Magne ic Aniso opy o Indi idual
Nanomagne s Embedded in Biological
Sys ems De e mined by Axi-asymme ic X‑ ay
T ansmission Mic oscopy
Lou des Ma cano,*Inaki O ue, Da id Gandia, Lucía Ganda ias, Ma kus Weigand,
Radu Ma ius Ab udan, Ana Ga cía-P ie o, Al edo Ga cía-A ibas, Alicia Muela, M. Luisa Fdez-Gubieda,*
and Se gio Valencia*
Ci e This: ACS Nano 2022, 16, 7398−7408
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sıSuppo ing In o ma ion
ABSTRACT: O e he pas ew yea s, he use o nanomagne s in biomedical applica ions has inc eased. Among
o he s, magne ic nanos uc u es can be used as diagnos ic and he apeu ic agen s in ca dio ascula diseases, o
locally des oy cance cells, o deli e d ugs a specific posi ions, and o guide (and ack) s em cells o damaged
body loca ions in egene a i e medicine and issue enginee ing. All hese applica ions ely on he magne ic
p ope ies o he nanomagne s which a e mos ly de e mined by hei magne ic aniso opy. Despi e i s impo ance,
he magne ic aniso opy o he indi idual magne ic nanos uc u es is unknown. Cu en ly a ailable magne ic
sensi i e mic oscopic me hods a e ei he limi ed in spa ial esolu ion o in magne ic field s eng h o , mo e ele an ,
do no allow one o measu e magne ic signals o nanomagne s embedded in biological sys ems. Hence, he use o
nanomagne s in biomedical applica ions mus ely on mean alues ob ained a e a e aging samples con aining
housands o dissimila en i ies. He e we p esen a hyb id expe imen al/ heo e ical me hod capable o wo king ou
he magne ic aniso opy cons an and he magne ic easy axis o indi idual magne ic nanos uc u es embedded in
biological sys ems. The me hod combines scanning ansmission X- ay mic oscopy using an axi-asymme ic
magne ic field wi h heo e ical simula ions based on he S one −Wohl a h model. The alidi y o he me hod is
demons a ed by de e mining he magne ic aniso opy cons an and magne ic easy axis di ec ion o 15 in acellula
magne i e nanopa icles (50 nm in size) biosyn hesized inside a magne o ac ic bac e ium.
KEYWORDS: X- ay magne ic ci cula dich oism, scanning ansmission X- ay mic oscopy, magne o ac ic bac e ia,
Magne o ib io blakemo ei MV-1, nanomagne s, magne ic nanopa icle, magne ic aniso opy
The las cen u y has aced a undamen al need o
de elop nano echnology-based pa hways o achie e
ele an pe o mance o echnological, biomedical,
and en i onmen al pu poses aiming o o e come he eme ging
social challenges. In his ega d, nanomagne s offe in e es ing
physical p ope ies showing he po en ial o ulfill such
demands.
1,2
The apid ad ances in nano ab ica ion achie ed
in he las decades ha e enabled he explo a ion o a g ea
a ie y o magne ic nanos uc u es o a my iad o applica ions
Recei ed: Oc obe 28, 2021
Accep ed: Ap il 20, 2022
Published: Ap il 26, 2022
A icle
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anging om magne ic eco ding
3,4
o clinical applica ions. In
he pa icula case o biomedical applica ions, he sui abili y o
nanomagne s lies in wo main ac s. Fi s , hei educed size
( om ew nanome e s o ens o nanome e s) is compa able o
hose o p o eins, nucleic acids, o i uses, allowing p omising
in e ac ion wi h biological sys ems. Second, he magne ic
na u e o he nanos uc u es g an s hei manipula ion by
ex e nal magne ic fields. All o his makes magne ic
nanos uc u es excellen candida es o be used as diagnosis
agen s in ca dio ascula diseases, o locally hea and des oy
cance cells in hype he mia cance ea men , o o a ge ed
magne ic cell deli e y in egene a i e medicine.
5−10
A success ul implemen a ion in biomedicine o he designed
magne ic nanos uc u e elies on i s unde lying physical
p ope ies a he nanoscale wi hin he biological en i y. In
pa icula , he ole o magne ic aniso opy a ises as an
o e iding ques ion.
