.1 [27,28]. Al e na i ely, low λs - alues can be achie ed in Ni1-xFex
alloys, while such alloys p esen a low sa u a ion magne iza ion, Ms, and hence
a e less in e es ing o applica ions [28].
In e nal s esses in glass-coa ed mic owi es (o he o de o 100-1000
MPa) a ise om he di e ence in he he mal expansion coe icien s o me allic
nucleus and glass coa ing [29]. They s ongly depend on he a io be ween he
glass coa ing hickness and me allic co e diame e , inc easing wi h he glass
coa ing hickness. Such la ge in e nal s esses gi e ise o a d as ic change o
he magne oelas ic ene gy, Kme, e en o small changes o he glass-coa ing
hickness a ixed me allic co e diame e [11].
Magne ic beha iou o each g oup o mic owi es depends on he
in e nal s esses alue and dis ibu ion. The e o e, magne ic p ope ies o he
glass–coa ed mic owi es can be ailo ed h ough he change o magne ic
aniso opy by ailo ing he in e nal s esses wi h adequa e pos -p ocessing
( u nace annealing, chemical e ching, e c.) o changing he composi ions o he
me allic nucleus.
1.3.3. Hys e esis loops and domain s uc u e
Depending on he magne os ic ion sign and alue amo phous glass-
coa ed mic ow ies can be di ided in h ee g oups. Figu e 1.2 e lec s he
hys e esis beha iou and domain s uc u e o he amo phous-glass coa ed
mic owi es ela ed o each g oup.
Co-based mic owi es wi h nega i e magne os ic ion coe icien usually
possess ci cula magne ic easy axis [30] and he e o e a e cha ac e ized by a
domain s uc u e consis ing o ci cula domains [31]. Magne iza ion p ocess in
axial di ec ion uns h ough e e sible o a ion o magne ic momen s inside
Fundamen als: Chap e I 8
domains. Almos linea loop wi h qui e low hys e esis is obse ed o hese
mic owi es when an axial magne ic ield is applied (Figu e 1.2a).
Nea ly ze o o low magne os ic ion coe icien s a e ound o Co-Fe-
based glass-coa ed mic owi es. The domain s uc u e o such mic owi es
consis s o axial domain s uc u e su ounded by ci cula domains [26].
Hys e esis loops o such mic owi es p esen e y low coe ci i y and high
pe meabili y (Figu e 1.2b).
Finally, Fe-based based glass-coa ed mic owi es wi h posi i e
magne os ic ion usually p esen ec angula hys e esis loop ela ed o hei
domain s uc u e consis ing o a la ge axially magne ized single domain
Figu e 1.2. Typical hys e esis loops and domain s uc u es o glass-coa ed
mic owi es wi h nega i e (a), nea ly ze o (b) and posi i e (c) magne os ic ion
coe icien . Adap ed om [32].
In oduc ion 9
su ounded by ou e domains wi h adial magne iza ion o ien a ion. In addi ion
o small closu e domains a he mic owi e ends in o de o dec ease he s ay
ields [32] (Figu e 1.2c). Magne ic bis abili y p esen ed o such mic owi es will
be u he discussed la e .
1.3.4. Induced aniso opies
The me as able amo phous s uc u e o glass-coa ed mic owi es makes
hem qui e sensi i e o hei en i onmen and pas his o y. One o he
impo an sou ces o aniso opies is he s ess induced du ing hei ab ica ion.
Aniso opy con ol is ex emely impo an o speci ic echnological
applica ions.
Annealing, a empe a u es below c ys alliza ion, allows o elax he
induced aniso opies as well as o c ea e new ones. Howe e , he a e o
change o s uc u al elaxa ion is a complex unc ion depending on he
annealing empe a u e and ime. Thus in o de o unde s and how aniso opies
a e a ec ed by annealing p ocesses, he elaxa ion phenomena i sel has o be
unde s ood [33].
The elaxa ion mechanism ha comp ises changes in olume, di usi i y
o iscosi y o he me allic glass is o i e e sible and mono onic cha ac e
(excep e y close o and abo e glass ansi ion empe a u e, Tg) [34]. On he
o he hand, a e e sible elaxa ion phenomena occu s when achie ing a
sa u a ed pseudo-equilib ium s a e a e p olonged annealing. Usually, he
sys em can mo e om one equilib ium s a e o ano he changing he annealing
empe a u e [35].
Se e al mechanisms a e p oposed o induced aniso opies including:
o de ing o a omic pai s ha esul s in di ec ional o de ing; easy-axis
alignmen ; s uc u al elaxa ion; shape aniso opy in luence due o mechanical
Fundamen als: Chap e I 10
g ain alignmen o s uc u al aniso opy associa ed o small aniso opic
s uc u al ea angemen s in sho a omic ange [36,37].
Annealing a modes empe a u es and annealing imes causes a
dec ease in he magne oelas ic aniso opy. Acco dingly, ele a ed annealing
empe a u e induces mac oscopic magne ic aniso opy wi h he p e e en ial
axis de e mined by he di ec ion o magne iza ion du ing he annealing [37].
He e, as an example he complex mechanism o induced aniso opies is
desc ibed o he case o Fe- ich mic owi es subjec ed o s ess-annealing (see
Figu e 1.3) [38-40]. In his case, s ess-annealing induced aniso opy is
associa ed o so called “back-s esses”. Annealing induces ans e sal
aniso opy and he s ess applied du ing he annealing induces longi udinal
aniso opy, esul ing in d as ic dec ease in he longi udinal s ess componen
and appea ance o comp essi e longi udinal s ess. Magne oelas ic ene gy is
minimized, wi h he edis ibu ion o he in e nal s esses and/o local
mic os uc u e.
Figu e 1.3. Schema ic illus a ion o e ec o s ess annealing in
Fe-based glass-coa ed mic owi es (Adap ed om [39]).

In oduc ion 11
1.3.5. Nanoc ys alline glass-coa ed mic owi es
Nanoc ys alline so magne ic ma e ials a e wo-phase ma e ials
consis ing o nanoc ys alli es andomly dis ibu ed in a so magne ic
amo phous phase. This g oup o magne ic ma e ials is conside ed o g ea
in e es due o hei excep ional so magne ic p ope ies [10].
The nanoc ys alline s a e is achie ed by c ys alliza ion o con en ional
Fe-Si-B amo phous alloys, p oduced since he ‘70s [41] wi h small addi ion o
Cu and Nb [42]. Fe-Si-B-Cu-Nb alloys ob ained a e usually known by adema k
name Fineme . Ul a ine g ain s uc u e wi h small c ys alli es (a ound 10 nm
g ain size) embedded in a esidual amo phous ma ix is ob ained a e ca e ully
annealing he amo phous p ecu so , a empe a u es be ween pa ial and ull
c ys alliza ion p ocesses in o de o a oid he de e io a ion o so magne ic
p ope ies.
The adjus men o he chemical composi ions and he annealing
pa ame e s o he de i i ica ion p ocess allow ob aining ma e ials wi h a he
di e en mic os uc u es. Al hough, mos esul s ha e been epo ed on
ibbons and wi es, ecen ly g ea a en ion has been paid also on
nanoc ys alline mic owi es [43,44].
The o igin o excellen so magne ic p ope ies in nanoc ys alline
mic owi es as well as he ou es o hei op imiza ion will be u he add ess in
he sec ion pa icula ly de o ed o hem.
1.4. Gian magne oimpedance (GMI) e ec
Fi s disco e ed in he ‘30s [45], i was no un il he la e ‘90s [46-48],
when high equency equipmen was a ailable, ha GMI esea ch ook o . The
GMI e ec is a skin e ec whe e he elec ical impedance o a ma e ial is linked
o i s magne iza ion, hus becoming an ideal way o p obing magne iza ion
Fundamen als: Chap e I 12
emo ely [49]. Ini ially s udied in wi es, GMI has been also epo ed in glass-
coa ed mic owi es [50], ibbons [51], mic o-pa e ned ibbons [52] and
mul ilaye s [53].
The key ad an age o magne ic senso s based on GMI is hei ul a-high
sensi i i y (up o 10% / A/m) [5,54]. When combining he la ge e ec o GMI,
wi h he capabili y o pe o m emo e measu emen s, and he ela i ely
inexpensi eness o so magne ic ma e ials, wi h hei low coe ci i ies, he
mix u e p oduces an ideal combina ion o p oduce senso s a a low-cos and
wi h high signal- o-noise a io.
Consequen ly, o he magne ic mic owi es s udied he e, he esea ch
pays a en ion on his e ec o ack magne iza ion, and h ough magne iza ion
changes sense o he magni udes (e.g., s ess).
Figu e 1.4 schema ically shows he GMI beha iou exhibi ed by Fe- ich
mic owi es wi h axial magne ic aniso opy and nea ly ze o magne os ic ion Co-
ich glass-coa ed mic owi es. GMI esponse o Fe- ich glass-coa ed mic owi es
p esen s a single maximum o H = 0 (Figu e 1.4a). On he o he hand, double-
peak beha iou is obse ed o nea ly ze o magne os ic ion samples (Figu e
1.4b). The la e samples a e he mos in e es ing due o he la ge GMI e ec
Figu e 1.4. Typical GMI beha iou o Fe- ich mic owi es (a)
and nea ly ze o magne os ic ion Co- ich mic owi es (b).
In oduc ion 13
and be e so ness. Howe e , Co belongs o c i ical aw ma e ials; he e o e,
g ea e o s a e paid o op imize he GMI esponse in less–expensi e Fe- ich
glass-coa ed mic owi es as p omising solu ion [55].
1.5. Magne ic bis abili y and Fas domain wall (DW) p opaga ion
A magne ic ma e ial is conside ed bi-s able when i s magne iza ion has
wo p e e ed o ien a ions, and he ansi ion be ween hese wo s a es occu s
h ough a single domain wall (DW) ha a els he ma e ial wi hou su e ing
any pinning. This is a desi ed beha io in ce ain si ua ions, because i simpli ies
analyzing he beha io o he ma e ial.
Such DW p opaga ion can be d i en ei he by a magne ic ield [56] o by
an elec ic cu en [50]. Roughly linea dependencies o DW eloci y, , on
magne ic ield, H, epo ed o a magne ic ield d i en DW dynamics a e well
unde s ood in e ms o he iscous DW mo ion [56].
DW p opaga ion in a iscous egime wi h a eloci y, , can be gi en as
[56]:
𝑣 = 𝑆(𝐻 − 𝐻0)
(1.2)
whe e S is he DW mobili y, H is he axial magne ic ield and H0 is he c i ical
p opaga ion ield.
Fundamen als: Chap e I 14
Figu e 1.5. Typical (H) dependence o magne ic
ield d i en DW dynamics [57].
Non-linea (H) dependencies can be obse ed ei he in low ield o a
high ield egions (see Figu e 1.5).
A e S. Pa kin ace ack memo y p oposal in 2008 [58], using he
concep o DWs o s o e in o ma ion, DW mo ion con ol has a ac ed
inc easing a en ion o a as numbe o p omising applica ions ( ace ack
memo ies, magne ic senso s, magne ic ags, e c.). Such applica ions equi e
as magne iza ion swi ching and con ollable DW p opaga ion. Despi e hei
g ea s abili y, he mal ac i a ion and pinning lead o s ochas ic beha io o he
DW mo ion ha needs o be add essed [59].
Amo phous glass coa ed mic owi es wi h posi i e magne os ic ion
cons an gene ally exhibi spon aneous magne ic bis abili y o igina ed by a
single and la ge Ba khausen jump be ween wo emanen s a es wi h opposi e
magne iza ion. As abo e desc ibed, pe ec ly ec angula hys e esis loops
obse ed o hese mic owi es a e ela ed o axial magne iza ion o ien a ion
wi hin he mos pa o he me allic co e o he mic owi e [60,61]. The
magne iza ion swi ching (be ween he wo emanen s a es) uns by as DW
p opaga ion, s a ing om he closu e domains a he mic owi e ends [62].
Thus, magne ically bis able mic owi es a e a unique ma e ial o DW
In oduc ion 21
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Fundamen als: Chap e II 25
2. Expe imen al echniques
This chap e is dedica ed o he desc ip ion o he di e en expe imen al
echniques employed in his esea ch wo k. A b ie desc ip ion o he undamen al
backg ound o each echnique and he pa icula expe imen al se -up condi ions used
is gi en, om sample p epa a ion o magne ic, mic os uc u al and composi ional
cha ac e iza ion o he glass coa ed mic owi es p oduced.
2.1. Glass-coa ed mic owi es ab ica ion: Taylo Uli o sky me hod
Taylo Uli o sky apid solidi ica ion echnique o glass-coa ed mic owi es
manu ac u ing allows he p epa a ion o hinnes amo phous mic owi es (wi h
Figu e 2.1. Glass coa ed mic owi es cas ing machine.
Expe imen al echniques 26
me allic nucleus diame e s anging om 0.5-40

m). This ab ica ion me hod consis s
o mel ing a p e-p epa ed ingo o me allic alloy inside a glass ( ypically Py ex o
Du an) ube using a high equency induc o [1,2].
Figu e 2.1. shows he cas ing machine o he glass-coa ed mic owi es
p oduc ion. Few g ams o he me al alloy wi h he sui able chemical composi ion a e
placed inside a glass ube. A high equency induc o mel s he me al o ming a d ople
which so ens he glass ube adjacen allowing a capilla y o o m. Then, he capilla y
illed wi h he mol en alloy is d awn and wound on a o a ing bobbin. As a esul , a
mic owi e wi h me allic co e and lexible and insula ing glass coa ing is ob ained.
Table 2.1. Composi ions and geome y o s udied glass-coa ed mic owi es.
Composi ion
Me allic
Nucleus
Diame e
d (μm)
To al
Diame e
D (μm)
Ra io
ρ=d/D
Magne os ic ion
Coe icien
λs × 10−6
Fe77.5B15Si7.5
15.1
35.8
0.42
38
Fe75B9Si12C4
15.2
17.2
0.88
38
Fe70B15Si10C5
3
18,75
0.16
35
Fe70B15Si10C5
6
23,08
0.26
35
Fe70B15Si10C5
10.8
22.5
0.48
35
Fe70B15Si10C5
15
23,8
0.63
35
Fe71.7B13.4Si11Nb3Ni0.9
103
158
0.65
35
Fe71,8Cu1Nb3,1Si15B9.1
7.0
24.8
0.282
30
Fe71,8Cu1Nb3,1Si15B9.1
18.2
39
0.467
30
Fe70.8Cu1Nb3.1Si14.5B10.6
11.8
14.4
0.8
30
Fe70.8Cu1Nb3.1Si14.5B10.6
15.6
21.8
0.7
30
Fe70.8Cu1Nb3.1Si14.5B10.6
10.7
16.4
0.6
30
Fe62Ni15.5Si7.5B15
14.35
33.25
0.43
27
Fe47.4Ni26.6Si11B13C2
29
32.2
0.9
25
Fe49.6Ni27.9Si7.5B15
14.2
33.85
0.42
20
(Fe0.7Co0.3)83.7Si4B8P3.6Cu0.7
26.5
22.3
0.84
Fe83.7Si4B8P3.6Cu0.7
15.5
17.5
0.89
Co65.4Fe3.8Ni1B13.8Si13C1.65Mo1.35
18.8
22.2
0.85
−1
Co69.2Fe3.6Ni1B12.5Si11C1.2Mo1.5
22.8
23.2
0.98
−1
Co69.2Fe4.1B11.8Si13.8C1.1
25.6
30.2
0.85
−0.3
Co67Fe3.9Ni1.5B11.5Si14.5Mo1.6
25.6
26.6
0.96
−0.29
Co64.04Fe5.71B15.88Si10.94C 3.4Ni0.03
95
130
0.73
Co66C 3.5Fe3.5B16Si11
20.1
24.8
0.81

