ma e ials
A icle
Magne ic and Magne o-Op ical P ope ies o
Fe75−xMn25GaxHeusle -like Compounds
Daniel K ál1, Lukáš Be an 1, Ma in Zelený1,2 , Jan Zemen 3, Roman An oš 1, Ja osla Ham le 1,
Jakub Záz o ka 1, Michal Rameš 4, K is ýna Onde ko á4, Oleg Heczko 4,* and Ma in Veis 1,*
1Facul y o Ma hema ics and Physics, Cha les Uni e si y, Ke Ka lo u 5, 12 16 P ague 2, Czech Republic;
daniel.k al@ka lo .m .cuni.cz (D.K.); [email p o ec ed] (L.B.); [email p o ec ed] (M.Z.);
an os@ka lo .m .cuni.cz (R.A.); ham le@ka lo .m .cuni.cz (J.H.); [email p o ec ed] (J.Z.)
2Facul y o Mechanical Enginee ing, Ins i u e o Ma e ials Science and Enginee ing, B no Uni e si y o
Technology, Technická2896/2, 616 69 B no, Czech Republic
3Facul y o Elec ical Enginee ing, Czech Technical Uni e si y in P ague, Technická2,
166 27 P ague, Czech Republic; [email p o ec ed]
4
Ins i u e o Physics o he Czech Academy o Sciences, Na Slo ance 1999/2, 18221 P ague 8, Czech Republic;
[email p o ec ed] (M.R.); [email p o ec ed] (K.O.)
*Co espondence: [email p o ec ed] (O.H.); eis@ka lo .m .cuni.cz (M.V.)
Recei ed: 6 Janua y 2020; Accep ed: 25 Janua y 2020; Published: 4 Feb ua y 2020


Abs ac :
Fe
75−x
Mn
25
Ga
x
Heusle -like compounds we e in es iga ed in a wide ange o Fe/Ga
a ios while keeping he Mn con en cons an and equal 25 a % in o de o elucida e he in e play
be ween magne ic p ope ies and composi ion. Ma e ials we e p epa ed by a c-mel ing om pu e
elemen s and subsequen ly annealed. Expe imen al in es iga ions we e ocused on magne iza ion
beha io in a wide empe a u e ange om 4 o 1000 K and magne ic ield up o 9 T. Op ical
and magne o-op ical (MO) measu emen s we e employed o shed mo e ligh on he magne ic
s a e and elec onic s uc u e o in es iga ed ma e ials. Magne iza ion measu emen s indica ed
ha in he icini y o s oichiome y (Fe
2
MnGa) he compounds a e e o/ e imagne ic, whe eas
he Fe-de icien compound is pa amagne ic and a high Fe concen a ion he an i e omagne ic
in e ac ion p e ails. Theo e ical calcula ions o co esponding o de ed and diso de ed s oichiome ic
compounds we e ca ied ou and compa ed o he expe imen on he le el o ne magne ic momen
as well as magne o-op ical spec a. This compa ison sugges s ha he Heusle c ys al s uc u e, L2
1
,
is no p esen e en close o s oichiome y. Mo eo e , he compa ison o densi y o s a es (DOS) o
o de ed and diso de ed s uc u es allowed us o explain missing ma ensi ic ans o ma ion (MT) in
in es iga ed ma e ials.
Keywo ds:
Heusle compounds; Fe-Mn-Ga; ma ensi ic ans o ma ion; Cu ie poin ; magne o-op ics;
ab ini io
1. In oduc ion
Some Heusle compounds unde go ma ensi ic ans o ma ion (MT), which is essen ial o shape
memo y and calo ic beha io [
1
]. Mo eo e , he winned low symme y phase can exhibi magne ically
induced eo ien a ion ha mani es s i sel as a huge magne ic ield-induced s ain, mo e han wen y
imes la ge compa ed o ha o gian magne os ic i e ma e ials [
2
–
4
]. C ucial o all e ec s is he
p esence o MT, which is due o a peculia elec onic s uc u e in he icini y o he Fe mi le el [
5
].
The main examples o magne ic shape memo y (MSM) ma e ial a e Ni-Mn-Ga Heusle compounds.
Howe e , hese compounds su e om se e al sho comings such as agili y [
6
] and ela i ely low
ma ensi ic and e omagne ic ansi ion empe a u es [7–9].