11
Indeed, he magne ic aniso opy has a
s ong influence on he magne ic esponse o he nanomagne s.
Fo example, i de e mines he s abiliza ion o he magne i-
za ion o he magne ic nanos uc u e, i s supe pa amagne ic
size limi , he magne iza ion e e sal mechanism, and he
coe ci e and sa u a ion fields, among o he s. All o hem a e
de e mining pa ame e s in he efficiency o he nanomagne o
i s subsequen medical applica ions.
12−20
Howe e , he access
o his ype o in o ma ion is es ic ed o mean alues
ob ained by means o mac oscopic echniques which a e age
o e a la ge numbe o nanomagne s o ge a measu able signal.
This impedes ob aining eliable in o ma ion owa d he design
o cus omized nanoma e ials o specific applica ions.
Despi e he exis ence o se e al space- esol ed magne ic
sensi i e echniques capable o cha ac e izing indi idual
nanomagne s wi hin na u al sys ems, he in o ma ion ha
can be ob ained is limi ed. Fo example, off-axis elec on
holog aphy in he ansmission elec on mic oscope
21,22
gi es
in o ma ion abou he field lines gene a ed by he magne ic
nanos uc u es, bu i canno di ec ly image hei magne -
iza ion. Simila ly, ni ogen- acancy op ical magne ic imaging,
23
a mo e ecen echnique, p esen s a a he poo spa ial
esolu ion o abou 400 nm. Finally, magne ic o ce
mic oscopy
24−27
p o ides a high spa ial esolu ion ( ypically
50 nm) and he abili y o wo k in a iable applied magne ic
fields, bu he in o ma ion his echnique p o ides is mos ly
quali a i e.
On he o he hand, synch o on adia ion echniques such as
X- ay pho oemission elec on mic oscopy (XPEEM) and
scanning ansmission X- ay mic oscopy (STXM) possess
compa a i e ad an ages since hey p o ide a high spa ial
esolu ion (down o ens o nanome e s) combined wi h
elemen specifici y and magne ic sensi i i y. XPEEM has
shown he possibili y o ob ain, by means o X- ay magne ic
ci cula dich oism (XMCD) con as ,
28
magne ic hys e esis
loops o indi idual magne ic nanopa icles down o 18 nm.
29
Howe e , i p esen s ce ain d awbacks when i comes o
s udying nanomagne s wi hin biological en i ies. I s su ace
sensi i i y s ands ou as a main obs acle. This is due o he ac
ha he XMCD signal is de ec ed ia collec ion o gene a ed
low-kine ic ene gy seconda y pho oelec ons upon illumina ion
wi h synch o on adia ion. These pho oelec ons o igina e
wi hin he opmos 2−3 nm su ace egion.
30
The e o e,
XPEEM canno be used o he cha ac e iza ion o magne ic
nanos uc u es embedded in biological sys ems as he
biological w ap a enua es he signal o igina ing om he
nanomagne su ace. Fu he mo e, XPEEM allows applica ion
o only mode a e magne ic fields (up o ≈20 mT
29
) due o he
magne ic field induced change o ajec o y o emi ed
pho oelec ons, hinde ing he measu emen o hys e esis
loops o nanosys ems wi h high coe ci e fields. In his espec ,
STXM is a mo e flexible echnique. The XMCD signal is
ob ained by measu ing he ansmi ed pho on in ensi y
h ough he specimen. Thus, STXM is a bulk sensi i e
Figu e 1. TEM imaging and XMCD analysis o M. blakemo ei. (a) TEM image o a M. blakemo ei MV-1 bac e ium. The enla ged egion
shows a sec ion o he chain wi h magne osomes whose long axes a e de ia ed om he chain axis. (b) Zoom-in o h ee magne osomes o
he chain. (c) Schema ic ep esen a ions o a unca ed hexa-oc ahed on, which is he c ys al habi o magne osomes om he s ain MV-1,
showing he diffe en ace s.