Fundamen als: Chap e II 27
Fe-, Ni-, Fe-Co- and Co- based mic owi es wi h mino me alloid addi ions (Si, B, P,
C) o non-magne ic me als ha e been p epa ed and s udied. The composi ions,
geome y and magne os ic ion coe icien , λs, o s udied mic owi es a e shown in
Table 2.1.
2.2. Pos -p ocessing echniques: Annealing p ocedu es
2.2.1. Con en ional u nace annealing
The mos ex ended annealing echnique is he hea ing o he sample a a gi en
empe a u e, Tann, in ai o acuum o a gi en ime, ann, in a con en ional u nace. A
single piece o a bunch o mic owi es can be ea ed a he same ime.
The samples we e hea ea ed a a empe a u e, Tann, ypically anging om
200 °C o 500 °C in a con en ional u nace, The molyne 62700. Typically, he
c ys alliza ion o amo phous mic owi es was epo ed o Tann ≥ 490 °C. The ad an age
o amo phous mic owi es is hei supe io mechanical p ope ies ypically epo ed o
amo phous ma e ials [3]. In mos cases, we ixed he annealing ime, ann, o 60 min
which is usually used o hea ea men o amo phous and nanoc ys alline ma e ials
[4]. The samples we e slow cooled o oom empe a u e wi hin he u nace.
2.2.2. S ess annealing
In se e al cases, ensile s ess was applied wi h a mechanical load a ached o
one mic owi e end du ing he annealing, as well as du ing he sample cooling in he
u nace.
The s ess alue in he me allic nucleus, σm, was e alua ed conside ing di e en
Young’s modulus o me al, E2, and glass, E1, as ollows [5]:
𝜎𝑚=𝐾∙𝑃
𝐾∙𝑆𝑚+𝑆𝑔𝑙 ; 𝜎𝑔𝑙 =𝐾
𝐾𝑆𝑚+𝑆𝑔𝑙
(2.1)
Expe imen al echniques 28
whe e K = E2 / E1, P is he applied mechanical load and Sm, and Sgl a e he c oss sec ions
o he me allic nucleus and he glass coa ing, espec i ely.
2.2.3. Cu en annealing
Also know as Joule hea ing, in his echnique a sample is annealed by he
cu en ha passes h ough i causing i s hea ing by Joule e ec . I is widely used due
o i s simplici y and low cos , he equipmen needed is simila as he one used o
esis i i y measu emen s [6].
Cu en annealing allows a be e con ol o he annealing ime wi hou
comp omising he mechanical and chemical p ope ies o he mic owi es as compa ed
wi h con en ional u nace annealing [7].
The cu en densi y is di ec ly ela ed o he sample hea ing [8]. The dc cu en
alue, I, needs o be se clea ly below he alue ha can p oduce magne ic ha dening
and/o c ys alliza ion o he samples in o de o a oid he de e io a ion o magne ic
p ope ies [9]. S uc u al elaxa ion and c ys alliza ion also depend on a g ea ex end
on he annealing ime [10].
Fo ou s udies, elec ical con ac s we e p epa ed by mechanically emo ing
he insula ing glass coa ing on he e y end o mic owi es. Cu en annealing, wi h
di e en du a ions and applying di e en cu en s was pe o med in ai on 8 cm long
samples. The insula ing glass-coa ing o he mic owi es allows pe o ming he he mal
ea men s in ai .
In o de o a oid he inhomogenei ies o he mic owi e diame e (and
co esponding cu en densi y a ia ion) and s esses ela ed o he sample cu ing, we
used he same mic owi e o s udies o he in luence o annealing ime, o a ixed DC
cu en alue, on magne ic p ope ies and GMI e ec .
Fundamen als: Chap e II 29
2.3. Magne ic cha ac e iza ion echniques
2.3.1. Hys e esis in e omagne ic ma e ials
The g aphical ep esen a ion o he magne iza ion e sus he applied ield o a
e omagne in he p ocesses o magne iza ion and demagne iza ion gi es as a esul a
closed cu e, called he hys e esis loop.
Figu e 2.2. Typical hys e esis loop o a e omagne ic ma e ial.
Hys e esis loops cha ac e ize he s a e o he sample s udied. Figu e 2.2 shows
a ypical hys e esis loop o a bulk e omagne ic sample [11]. Ini ially, he ma e ial is
demagne ized and he applied ield is ze o (M = H = 0), inc easing he alue o he ield
H he i s magne iza ion cu e Oabc is ob ained. F om ze o o he poin a he sample is
magne ized by he e e sible p ocess o he domain on ie s mo emen . Be ween a
and b he magne iza ion inc eases by an i e e sible p ocess o he domains on ie s
mo emen and be ween b and c inc eases mainly by he domains magne iza ion
o a ion, being c he poin o magne iza ion sa u a ion, Ms. Dec easing om c he
alue o he ield H up o ze o we each he poin o emanen magne iza ion o
Expe imen al echniques 30
emanence, M , since he magne iza ion o he sample is no cancelled due o he non
e e sibili y o he domains on ie s mo emen , he sample magne iza ion does no
e u n o he ini ial demagne ized s a e, each magne iza ion domain o a es back o
he nea es easy di ec ion. To cancel his magne iza ion i is needed o apply a ield
wi h he app op ia e alue and in he opposi e di ec ion, called coe ci e ield o
coe ci i y, Hc. Inc easing he ield in his di ec ion he sa u a ion is also eached.
The sa u a ion magne iza ion, Ms, is de e mined by he composi ion, in e nal
s uc u e and empe a u e o he ma e ial and he coe ci e ield, Hc, and emanence
M , a e de e mined by he aniso opy o he sample. The coe ci i y also depends on
he impe ec ions (in e nal s esses dis ibu ion o de ec s).
The a io be ween he magne iza ion and he applied ield, gi en by he slope
o he hys e esis cu e, is called he suscep ibili y, 𝜒, o he ma e ial [12]:
𝜒=𝑀
𝐻
(2.2)
The a ea enclosed by he hys e esis loop is equal o he ene gy dissipa ed by
he sample in a magne iza ion cycle. Ha d magne ic ma e ials ypically ha e a squa e
shape hys e esis loop, wi h high coe ci e ield, Hc, (a equi emen o many
applica ions, such as memo y de ices), as he ma e ial is so e he hys e esis loop
ends o be mo e linea , he a ea inside he cycle is smalle and hence, he hys e esis
loss is lowe , a desi able cha ac e is ic o so magne ic ma e ials ( o applica ions like
magne ic senso s).
2.3.2. Flux-me ic me hod o hys e esis loops measu emen s
One o he main and i s s eps o he cha ac e iza ion o magne ic mic owi es
is i s hys e esis loop analysis, ha will allow us o ob ain magne ic pa ame e s such us
coe ci e ield, Hc, aniso opy ield, Hk, emanen magne iza ion, M and magne ic
sa u a ion, Ms. Hys e esis loops can be ob ained by he induc ion luxme ic me hod
based on he Fa aday-Lenz law, ha es ablishes ha wi h he magne ic lux,


Fundamen als: Chap e II 37
A specially designed mic os ip sample holde (shown in Figu e 2.6) placed
inside a solenoid su icien ly long o p o ide a homogeneous ield allows measu ing o
he magne ic ield dependence o sample impedance, Z(H), using ec o ne wo k
analyze (Agilen N5230A VNA) om he e lec ion coe icien , S11, aking in o accoun
he ollowing exp ession [21]:
𝑍= 𝑍0(1+𝑆11)
(1−𝑆11)
(2.14)
being
Z
0 = 50  he cha ac e is ic impedance o he coaxial line and S11 is he e lec ion
coe icien . Desc ibed echnique allows measu ing he GMI e ec in an ex ended
equency, , ange, up o GHz equencies.
2.3.5. F ee-space elec omagne ic pa ame e s measu emen sys em
F ee-space echnique o e s se e al ad an ages o measu emen o
elec omagne ic pa ame e s o composi e ma e ials. This non-con ac me hod allows
non-des uc i e measu emen s unde di e en empe a u e o en i onmen al
condi ions [22,23].
The expe imen al se -up used in his wo k o e lec ion (R) and ansmission (T)
coe icien s measu emen consis s o a pai o b oadband ho n an ennas (1-17 GHz), a
Figu e 2.6. Mic os ip line o GMI measu emen s o he mic owi es.

Expe imen al echniques 38
ec o ne wo k analyze (Agilen N5230A VNA) and an anechoic chambe (see Figu e
2.7).
The composi e is placed in he middle o he anechoic chambe wi h he
mic owi es o ien a ion along he elec ic- ield o he inciden elec omagne ic wa e.
The desi ed equency ange o measu emen o he sca e ing pa ame e s,
de e mines he equi emen s o he ope a ing equency o he VNA, an ennas and o
he chambe size (dis ance be ween an ennas and sample) [23].
The size o he sample needs o be la ge han he wa eleng h o he inciden
elec omagne ic wa e in o de o achie e con incing esul s. In ac , o u he
minimize he e ec s o he sca e ings om he sample bounda y, he sample size
should be a leas wice la ge han he wa eleng h [24]. Acco ding o his, in ou
expe imen s, he composi e was placed in 20 x 20 cm2 window o a oid he edge
e ec s. This window limi s he applicable equency ange in 4-17 GHz.
Figu e 2.7. F ee space mic owa e measu emen se -up o measu emen o he
elec omagne ic pa ame e s in composi e ma e ial
a he Applied Physics Dep . o UPV/EHU.
Fundamen als: Chap e II 39
2.3.6. Domain Wall (DW) p opaga ion measu emen s
The magne ic ield d i en domain wall (DW) p opaga ion has been s udied using
modi ied Six us-Tonks me hod c The main di e ences o used me hod om he classical
Six us-Tonks [25] se -up a e he ollowing: a sys em o h ee pick-up coils is employed
(see Figu e 2.8) [26], ins ead o a nuclea ion coil, since small closu e domains
spon aneously appea a he end o he wi e in o de o dec ease he s ay ield. In
addi ion, one sample end is placed ou side he magne iza ion coil o ensu e a single DW
p opaga ion a oiding mul iple DW p opaga ion and hence o e es ima ing he
magni ude o DW eloci y.
S udied mic owi e samples (usually o abou 10 cm long) we e placed inside he
h ee coaxially pick-up coils. Ra he homogeneous axial magne ic ield was gene a ed by
a 140 mm long solenoid (10 mm in diame e ). The DW a elling along he sample
induces an elec omo i e o ce (EMF) in he pick-up coils ha is eco ded by an
oscilloscope. Then, eloci y, , o a DW a elling along he sample can be es ima ed as
[27]:
Figu e 2.8. Schema ic pic u e o he expe imen al se -up o
DW dynamics measu emen s in mic owi es [27].
Expe imen al echniques 40
= l
Δ
(2.15)
wi h l he dis ance be ween pick-up coils and Δ he ime in e al be ween he EMF
peaks gene a ed when mo ing DW c osses he pick-up coils [26].
Fo e alua ion o he DW injec ion inside he sample and nuclea ion ield p o ile,
we used a sho magne izing coil o apply local magne ic ield [28,29]. Loca ed nex o
he sho pick-up coil, he sho magne izing coil allows de ec ing local magne iza ion
e e sal a su icien ly la ge dis ance om he ends o he wi e. Then, by slowly mo ing
he wi e h ough he sho magne izing coil is possible o measu e he leng h
dis ibu ion o he local magne iza ion e e sal (DW injec ion) ields o each sample.
2.3.7. Small angle magne iza ion o a ion (SAMR) echnique o
magne os ic ion measu emen s
Magne ic p ope ies o amo phous alloys s ongly depend on he magni ude o
he magne os ic ion, which causes he change in he dimensions o a magne ic
ma e ial du ing he magne iza ion. Di ec magne oelas ic e ec has small in luence (o
he o de o ≈ 10-5-10-7) bu he in e se e ec , i.e., he change in he magne iza ion o
a e omagne ic ma e ial due o he applied mechanical s ess is signi ican . The e o e,
o he op imiza ion o he magne ic p ope ies o magne ic mic owi es i is ele an o
quan i y he alue o he magne os ic ion. The e a e se e al indi ec me hods o he
de e mina ion o he sa u a ion magne os ic ion cons an , 𝜆𝑆. In he p esen wo k,
Small Angle Magne iza ion Ro a ion (SAMR) echnique, in oduced in 1980s [26,28], is
employed.
Figu e 2.9. Schema ic pic u e o he se -up o magne os ic ion
measu emen s in mic owi es.
Fundamen als: Chap e II 41
As can be seen om Figu e 2.9, du ing he measu emen s he ini ial ensile
s ess, σ0, is c ea ed by a weigh , P, a ached o he mic owi e end. In his me hod he
sample (o abou 10 cm long) is sa u a ed by an axial DC magne ic ield, Hz, c ea ed
along he mic owi e z -axis using a solenoid, while applying simul aneously a small ac
ans e se ield, Hy, c ea ed by an AC elec ic cu en lowing along he sample. The
combina ion o hese ields leads o a e e sible o a ion o he magne iza ion wi hin a
small angle,

, ou o he axial di ec ion. The induc ion ol age, V(2

), due o he
magne iza ion o a ion, is de ec ed by a pick-up coil wounded a ound he mic owi e.
This signal is ampli ied o i s de ec ion in he measu ing block. The AC cu en alue,
lowing h ough he wi e is selec ed o a oid possible Joule hea ing o he sample: he
cu en ampli ude does no exceed 10-30 mA.
The magne os ic ion coe icien ,

s, is de e mined om he measu emen o
he dependence on axial magne ic ield, Hz, e sus applied s ess

o di e en
mechanical loads, a ixed alue o induc ion ol age V(2

), acco ding o he
exp ession [30,31]:
𝜆𝑆= −𝜇0𝑀𝑆
3 (𝑑𝐻
𝑑𝜎)
(2.16)
whe e

oMs is he sa u a ion magne iza ion o he sample ob ained om
magne iza ion cu es measu ed a high applied ield and oom empe a u e.
Expe imen al echniques 42
Addi ional de ails on SAMR me hod and se -up ea u es designed o e alua ion
o magne os ic ion coe icien ,

s, can be ound in e s. [30,31].
The SAMR me hod is success ully employed o he e alua ion o Co- ich glass-
coa ed mic owi es wi h nega i e magne os ic ion coe icien as i was o iginally
de eloped o magne ic ma e ials in which magne iza ion o a ion go e ns he
magne iza ion p ocess. Recen ly, i has also been ex ended o e alua ion o
mic owi es wi h posi i e magne os ic ion coe icien [32,33]. Indeed, in Co- ich
mic owi es ci cula magne iza ion o ien a ion was expe imen ally obse ed by a ious
expe imen al echniques (Figu e 2.10a), while Fe- ich mic owi es p esen adial
magne iza ion o ien a ion (Figu e 2.10b) [34]. Acco dingly, magne iza ion o a ion in
he ou e domain shell can be obse ed in bo h kinds o mic owi es [32,33].
Figu e 2.10. Schema ic pic u e illus a ing domain s uc u e
o Co- ich (a) and Fe- ich (b) mic owi es.

Fundamen als: Chap e II 43
2.4. Mic os uc u al cha ac e iza ion echniques
2.4.1. Powde X- ay di ac ion (XRD)
X- ay di ac ion allows he s uc u al cha ac e iza ion o amo phous and
c ys alline ma e ials. Elec omagne ic wa es, in his case X- ays, a e di ac ed when
hey encoun e an obs acle, and his e ec is inc eased when he size o he obs acle is
compa able o he wa eleng h inciden on he ma e ial. Then, i is possible o explo e
he s uc u e o solids by s udying he di ac ion pa e ns o an inciden wa e wi h
wa eleng h compa able o he dis ance be ween a oms.
When an X- ay beam s ikes a solid ma e ial, pa o his beam is sca e ed in all
di ec ions by he elec ons associa ed wi h he a oms o he ma e ial o ions ha
encoun e s along he way, bu he es o he beam can gi e ise o he X- ay
di ac ion phenomenon, which akes place i he e is an o de ed a angemen o
a oms (long ange) and a e ul illed he condi ions gi en by B agg's Law [35] (Figu e
2.11) ha ela e he wa eleng h,

o he X- ays and he in e a omic dis ance, dhkl,
be ween he amily o planes (hkl), wi h he angle o incidence o he di ac ed beam,

(B agg angle). This law is desc ibed by he ollowing equa ion [35]:
𝑛𝜆=2𝑑ℎ𝑘𝑙𝑠𝑖𝑛𝜃
(2.17)
whe e n is an in ege ha ep esen s he o de o e lec ion. This equa ion allows us o
ob ain he angula posi ion o he di ac ion peaks o he c ys alline solid ha is
analyzed.
Expe imen al echniques 44
The s uc u e o he samples in he p esen wo k has been analyzed using
B uke (D8 Ad ance) X- ay di ac ome e (Figu e 2.12) wi h CuKα (λ = 1.54 Å)
adia ion, ope a ed a applied ol age o 40 KV and ilamen cu en o 30 mA. The
sample is a ached o he di ac ome e sample holde and each scan is made o e
he wo he a angula ange o 30 o 90 deg ees, s ep size o 0.05°and a s ep ime o 30
second o each s ep. The di ac ion peaks a e indexed using JCPDS (Join Commi ee
on Powde Di ac ion S anda ds) da abase.
Figu e 2.12. B uke (D8 Ad ance) X- ay di ac ome e pic u e [36].
Figu e 2.11. Schema ic pic u e illus a ing B agg's Law o di ac ion.
Fundamen als: Chap e II 45
A wide halo cha ac e is ic o comple ely amo phous ma e ials was obse ed in
he case o amo phous (as-p epa ed o annealed) glass-coa ed mic owi es.
2.4.2. Op ical Mic oscopy (OM)
The diame e s o he me allic nucleus and glass coa ing o he di e en
mic owi es employed in his wo k and he homogenei y along hei leng h was
checked by means o an op ical mic oscopy, in ou case Mic oscope Axio Scope A1 (as
shown in Figu e 2.13), ha uses isible ligh and a sys em o lenses o magni y images.
This mic oscopy allows o ob ain a wo-dimensional image o he mic owi es. The
mic owi e is placed in he mic oscope s age on a slide (a hin la piece o glass) o
check i s geome y.
Figu e 2.13. Mic oscope Axio Scope A1. Sou ce Ca l Zeiss
Mic oscopy GmbH and own elabo a ion (Adap ed om
Mic oscope Axio Scope A1 use manual).
Expe imen al echniques 46
The sys em con en s a ious lenses, which a e placed in he mic oscope column
below he emission chambe and si ua ed one abo e he o he . The condense lens
allows o ob ain a pa allel and hin beam o ligh o m he illumina o o p ope
illumina e and ocus he ligh on he sample. The objec i e lens collec s he ligh
di ac ed om he sample and o ms he i s image o he objec and he
in e media e lens o g oup o lenses (called he eyepiece) ampli y his image ha
inally is p ojec ed by he p ojec ion lens. The quali y o he image depends on he
con as , esolu ion and he ocal dep h o he mic oscope. Illumina ion sou ces and
objec i es can be manipula ed o adjus he image.
2.4.3. Scanning Elec on Mic oscopy (SEM)
Chemical composi ion, mic os uc u e and ex e nal mo phology o he mic owi es
once hey a e ob ained and a e he he mal ea men s, we e cha ac e ized by
Scanning Elec on Mic oscopy, (SEM). The equipmen employed a he UPV/EHU was a
MEB JEOL JSM-7000F (Figu e 2.14) wi h ene gy-dispe si e X- ay spec oscopy (EDX)
op ion wi h an Inca Ene gy 350 spec ome e . The mic oscope has a ield emission
sou ce (Scho ky ype).
In his echnique, a hin beam o high-ene gy accele a ed elec ons is concen a ed
by elec omagne ic lenses and ocuses on he su ace o a hick an opaque sample. The
beam scans he su ace o he sample in a as e scan pa e n, wi h a eloci y
synch onized wi h he posi ion in a compu e sc een o c ea e he image. As a esul o
he in e ac ion, di e en ypes o adia ion a e p oduced. The emi ed elec ons and
hose ha bounce o he su ace (Auge elec ons, seconda y and backsca e ed
elec ons) a e collec ed by a senso . Seconda y elec ons emi ed by he nea es o he
su ace a oms o he sample allow o ob ain he images o he su ace. Thei in ensi y
depends on he inciden angle and hus, on he opog aphy o he su ace, and i is
p opo ional o he co esponden spo on he image o he sample a he sc een. To
acili a e he emission o he elec ons he sample is coa ed wi h a conduc i e me al,
usually Au.
Fundamen als: Chap e II 53
[34] Y. Kabano , A. Zhuko , V. Zhuko a, J. Gonzalez, Magne ic domain s uc u e o wi es
s udied by using he magne o-op ical indica o ilm me hod, Appl. Phys. Le . 87 (2005)
142507, doi:10.1063/1.2077854.
[35] D.B. Culli y, Elemen s o x- ay di ac ion, 2-Edi ion: Addison-Wiley Publishing Company
Reading (1978).
[36] B uke Co po a ion, h ps://www.b uke .com/en/p oduc s-and-solu ions/di ac ome e s
and-sca e ing-sys ems/x- ay-di ac ome e s/d8-ad ance- amily/d8-ad ance.h ml.