Ma e ials 2020,13, 703; doi:10.3390/ma13030703 www.mdpi.com/jou nal/ma e ials
Ma e ials 2020,13, 703 2 o 12
Heusle Fe-Mn-Ga compounds ha e been p oposed as good candida es o new MSM ma e ial [
10
]
as hey ha e a much highe Cu ie poin han Ni-Mn-Ga. Howe e , i was ound e y soon ha ma ensi ic
ans o ma ion is no a uni e sal ea u e, and i occu s only in some pa icula composi ions [
11
–
14
].
Apa om he mally induced ans o ma ion [
15
], e en he ield-induced ans o ma ion was obse ed
o Fe2MnGa by Zhu e al. [16].
I was ound ha e na y compounds close o Fe
2
MnGa composi ion c ys allize in a ious cubic
s uc u es de ined by a di e en a omic o de [
12
]. The o de ing is e y sensi i e o composi ional
a ia ion and e en a e y small de ia ion om s oichiome y, o en negligible o e en unde ec able
by usual EDS, can p oduce ei he bcc-like (diso de ed B2, o de ed L2
1
Heusle s uc u e) o cc-like
(L1
2
s uc u e) phases o hei mix u e [
12
,
17
]. Appa en ly, he mal his o y can also play a ole in
es ablishing a ious phases [18].
Unlike Ni-Mn-Ga, Fe-Mn-Ga compounds con ain wo kinds o a oms wi h di e en magne ic
momen localiza ion bu wi h compa able magni ude. Thei in e ac ion can p o ide a ious magne ic
a angemen s om an i e omagne ic o e i- o e omagne ic s a es. The close coexis ence o he
phases in a single compound is indica ed by he exchange bias [
19
]. Such coexis ence, in connec ion
wi h a complex in e play o bcc- and cc-like phases, esul s in complica ed magne ic beha io . O e all,
he magne ic s a e is no well unde s ood e en o s oichiome ic Fe
2
MnGa. Despi e he mixed
s uc u al o de o cc- and bcc-like phases in nea s oichiome ic Fe
2
MnGa, Kud ya se e al. we e
able o de e mine i s elec onic and op ical p ope ies and compa e i wi h ab ini io calcula ions [
13
,
20
].
Howe e , he published esul s a e incomple e as he mos s udied composi ions a e close o he
s oichiome ic Fe2MnGa compound.
He e we p esen a comp ehensi e s udy encompassing p e ious expe imen al epo s and
heo e ical p edic ions. We in es iga ed expe imen ally Fe
75-x
Mn
25
Ga
x
compounds de i ed om
Heusle compounds in a wide ange o composi ions wi h a ied Fe/Ga a ios while keeping he Mn
con en cons an and equal 25 a %. The magne ic and MO measu emen s a e complemen ed wi h ab
ini io calcula ions o s oichiome ic Fe
2
MnGa wi h di e en la ice s uc u es and magne ic o de ing in
an a emp o cla i y he obse ed complex beha io and di e ences be ween ou expe imen al esul s
and p e ious calcula ions.
2. Ma e ials and Me hods
Polyc ys alline bulk samples we e p epa ed by a c-mel ing om pu e elemen s in A a mosphe e
using a Buhle u nace. A e he homogeniza ion hea ea men a 1073 K/24 h, he samples we e cu
and polished mechanically and elec oly ically o ob ain high-quali y su aces o scanning elec on
mic oscopy (SEM) and op ical and magne o-op ical measu emen s. SEM was used o e eal he
mic os uc u e, phase composi ion, and g ain size. We used SEM Tescan Fe a 3 equipped wi h
elec on dispe sion spec oscopy (EDS) analyse and elec on backsca e ed di ac ion (EBSD) de ice.
The c ys al s uc u e was e alua ed om EBSD. Composi ion o he polyc ys alline bu ons we e
de e mined by EDS wi h e o up o 1 a % pa icula ly on Mn con en . The e o s in hese pa icula
compounds we e es ima ed om ou analyses o Ni-Mn-Ga Heusle compounds, using compa ison
wi h X- ay luo escence analysis wi h s anda ds.