43
(d) Sphe ical coo dina es (α,λ) o he [111] elonga ed di ec ion o he magne osomes in he xyz e e ence
sys em used in he simula ions (Figu e 2). (e) Fe L3-edge ansmission X- ay abso p ion spec a wi h he incoming beam igh -pola ized
unde an ex e nal posi i e/nega i e sa u a ing magne ic field (σ±) ob ained om a collec ion o andomly dis ibu ed M. blakemo ei cells.
Spec a ha e been no malized by he peak in ensi y a he L3-edge o he nonmagne ic con ibu ion o he X- ay abso p ion (XAS = σ++σ−).
Compu ing σ−−σ+gi es he XMCD signal ( ), whe e he bes linea combina ion fi has been added (con inuous ed line). The e ical
do ed line in ( ) ma ks he ene gy a which he STXM images we e eco ded (E= 709.3 eV).
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echnique capable o gaining magne ic in o ma ion on
in acellula magne ic nanos uc u es. Las bu no leas , as
STXM measu es pho ons, he e is no limi a ion in e ms o
magne ic fields.
31
He e we epo on a hyb id me hod combining expe imen al
da a acquisi ion wi h a heo e ical modeling o ob ain
quan i a i e in o ma ion on he effec i e magne ic aniso opy
(magne ic aniso opy cons an and magne ic easy axis
di ec ion) o indi idual nanomagne s. The me hod elies on
a magne ic imaging echnique wi h nanome ic spa ial
esolu ion (e.g., XPEEM o STXM) unde axi-asymme ic
magne ic fields and fi ing o he expe imen al da a on a model
based on he S one −Wohl a h o malism. The axi-asym-
me ic magne ic field leads o asymme ic hys e esis loops
which allow emo al o he degene acy on he angula
o ien a ion o he magne ic easy axis. I acili a es he
heo e ical analysis because i educes he co ela ions be ween
he pa ame e s in ol ed, hus imp o ing he accu acy o he
esul s.
To highligh he ull po en ial o he p oposed me hod, his
app oach has been es ed o e a model sys em consis ing o
magne ic nanopa icles embedded in a biological sys em, i.e.,a
magne o ac ic bac e ium wi h ≈50 nm size magne i e
nanopa icles biosyn hesized in i s in e io . Magne o ac ic
bac e ia a e mic oo ganisms ha ha e he abili y o syn hesize
in e nally memb ane-enclosed single-domain magne ic nano-
pa icles called magne osomes. Wi hin he bac e ium, magne-
osomes a e aligned, o ming an in e nal magne ic chain which
beha es as a la ge pe manen magne ic dipole causing hei
o ien a ion along he geomagne ic field lines.
32−36
P e ious
wo ks ha e demons a ed he supe io i y o STXM-XMCD
o e XPEEM o magne ic imaging o in acellula magne o-
somes.
37−42
RESULTS AND DISCUSSION
Figu e 1a depic s a TEM image o magne o ac ic bac e ium
Magne o ib io blakemo ei s ain MV-1, employed in his wo k.
MV-1 cells possess a single magne osome chain con aining a
a iable numbe o unca ed hexa-oc ahed al magne i e
(Fe3O4) magne osomes wi h app oxima e dimensions 35 ×
35 ×65 nm3( e s 36 and 43)(Figu e 1b,c) and single
magne ic domains wi h a high magne ic momen s able a
oom empe a u e.
22,44
Magne osomes in he chain a e aligned
closely pa allel o hei axis o elonga ion, a ⟨111⟩c ys allo-
g aphic di ec ion o magne i e (Figu e 1c), along he axis o
mo ili y o he cell,
43,45−48
al hough impo an de ia ions a e
some imes obse ed (see Figu e 1a). The elonga ion along he
⟨111⟩di ec ion ( he [111] di ec ion in Figu e 1c), which
coincides in his sys em wi h a magne oc ys alline easy axis,
yields a s ong effec i e uniaxial magne ic aniso opy o he
magne osomes along ha di ec ion.