Resul s and discussion: Chap e III 54
Pa II: Resul s and discussion
3. Enginee ing o magne ic p ope ies o Co- ich mic owi es
As men ioned be o e, non-exis ence o magne oc ys alline aniso opy in
amo phous ma e ials makes he magne oelas ic aniso opy he main sou ce o
magne ic aniso opy [1]. Magne oelas ic aniso opy depends on he magne os ic ion
coe icien , λs, and he applied and in e nal s esses (eq. (1.1)).
The λs sign and alue o amo phous ma e ials is mainly gi en by he chemical
composi ion. The e o e, chemical composi ion modi ica ion allows o adjus λs sign
and alue [1,2]. Co-based alloys posses low magne os ic ion alues (up o λs ≈ -5 x 10-
6) and ea ly ze o magne os ic ion alues can be ob ained doping Co-based alloys wi h
Fe o Mn [1,2].
The o he impo an pa ame e is he in e nal s esses, σi, alue. Once he
composi ion is chosen, he magne ic p ope ies can be op imized by modi ying he
in e nal s esses wi h he selec ion o he sample geome y, desc ibed by he

- a io
be ween he me allic nucleus diame e , d, and he o al mic owi e diame e , D, and
he app op ia e pos -p ocessing. In his chap e , Co-based mic owi es o di e en
cha ac e is ics, i.e., composi ions and diame e s, and hence di e en magne os ic ion
coe icien s,

s, will be p esen ed wi h he desc ip ion and discussion o he pos -
p ocessing selec ed o hem wi h he aim o op imize i s magne ic so ness and
imp o e he Gian Magne oimpedance (GMI) e ec and domain wall dynamics.
The magne ic so ness is in insically ela ed o he GMI e ec o igina ed by he
dependence o he skin dep h, δ, o a magne ic conduc o on applied magne ic ield, H,
as p e iously de ined by eq. (2.8) [1]. Fo cha ac e iza ion o he GMI e ec i will be
used he GMI a io,

Z/Z, as de ined in eq. (2.9) [1]. The GMI a io op imiza ion is
linked o imp o emen o magne ic so ness.
Enginee ing o magne ic p ope ies o Co- ich mic owi es 55
The in luence o each con ollable pa ame e in all he pos -p ocessing ypes
selec ed has been s udied, in o de o ge a comple e o e iew o he adjus ing
pa ame e s o he op imiza ion o he magne ic p ope ies.
Table 3.1 summa izes he main cha ac e is ics o he Co- ich mic owi es
s udied.
Table 3.1. Composi ions, geome y and magne os ic ion coe icien s o s udied Co- ich glass-
coa ed mic owi es.
Sample Nº
Composi ion
d (μm)
D (μm)

= d/D
λs x 10-6
1
Co69.2Fe3.6Ni1B12.5Si11Mo1.5C1.2
22.8
23.2
0.98
-1
2
Co69.2Fe4.1B11.8Si13.8C1.1
25.6
30.2
0.85
-0,3
3
Co65.4Fe3.8Ni1B13.8Si13Mo1.35C1.65
18.8
22.2
0.85
-1
4
Co67Fe3.9Ni1.5B11.5Si14.5Mo1.6
25.6
26.6
0.96
-0.29
5
Co64.04Fe5.71B15.88Si10.94C 3.4Ni0.03
95
130
0.73
6
Co66C 3.5Fe3.5B16Si11
20.1
24.8
0.81
3.1. As-p epa ed Co- ich mic owi es
Figu e 3.1a-d shows he hys e esis loops o 4 o he Co- ich mic owi es
selec ed. The mic owi e samples ha e nega i e magne os ic ion coe icien and in as-
p epa ed s a e exhibi qui e so magne ic p ope ies, e lec ed in a ypical linea and
inclined hys e esis loop wi h low coe ci i y [1], below Hc ≈ 10 A/m.
Resul s and discussion: Chap e III 56
X- ay di ac ion (XRD) pa e ns o s udied mic owi es p esen a wide halo, in
as-p epa ed and annealed s a e, cha ac e is ic o comple ely amo phous ma e ials [3],
as can be seen in Figu e 3.2 o sample 3.
-600 -300 0 300 600
-1
0
1
Co69.2Fe3.6Ni1B12.5Si11Mo1.5C1.2
M/M0
H (A/m)
(a)
Sample 1
-1000 -500 0 500 1000
-1
0
1
H (A/m)
M/M0
Sample 2
Co69.2Fe4.2B11.8Si13.8C1.1
(b)
-1000 -500 0 500 1000
-1
0
1
Co65.4Fe3.8Ni1B13.8Si13Mo1.35C1.65
M/M0
H(A/m)
Hk
(c)
Sample 3
-200 -100 0 100 200
-1
0
1
Co67Fe3.9Ni1.5B11.5Si14.5Mo1.6
M/M0
H (A/m)
Sample 4
(d)
-75 0 75
-1
0
1
Figu e 3.1. Hys e esis loops o as-p epa ed Co69.2Fe3.6Ni1B12.5Si11Mo1.5C1.2
(a), Co69.2Fe4.1B11.8Si13.8C1.1 (b), Co65.4Fe3.8Ni1B13.8Si13Mo1.35C1.65 (c) and
Co67Fe3.9Ni1.5B11.5Si14.5Mo1.6 (d) mic owi es.
Enginee ing o magne ic p ope ies o Co- ich mic owi es 57
F om he s udied mic owi es, in Figu e 3.3a a e p esen ed he samples wi h
simila composi ion o compa ison o he e olu ion o he hys e esis loop wi h he

− a io inc ease. In Figu e 3.3b can be seen he dec ease o he aniso opy ield, Hk, as
he

− a io inc eases.
40 60 80 100
0
500
1000
1500
2000 Sample 3
I (a b. uni .)
2 (deg.)
Figu e 3.2. XRD di ac ion pa e n o as-p epa ed
Co65.4 Fe3.8Ni1B13.8Si13Mo1.35C1.65 mic owi e.
-900 -600 -300 0 300 600 900
-1
0
1

= 0,98 Sample 1

= 0,85 Sample 3

= 0,96 Sample 4
M/M0
H (A/m)
(a)
0,80 0,85 0,90 0,95 1,00
200
300
400
500
600
Hk (A/m)

(b)
Figu e 3.3. Hys e esis loops o as-p epa ed Co- ich mic owi es o simila
composi ion s udied (a) and Hk (

) dependence o mic owi es
samples 1, 3 and 4 (b).
Resul s and discussion: Chap e III 58
3.2. Pos -p ocessing e ec on magne ic p ope ies, GMI e ec and DW
dynamics o Co- ich mic owi es
3.2.1. Con en ional u nace annealing in Co- ich mic owi es
A e annealing a su icien ly high empe a u e, simila ly o epo ed esul s
o Co- ich mic owi es wi h anishing λs [4], he hys e esis loop shape u ns in o
ec angula . Co69.2Fe3.6Ni1B12.5Si11Mo1.5C1.2 mic owi es (sample 1) annealed a 250 °C
and 350 °C du ing 60 min p esen conside able magne ic ha dening, pe ec ly
ec angula hys e esis loops wi h almos he same coe ci i y, Hc ≈ 90 A/m, can be seen
in
Figu e 3.4, o he di e en annealing empe a u es, and an inc ease in he
emanen magne iza ion, M , is obse ed.
The in luence o he annealing empe a u e on GMI a io p esen ed in
Figu e 3.4 was s udied a a equency o 200 MHz, gi en ha Co- ich mic owi es
p esen maximum GMI a io alues a a equency, , anging om 100 o 200 MHz [5].
-600 -300 0 300 600
-1
0
1Sample 1
M/M0
H (A/m)
As-p epa ed
250 ºC
350 ºC
Figu e 3.4. Hys e esis loop o Co69.2Fe3.6Ni1B12.5Si11Mo1.5C1.2 mic owi e
as-p epa ed and annealed a di e en empe a u es du ing 60 min.

Enginee ing o magne ic p ope ies o Co- ich mic owi es 59
Simila endency was obse ed in se e al Co- ich mic owi es wi h anishing
magne os ic ion coe icien [1,4]. Consequen ly, obse ed endency in ha dening o
Co- ich mic owi es and ans o ma ion o inclined hys e esis loops in o ec angula is
o gene al cha ac e .
ΔZ/Z(H) dependences obse ed in Figu e 3.5 show a dec ease a e annealing a
200 °C, howe e , annealing a highe empe a u es, Tann o 250 °C and 300 °C, gi e as a
esul an inc ease in he maximum GMI a io, ΔZ/Zmax. Hmax, he ield o maximum
ΔZ/Z(H), becomes lowe wi h inc easing he annealing ime, changing ΔZ/Z(H)
dependence shape, om he double-peak dependence shown in as-p epa ed and
annealed a 200 °C samples o a shape o decay wi h he magne ic ield inc ease
p esen ed o he samples annealed a highe annealing empe a u e, Tann.
ΔZ/Z(H) dependence shape, can be explained in e ms o he magne ic
aniso opy dis ibu ion o he mic owi e me allic nucleus and he skin pene a ion
dep h,

, and i s dependence on he equency gi en by eq. (2.8) [1,6].
Acco ding o eq. (2.8),

as a unc ion o he a io be ween RDC, he DC-
esis ance o he wi e, and RAC, he eal componen o he impedance, RDC/RAC, can be
exp essed as [7]:
-15 -10 -5 0 5 10 15
0
100
200 Sample 1
Z/Z (%)
H (kA/m)
As-p epa ed
200 ºC
250 ºC
350 ºC
Figu e 3.5. ΔZ/Z(H) dependences measu ed a 200 MHz o
Co69.2Fe3.6Ni1B12.5Si11Mo1.5C1.2 mic owi e as-p epa ed and
annealed a di e en empe a u es du ing 60 min.
Resul s and discussion: Chap e III 60
𝛿 = 𝑟[1−(1−𝑅𝐷𝐶/𝑅𝐴𝐶)1/2]
(3.1)
whe e is he wi e adius.
The inne axially mic owi e adius, Rc, is ela ed o he emanen magne iza ion
and he e o e, can be es ima ed om he educed emanence, M /Ms, using he
ela ion [1,3]:
𝑅𝐶= 𝑟(𝑀𝑟/𝑀𝑆)1/2
(3.2)
One o he impo an pa ame e s o GMI e ec cha ac e iza ion is he
maximum GMI a io, ΔZ/Zmax, de e mined om he ΔZ/Z(H) dependencies [1,3].
ΔZ/Zmax e olu ion upon annealing, as i is e lec ed in Figu e 3.6, o annealing
empe a u es o 250 °C and 300 °C gi es highe ΔZ/Zmax alues o he whole equency
ange s udied.
I is impo an o no e, ha o Co- ich mic owi es wi h magne ic bis abili y
induced by annealing i was p e iously epo ed a dec ease in he GMI a io [4].
The magne ic ha dening obse ed in
Figu e 3.4 can be explained by he change o he magne os ic ion coe icien
om nega i e o posi i e associa ed o he in e nal s esses elaxa ion o o he
domain s uc u e modi ica ion consis ing o he onse and g ow h o he inne axially
magne ized single domain a he expense o he ou e domain shell wi h ans e se
magne ic aniso opy [1,4,5]. Ob iously, con en ional u nace annealing canno be
conside ed as app op ia e p ocessing o magne ic so ness imp o emen o Co- ich
mic owi es.
Enginee ing o magne ic p ope ies o Co- ich mic owi es 61
Acco dingly, addi ional e o s ha e been paid o imp o e magne ic so ness o
Co- ich mic owi es.
3.2.2. S ess-annealing in Co- ich mic owi es
A sys ema ic s udy o he in luence o applied ensile s ess du ing he
annealing o di e en applied s esses, empe a u es and annealing imes was ca ied
ou o Co69.2Fe3.6Ni1B12.5Si11Mo1.5C1.2 mic owi e, co esponding o labeled sample 1
and Co69.2Fe4.1B11.8Si13.8C1.1, sample 2.
The ensile s ess wi hin he me allic nucleus, applied o he sample hanging a
mechanical load o one end o he mic owi e du ing he sample hea ing and slow
cooling wi hin he u nace, has been e alua ed ollowing he equa ion p e iously
desc ibed (eq.(2.1)):
𝜎𝑚=𝐾 ∙𝑃
𝐾 ∙ 𝑆𝑚+𝑆𝑔𝑙
(3.3)
being K = E2/E1, he a io o he Young’s moduli a oom empe a u e o he me allic
alloy, E1, and he glass, E2. P is he mechanical load applied and Sm and Sgl a e he c oss
200 400 600 800 1000
0
50
100
150
200
Z/Zmax (%)
(MHz)
As-p epa ed
200 ºC
250 ºC
350 ºC
Sample 1
Figu e 3.6. Maximum GMI a io dependences on equency o
Co69.2Fe3.6Ni1B12.5Si11Mo1.5C1.2 mic owi e as-p epa ed and
annealed a di e en empe a u es o Tann = 60 min.
Resul s and discussion: Chap e III 62
sec ions o he me allic nucleus and glass coa ing, espec i ely. The applied s ess
wi hin he me allic nucleus anges om 0 o 472 MPa.
Simila ly o he case shown in
Figu e 3.4, magne ic ha dening is achie ed upon con en ional annealing [8].
The linea hys e esis loop o as p epa ed sample u ns in o ec angula (Figu e 3.7a)
o he sample annealed wi hou applied s ess, wi h an inc ease in he coe ci i y,
om H ≈ 5 A/m up o Hc ≈ 93 A/m.
S ess-annealing allows o manipula e he hys e esis loop cha ac e and he
magne ic so ness: a in e media e Tann and σm wi h he applica ion o s ess du ing he
annealing, he coe ci i y expe imen s a no iceable dec ease and he emanen
magne iza ion inc eases. Figu e 3.7b shows he in luence o he empe a u e in he
s ess-annealing ea men , coe ci i y dec eases wi h he empe a u e inc ease.
This endency changes wi h he inc ease o Tann and σm, a Tann = 300 oC, Hc
con inues o dec ease, while M /M0 begins o dec ease wi h inc easing σ (see Figu e
3.8a). S ess-annealed a Tann = 300 oC samples p esen ec angula hys e esis loops
shape wi h a he low Hc (Figu e 3.8a).
-200 -100 0 100 200
-1,0
-0,5
0,0
0,5
1,0
Sample 1
M/M0
H (A/m)
As-p epa ed
0 MPa
118 MPa
354 MPa
472 MPa
Tann= 350 ºC
ann = 60 min
(a)
-200 -100 0 100 200
-1,0
-0,5
0,0
0,5
1,0
M/M0
H (A/m)
As- p epa ed
Tann=200 oC
Tann=300 oC
Tann=350 oC
Tann=375 oC
(b)

= 354 MPa
ann = 60 min
Sample 1
Figu e 3.7. Hys e esis loop o as-p epa ed and s ess annealed wi h di e en applied
s esses a 350 °C (a), as-p epa ed and s ess annealed wi h 354 MPa a
di e en empe a u es (b) Co69.2Fe3.6Ni1B12.5Si11Mo1.5C1.2 mic owi es.
Enginee ing o magne ic p ope ies o Co- ich mic owi es 69
The e o e, he DW p opaga ion was measu ed o he samples p esen ing
induced magne ic bis abili y. Ob ained (H) dependencies a e p esen ed in Figu e 3.14,
whe e i can be app ecia ed he in luence o annealing empe a u e.
High DW eloci y is obse ed o he mic owi es annealed a 325 oC (see Figu e
3.14) wi h a non-mono onic dependence o he DW eloci y on he annealing
empe a u e. The la e can be associa ed o he annealing in luence on he sign and
alue o he magne os ic ion coe icien , λs, [12]. As a ule, an inc ease o λs upon
annealing is ound o Co-based mic owi es [13].
Consequen ly, he annealing in luence on he magne oleas ic aniso opy, i.e,
s esses elaxa ion and magne os ic ion coe icien modi ica ion, is e lec ed on he
e olu ion o he DW dynamics and as well as in he GMI e ec p e iously analyzed.
S ess annealing was p esen ed as a use ul ool o he imp o emen o he GMI
e ec . The s ess-induced aniso opy is expec ed o a ec bo h GMI a io and DW
dynamics.
A selec ed s ess-annealing condi ions, whe e he hys e esis loops shape
emains ec angula , i can be assumed ha he samples can p esen single domain
wall p opaga ion ela ed o a single Ba khausen jump.
020 40 60
0
1000
2000
3000

= 354 MPa
Tann = 200ºC
Tann = 300ºC
Tann = 325ºC
Tann = 350ºC
(m/s)
H (A/m)
(a)
ann = 60 min
030 60 90 120
0
1000
2000
3000
ann = 60 min
Tann = 350ºC

= 0 MPa

= 118 MPa

= 236 MPa

= 354 MPa
(m/s)
H (A/m)
(b)
Figu e 3.15. (H) dependences measu ed o Co69.2Fe4.1B11.8Si13.8C1.1 mic owi es s ess-annealed
wi h 354 MPa a di e en Tann (a) and o he sample annealed a
Tann = 350 oC wi h di e en applied s esses du ing he annealing.