The magne ic p ope ies wi h ield and empe a u e we e measu ed in he in e al om 10 o
1000 K and ield up o 9 T using a PPMS ib a ing sample magne ome e in PPMS by Quan um
Design. The spon aneous sa u a ion magne iza ion was de e mined by ex apola ing he high- ield
magne iza ion o ze o ield.
A magne o-op ical spec ome e based on he o a ing analyze [
21
] me hod was ob ained o
acqui e complex magne o-op ical Ke e ec (MOKE) in pola con igu a ion wi h nea ly no mal ligh
incidence in he pho on ene gy ange om 1.2 o 4.5 eV. Applied magne ic ield was 1.2 T o b ing he
samples close o he magne ic sa u a ion. All magne o-op ical da a we e measu ed a oom empe a u e.
The Vienna Ab ini io Simula ion Package (VASP, e . 5.4.4) was used o s uc u al elaxa ion and
calcula ions o magne ic momen s, densi ies o s a es (DOS) as well as op ical p ope ies o s oichiome ic
Ma e ials 2020,13, 703 3 o 12
Fe
2
MnGa [
22
,
23
]. In ou calcula ion, he elec on-ion in e ac ion was desc ibed by p ojec o augmen ed-
wa e (PAW) po en ials [
24
,
25
]. We used he g adien -co ec ed exchange–co ela ion unc ional
p oposed by Pe dew e al. [
26
]. To include expec ed diso de , he Special Quasi andom Supe cell
(SQS) [
27
,
28
] wi h 32 a oms as a model o diso de ed sys em was gene a ed using a sepa a e so wa e
ool [
29
]. This me hod is based on op imizing pai co ela ion coe icien s o ep esen a s a is ically
andom solid solu ion.
3. Resul s and Discussion
P epa ed ma e ials anged om he Fe
25
Mn
25
Ga
50
o Fe
65
Mn
25
Ga
10
keeping Mn con en a 25 a %
as close as possible. The chemical composi ion de e mined o mos compounds by EDS is lis ed in
Table 1 oge he wi h sa u a ion magne iza ion and Cu ie empe a u e. The EDS analysis indica ed
ha he nominal composi ion does no di e signi ican ly om he measu ed one. Lis ed samples we e
u he analyzed by magne o-op ical measu emen s.
Table 1.
Composi ion, spon aneous magne iza ion M
s
, and Cu ie empe a u es T
c
o selec ed
compounds. The spon aneous magne iza ion in Boh magne ons (
µB
) pe o mula uni ( .u.) and he
Cu ie empe a u e o he second phase a e lis ed in b acke s. The M
s
was ob ained by ex apola ion he
magne iza ion om high magne ic ield o ze o ield. The e o in de e mina ion o composi ion is
abou 1 a %; o magne iza ion measu emen , he e o is abou 5%.
Name Nominal De e mined by EDS
Msa 10 K
(Am2/kg)
(µBpe .u.)
Tc (K)
Fe40 Fe40Mn25Ga35 Fe39.5Mn26Ga34.5 87
(3.77)
532
(183)
Fe50 Fe50Mn25Ga25 Fe49Mn26Ga25 100
(4.23)
762
(554)
Fe52 Fe52Mn25Ga23 Fe51Mn26Ga23 57
(2.40)
736
Single
Fe56 Fe56Mn25Ga19 Fe56Mn26Ga18 1 a 300 K
(0.04)
An i e omagne ic
( aces o e o.)
Fe65 Fe65Mn25Ga10 - 0.05
(0.02)
An i e omagne ic
TN=300 K
3.1. S uc u al P ope ies
All s udied ma e ials had a cubic s uc u e a oom empe a u e. None o he s udied ma e ials
exhibi ed ans o ma ion o he lowe symme y phase, ha is, ma ensi ic ans o ma ion (as de e mined
om magne ic measu emen shown below) upon cooling. SEM obse a ion using backsca e ed elec ons
e ealed ha wo compounds, Fe65 and Fe52, we e single cubic phase. The example o single-phase
mic os uc u e is shown in Figu e 1( igh ). SEM indica ed a non-homogenei y o Fe50; howe e ,
di e en phases could no be esol ed. A no able excep ion was he Fe40 compound, in which wo
di e en phases could be clea ly iden i ied, as shown in Figu e 1(le ). The EBSD measu emen indica ed
wo cubic phases. These phases had e y simila composi ions as de e mined by EDS. Magne o-op ical
Ke E ec (MOKE) mic oscopy indica ed ha only one phase was e omagne ic a oom empe a u e
as he magne ic domains could be obse ed. The phase o med e omagne ic islands imme sed in
a non-magne ic ma ix. The wo-phase cha ac e o he compound was con i med by magne iza ion
measu emen (see below).