Resul s and discussion: Chap e III 70
Figu e 3.15a p esen s he in luence o he annealing empe a u e o a ixed
alue o he applied s ess du ing he annealing. I can be obse ed upon inc ease o
he annealing empe a u e a g adual inc ease o he mobili y, S, (slope o he cu e)
and he DW eloci y. In he same way, in Figu e 3.15b he e is e lec ed an inc ease o S
- alues upon

ising o a ixed Tann.
Figu e 3.16 shows he in luence o he ensile s ess applied du ing he
annealing a Tann = 300 oC o ann = 60 min. All he samples p esen single DW
p opaga ion wi h almos pe ec ly linea (H) dependencies (desc ibed by eq. (1.2))
and qui e high DW eloci ies.
Fe3.6Co69.2Ni1B12.5Si11Mo1.5C1.2 mic owi es annealed wi hou s ess p esen he
highes DW eloci y o abou 3 km/s (Figu e 3.16). Howe e , he ield ange o single
DW p opaga ion is a he sho (be ween 83 and 93 A/m). Ex ended ield ange is
obse ed o s ess-annealed Fe3.6Co69.2Ni1B12.5Si11Mo1.5C1.2 mic owi es. DW eloci y
and S - alues a e a ec ed by

alues, simila ly o he case o Tann = 350 oC (Figu e
3.15b). The e is a g adual inc ease o he mobili y upon inc ease o he s ess applied
du ing he annealing. The obse ed shi o he linea (H) dependences o s ess-
annealed mic owi es wi h induced magne ic bis abili y o low ield egion (Figu e 3.15b
and Figu e 3.16) is explained by he lowe coe ci i y alues o s ess-annealed samples
(see Figu e 3.8).
020 40 60 80 100
0
1000
2000
3000 ann = 60 min
Tann = 300ºC

= 0 MPa

= 118 MPa

= 236 MPa

= 354 MPa
(m/s)
H (A/m)
Figu e 3.16. (H) dependencies o Fe3.6Co69.2Ni1B12.5Si11Mo1.5C1.2
mic owi es annealed a Tann = 300 oC o ann =60 min wi hou
s ess (σm = 0 MPa) and unde di e en s esses.
Enginee ing o magne ic p ope ies o Co- ich mic owi es 71
3.2.4. Joule hea ing in Co- ich mic owi es
Th oughou his sec ion he in luence o Joule hea ing on he magne ic
p ope ies o Co-based mic owi es and i s compa ison wi h con en ional u nace
annealing is sys ema ically in es iga ed. Acco dingly, he expe imen al esul s o
Co69.2Fe4.1B11.8Si13.8C1.1 and Co67Fe3.9Ni1.5B11.5Si14.5Mo1.6 mic owi es, samples 2 and 4,
espec i ely, a e p esen ed.
The mic owi es we e subjec ed o a se ies o cu en annealing ea men s in
which di e en cu en s we e applied du ing di e en ime. Di ec cu en (DC) alues
o he hea ea men s we e selec ed clea ly below he alues ha could p oduce
ha dening and/o c ys alliza ion o he samples, as desc ibed in annealing p ocedu es
sec ion [14]. Cu en densi ies o 58.3 and 77.7 A/mm2 we e selec ed o ime anging
om 3 o 20 minu es o bo h samples.
Acco dingly, Co69.2Fe4.1B11.8Si13.8C1.1 mic owi e (sample 1), wi h d = 22.8 μm, was
subjec ed o cu en s o 24 and 32 mA. Hys e esis loops o cu en annealed samples
a e p esen ed in Figu e 3.17. Joule hea ed a I = 24 mA samples, Figu e 3.17a, p esen
simila cha ac e as hys e esis loops o as-p epa ed mic owi e, wi h low coe ci i y
alues. A sligh dec ease in he magne ic aniso opy ield can be obse ed (Figu e
3.17c).
Cu en annealed samples a I= 32 mA (Figu e 3.17b), show simila beha iou ,
linea hys e esis loop wi h a dec ease in Hk, ha becomes mo e ema kable o ann =
10 min (Figu e 3.17c).
Al hough Joule hea ing a j ≈ 80 A/mm2 causes a sample hea ing up o
app oxima ely 200 oC [12], as compa ed wi h con en ional u nace annealing o
s udied mic owi e a 200 oC p esen ed in Figu e 3.17b, Joule hea ed samples p esen
lowe Hc.
Resul s and discussion: Chap e III 72
Magne ic ha dening obse ed o Co- ich mic owi es a e con en ional u nace
annealing is a oided wi h cu en annealing, as is also obse ed in amo phous ibbons
[14].
ΔZ/Z(H) dependence o Joule hea ed sample wi h j = 24 mA du ing 3 min,
p esen ed in Figu e 3.18a o = 150 MHz, shows a ema kable imp o emen o
ΔZ/Zmax om ΔZ/Zmax ≈ 100% o ΔZ/Zmax ≈ 300 %, as compa ed o as-p epa ed sample.
Double-peak shape o ΔZ/Z(H) dependencies, simila o as-p epa ed sample, is
obse ed o all Joule hea ed samples a all equencies measu ed (see Figu e 3.18b
and Figu e 3.18c, whe e esul s o Joule hea ing o ann = 3 min a e shown).
-200 0 200
-1
0
1
As-p epa ed
3 min 24 mA
10 min 24 mA
M/M0
H (A/m)
(a)
Sample 2
-200 0 200
-1
0
1
M/M0
H (A/m)
As-p epa ed
3 min 32 mA
10 min 32 mA
20 min 32 mA
Tann=200 0C
(b)
Sample 2
0 5 10 15 20
180
200
220
240
260
Hk (A/m)
(min)
24 mA
32 mA
(c)
Sample 2
Figu e 3.17. Hys e esis loops o sample 1 as-p epa ed and Joule hea ed a 24 mA (a), Joule
hea ed a 32 mA and annealed a 200 oC o 60 min (b) and Hk ( ann) dependence
e alua ed om hys e esis loops o cu en annealed samples (c).
Enginee ing o magne ic p ope ies o Co- ich mic owi es 73
The double-peak ΔZ/Z(H) dependence obse ed is associa ed o ci cum e en ial
magne ic aniso opy and he maximum ield, Hm, o magne ic aniso opy ield [15].
Joule hea ed samples p esen lowe Hm alues han hose o as-p epa ed sample
(Figu e 3.18a), ha co ela e wi h lowe Hk alues o Joule hea ed sample han o as-
p epa ed, ob ained om bulk hys e esis loops measu ed o bo h samples (see Figu e
3.17a,b).
Maximum GMI a io, ΔZ/Zmax, dependence on equency p esen ed in Figu e
3.19a shows a GMI a io imp o emen , wi h ΔZ/Zmax close o 300% o all cu en
annealed samples in an ex ended equency ange. I is impo an o no e, ha he
op imum equency, a which maximum on ΔZ/Zmax( ) dependence is obse ed is
-15 -10 -5 0 5 10 15
0
100
200
300
Z/Z (%)
H (kA/m)
As-p epa ed
24 mA 3 min
(a)
Sample 2
-5 0 5
0
50
100
150
200
250
300 Sample 2 10 MHz
100 MHz
150 MHz
200 MHz
500 MHz
Z/Z (%)
H (kA/m)
24 mA 3 min
(b)
-10 -5 0 5 10
0
100
200
300 Sample 2 10 MHz
100 MHz
150 MHz
200 MHz
500 MHz
Z/Z (%)
H (kA/m)
32 mA 3 min
(c)
Figu e 3.18. Co69.2Fe4.1B11.8Si13.8C1.1 mic owi e ΔZ/Z(H) dependencies measu ed in as-p epa ed
and Joule hea ed (24 mA, 3 min) samples measu ed a 150MHz (a), ΔZ/Z(H) dependencies
measu ed a di e en equencies o Joule hea ed 3 min a 24 mA (b)
and a 32 mA (c), espec i ely.
Resul s and discussion: Chap e III 74
shi ed o highe equencies o abou 150-200 MHz as compa ed o as p epa ed
sample, in which such maximum akes place a a equency o abou 100 MHz (Figu e
3.19a).
Compa ison o ΔZ/Zmax ( ) dependencies o as-p epa ed, s ess-annealed and
Joule hea ed samples p esen ed in Figu e 3.19b e lec s he bene icial in luence o
Joule hea ing, Joule hea ed sample p esen s he highes ΔZ/Zmax - alue up o = 400
MHz.
In luence o Joule hea ing on he hys e esis loops and GMi e ec o
Co67Fe3.9Ni1.5B11.5Si14.5Mo1.6 mic owi e, sample 4, is s udied below. The hys e esis loops
o he samples cu en annealed a e p esen ed in Figu e 3.20, coe ci e ield, Hc, and
e ec i e aniso opy ield, Hk, e alua ed om he knee a ea jus be o e he app oach o
magne iza ion sa u a ion, Ms, we e ob ained om he hys e esis loops and compiled in
Table 3.2.
0200 400 600 800 1000
0
100
200
300
Sample 2
As-p epa ed
24mA
3 min
5 min
10 min
32 mA
3 min
5 min
10 min
20 min
Z/Zmax (%)
(MHz)
(a)
0200 400 600 800 1000
0
100
200
300
Sample 2
As-p epa ed
24 mA 10min
200 oC 354 MPa
375 oC 354 MPa
Z/Zmax (%)
(MHz)
(b)
Figu e 3.19. Co69.2Fe4.1B11.8Si13.8C1.1 mic owi e ΔZ/Zmax ( ) dependences obse ed in as-p epa ed
and Joule hea ed a di e en annealing condi ions samples (a) and ΔZ/Zmax ( ) dependencies
o as-p epa ed, s ess-annealed (Tann = 200 and 375 oC, wi h 354 MPa, o 60 min) and
Joule annealed (24 mA, 10 min) samples (b).

Enginee ing o magne ic p ope ies o Co- ich mic owi es 75
Cu en annealed Co67Fe3.9Ni1.5B11.5Si14.5Mo1.6 glass coa ed mic owi es p esen
ex emely so magne ic p ope ies. The samples cu en annealed a 30 mA o 3 min
and 5 min p esen he lowes coe ci i ies o abou 2 A/m and Hk ≈ 32 A/m, as can be
seen om Hk e olu ion wi h Joule hea ing ime, in Figu e 3.18d. Inc easing he
annealing ime a sligh inc ease in he coe ci i y and he aniso opy ield is obse ed.
The cha ac e o he hys e esis loop emains he same o longe cu en annealed
ime [16]. Simila beha iou is obse ed o he sample cu en annealed a 40 mA.
-50 0 50
-1,0
-0,5
0,0
0,5
1,0 Sample 4
-100 -50 0 50 100
-1,0
-0,5
0,0
0,5
1,0
M/MS
H (A/m)
10min 30mA
20min 30mA
M/Ms
H (A/m)
As-p epa ed
3min 30mA
5min 30mA
10min 30mA
(a)
-50 0 50
-1,0
-0,5
0,0
0,5
1,0 Sample 4
(b)
M/Ms
H (A/m)
As-p epa ed
3min 40mA
5min 40mA
10min 40mA
-50 0 50
-1,0
-0,5
0,0
0,5
1,0 Sample 4
(c)
M/Ms
H (A/m)
As-p epa ed
5 min 30 mA
5 min 40 mA
010 20
0
20
40
60
80
Hk (A/m)
ann (min)
(d)
Figu e 3.20. Hys e esis loops o Co67Fe3.9Ni1.5B11.5Si14.5Mo1.6 mic owi es Joule hea ed
a 30 mA o 3, 5, 10 and 20 min (inse ) (a), Joule hea ed a 40 mA o 3, 5 and
10 min (b) and compa ison be ween he hys e esis loops o he sample
Joule hea ed a 30 mA and 40 mA o 5 min (c) and Hk
dependence on Joule annealing ime o I = 30 mA (d).
Resul s and discussion: Chap e III 76
Table 3.2. Magne ic p ope ies o s udied Co67Fe3.9Ni1.5B11.5Si14.5Mo1.6
mic owi es subjec ed o di e en pos -p ocessing.
Pos -p ocessing ype
I applied
(mA)
Du a ion
(min)
Hc
(A/m)
Hk
(A/m)
As-p epa ed
7
65
Joule hea ed
30
3
2
32
5
2
32
10
6
75
20
6
75
40
3
5
50
5
5
55
10
4
63
Annealed (Tann = 300 °C)
60
6
21
The esul s ob ained o Co67Fe3.9Ni1.5B11.5Si14.5Mo1.6 mic owi e annealed in
con en ional u nace, a 300 °C du ing 60 min (Figu e 3.21a) and i s compa ison wi h
Joule hea ed sample wi h 30 mA du ing 40 min (Figu e 3.21b) show ha in con as o
Joule hea ed sample, con en ional annealing leads o a d as ic magne ic ha dening o
he sample [17].
-50 0 50
-1,0
-0,5
0,0
0,5
1,0 Sample 4
As-p epa ed
Annealed
M/M0
H (A/m)
(a)
(300 ºC 60 min)
-50 0 50
-1,0
-0,5
0,0
0,5
1,0 Sample 4
M/M0
H(A/m)
Joule hea ed
(30 mA 40 min)
Annealed
(300 ºC 60 min)
(b)
Figu e 3.21. Hys e esis loops o Co67Fe3.9Ni1.5B11.5Si14.5Mo1.6 mic owi e as-p epa ed and
annealed a 300°C 60 min (a) and annealed a he same condi ions and cu en
annealed wi h 30 mA o 40 min (b).
Enginee ing o magne ic p ope ies o Co- ich mic owi es 77
ΔZ/Z(H) ep esen a ion o as-p epa ed and cu en -annealed
Co67Fe3.9Ni1.5B11.5Si14.5Mo1.6 mic owi es gi es as a esul a double-peak dependence
(Figu e 3.22) ypically epo ed o Co- ich mic owi es wi h low nega i e
magne os ic ion coe icien and weak ci cum e en ial magne ic aniso opy [15,18].
E en in as-p epa ed s a e, Co67Fe3.9Ni1.5B11.5Si14.5Mo1.6 mic owi e p esen s high ΔZ/Z(H)
alues wi h a maximum GMI a io, ΔZ/Zmax, o abou 550% a a equency o 300 MHz
(Figu e 3.22 and Figu e 3.23).
An inc ease in he GMI a io is obse ed a e Joule-hea ing a he selec ed
condi ions. Highes GMI a io enhancemen is a ained o sho cu en -hea ing imes
as can be app ecia ed in Figu e 3.22, o samples annealed a 30 and 40 mA du ing 3
min and 5 min, ela ed o he magne ic so ening obse ed in he hys e esis loops o
cu en annealed mic owi es a hese condi ions. The highes ΔZ/Zmax alue o abou
-3 0 3
0
100
200
300
400
500
600
-3 0 3
0
100
200
300
400
500
600
700
-3 0 3
0
100
200
300
400
500
600
-3 0 3
0
100
200
300
400
500
600
700 (c)
(a)
(d)
(b)
Z/Z(%)
100MHz
200MHz
300MHz
1.00GHz
Z/Z(%)
H(kA/m)
100MHz
200MHz
300MHz
1.00GHz
Sample 4
Sample 4
Sample 4
Sample 4
Z/Z(%)
H(kA/m)
100MHz
200MHz
300MHz
1.00GHz
H(kA/m)
Z/Z(%)
H(kA/m)
100MHz
200MHz
300MHz
1.00GHz
Figu e 3.22. ΔZ/Z(H) dependences o Co67Fe3.9Ni1.5B11.5Si14.5Mo1.6 mic owi e as-p epa ed (a)
cu en annealed a 40 mA o 3 min (b), 5 min (c) and 10 min (d) measu ed a di e en
equencies.
Resul s and discussion: Chap e III 78
650% is ob ained o sample cu en -annealed a 40mA du ing 5 minu es. An inc ease
in he annealing ime co ela es wi h a dec ease in ΔZ/Zmax (Figu e 3.22d).
A no iceable imp o emen o he GMI a io is ob ained o he whole MHz
equency ange. The op imum equency mo es om 300 MHz o as-p epa ed
sample o 200 MHz o cu en -annealed ones.
0200 400 600 800 1000
300
400
500
600 Sample 4
Z/Zmax (%)
(MHz)
As-p epa ed
30mA 3min
30mA 5min
40mA 5min
Figu e 3.23. Maximum GMI a io dependences on equency o
Co67Fe3.9Ni1.5B11.5Si14.5Mo1.6 mic owi e as-p epa ed and
cu en annealed a di e en condi ions.
In he cu en annealing p ocess, he sample, besides he hea ing, is a ec ed by
he ci cum e en ial magne ic ield associa ed o he cu en lowing h ough i . The
ci cum e en ial magne ic ield, Hci c, p oduced om he cu en passing h ough he
mic owi e (Oe s ed’s law) can be es ima ed in he me allic nucleus as ollowing [3]:
𝐻𝑐𝑖𝑟𝑐 = 𝐼/2𝜋𝑟
(3.4)
wi h I he cu en alue and he adial dis ance.
Hci c alues change o ze o o i s maximum alue a he su ace o he
mic owi e, which is he one in ol ed in he GMI e ec . Ob ained alues o he s udied
mic owi e o he applied cu en s a e Hci c ≈ 0.375 kA/m and 0.5 kA/m o I = 30 mA
Enginee ing o magne ic p ope ies o Co- ich mic owi es 85
Fe3.6Co69.2Ni1B12.5Si11Mo1.5C1.2 mic owi e s ess-annealed o σ ≥ 470 MPa changes o m
axial o ans e se) [8,9]. Fu he mo e, he di e ence in he hys e esis loops o bo h
s ess-annealed samples can be also ela ed o he di e ence in chemical composi ions
and hus di e en λs – alues.
As p e iously shown, he s ess-annealing induced magne ic aniso opy o
mic owi es depends on he annealing condi ions, Tann, ann and σ [10]. Consequen ly,
s ess-annealing o Fe- ich mic owi es unde empe a u e g adien was sa is ac o ily
employed o ob aining con ollable spa ial dis ibu ion o he magne ic aniso opy
[10].
The same concep is used o s udied Co- ich mic owi es. In ac , as can be seen
in Figu e 3.29 and Figu e 3.30, he e is a g adual modi ica ion o he hys e esis loop
(measu ed by he sho pick-up coil along he samples leng h) o bo h samples s ess-
annealed a a iable Tann.
As has been e alua ed om he hys e esis loops (shown in Figu e 3.29 and
Figu e 3.30), bo h samples p esen a ia ion o he magne ic p ope ies along he
wi es leng h ha co ela e wi h Tann g adien du ing he s ess-annealing. Acco dingly,
-200 -100 0 100 200
-1
0
1
-200 -100 0 100 200
-1
0
1
-200 -100 0 100 200
-1
0
1
-200 -100 0 100 200
-1
0
1
-200 -100 0 100 200
-1
0
1
-200 -100 0 100 200
-1
0
1
M/M0
(a)
0 mm 80 mm
(b)
(c)
90 mm 110 mm
(d)
(e)
150 mm
H(A/m)
200 mm
( )
Figu e 3.30. Hys e esis loops o sample 6 s ess-annealed (σ = 400 MPa) a
a iable Tann. Tann e alua ed om Figu e 3.23b a e: 25 oC (a); 160 oC (b);
251 oC (c); 290 oC (d); 295 oC (e) and 300 oC ( ), espec i ely.

Resul s and discussion: Chap e III 86
Figu e 3.31a and Figu e 3.31b show he e olu ion o he hys e esis loops in e ms o
emanen magne iza ion, M /M0, and magne ic aniso opy ield, Hk, a ia ion along he
mic owi e leng h, L, o sample 5.
Likewise, Figu e 3.32 shows he e olu ion o he hys e eis loops o sample 6
subjec ed o s ess-annealing in Tann g adien , e lec ed in M /M0, and coe ci i y, Hc,
a ia ion along he mic owi e leng h.
The e olu ion upon s ess-annealing unde Tann g adien p esen s ea u es
simila o hose epo ed o s ess-annealing induced aniso opy in Co-based
mic owi es [29]. Bo h samples p esen an inc ease in M /M0 ollowed by a dec ease
wi h Tann inc easing.
050 100 150 200
0,0
0,3
0,6
-1000 -500 0 500 1000
-1
0
1
M/M0
H (A/m)
137 mm
-1000 -500 0 500 1000
-1
0
1
M/M0
H (A/m)
95 mm
-1000 -500 0 500 1000
-1
0
1
M/M0
H (A/m)
215 mm
-1000 -500 0 500 1000
-1
0
1
M/M0
H (A/m)
0 mm
M /Mo
L (mm)
Mic owi e
(a)
050 100 150
0
300
600
900
-1000 -500 0 500 1000
-1
0
1
M/M0
H (A/m)
0 mm
95 mm
107 mm
127 mm
137 mm
215 mm
Hk (A/m)
L (mm)
(b)
Figu e 3.31.Va ia ion o M /M0 (a) and Hk (b) along he sample leng h in he sample 5
annealed a a iable Tann. The lines a e jus guides o he eyes.
Enginee ing o magne ic p ope ies o Co- ich mic owi es 87
The hys e esis loops modi ica ion is explained by he mic owi es domain
s uc u e, which is a ec ed by he λs alue and sign, he in e nal s esses dis ibu ion
and he shape magne ic aniso opy. As a consequence, axial magne iza ion alignmen
is p omo ed by he exchange ene gy con ibu ion, especially ele an o hin and long
enough magne ic mic owi es, wi h high shape aniso opy [30,31].
The in e nal s esses o igin in glass-coa ed mic owi es is explained aking in o
accoun ha in addi ion o quenching in e nal s esses, σiq, a ising om he apid mel
quenching i sel , he e a e wo mo e in e nal s esses con ibu ions: he di e ence in
he mal expansion coe icien s o he me allic alloy and he glass coa ing, σi , and he
d awing s esses, σid, [32,33]. Di e en heo e ical app oaches and indi ec
expe imen al esul s (e.g., e ec o glass-coa ing e ching, in luence o applied s esses)
mani es ha he σi con ibu ion a ising om he di e ence in he mal expansion
coe icien s o me al and glass is he mos ele an [15,31]. Co espondingly, σi ≫ σiq
and σi ≫ σid.
The alue o in e nal s esses is a ec ed by he mic owi e geome y: glass-
coa ing hickness, me allic nucleus diame e , d, and o al mic owi e diame e , D. In he
mos simpli ied app oxima ion σi has been exp essed as [34]:
𝜎𝜙= 𝜎𝑟= 𝑃 = 𝜀𝐸𝑘Δ
(𝑘
3+1)Δ+4
3 ; 𝜎𝑧= 𝑃(𝑘 +1)Δ+ 2
(𝑘Δ+1)
(3.7)
whe e σ

, σ and σz a e ci cula , adial and axial s esses, Δ = (1−𝜌2)/𝜌2 , 𝑘 =
𝐸𝑔/𝐸𝑚, 𝐸𝑚, 𝐸𝑔- Young modulus o me allic nucleus and glass, espec i ely, 𝜀 =
(𝛼𝑚−𝛼𝑔)(𝑇𝑚−𝑇𝑟𝑜𝑜𝑚) αm αg a e he mal expansion coe icien s o me allic
nucleus and glass, espec i ely, and Tm, T oom a e mel ing and oom empe a u es.
The e o e, he hys e esis loops a ia ion, seen in Figu e 3.31 and Figu e 3.32, is
he esul o he balance be ween he shape magne ic aniso opy, he magne oelas ic
aniso opy and he s ess-annealing induced aniso opy.
Resul s and discussion: Chap e III 88
Acco ding o he co e-shell domain s uc u e model he modi ica ion in M /Mo
along he mic owi e can be associa ed wi h he change in he inne axially magne ized
co e adius, Rc, ela ed wi h M /Mo, by eq. (3.2).
Consequen ly, he spa ial dis ibu ion o he hys e esis loops, mus be
consequence o he g adual modi ica ion o he domain s uc u e along he mic owi es
s ess-annealed unde a empe a u e g adien .
0100 200
0,5
1,0
0100 200
5
10
15
-100 -50 0 50 100
-1
0
1
M/M0
H (A/m)
110 mm
-100 -50 0 50 100
-1
0
1
M/M0
H (A/m)
200 mm
-100 -50 0 50 100
-1
0
1
M/M0
H (A/m)
0 mm
M /M0
(a)
(b)
Hc (A/m)
L (mm)
Mic owi e
Figu e 3.32. Va ia ion o M /M0 (a) and Hc (b) along he sample leng h o he sample 6
annealed a a iable Tann. The lines a e jus guides o he eyes.
Enginee ing o magne ic p ope ies o Co- ich mic owi es 89
3.3. Concluding ema ks
Amo phous Co- ich mic owi es can p esen excellen magne ic so ness and
gian magne oimpedance (GMI) e ec . High GMI e ec , ob ained e en in as-p epa ed
Co- ich mic owi es, can be u he imp o ed by app op ia e hea ea men (including
con en ional annealing, s ess-annealing and Joule hea ing).
I is wo h men ioning he conside able imp o emen o ΔZ/Zmax alues up o
650%, ob ained o Co67Fe3.9Ni1.5B11.5Si14.5Mo1.6 mic owi e a e app op ia e cu en
annealing condi ions. Such mic owi es cu en annealed a op imal condi ions,
addi ionally p esen enhanced magne ic so ness.
Con en ionally u nace annealed and s ess-annealed, unde app op ia ely
selec ed condi ions, Co-based mic owi es can p esen ec angula hys e esis loops and
he e o e single and as domain wall p opaga ion. Howe e , gene ally Co-based
s ess-annealed mic owi es p esen high magne oimpedance a io. The e o e,
combina ion o bo h high GMI e ec and as single DW p opaga ion can be ob ained
in he same Co-based mic owi e. The app op ia e egimes allowing obse a ion o as
and single DW p opaga ion and high GMI e ec in he same mic owi e we e ound.
DW eloci y is obse ed in annealed Co-based mic owi es unde applica ion
o ensile s esses due o he induced magne ic bis abili y.
We p opose a a he simple me hod o p epa a ion o Co ich mic owi es
wi h g aded magne ic aniso opy consis ing o s ess- annealing unde empe a u e
g adien . A g adual change in he hys e esis loop o Co- ich glass-coa ed mic owi e
s ess-annealed a a iable empe a u e is obse ed.
Resul s and discussion: Chap e III 90
3.4. Re e ences
[1] A. Zhuko , M. Ipa o , M. Chu yukano a, A. Talaa , J.M. Blanco, V. Zhuko a, T ends in
op imiza ion o gian magne oimpedance e ec in amo phous and nanoc ys alline
ma e ials, J. Alloys Compd., 727 (2017) 887–901.
[2] G. He ze , Amo phous and Nanoc ys alline So Magne s, G.C. Hadjipanayis Ed., pp. 711–
730, in P oc. NATO Ad . S udy Ins . Magn. Hys e esis No . Ma e ., Sp inge Ne he lands,
Do d ech (1997), doi:10.1007/978-94-011-5478-9_77.
[3] P. Co e-León, V. Zhuko a, M. Ipa o , J.M. Blanco, J. Gonzalez, A. Zhuko , Enginee ing o
magne ic p ope ies o Co- ich mic owi es by joule hea ing, In e me allics 105 (2019)
92–98, doi:10.1016/j.in e me .2018.11.013.
[4] A. Zhuko , A. Talaa , M. Ipa o , J.M. Blanco, V. Zhuko a, Tailo ing o magne ic p ope ies
and GMI e ec o Co- ich amo phous mic owi es by hea ea men , J. Alloys Compd.
615 (2014) 610–615, doi: 10.1016/j.jallcom.2014.07.079.
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Resul s and discussion: Chap e IV 93
4. Enginee ing o magne ic p ope ies o mic owi es wi h
posi i e magne os ic ion coe icien (Fe-, Fe-Ni- and
Fe-Co- ich)
This chap e summa izes he esul s ob ained by selec ing di e en
chemical composi ions and pos -p ocessing s eps wi h he aim o op imize he
magne ic p ope ies o di e en Fe- ich composi ions and geome ic
cha ac e is ics o amo phous glass coa ed mic owi es as p esen ed in he able
below (Table 4.1).
The mic owi es selec ed p e end o gi e a comple e o e iew o he
beha iou o Fe- ich mic owi es om he me allic alloy g oups CoxFe1-x and
NixFe1-x, o 0 ≤ x ≤ 1, and Fineme - ype FeCuNbSiB mic owi es.
Table 4.1. Composi ions, geome y and magne os ic ion
coe icien s o s udied Fe- ich glass-coa ed mic owi es.
Composi ion
d (μm)
D (μm)

= d/D
λs x 10-6
Fe77.5B15Si7.5
15.1
35.8
0.42
38
Fe70B15Si10C5
3
18,75
0.16
35
Fe70B15Si10C5
6
23,08
0.26
35
Fe70B15Si10C5
10.8
22.5
0.48
35
Fe70B15Si10C5
15
23,8
0.63
35
Fe75B9Si12C4
15.2
17.2
0.88
38
Fe71.7B13.4Si11Nb3Ni0.9
103
158
0.65
35
Fe47.4Ni26.6Si11B13C2
29
32.2
0.9
25
Fe49.6Ni27.9Si7.5B15
14.2
33.85
0.42
20
Fe62Ni15.5Si7.5B15
14.35
33.25
0.43
27
Fe70.8Cu1Nb3.1Si14.5B10.6
11.8
14.4
0.8
30
Fe70.8Cu1Nb3.1Si14.5B10.6
15.6
21.8
0.7
30
Fe70.8Cu1Nb3.1Si14.5B10.6
10.7
16.4
0.6
30
Fe71.8Cu1Nb3.1Si15B9.1
7.0
24.8
0.282
30
Fe71.8Cu1Nb3.1Si15B9.1
18.2
39
0.467
30
(Fe0.7Co0.3)83.7Si4B8P3.6Cu0.7
26.5
22.3
0.84
Fe83.7Si4B8P3.6Cu0.7
15.5
17.5
0.89
Fe38.5Co38.5B18Mo4Cu1
10
16.6
0,6
Enginee ing o magne ic p ope ies o mic owi es wi h posi i e magne os ic ion
coe icien (Fe-, Fe-Ni- and Fe-Co- ich)
94
4.1. As-p epa ed Fe- ich mic owi es
4.1.1. FeBSiC mic owi es
As-p epa ed Fe75B9Si12C4 amo phous glass coa ed mic owi e wi h
me allic nucleus diame e d = 15.2 μm and o al diame e D = 17.2 μm, and
wi h magne os ic ion coe icien , λs, posi i e alue o abou 35 x 10-6, p esen s
a ec angula hys e esis loop (Figu e 4.1) wi h Hc ≈ 48 A/m.
Amo phous s a e o he as-p epa ed mic owi e was con i med by XRD
pa e n (Figu e 4.2a) and DSC cu e o as-p epa ed Fe75B9Si12C4 mic owi e
(Figu e 4.2b) shows a c ys alliza ion empe a u e, Tc 1, o abou 522 °C, and he
es ima ion o he Cu ie empe a u e is abou Tc = 413 °C. The e o e, he
annealing empe a u es, Tann, o his sample, in o de o p e en
c ys alliza ion, should be main ained below hese empe a u es.
-100 0 100
-1
0
1
M/M0
H (A/m)
Hs
Hc
Figu e 4.1. Hys e esis loop o as-p epa ed Fe75B9Si12C4
amo phous glass-coa ed mic owi e.
40 60 80 100
0
1000
2000
3000
4000
5000
I (a b. uni .)
2 (deg.)
(a)
200 300 400 500
0
1
2Tc 1 = 522 oC
DSC signal (mW/mg)
T (oC)
Tc = 413 oC
(b)
Figu e 4.2. XRD di ac ion pa e n (a) and DSC cu e (b)
o as-p epa ed Fe75B9Si12C4 mic owi e.
Resul s and discussion: Chap e IV 101
4.6c, in sample annealed a 550 °C du ing 3 h, i can be seen ha i s
c ys alliza ion peaks, ela ed o he p ecipi a ion o ine Fe3B c ys als, begin o
appea in he XRD pa e n. The o e lap be ween he b oad halo and he sha p
peaks can be unde s ood as he coexis ence o bo h phases, amo phous and
c ys alline (consis ing o α-Fe, Fe3B).
By means o a Scanning Elec on Mic oscope (MEB JEOL JSM-7000F), he
chemical composi ion and mic os uc u e o he mic owi e in as-p epa ed and
annealed s a e was cha ac e ized (Figu e 4.7). The images we e ob ained
wo king a 5 kV and I ≈ 0.1 nA. Fo he composi ional analysis, we employed he
ene gy-dispe si e X- ay spec oscopy (EDX) mode, wi h an Inca Ene gy 350
spec ome e , adjus ing he measu emen condi ions a 20 kV and I ≈ 1 nA.
SEM analysis o as-p epa ed and annealed samples, p esen ed in Figu e 4.7,
co ela es wi h he XRD pa e ns. SEM image o he me allic nucleus o as-
p epa ed sample (Figu e 4.7a) is ypical o amo phous samples. In Figu e 4.7b,
o SEM pic u e o annealed mic owi e a 550 °C du ing 3 h, c ys alli es o abou
25 nm size can be app ecia ed. Nanoc ys alline s uc u e can be explained due
o he pa icula composi ion o he mic owi es unde s udy, gi en ha he Nb
impedes hinde s he c ys alli es upon annealing [9].
Figu e 4.7. SEM images o he me allic nucleus o Fe71.7B13.4Si11Nb3Ni0.9
mic owi es as-p epa ed (a) and annealed a 550 °C o ann = 3 h (b).