Ma e ials 2020,13, 703 4 o 12
Figu e 1.
Mic os uc u e o wo-phase Fe40 (
le
) and single-phase Fe52 (
igh
) samples obse ed by
backsca e ed elec ons in SEM. I clea ly shows he wo-phase cha ac e o he Fe40 sample showing
i egula lowe -like islands in a ma ix. Sample Fe52 is single phase wi h ela i ely la ge g ains.
Composi ion de e mined by EDS is indica ed in he igu e.
3.2. Magne ic P ope ies
Figu e 2summa izes he magne iza ion loops and empe a u e dependence o low- ield and
high- ield magne iza ion o all magne ically o de ed samples. The low- ield magne iza ion con i med
expec ed high Cu ie empe a u es in all compounds close o s oichiome y. The high Cu ie empe a u e
phase can be iden i ied om he li e a u e as cc phase [
12
,
13
]. The highes empe a u e, abou 760 K,
was measu ed o he sample (Fe50) closes o s oichiome y. The empe a u es a e lis ed in Table 1.
The low- ield magne iza ion measu emen also con i med he single phase in Fe52 and he wo-phase
cha ac e o Fe40 in ag eemen wi h SEM (Figu e 1), indica ing low Cu ie empe a u e (183 K) o he
second phase. This ag eed wi h MOKE obse a ion a oom empe a u e. Acco ding o Kud ya se ,
he ma ix phase wi h a low Cu ie poin is he diso de ed bcc phase [12,13].
Mo eo e , he low- ield measu emen e ealed wo di e en high Cu ie empe a u es in Fe50
(as shown in he second panel o Figu e 2), indica ing, in acco dance wi h inhomogenei ies obse ed
by SEM, ha he sample con ained wo di e en phases. Acco ding o Kud ya se [
12
], i should
con ain cc and bcc phases. Al hough he cc phase exhibi ed a high Cu ie poin in acco dance wi h he
li e a u e, he expec ed bcc phase had qui e a high Cu ie empe a u e compa ed o ha o Fe40. I seems
o exclude he p esence o he bcc phase, bu i may be also asc ibed o di e en composi ion close o
s oichiome y. On he o he hand, he Cu ie empe a u e o he assumed cc-phase is compa able wi h
sample Fe52 in line wi h he li e a u e [
13
]. High- ield he momagne ic cu es suppo he desc ibed
beha io ; howe e , he sepa a ion be ween phases canno be de e mined in any case.
Magne iza ion loops o selec ed samples a oom empe a u e and close o 0 K, shown in
Figu e 2, indica e ha he ma e ials close o s oichiome y we e all e omagne ic o e imagne ic in
ag eemen wi h [
12
]. Wi h dec easing empe a u e, he sa u a ion magne iza ion was o en educed
below oom empe a u e magne iza ion. The dec ease o sa u a ion magne iza ion wi h dec easing
empe a u e is well illus a ed by high- ield he momagne ic cu es. This dec ease indica ed he onse
o an i e omagne ic in e ac ion below oom empe a u e.
In e es ingly, he Fe52 sample, which om SEM obse a ion and low- ield magne ic measu emen
seems o be single-phase ma e ial, exhibi ed a sha ply inc easing coe ci i y and a s ong dec ease o
low- ield magne iza ion wi h dec easing empe a u e. This beha io is no obse ed o any o he
composi ions. The lowe ing suscep ibili y and inc eased coe ci i y can indica e enhanced magne ic
domain pinning. I may be asc ibed o an i e omagne ism in dis u bed egions [
12
] as g ain bounda ies
and e en wi hin an iphase bounda ies [30–32] on which he magne ic domain walls can be pinned.
Ma e ials 2020,13, 703 5 o 12
Figu e 2.
Magne iza ion cu es a oom and 10 K empe a u es (
igh
) and he momagne ic cu es
measu ed upon hea ing (
le
) o selec ed samples ma ked in igu e. Black line and le y-scale indica e
sa u a ion magne iza ion a 9 T. Red line and igh y-scale indica e low- ield magne iza ion (0.01 T).

Ma e ials 2020,13, 703 6 o 12
Figu e 3.
Spon aneous magne iza ion a 10 K ob ained by ex apola ion om high- ield magne iza ion
(up o 9 T) o ze o ield is ep esen ed by ed iangles. S oichiome ic composi ion o Fe
2
MnGa
is ma ked by he e ical b oken line. Room empe a u e magne iza ion a 1.4 T ela ed o MO
measu emen s is ep esen ed by black squa es. The es ima ed e o s in composi ion and magne iza ion
de e mina ion a e ma ked.
The compounds wi h he composi ion s ongly de ia ed om s oichiome y we e ei he
pa amagne ic o an i e omagne ic. Clea an i e omagne ic beha io was obse ed o Fe65 wi h N
é
el
empe a u e T
N
abou 300 K, de e mined om he empe a u e dependence o sa u a ion magne iza ion.
This is simila o empe a u e, whe e he dec ease o sa u a ion magne iza ion is obse ed o o he
composi ions. I sugges s ha he an i e omagne ic in e ac ion becomes g adually s onge wi h
inc easing Fe con en (i.e., om Fe40 o Fe65 samples).
The dependence o he spon aneous magne iza ion a 10 K on Fe con en shown in Figu e 3
summa izes p e ious obse a ions. Fo low Fe concen a ion he ma e ial is pa amagne ic, o highe
Fe concen a ion, he e omagne ic in e ac ion is es ablished and sa u a ion magne iza ion inc eases.
The maximum momen occu s a s oichiome y. Wi h inc easing Fe con en abo e s oichiome y, he
magne iza ion sha ply d opped o almos ze o due o an i e omagne ic in e ac ion. The esidual
magne ic momen o he compound wi h high con en o Fe can be due o no ully compensa ed
an i e omagne ism o due o s uc u al inhomogenei y, ha is, he p esence o a small olume o
e omagne ic phase o e en a minu e amoun o pu e Fe.
Room empe a u e magne iza ion measu ed a 1.4 T ollows he ends obse ed o he
spon aneous magne iza ion. I is also shown in Figu e 3as i is impo an o MO measu emen done
a oom empe a u e.
3.3. Magne o-Op ical Spec oscopy
Room empe a u e expe imen al spec a o pola Ke o a ion and ellip ici y a e shown in Figu e 4.
The spec a o pola Ke o a ion exhibi mono onous beha io wi h an inc ease owa ds he low
ene gy egion and an indica ion o a spec al s uc u e nea 2 eV. On he o he hand, he ellip ici y
spec a ise wi h inc easing ene gy wi h a b oad maximum si ua ed nea 3.5 eV.
This spec al dependence esembles al eady epo ed esul s on polyc ys alline Fe
48
Mn
24
Ga
28
[
33
]
and Fe
50
Mn
25
Sn
25
[
34
] bulk samples. Howe e , he spec a we e comple ely di e en han
hose p e iously epo ed on o he Heusle compounds con aining Mn, bu wi hou Fe a oms,
such as Ni-Mn-Ga [
35
,
36
], Ni-Mn-Sn, Ni-Mn-Sb, o o he compounds con aining Mn a oms [
37
].
This esul indica es a majo di e ence in he elec onic band s uc u e be ween Fe-Mn-Ga and
Ni-Mn-Ga compounds.
Ma e ials 2020,13, 703 7 o 12
Figu e 4.
Expe imen al spec a o pola Ke o a ion (
op
) and ellip ici y (
bo om
) measu ed a 1.2 T
and oom empe a u e oge he wi h ab ini io heo e ical calcula ions.
Figu e 4also shows s ong a ia ion o magne o-op ical e ec upon he composi ion o he sample.
Al hough he spec al beha io is simila o all he samples, sample Fe50 exhibi s he highes MOKE
ampli ude, whe eas sample Fe56 has almos negligible magne o-op ical esponse. This is consis en
wi h magne ic measu emen s and is demons a ed in Figu e 5, whe e he ampli ude o MOKE a 1.5 eV
is plo ed as a unc ion o Fe composi ion. As one can see om his igu e, he magne iza ion oge he
wi h MOKE has a maximum o nea ly s oichiome ic composi ion.