Enginee ing o magne ic p ope ies o mic owi es wi h posi i e magne os ic ion
coe icien (Fe-, Fe-Ni- and Fe-Co- ich)
102
As p epa ed hys e esis loop o Fe71.7B13.4Si11Nb3Ni0.9 mic owi e (Figu e
4.8) is cha ac e ized by i s ec angula shape wi h low coe ci i y, Hc ≈ 25 A/m,
co espondingly wi h he amo phous s uc u e.
4.2. Pos -p ocessing e ec on magne ic p ope ies and GMI e ec
o Fe- ich mic owi es
4.2.1. E ec o annealing on magne ic p ope ies and GMI
e ec in nanoc ys alline and de i i ied mic owi es
The de i i ica ion o amo phous nucleus eached by pos annealing
p ocess is a use ul ool allowing conside able modi ica ion o he magne ic
p ope ies and e en magne ic so ening in some Fe- ich mic owi es [9,18,19].
In he case o FeSiBNbCu (so-called Fineme ) alloys low magne os ic ion
alues and be e magne ic so ness can be achie ed by he de i i ica ion o
amo phous p ecu so [9,18-20]. The magne ic so ening o he de i i ied
Fineme alloys is commonly explained conside ing he anishing
magne oc ys alline aniso opy, as well as he anishing λs – alue o he
ma e ial, consis ing o nano-sized g ains wi h an a e age size on he o de o 10
-200 -100 0 100 200
-1
0
1
M/M0
H (A/m)
As-p epa ed
Figu e 4.8. Hys e esis loop o as-p epa ed Fe71.7B13.4Si11Nb3Ni0.9 mic owi e.
Resul s and discussion: Chap e IV 103
nm, embedded in an amo phous ma ix ob ained by nanoc ys alliza ion o he
amo phous p ecu so s [9,17,18].
The a e age magne os ic ion coe icien akes nea ly ze o alues
[9,17,18], due o he con ol o he c ys alline olume ac ion: he exis ence o
wo phases (amo phous and c ys alline) p o ides a good balance o a nega i e
magne os ic ion o α-Fe-Si nanoc ys alli es o abou (𝜆𝑠
𝐹𝑒𝑆𝑖 ≈ -6 x 10-6) and a
posi i e one o he amo phous ma ix o abou (𝜆𝑠
𝑎𝑚 ≈ 20 x 10-6) esul ing
inally in anishing ne magne os ic ion alues [9]:
𝜆𝑠
𝑒𝑓𝑓 ≈ 𝑉𝑐𝑟 𝜆𝑠
𝐹𝑒𝑆𝑖 + (1 − 𝑉𝑐𝑟) 𝜆𝑠
𝑎𝑚
(4.1)
whe e λse is he sa u a ion magne os ic ion coe icien , and Vc is he
c ys alline olume ac ion.
-100 -50 0 50 100
H (A/m)
M/Mo
As-p epa ed
Hc= 44.5 A/m
(a)
1
0
-1
1
0
-1
0
-1 Hc = 15.9 A/m
Hc = 34.9 A/m
Hc = 32.5 A/m
1
0
400 oC
-1
1
0
-1
500 oC
550 oC
0100 200 300 400 500 600
0
20
40
60
4000
8000
12000
16000
Hc (A/m)

= 0.6

= 0.7

= 0.8
(b)
Tann (oC)
Figu e 4.9. Hys e esis loops o as-p epa ed and annealed Fe70.8Cu1Nb3.1Si14.5B10.6
mic owi e samples a Tann be ween 400-600 °C (a) and Hc (Tann)
dependence o Fe70.8Cu1Nb3.1Si14.5B10.6 mic owi es
o di e en ρ- a ios (b).
Enginee ing o magne ic p ope ies o mic owi es wi h posi i e magne os ic ion
coe icien (Fe-, Fe-Ni- and Fe-Co- ich)
104
This nanoc ys alliza ion o FeSiBNbCu alloys is usually obse ed a e
annealing in he ange o 500-600 oC o 1 h (i.e., a empe a u es be ween he
i s and second c ys alliza ion s ages). One o he examples o he e olu ion o
he hys e esis loops o Fineme - ype mic owi es upon nanoc ys alliza ion is
shown in Figu e 4.9. As can be obse ed om Figu e 4.9, in he case o he
Fe70.8Cu1Nb3.1Si14.5B10.6 mic owi e, annealing a Tann up o 550 oC allows
conside able dec ease o coe ci i y. Fo hese annealing condi ions he
cha ac e o hys e esis loops does no change: all he hys e esis loops p esen
ec angula shape.
In some cases ec angula hys e esis loops a e epo ed no only upon
de i i ica ion o Fineme - ype, bu e en a e second c ys alliza ion p ocess
when alues up o 2400 A/m a e obse ed [17-19]. One o he examples is
shown in Figu e 4.10, whe e hys e esis loop o Fe71.8Cu1Nb3.1Si15B9.1 mic owi e
(

= 0.282) annealed a Tann = 700 oC is shown. Howe e , Fe71.8Cu1Nb3.1Si15B9.1
mic owi e (

= 0.467) p esen a he di e en s ep-wise hys e esis loops (see
Figu e 4.10) ha can be a ibu ed o pa ially c ys alline (bi-phase) s uc u e.
Such pa ially c ys alline magne ic mic owi es, wi h s ep-wise hys e esis loops
ela ed o magne ic in e ac ion be ween c ys als o mixed amo phous-
-8000 -4000 0 4000 8000
-1
0
1
M/M0
H (A/m)

= 0,282

= 0,467
Figu e 4.10. Hys e esis loops o Fe71,8Cu1Nb3,1Si15B9,1 mic owi es
wi h di e en

- a ios annealed a 700 oC.
Resul s and discussion: Chap e IV 105
c ys alline s uc u e, can be in e es ing o applica ions in elec onic
su eillance sys ems [17-20].
The mic owi es ob ained by de i i ica ion exhibi highe sa u a ion
magne iza ion and a ce ain annealing condi ions can p esen be e magne ic
so ness and GMI esponse han as-p epa ed Fe- ich mic owi es and he e o e
hey a e use ul o GMI senso s and me acomposi es applica ions [9,20,21].
In ac , mic owi es wi h nanoc ys alline s uc u e can be ob ained e en
di ec ly in as-p epa ed s a e wi hou annealing [9,20,21]. The ad an age o
such mic owi es is ha hey can p esen be e mechanical p ope ies
[9,20,21].
I is wo h men ioning, ha he use o specially designed composi ions
allows u he inc ease o sa u a ion magne iza ion, μoMs, and also ob ain
ex emely magne ically so nanoc ys alline ma e ials [21]. In he case o
mic owi es, he use o a simila chemical composi ion allows p epa a ion o
nanoc ys alline mic owi es wi h imp o ed DW mobili y wi hou any pos
-10 -5 0 5 10
-1
0
1
-1,0 -0,5 0,0 0,5 1,0
-1
0
1
(Fe0,7Co0,3)83,7Si4B8P3,6Cu0,7 mw
Fe83,7Si4B8P3,6Cu0,7 mw
0Ms(T)
H(kA/m)
(Fe0,7Co0,3)83,7Si4B8P3,6Cu0,7 mic owi e
Fe83,7Si4B8P3,6Cu0,7 mic owi e
0Ms(T)
H (kA/m)
Figu e 4.11. Hys e esis loops o (Fe0.7Co0.3)83.7Si4B8P3.6Cu0.7
Fe83.7Si4B8P3.6Cu0.7 mic owi es as-p epa ed.
Enginee ing o magne ic p ope ies o mic owi es wi h posi i e magne os ic ion
coe icien (Fe-, Fe-Ni- and Fe-Co- ich)
106
p ocessing [21]. The pa ially c ys alline (Fe0.7Co0.3)83.7Si4B8P3.6Cu0.7 mic owi e
p esen s ele a ed alues o Hc (abou 480 A/m) and a he high sa u a ion
magne iza ion o abou 1.6 T (see Figu e 4.11).
Such ele a ed Hc - alues a e qui e simila o ha exhibi ed by o he
pa ially nanoc ys alline mic owi es, i.e., Hi pe m-like Fe38.5Co38.5B18Mo4Cu1
mic owi es wi h simila a e age g ain size (abou 38 nm and 23-33 nm o
(Fe0.7Co0.3)83.7Si4B8P3.6Cu0.7 and Hi pe m-like mic owi es, espec i ely) [21].
Acco dingly, e en pa ially c ys alline o nanoc ys alline mic owi es can p esen
pe ec ly ec angula hys e esis loops. Fo (Fe0.7Co0.3)83.7Si4B8P3.6Cu0.7 mic owi e
ele a ed μoMs - alues allowed o ob ain ex emely as domain wall eloci y
e en in as-p epa ed s a e [21].
As-p epa ed Fineme -like and Hi pe m-like glass-coa ed mic owi es also
p esen pe ec ly ec angula hys e esis loops, as p esen ed in Figu e 4.12.
Fe38.5Co38.5B18Mo4Cu1 mic owi e p esen nanoc ys alline s uc u e in as-
p epa ed s a e [22]. Highe Hc - alues o Fe38.5Co38.5B18Mo4Cu1 and
(Fe0.7Co0.3)83.7Si4B8P3.6Cu0.7 mic owi es ha e been a ibu ed o ele a ed
magne os ic ion coe icien o hese mic owi es as-compa ed o Fineme - ype
mic owi es.
-200 -100 0 100 200
-1
0
1
M/M0
H(A/m)
(a)
-600 -300 0 300 600
-1
0
1
H (A/m)
M/M0
(b)
Figu e 4.12. Hys e esis loops o Fe70.8Cu1Nb3.1Si14.5B10.6 (ρ = 0.38) (a)
and Fe38.5Co38.5B18Mo4Cu1 (ρ = 0.6) (b) as-p epa ed mic owi es.

Resul s and discussion: Chap e IV 107
Fo nanoc ys alline ma e ials, consis ing o nano-sized g ains dis ibu ed
andomly in an amo phous ma ix, magne ic so ening and conside able GMI
enhancemen co ela es wi h he de i i ica ion p ocess [9,17-22].
Figu e 4.13a shows he XRD di ac ion pa e ns Fe70.8Cu1Nb3.1Si14.5B10.6
amo phous glass-coa ed mic owi e wi h me allic nucleus and o al diame e s:
d= 11.2 μm and D= 14.4 μm, espec i ely, annealed a di e en empe a u es.
The sample in as-p epa ed s a e and annealed a empe a u es below Tann ≤
450 °C, main ains amo phous s uc u e. A e annealing a empe a u es
be ween 500-600 oC he beginning o c ys alliza ion can be app ecia ed, wi h
he c ys alline peak be ween 42-45° co esponden wi h α-Fe (Si) phase.
Va ious cha ac e is ics o he c ys alline phase o he ma e ial can be
de e mined by he shape o he c ys alline peak, in pa icula , he ull wid h a
30 40 50 60 70 80 90
500
1000
1500
I (a b. uni .)
2 (deg)
Tann= 400 0C
Tann= 550 0C
Tann= 650 0C
(a)
0
10
20
30
40
50
0200 400 6000
50
100
150
200
Dg (nm)
Tann (ºC)
Dg
(b)
Hc (A/m)
Hc
-10 0 10
0
20
40
60
80
100
Z/Z (%)
H (kA/m)
As-p epa ed
Tann= 550 ºC
(c)
= 200 MHz
Figu e 4.13. XRD di ac ion pa e ns o annealed Fe70.8Cu1Nb3.1Si14.5B10.6 mic owi es
(a), Dg (Tann) and Hc (Tann) dependencies (b) and GMI a io dependencies
( = 200 MHz) o as-p epa ed and annealed a 550 °C (c)
Fe70.8Cu1Nb3.1Si14.5B10.6 mic owi es.
Enginee ing o magne ic p ope ies o mic owi es wi h posi i e magne os ic ion
coe icien (Fe-, Fe-Ni- and Fe-Co- ich)
108
he hal maximum. By means o Debye Sche e equa ion can be es ima ed he
c ys al main g ain size Dg [23,24]:
𝐷𝑔= 𝑘𝜆/𝜖cos2𝜃
(4.2)
being k a dimensionless shape ac o wi h alue close o uni y,

de
wa eleng h,
ϵ
he ull wid h a he hal maximum o he c ys alline peak and 2

he angula posi ion o he c ys alline peak (B agg angle).
Es ima ion o he a e age g ain sizes o he nanoc ys als embedded in
he esidual amo phous ma ix (see Figu e 4.13b) is below 20 nm.
Magne ic so ening, e lec ed in he Hc dec ease, oge he wi h he
p ecipi a ion o small α-Fe (Si) g ains (Figu e 4.13b), co ela e wi h he GMI
a io imp o emen obse ed in Figu e 4.13c upon annealing and he
consequen de i i ica ion o he amo phous p ecu so .
Annealing a app op ia e condi ions ha ensu e he de i i ica ion o
Fineme - ype amo phous mic owi es can be conside ed as an e ec i e pos -
p ocessing ou e o he op imiza ion o he magne ic so ness and GMI e ec
o his g oup o Fe- ich mic owi es, bu de e io a ion and poo mechanical
p ope ies con inue o be he main disad an age in his ype o mic owi es [25].
The e o e, we paid special a en ion o sea ch o pos -p ocessing o mic owi es
ha allows main aining amo phous s uc u e.
4.2.2. Tuning o magne ic p ope ies o amo phous mic owi es
by u nace annealing
Below a e p esen ed some examples o he in luence o con en ional
u nace annealing, ocusing in he hys e esis loops o Fe- ich mic owi es o
di e en composi ions and on he domain wall dynamics and GMI e ec and
he combina ion o bo h magne ic p ope ies in he same mic owi e.
Resul s and discussion: Chap e IV 109
4.2.2.1. E ec o u nace annealing on magne ic p ope ies o FeBSiC
mic owi es
Hys e esis loops cha ac e is no a ec ed by he hea ea men ,
main aining ec angula shape, as can be seen in Figu e 4.14a and Figu e 4.15a
o Fe75B9Si12C4 mic owi es, only a sligh dec ease in Hc ( ann) dependence is
obse ed (Figu e 4.14b). A e con en ional annealing a di e en
empe a u es ( anging om Tann = 250 °C o Tann = 375 °C), Fe75B9Si12C4
mic owi e hys e esis loops emain ec angula shaped (Figu e 4.14a), as
ypically obse ed o mic owi es wi h posi i e

s [2-4,11,12], wi h a sligh Hc
dec ease.
The magne ic bis abili y o igin is ela ed o peculia emagne iza ion
p ocess consis ing o as magne iza ion swi ching h ough a single DW
p opaga ion. DW p opaga ion has been obse ed o his mic owi e in as-
p epa ed and annealed s a es. In Figu e 4.15b a no iceable inc ease in he DW
eloci y and mobili y can be app ecia ed a e he annealing. The DW dynamics
exhibi s an almos pe ec ly linea beha io o he (H) dependence o his
sample as-p epa ed and annealed.
-100 -50 0 50 100
-1
0
1
400 ºC 3 min
400 ºC 180 min
M/M0
H (A/m)
As-p epa ed
(a)
050 100 150
80
85
90
Hc (A/m)
ann (min)
(b)
Figu e 4.14. Hys e esis loops o as-p epa ed and annealed a Tann = 400 °C o di e en
ann Fe75B9Si12C4 amo phous mic owi es (a) and Hc ( ann) dependence (b).
Enginee ing o magne ic p ope ies o mic owi es wi h posi i e magne os ic ion
coe icien (Fe-, Fe-Ni- and Fe-Co- ich)
110
Such linea (H) dependence below he Walke b eakdown ield, HW, is
a ibu ed o a iscous DW p opaga ion egime desc ibed in e ms o DW
mobili y, S, (eq. (1.2)) [11,12].
I can be seen (Figu e 4.15b) he in luence o Tann on a S alues
consis s in inc ease in and S alues inc easing Tann up o 375 °C. Simila DW
eloci y inc ease wi h he annealing empe a u e inc ease was ecen ly
epo ed elsewhe e [11,12,26-28].
To s udy he In luence o annealing ime, we selec a empe a u e, Tann =
325 °C, and a y he annealing ime, ann, as p e iously s udied [2-4]. The esul s
a e p esen ed below in Figu e 4.16. Simila imp o emen as obse ed wi h
inc easing he annealing empe a u e is obse ed, o longe ann and S alues
a e highe .
-200 -100 0 100 200
-1
0
1
M/M0
As-p epa ed
250 ºC
300 ºC
325 ºC
375 ºC
(a)
H (A/m)
20 40 60 80
200
400
600
800
1000
1200
As-p epa ed
250 oC
300 oC
325 oC
375 oC
m/s
H (A/m)
(b)
Figu e 4.15. Hys e esis loops (a) and (H) dependence (b) o Fe75B9Si12C4 mic owi es
as p epa ed and annealed du ing 60 min o di e en annealing empe a u es.
Resul s and discussion: Chap e IV 117
4.2.3. S ess-annealing in FeBSiC mic owi es
4.2.3.1. Tuning o domain wall dynamics by s ess-annealing
Fo amo phous glass coa ed mic owi es, he change in he
magne oelas ic aniso opy (gi en by eq. (1.1)) by he s ess elaxa ion induced
by he annealing, being his he main sou ce o magne ic aniso opy in absence
o magne oc ys alline aniso opy, can explain he inc ease in he domain wall
eloci y and mobili y.
Then, s ess-annealing was pe o med in his Fe75B9Si12C4 mic owi e. In
Figu e 4.24 i can be app ecia ed he disappea ance o he ec angula shape o
he hys e esis loop o as-p epa ed sample, ha main ains up o 30 min o
annealing ime, wi h a mo e ema kable magne ic so ening achie ed
inc easing he annealing ime, ann.
I mus be ake in o accoun ha he di e ence in he he mal
expansion coe icien s be ween he me allic nucleus and he glass coa ing is
he esponsible o induce mos pa o he in e nal s esses [3-5].
-15 -10 -5 0 5 10 15
0
20
40
Z/Z (%)
H (kA/m)
As-p epa ed
Tann= 410 ºC
ann=16 min
ann=128 min
ann=256 min
Figu e 4.23. GMI a io measu ed in as-p epa ed (a) and annealed a 410 °C
o 16 (b), 128 (c) and 256 (d) minu es Fe47.4Ni26.6Si11B13C2
mic owi es measu ed a 600 MHz.