Figu e 5.
Composi ion-dependen pola Ke e ec o Fe-Mn-Ga compounds a he pho on ene gy o
1.5 eV.
Ma e ials 2020,13, 703 8 o 12
3.4. Theo e ical Calcula ions
To explain ou expe imen al da a and o compa e wi h p e iously published esul s, we pe o med
new ab ini io calcula ions wi h s oichiome ic composi ion. Kud ya se e al. [
13
] show ha he L2
1
o de ed s uc u e has sligh ly highe o al ene gy and hus i does no appea in he s oichiome ic
compound. This calcula ion seems o sugges ha he e is no Heusle compound wi h p ope o de ing.
We nex conside ed he L12( cc) o de ed s uc u e.
P e ious ab ini io calcula ions pe o med o he s oichiome ic compound wi h he L1
2
( cc) o de
indica ed he e omagne ic o de ing as he mos s able wi h a magne ic momen o 6.13
µB
/ .u. This is
signi ican ly highe han measu ed alues o sa u a ion magne iza ion o 4.23
µB
/ .u. In con as , he
e imagne ic o de ing wi h opposi e o ien a ion o magne ic momen s a Fe and Mn a oms exhibi s
much smalle magne ic momen s o 0.48 µB/ .u. [13].
In ou calcula ion, we used he L1
2
( cc) s uc u e desc ibed p e iously [
13
] bu we conside ed
opposi e o ien a ion o magne ic momen a neighbo ing Fe a oms wi hin he same plane. This esul ed
in a magne ic momen o 1.90
µB
/ .u. An e en highe magne ic momen o 2.75
µB
/ .u. was ound o
an i e omagne ic in e ac ion be ween Fe planes, whe eas in-plane in e ac ion be ween Fe a oms was
e omagne ic. The magne ic momen is, howe e , s ill lowe han expe imen ally obse ed alues o
nea ly s oichiome ic compounds.
Fu he inc easing o magne ic momen s can be achie ed by conside ing he chemical diso de
be ween Ga and Fe a oms in he L1
2
la ice. We used he Special Quasi andom Supe cell (SQS) [
27
,
28
]
wi h 32 a oms as a model o diso de ed sys em. Such a supe cell exhibi s a magne ic momen
o 4.31
µB
/ .u. due o he opposi e o ien a ion o magne ic momen s a pa icula Fe a oms.
An i e omagne ic in e ac ion appea s i he Fe a om is su ounded a leas by six o he Fe a oms.
In an o de ed L1
2
s uc u e, each Fe a om is su ounded by only ou o he Fe a oms. Mo eo e ,
we also ound ha his e imagne ic s a e o diso de ed s uc u e was ene ge ically mo e a o able
han e omagne ic o de ing abou 0.017 eV/a om. This clea ly indica es ha he compound Fe50 is
diso de ed L12, which esul s in he highes magne ic momen o all e imagne ic s a es.
Fo sligh ly non-s oichiome ic compounds wi h excess Fe con en (i.e., he Fe52 sample), a sha p
dec ease o magne ic momen down o 2.4
µB
/ .u. was obse ed in he expe imen . Based on
he heo e ical calcula ion o s oichiome ic compound, his sha p dec ease o magne ic momen
can be explained by he disappea ance o he diso de and he appea ance o L1
2
o de ing. The
heo e ical p edic ion o o de ed compounds is 2.75
µB
/ .u o 1.9
µB
/ .u., depending on he mode
o an i e omagne ic in e ac ion as desc ibed abo e. The u he sha p decline o magne ic momen
obse ed in he expe imen in he compounds wi h highe Fe con en can be asc ibed o ully es ablished
an i e omagne ic in e ac ion.
The ab ini io calcula ion showed ha u he dec ease o magne ic momen is due o inc easing
chance o o m Fe clus e s wi h opposi ely o ien ed magne ic momen s a Fe a oms. The p edic ed
end was obse ed in he expe imen ; howe e , he expe imen ally obse ed magne iza ion dec ease
is much sha pe han p edic ed.