Enginee ing o magne ic p ope ies o mic owi es wi h posi i e magne os ic ion
coe icien (Fe-, Fe-Ni- and Fe-Co- ich)
118
(H) dependence o s ess-annealed samples (Figu e 4.25a) e lec s a
d as ic inc ease in he DW eloci y and mobili y inc easing wi h he inc ease in
he annealing ime.
-400 0 400
-1
0
1
M/M0
H (A/m)
As-p epa ed
15min
30min
45min
60min
Figu e 4.24. Hys e esis loops o Fe75B9Si12C4 mic owi es as-p epa ed and
s ess-annealed wi h

= 190 MPa a Tann = 325 °C o di e en ann.
20 30 40 50 60 70
200
400
600
800
1000
1200
1400
As-p epa ed
15 min
30 min
(m/s)
H (A/m)
(a)
030 60
20
40
S (m2/As)
ann (min)
Annealed
S ess-annealed
(b)
Figu e 4.25. (H) dependence o as-p epa ed and s ess-annealed Fe75B9Si12C4
mic owi es wi h

= 190 MPa a Tann = 325 °C o di e en ann (a) and S( ann)
o Fe75B9Si12C4 mic owi es annealed a Tann= 325 °C (b).
Resul s and discussion: Chap e IV 119
Compa ison o S ( ann) alues e alua ed o con en ional annealed and
s ess-annealed mic owi es is plo ed in Figu e 4.25b. S ≈ 7 m2/A∙s o as-
p epa ed sample subs an ially inc eases a e annealing a 325 °C achie ing S ≈
10 m2/A∙s, while a e s ess-annealing a mo e ema kable inc ease, up o S ≈
40 m2/A∙s, is ob ained. This ema kable inc ease mus be associa ed wi h
ans e se magne ic aniso opy induced by he s ess annealing and e lec ed
in he coe ci i y and emanen magne iza ion dec ease (Figu e 4.24).
S ess-induced aniso opy can be uned no only by modi ying he
annealing ime bu also changing he annealing empe a u e, Tann, and he
s ess applied du ing he annealing, whose in luence is s udied in Figu e 4.27.
S ess-annealing a high enough Tann and

ans o ms he ec angula
hys e esis loop in o almos linea .
Conside ing ha he magne ic domain s uc u e o magne ic wi es is
assumed o be consis ing o ou e domain shell wi h ans e se magne iza ion
o ien a ion and inne axially magne ized co e [28,37], he domain s uc u e
modi ica ion can be e alua ed om he squa eness a io, M /Ms, as desc ibed
by eq. (3.1).
-400 0 400
-1
0
1
S ess-annealed
(

= 190 MPa)
S ess-annealed
(

= 760 MPa)
M/M0
H (A/m)
As-p epa ed
Annealed
(a)
-400 0 400
-1
0
1
M/M0
H (A/m)
As-p epa ed
S ess annealed
(

= 380 MPa)
300 oC
350 oC
(b)
Figu e 4.26. Hys e esis loops o Fe75B9Si12C4 mic owi es as-p epa ed, annealed
and s ess-annealed a Tann= 300 °C o ann = 60 min (a) and s ess-annealed
(

= 380 MPa, ann = 30 min) a di e en empe a u es (b).
Enginee ing o magne ic p ope ies o mic owi es wi h posi i e magne os ic ion
coe icien (Fe-, Fe-Ni- and Fe-Co- ich)
120
In his way om M /Ms- alues ob ained om hys e esis loops p esen ed
in Figu e 4.27 we e alua ed he dependence o he adius o inne axially
magne ized co e, Rc, on annealing condi ions. As can be app ecia ed om
Figu e 4.27, Rc - alues p og essi ely dec ease wi h inc easing o σappl, Tann and
ann alues.
A ixed annealing empe a u e he adius o inne axially magne ized
co e, Rc, is lowe a highe applied s ess (Figu e 4.27b,c).
F om a o emen ioned analysis, we can deduce ha he s ess-annealing
allows he inc ease o he olume o ou e domain shell wi h ans e se
magne iza ion o ien a ion inc ease in expense o dec easing o he adius o
inne axially magne ized co e.
0200 400
2
4
6
8
Rc (m)
Tann (oC)
(a)
0300 600
2
4
6
8
Rc (m)

appl (MPa)
(b)
010 20 30
200
400
600
800
Rc (m)
ann (min)

= 190 MPa

= 380 MPa
Tann= 325 oC
(c)
Figu e 4.27. E ec o annealing empe a u e (a), s ess applied du ing annealing a
Tann = 300 °C (b) and annealing ime (c) on Rc- alues o s udied mic owi e.
Resul s and discussion: Chap e IV 121
Consequen ly, bene icial e ec o ans e se magne ic aniso opy on
DW eloci y (see Figu e 4.25) mus be a ibu ed o he inc ease o he olume
o ou e domain shell wi h ans e se magne ic aniso opy.
One o he obs acles limi ing applica ions o as DW p opaga ion
obse ed in mic o- and nano-wi es is ha he a elling DW is essen ially no
ab up [38-40]. Howe e , he cha ac e is ic wid h δ o a head- o-head DW is
closely ela ed o he magne oelas ic aniso opy [39]. Thus, he educed head-
o-head domain wall wid h δ/d (d is he me allic nucleus diame e ) is
de e mined by he alue o he aniso opy cons an K: o K = 104 e g/cm3, δ/d
≈ 13.5 and o K = 103 e g/cm3, δ/d = 40–50 [39]. Fo hese es ima ions, i was
assumed ha he whole olume o he me allic nucleus diame e p esen s axial
magne iza ion.
In he p esen case, we a e able o une he olume o he inne axially
magne ized co e by annealing ime and s ess applied du ing he annealing (see
Figu e 4.27). The e o e, we may expec he modi ica ion o DW cha ac e is ic
wid h δ upon s ess annealing.
The cha ac e is ic DW wid h can be e alua ed om he EMF signals
gene a ed by a head- o-head DW mo ing h ough he mic owi e [39].
The EMF,

, gene a ed wi hin he u n o he pick-up coil by a change in
he magne ic lux can be exp essed as [39]:
𝜀(𝑡)=Δϕ
Δ𝑡
(4.4)
whe e ϕ = BS is he magne ic lux, S is he a ea o he su ace, B = M + H is he
magne ic induc ion, and M is he magne iza ion. Thus, he ea u es ( he
ampli ude and wid h) o he EMF peaks mus be de e mined by 𝜕𝑀
𝜕𝑡.
As can be app ecia ed om Figu e 4.28, a dec easing o he EMF signal
wid h om he pick-up coil can be app ecia ed a e s ess-annealing. The EMF
signals,

, ha e been compa ed o as-p epa ed and s ess-annealed o
Enginee ing o magne ic p ope ies o mic owi es wi h posi i e magne os ic ion
coe icien (Fe-, Fe-Ni- and Fe-Co- ich)
122
di e en ann samples (Figu e 4.28a), as well as o as-p epa ed and hose
annealed unde s ess and wi hou s ess (Figu e 4.28b).
Such changes a e e idenced by he e alua ion o he hal -wid h, W, o
he EMF signal wi h annealing ime p o ided in Figu e 4.28c. As can be
app ecia ed, a dec ease o hal -wid h o he EMF signal a e s ess-annealing is
e idenced.
0,02504 0,02506
0,000
0,005
0,010

(V)
(ms)
As-p epa ed
15 min
30 min
(a)
0,02502 0,02504 0,02506
0,000
0,005
0,010

(V)
(ms)
As-p epa ed
0 MPa
190 MPa
(b)
020 40 60
0,012
0,014
0,016
0,018
0,020
W (ms)
(min)
0 MPa
190 MPa
(c)
Figu e 4.28. EMF peaks induced by he magne iza ion change in pick-up coils
measu ed o Fe75B9Si12C4 mic owi es as-p epa ed and s ess-annealed
(

= 190 MPa) o di e en ann (a), as-p epa ed and annealed a
Tann = 325 °C o 30 min wi hou s ess and unde s ess (b)
and dependence o he hal -wid h o he EMF peaks
wi h he annealing ime (c).

Resul s and discussion: Chap e IV 123
As discussed abo e, such dec easing o he hal -wid h ( ull wid h a hal
maximum), W, mus be associa ed ei he o he dec easing o he cha ac e is ic
DW wid h o o he DW eloci y inc easing. The eason o such modi ica ions
can be s ess-annealing induced ans e se magne ic aniso opy as well as
educ ion o he olume o he inne axially magne ized co e a e s ess-
annealing. Indeed as men ioned abo e, he δ – alues a e de e mined by he
magne oelas ic aniso opy and by he diame e o he axially magne ized co e.
In o de o sepa a e hese wo ac o s we mus analyze in mo e de ail
he EMF gene a ed wi hin he pick-up coil. P e iously, he EMF, ε, gene a ed
wi hin he pick-up coil u n when DW wid h, δ, is compa able wi h he dis ance
o he coil u n, z, was analyzed [39]. The exp ession ob ained in his case is
[39]:
𝜀(𝑡)=−𝑄𝑣𝑅2√𝜋
2∫𝑑𝑧1〈𝜕𝛼𝑧
𝜕𝑧1 (𝑧1−𝑣𝑡)〉
((𝑧−𝑧1)2+𝑅2)3/2
(4.5)
whe e R is he adius o he coil u n, = – dz/d is he domain wall eloci y,
1
zz



is he a e age linea densi y o he DW magne ic cha ge o e he wi e
c oss sec ion and Q he magne ic cha ge.
The eq. (4.5) is a he complex. In he simpli ied case, when he
cha ac e is ic domain wall wid h, δ, is small compa ed wi h he dis ance z om
he coil u n o he DW posi ion, he eq. (4.5) can be simpli ied as [39]:
𝜀(𝑡)=−√𝜋
2𝑄𝑣𝑅2
(𝑧+𝑅2)3/2
(4.6)
We can compa e he EMF signals o as-p epa ed and s ess-annealed
samples i we conside he same coil pa ame e s.
In his case he only di e ence in EMF alues mus be associa ed o he
di e en DW eloci y, , alues and di e ence in emanen magne iza ion o
as-p epa ed and s ess- annealed samples. The la e con ibu es h ough he
magne ic cha ge, Q, gi en by [39]:
Enginee ing o magne ic p ope ies o mic owi es wi h posi i e magne os ic ion
coe icien (Fe-, Fe-Ni- and Fe-Co- ich)
124
𝑄=2𝑀𝑟𝑆
(4.7)
whe e S is he sample c oss sec ion and M – emanen magne iza ion. This is
a ibu ed o he ac ha only he emagne iza ion e e sal o he inne axially
magne ized co e con ibu es o he EMF signal.
These conside a ions allow us o e alua e i he di e ence in hal -wid h
o he EMF signal o as-p epa ed and s ess- annealed (Tann = 325 oC, σappl = 190
MPa, ann = 30 min) mic owi es is a ibu ed only o di e en DW eloci ies o i
DW shape change a e s ess annealing also akes place. Ob ained eloci ies
a io aken om Figu e 4.25a o H = 25 A/m o s ess annealed and as-
p epa ed samples ( sa and ap, espec i ely) gi es sa/ ap ≈ 1.25. Howe e ,
conside ing he di e ence in he emanen magne iza ion (e alua ed om
Figu e 4.24), he a io Qsa sa/ Qap ap ≈ 0.98 (whe e Qsa and Qap a e alues o
s ess-annealed and as-p epa ed samples). While he W – alues a io, i.e.,
Wsa/Wap (whe e Wap and Wsa a e he hal -wid h o he EMF peaks o as-
p epa ed and s ess-annealed samples) is abou 0.83.
Consequen ly, we can assume he cha ac e is ic DW wid h educ ion in
s ess-annealed mic owi es.
4.2.3.2. E ec o s ess-annealing on GMI e ec o Fe- ich mic owi es
Simila ly o Co- ich mic owi es, we used s ess-annealing in o de o
imp o e he GMI e ec . As shown abo e, s ess-annealing allows o induce
ans e se magne ic aniso opy in Fe- ich mic owi es.
A ema kable GMI a io imp o emen is obse ed upon s ess-annealing o
Fe- ich mic owi es (see Figu e 4.29). As-compa ed o as-p epa ed mic owi e,
s ess-annealing (Tann = 350 °C, ann = 60 min and σm = 190 MPa) allows an o de
o magni ude imp o emen o maximum GMI a io,

Z/Zmax, (see Figu e 4.29a
and Figu e 4.29b). The o he ele an ea u e is ha s ess-annealed
Resul s and discussion: Chap e IV 125
mic owi es p esen unusual

Z/Z(H) dependencies (see Figu e 4.29b): low
equency

Z/Z(H) dependencies (10-50 MHz) a e simila o ha o as-p epa ed
mic owi e, i.e., single peak dependence wi h a decay om H = 0. Howe e ,
ising he equency an addi ional maximum on

Z/Z(H) dependencies appea s
(Figu e 4.29b). The e o e, a in e media e equency ange (100-300 MHz)

Z/Z(H) dependencies p esen i egula shape ha ecen ly has been
in e p e ed as he supe posi ion o he double-peak

Z/Z(H) dependence
ypical o ans e se magne ic aniso opy and single-peak epo ed o axial
magne ic aniso opy [4]. A ele a ed equencies

Z/Z(H) dependencies p esen

Z/Z(H) dependence ypical o he wi es wi h ans e se magne ic aniso opy
(see Figu e 4.29c).
-10 0 10
0
10
20
30
Z/Z (%)
H (kA/m)
50 MHz
100 MHz
400 MHz
800 MHz
(a)
-10 0 10
0
30
60
90
120
Z/Z (%)
H (kA/m)
10 MHz
50 MHz
100 MHz
150 MHz
300 MHz
(b)
-10 0 10
0
50
100
Z/Z (%)
H (kA/m)
100 MHz
200 MHz
500 MHz
800 MHz
(c)
Figu e 4.29.

Z/Z(H) dependencies obse ed in as-p epa ed (a) and s ess-annealed
a Tann =350 °C ( o 60 min and σm = 190 MPa) Fe75B9Si12C4 mic owi es.
Enginee ing o magne ic p ope ies o mic owi es wi h posi i e magne os ic ion
coe icien (Fe-, Fe-Ni- and Fe-Co- ich)
126
Such equency in luence on

Z/Z(H) dependencies can be in e p e ed
conside ing exis ence o inne axially magne ized domain inside he s ess-
annealed mic owi es and equency dependence o he skin pene a ion dep h,
δ, as desc ibed in [4].
I is wo h men ioning, ha such i egula i y can be obse ed in

Z/Z(H)
dependencies o s ess-annealed mic owi es a di e en annealing condi ions.
Thus, simila i egula dependencies ha e been obse ed o mic owi es
annealed a 250 °C (Figu e 4.30a) and 300 °C (Figu e 4.30b) o 60 min and 900
MPa. Howe e , he equency ange a which such unusual

Z/Z(H)
dependencies a e obse ed depend on s ess- annealing condi ions: o lowe
annealing empe a u e he equency ange (70-200 MHz) is shi ed o lowe
equencies.
F om abo e p esen ed esul s i is clea ha he equency is one o he
impo an pa ame e s allowing GMI a io op imiza ion. One o he pa ame e s
ha can be used as a e e ence is he maximum GMI a io,

Z/Zmax. Fo as-
p epa ed samples

Z/Zmax co esponds o Hm = 0, howe e , o he s ess-
annealed sample

Z/Zmax is obse ed a some ield, Hm ≠ 0. F equency
-10 0 10
0
50
100
Z/Z (%)
H (kA/m)
70 MHz
80 MHz
100 MHz
150 MHz
200 MHz
(a)
-10 0 10
0
50
100
Z/Z (%)
H (kA/m)
100 MHz
150 MHz
200 MHz
(b)
Figu e 4.30.