To explain he missing MT in he in es iga ed samples, he ab ini io calcula ions o MOKE
spec a o L2
1
and diso de ed L1
2
s uc u es we e pe o med using he complex pe mi i i y enso
ob ained wi hin he linea esponse heo y as implemen ed in he VASP 5.4 code. The esul s a e
shown in Figu e 4 oge he wi h expe imen al da a. Theo e ical spec a o L2
1
s uc u e do no
ollow expe imen al da a, as hey exhibi se e al maxima and minima and change sign o MOKE
se e al imes ac oss he in es iga ed ene gy ange. This indica es he absence o L2
1
o de in he
in es iga ed samples.
On he o he hand, he spec a o he diso de ed L1
2
s uc u e p o ide be e ag eemen wi h
he expe imen . They exhibi simila mono onous inc ease and dec ease o pola Ke o a ion and
ellip ici y, espec i ely. Admi edly, he ampli ude o he e ec is lowe han he expe imen al da a
o he Fe50 sample. Howe e , his can be explained by he ela i ely small uni cell (32 a oms) used
in he calcula ion due o p ohibi i ely high memo y equi emen s. Such a small cell migh desc ibe
Ma e ials 2020,13, 703 9 o 12
he mo e se e e de ia ion om he ully o de ed s uc u e han he diso de p esen in ou sample.
This de ia ion hen changes he elec onic s uc u e excessi ely as mani es ed by he smoo h DOS
below, which can esul in a supp ession o he p obabili y o elec onic ansi ions esponsible o
magne o-op ical esponse.
To explain he di e ence in he MOKE o s oichiome ic Ni-Mn-Ga and in es iga ed Fe-Mn-Ga
samples, spin- esol ed o al DOS we e calcula ed and a e displayed in Figu e 6.
Figu e 6.
Calcula ed spin- esol ed o al DOS o L2
1
and diso de ed L1
2
s uc u es compa ed o hose
o s oichiome ic Ni2MnGa.
Compa ing he o al DOS o L2
1
and diso de ed L1
2
s uc u es wi h hose epo ed o Ni
2
MnGa [
5
],
one can see a majo di e ence in he majo i y spin channel jus abo e he Fe mi le el. While he L2
1
and diso de ed L1
2
s uc u es o Fe
2
MnGa ha e a clea ly isible band app oxima ely 0.2–0.3 eV abo e
he Fe mi le el ( isible as a sha p peak indica ed by a ows), his band is comple ely missing in he case
o Ni
2
MnGa. I indica es ha a subs i u ion o Ni by Fe esul s in he p esence o emp y s a es abo e
he Fe mi le el in he majo i y spin channel, which can ac as exci ed s a es o pa icula elec onic
ansi ions. Figu e 6also shows ha he diso de ed L1
2
s uc u e exhibi s highe DOS a Fe mi ene gy
compa ed o he L21s uc u e.
On he o he hand, he mino i y spin channel looks simila o he case o Ni
2
MnGa [
5
] as well as
o bo h Fe-Mn-Ga s uc u es. The e o e, one should expec ce ain simila i ies in he MOKE spec a
o hese wo compounds. Indeed, besides s ong mono onous inc ease/dec ease owa ds he low
ene gy egion, one can see ce ain indica ions o spec al s uc u es in expe imen al MOKE spec a
a ound 2 eV in o a ion and 3 eV in ellip ici y. These may o igina e, simila ly o Ni
2
MnGa [
35
,
36
], om
ansi ions be ween s a es in he mino i y spin channel. Howe e , hei ansi ion p obabili y is much
lowe compa ed o he low ene gy ansi ions. This is he case o he diso de ed L1
2
s uc u e whe e
he ene gy gap in he mino i y spin channel a ound he Fe mi le el is no obse ed con a y o he L2
1
s uc u e and Ni
2
MnGa (see Figu e 6). High DOS a ound he Fe mi ene gy aise he op ical abso p ion
a lowe ene gies [
20
] and enhance he magne o-op ical esponse as was expe imen ally obse ed in he
spec a o pola Ke o a ion. The huge di e ence in DOS in he icini y o he Fe mi le el mos likely
supp esses he MT. Since he ene gy gap in he mino i y spin channel makes he ma ensi e phase
mo e ene ge ically a o able o e aus eni e [
5
] (i is shi ed om below he Fe mi le el o he Fe mi
le el du ing he MT), he s abiliza ion o he diso de ed L1
2
s uc u e in he in es iga ed compound is
he eason o he missing MT.