Z/Z(H) dependencies obse ed in s ess-annealed a
Tann = 250 °C o 60 min and σm = 900 MPa (a) and Tann = 300 °C
o 60 min and σm = 900 MPa (b) Fe75B9Si12C4 mic owi es.
Resul s and discussion: Chap e IV 133
o change o coe ci i y, ΔHc, o as-p epa ed Fe75B9Si12C4 sample is 160 A/m and
o s ess-annealed Fe75B9Si12C4 sample ΔHc = 191 A/m. This di e ence is mos
ema kable o he ange o low

– alues, making s ess-annealing sui able o
de ec ion o low applied s esses. Simila ly, squa eness a io, M /Ms, o s ess-
annealed Fe75B9Si12C4 sample p esen s mo e signi ican changes a low

egion.
Obse ed s ess dependencies o he squa eness a io mus be
associa ed wi h changes o domain s uc u e. Indeed, i is commonly accep ed
ha he domain s uc u e o Fe- ich mic owi es consis s o inne axially
magne ized co e and ou e shell wi h ans e se magne iza ion easy di ec ion
[38,47].
As can be obse ed om Figu e 4.36b, M /Ms a io o s ess-annealed
Fe75B9Si12C4 sample apidly inc eases upon applied s ess. Conside ing eq. (3.2)
we ob ained Rc modi ica ion unde applied s ess in luence om 6 up o almos
7.5 μm as depic ed in Figu e 4.36b. Consequen ly, we mus assume change o
domain s uc u e in s ess-annealed Fe75B9Si12C4 sample unde in luence o
applied s esses in s ess-annealed Fe75B9Si12C4 sample consis ing o ising o
he inne axially magne ized co e adius om 6 up o almos 7.5 μm.
4.2.4. Re e sibili y o he s ess-annealing aniso opy
As shown abo e, s ess annealing o as-p epa ed Fe75B9Si12C4
mic owi es, allows he induc ion o ans e se magne ic aniso opy ha
depends on he s ess-annealing condi ions. Figu e 4.37 compa es he
ec angula hys e esis loop o as p epa ed Fe75B9Si12C4 mic owi es wi h he
hys e esis loops o he mic owi es annealed a a ixed Tann = 350 oC and ime ann
= 60 min, unde di e en applied s esses,

showing he g adual
ans o ma ion o he hys e esis loop in o linea and he inc ease in Hk (Figu e

Enginee ing o magne ic p ope ies o mic owi es wi h posi i e magne os ic ion
coe icien (Fe-, Fe-Ni- and Fe-Co- ich)
134
4.37) wi h inc easing he s ess-applied du ing he annealing, ha co ela es
wi h he dec ease o he squa eness a io, M /Ms.
Hc dec eases a low applied s esses o 190 MPa and 380 MPa (inse o
Figu e 4.38) howe e o he highe s ess applied Hc alues a e p ac ically he
same o as-p epa ed sample.
The adius o he inne axially magne ized co e, Rc (as de ined in eq.
(3.2)), e alua ed om M /Ms, shows a dec ease wi h he inc ease in he applied
s ess du ing he s ess-annealing Figu e 4.37) ha can be in e p e ed as he
inne axially magne ized co e educ ion as he olume o mic owi e wi h
ans e se magne ic aniso opy g ows.
To s udy he e e sibili y o he s ess annealing aniso opy o a sample
s ess-annealed a a ixed

, we pe o med a subsequen annealing wi hou
s ess o he s ess-annealed sample (SA) a he same empe a u e (Tann = 350
oC) and o ann = 60 min, (SA + A), and a longe subsequen annealing, (SA + 2A),
a he same empe a u e o ann = 150 min.
-500 0 500
-1
0
1
As-p epa ed
190 MPa
380 MPa
760 MPa
M/M0
H (A/m)
Figu e 4.37. Hys e esis loops o Fe75B9Si12C4 mic owi es as-p epa ed, s ess-
annealed a Tann = 350 oC, ann = 60 min, unde di e en applied s esses.
Resul s and discussion: Chap e IV 135
Fo he case o he mic owi e subjec ed o s ess-annealing wi h σ = 190
MPa (hys e esis loops p esen ed in Figu e 4.37 and Figu e 4.39a) a pa ially
eco e o he s ess-annealing aniso opy can be eached a e he subsequen
annealing. Howe e , he hys e esis loop o mic owi e subjec ed o s ess-
annealing wi h σ = 76 MPa is less a ec ed by subsequen annealing: i emains
almos unchanged a e subsequen annealing (see Figu e 4.39b). As can be
in e p e ed om M /Ms and Rc ( ann) dependencies ob ained om he hys e esis
loops and ep esen ed in Figu e 4.40, M /Ms and Rc alues ob ained a e
annealing ( ann = 150 min) o s ess- annealed wi h σ = 190 MPa sample each
alues simila o hose o as-p epa ed mic owi e. We can conclude ha he
subsequen annealing allows inc easing he olume o he inne axially
magne ized co e.
Lowe coe ci i y alues o he sample subjec ed o longe subsequen
annealing ( ann = 150 min), as compa ed o as p epa ed sample, can be
associa ed o he s ess elaxa ion.
0300 600
0
600
1200
0300 600
2
4
6
8
Hk
0300 600
30
60
90
Hc(A/m)
(MPa)
Hc
Hk (A/m)
Rc
Rc (m)

(MPa)
Figu e 4.38. Hk and Rc dependencies and Hc (on he inse ) dependences on s ess
applied du ing he annealing. The lines in he igu e a e jus guides o eyes.
Enginee ing o magne ic p ope ies o mic owi es wi h posi i e magne os ic ion
coe icien (Fe-, Fe-Ni- and Fe-Co- ich)
136
As obse ed om Figu e 4.39b, hys e esis loops o he mic owi e s ess-
annealed wi h σ = 760 MPa ollowed by he subsequen annealing s eps e lec
much s onge induc ion o ans e se magne ic aniso opy. The hys e esis
loops o he mic owi e once subjec ed o s ess-annealing do no change unde
subsequen annealing o ann = 60 min no o longe ann = 150 min.
In Rc ( ann) ep esen a ion o Figu e 4.40, compa ing wi h sample s ess-
annealed wi h σ = 190 MPa, only a sligh inc ease can be app ecia ed a e he
annealing p ocedu es o he SA sample wi h σ = 760 MPa, o which he Rc ( ann)
dependence shows ha a e he s ess annealing a hose

alues mos pa
o he mic owi e me allic nucleus possesses ans e se magne ic aniso opy.
The compa ison be ween Figu e 4.37a and Figu e 4.37b and Rc ( ann)
dependence o bo h samples (Figu e 4.40), lead us o conclude ha he
inc ease in he applied s ess du ing he s ess annealing ea men implies a
g ow h in he i e e sible pa o he s ess-annealed induced magne ic
aniso opy.
-500 0 500
-1
0
1
M/M0
H (A/m)
As-p epa ed
SA
SA+A
SA+2A

= 190 MPa
(a)
-400 -200 0 200 400
-1
0
1
As-p epa ed
SA
SA+A
SA+2A
M/M0
H (A/m)

= 760MPa
(b)
Figu e 4.39. Hys e esis loops o Fe75B9Si12C4 mic owi es as-p epa ed and s ess
annealed wi h σ = 190 MPa (a) and σ = 760 MPa (b) wi h subsequen annealing
du ing 60 min and 150 min.
Resul s and discussion: Chap e IV 137
One mo e ad an age o Fe- ich mic owi e subjec ed o combined
annealing (s ess-annealing + subsequen annealing) is be e GMI e ec o
such mic owi es.
In spi e o ec angula cha ac e o hys e esis loops o Fe75B9Si12C4
mic owi es s ess annealed (SA) wi h σ = 190 MPa and hen annealed a 350 oC
o 150 min, such mic owi e p esen be e GMI esponse as-compa ed o as-
060 120
0
3
6
Rc (m)
0
60
120
0
1
2
R
c
(

m)
ann
(min)
Rc (

= 190 MPa)
ann (min)
Rc (

= 760 MPa)
Figu e 4.40. Compa ison o Rc ( ann) dependence be ween samples s ess-annealed
upon σ = 190 and 760 MPa wi h subsequen annealing. The lines in he
igu e a e jus guides o eyes.
-10 -5 0 5 10
0
50
100
Z/Z (%)
H (kA/m)
10 MHz
50 MHz
100 MHz
(a)
-10 -5 0 5 10
0
50
100
150
Z/Z (%)
H (kA/m)
200 MHz
500 MHz
1 GHz
(b)
Figu e 4.41. ΔZ/Z(H) dependences o SA (σ = 190 MPa) and hen annealed Fe75B9Si12C4
mic owi es measu ed a ≤ 100 MHz (a) and a ≥ 100 MHz (b).
Enginee ing o magne ic p ope ies o mic owi es wi h posi i e magne os ic ion
coe icien (Fe-, Fe-Ni- and Fe-Co- ich)
138
p epa ed and e en s ess-annealed Fe75B9Si12C4 mic owi e: ΔZ/Zmax – alues up
o 150 % a e eco ded a 500 MHz (see Figu e 4.41).
As shown in Figu e 4.41a o ≤ 80 MHz he single peak ΔZ/Z(H)
dependence is obse ed, while ≥ 80 MHz ΔZ/Z(H) dependence change om
single-peak o double-peak ype (see Figu e 4.41b).
The p oposed pos p ocessing consis ing o s ess-annealing ollowed by
annealing allows supp essing he i egula ΔZ/Z(H) dependence obse ed in
s ess-annealed Fe- ich mic owi es (see Figu e 4.29) by he subsequen
annealing. One mo e example is p o ided in Figu e 4.42 and Figu e 4.43 o
s ess-annealing pe o med a σ = 760 MPa.
The s ess-annealed (a σ = 760 MPa) Fe75B9Si12C4 mic owi e p esen s
conside able GMI e ec (see Figu e 4.42a and Figu e 4.42b) in spi e o high
ans e se magne ic aniso opy ha can be deduced om he hys e esis loops
shown in Figu e 4.39. As can be obse ed om Figu e 4.42a, double-peak
ΔZ/Z(H) dependencies a e obse ed e en o low equencies (10-50 MHz).
Rising he equency, i.e., o in e media e equencies (100 ≤ ≤ 200 MHz)
ΔZ/Z(H) dependencies p esen i egula shape (Figu e 4.42b). Finally, o high
equencies ( ≥ 300 MHz) again double peak ΔZ/Z(H) dependencies a e
obse ed (Figu e 4.42c). Gene ally, obse ed ΔZ/Zmax – alues a e below 80%.
Highe ΔZ/Zmax – alues (up o 120%) and double-peak ΔZ/Z(H)
dependencies in a whole equency ange a e obse ed o he Fe75B9Si12C4
mic owi e a e SA (σ = 760 MPa) and hen subsequen ly annealed ( o 150
min) (see Figu e 4.43a and Figu e 4.43b).
F om abo e p esen ed expe imen al esul s we can deduce ha
annealing a e s ess annealing allows:

Resul s and discussion: Chap e IV 139
i) A ema kable GMI e ec imp o emen as compa ed o as-p epa ed
and e en o s ess-annealed Fe- ich mic owi es and
ii) Supp ession o i egula i ies in ΔZ/Z(H) dependencies obse ed in
all s ess-annealed samples a in e media e equencies (see
Figu es 4.29, 4.41, 4.42 and 4.43).
A bene icial in luence o app op ia e annealing a e s ess-annealing is
e idenced om a compa ison o he ΔZ/Zmax ( ) dependencies p esen ed in
Figu e 4.44. I is clea ly seen ha GMI e ec imp o emen is obse ed in he
whole equency ange. The highes ΔZ/Zmax a io o abou 160% is obse ed a
300 MHz ( o he Fe75B9Si12C4 mic owi e SA a 190 MPa and hen annealed)
[48].
-10 -5 0 5 10
0
40
80
Z/Z (%)
H (kA/m)
10 MHz
50 MHz
100 MHz
(a)
-10 -5 0 5 10
0
30
60
Z/Z (%)
H (kA/m)
80 MHz
150 MHz
200 MHz
(b)
-10 -5 0 5 10
0
40
80
Z/Z (%)
H (kA/m)
300 MHz
500 MHz
1 GHz
(c)
Figu e 4.42.

Z/Z(H) dependences o SA (σ = 760 MPa) Fe75B9Si12C4 mic owi e
measu ed a ≤ 100 MHz (a), 80 ≤ ≤ 200 MHz (b) and a ≥ 300 MHz (c).
Enginee ing o magne ic p ope ies o mic owi es wi h posi i e magne os ic ion
coe icien (Fe-, Fe-Ni- and Fe-Co- ich)
140
In all he cases subsequen annealing allows ΔZ/Zmax – alues
imp o emen by up o 50%.
The obse ed bene icial e ec o annealing on he GMI e ec can be
explained conside ing ha annealing p omo es he enhancemen o
ci cum e en ial aniso opy and, hence, supp esses he i egula i ies in he
ΔZ/Z(H) dependencies.
-10 0 10
0
50
100
Z/Z (%)
H (kA/m)
10 MHz
50 MHz
100 MHz
(a)
-10 0 10
0
50
100
Z/Z (%)
H (kA/m)
200 MHz
500 MHz
1 GHz
(b)
Figu e 4.43. ΔZ/Z(H) dependences o SA (σ = 760 MPa) + annealed Fe75B9Si12C4
mic owi e measu ed a ≤ 100 MHz (a) and a ≥ 200 MHz (b).
0300 600 900
30
60
90
120
150
Z/Zmax (%)
(MHz)
SA (

=190MPa)
SA (

=190MPa) + annealed (150min)
SA (

=760MPa)
SA (

=760MPa) + annealed (150min)
Figu e 4.44. ΔZ/Zmax( ) dependencies o SA and SA + annealed Fe75B9Si12C4 mic owi e
o σ = 190 MPa and 760 MPa. The lines a e jus guides o eyes.
Resul s and discussion: Chap e IV 141
4.2.5. GMI e ec and DW p opaga ion in “ hick” glass-coa ed
Fe- ich mic owi es
A e annealing, a 550 °C he cha ac e o he hys e esis loop o
Fe71.7B13.4Si11Nb3Ni0.9 mic owi e does no change, as can be seen in Figu e 4.45,
al hough Hc expe imen s a sligh inc ease, his magne ic ha dening can be
unde s ood as he beginning o c ys alliza ion (as con i med by he XRD pa e n
in Figu e 4.4c). Then, we assumed ha a lowe annealing empe a u es he
mic owi e s uc u e emains amo phous. Annealing a 300 °C causes a
coe ci i y dec ease, he magne ic so ening in his case can be explained due o
he in e nal s esses elaxa ion.
The bis able beha iou o he mic owi e as-p epa ed and annealed o
sho annealing ime obse ed in Figu e 4.45, sugges s he possibili y o
obse e single domain wall, DW, p opaga ion, since i is obse ed o o he Fe-
ich mic owi es [35,36]. By means o he modi ied Six us-Tonks me hod
(desc ibed in de ail in Chap e 2) he eloci y dependence on magne ic ield H,
(H), was e alua ed and i is p esen ed in Figu e 4.45. As-p epa ed mic owi e
p esen s p ac ically linea (H) dependence and ela i ely high alues, up o
-200 -100 0 100 200
-1
0
1
M/M0
H (A/m)
As-p epa ed
300oC 1h
300oC 4h
550oC 1h
550oC 3h
Figu e 4.45. Hys e esis loop o as-p epa ed Fe71.7B13.4Si11Nb3Ni0.9 mic owi e
and annealed a 550 °C and 300 °C o di e en ann.
Enginee ing o magne ic p ope ies o mic owi es wi h posi i e magne os ic ion
coe icien (Fe-, Fe-Ni- and Fe-Co- ich)
142
700 m/s, as compa ed o he epo ed o Fe- ich mic owi es o simila
diame e ob ained by in- o a ing wa e quenching echnique [49].
30 40 50 60 70 80
200
400
600
800
1000
S = 15,5 m2/A.s
S = 11,9 m2/A.s
As p epa ed
550 oC 1 h
(m/s)
H (A/m)
Figu e 4.46. DW eloci y dependence on magne ic ield, (H), o as-p epa ed
Fe71.7B13.4Si11Nb3Ni0.9 mic owi es and annealed a 550 °C o ann = 1 h.
The linea dependence o he DW eloci y, (H), along he mic owi e
[36-38,50], as a unc ion o he magne ic ield, in a iscous egime is desc ibed
by eq. (1.2).
-6 -4 -2 0 2 4 6
30
40
50
Z/Z (%)
H (kA/m)
100MHz
500MHz
1 GHz
Figu e 4.47. GMI a io dependence o as-p epa ed Fe71.7B13.4Si11Nb3Ni0.9
mic owi e a di e en equencies.