49,50
As a consequence, he
nanopa icles biosyn hesized by M. blakemo ei a e uniaxial
single magne ic domains whose magne iza ion p ocess can be
Figu e 2. Schema ic ep esen a ion o he axi-asymme ic STXM-XMCD expe imen . (a,b) Schema ic se up o he STXM mic oscope and
magne sys em implemen ed o he XAS and STXM-XMCD measu emen s. (c) μ0Hy,zmagne ic field componen s as a unc ion o μ0Hx. The
con inuous lines a e fi s o he expe imen al calib a ion poin s whose analy ical exp ession has been used in he heo e ical models (see he
Suppo ing In o ma ion). (d) Space- esol ed XAS image o he 15-magne osome in acellula chain we measu e collec ed a he Fe L3-edge
esonance ene gy.
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desc ibed by a modified S one −Wohl a h model,
51−54
as will
be shown in he ollowing.
The chemical pu i y o he ba ch o which he in es iga ed
bac e ium belongs o, has been cha ac e ized by means o
XMCD on a mac oscopic sample composed o a collec ion o
andomly dis ibu ed cells (ALICE s a ion, beamline PM3,
Helmhol z-Zen um Be lin). The abso p ion spec a ha e been
measu ed in ansmission geome y ac oss he Fe L3-edge o
incoming ci cula pola ized adia ion wi h igh helici y and an
ex e nal posi i e/nega i e sa u a ing magne ic field (σ±)
applied pa allel o he beam di ec ion (see Figu e 1e). The
esul an XMCD signal, compu ed as σ−−σ+, p esen ed in
Figu e 1 , depic s h ee majo peaks cen e ed a 709.3, 710.3,
and 711.1 eV. These spec oscopic signa u es wi hin he
XMCD a e cha ac e is ic o he in e se spinel s uc u e o
magne i e and a ibu ed o Fe2+ a oc ahed al (Oh) si es and
Fe3+ occupying e ahed al (Td) and oc ahed al posi ions,
espec i ely.
55,56
XMCD is p opo ional o he p ojec ion o
he magne iza ion along he p opaga ion di ec ion o he
incoming beam. Hence, he opposi e XMCD sign be ween he
Fe
Oh
2+
and
Fe
Oh
3+
peaks as compa ed o ha o he FeTd
3
+
peak
highligh s he expec ed an i e omagne ic alignmen be ween
he Fe ca ions in Oh and Td si es. We no e he p esence wi hin
he XMCD o an addi ional spec oscopic ea u e which shows
up as a shoulde a he low ene gy side o he
Fe
Oh
2+
peak. This
s uc u e appea s due o sa u a ion o hickness effec s inhe en
o ansmission expe imen s.
57
I can be shown ha i s
p esence does no subs an ially affec he size o he XMCD
ea u es associa ed wi h
Fe
Oh
2+
,FeTd
3
+
, and
Fe
Oh
3+
so ha he
XMCD can be fi by a linea combina ion o he heo e ical
spec a o each indi idual Fe componen be ween 705 and 715
eV.
58
Ou fi yieldsa
Fe
Oh
2+
:FeTd
3
+
:
Fe
Oh
3+
a io o
1.06(7):1.00(8):1.18(9) ( ed cu e in Figu e 1 ), in good
ag eemen wi h s oichiome ic magne i e (1:1:1). Compa able
XAS and XMCD spec a we e ob ained by means o STXM on
a single in acellula magne osome chain (see he Suppo ing
In o ma ion).
Figu e 2a,b shows schema ically he configu a ion used o
he STXM-XMCD measu emen s ca ied ou using he
MAXYMUS mic oscope a he UE46-PGM2 beamline a he
Helmhol z-Zen um Be lin.
59
An axi-asymme ic ex e nal
magne ic field was gene a ed by ou od NdFeB pe manen
magne s which can be o a ed independen ly.
31
The magne ic
field a he sample loca ion is mos ly o ien ed along he x-
di ec ion and can be a ied be ween μ0Hx=±260 mT. The
μ0Hy,zcomponen s o he applied field a e shown in Figu e 2c
as a unc ion o μ0Hx. While he μ0Hyand μ0Hzcomponen s
each much lowe maximum alues han he μ0Hxcomponen ,
hese a e enough o impose an asymme y o he applied field
ha will be he key poin o define he magne ic aniso opy o
each indi idual magne osome (see he Suppo ing In o ma-
ion).
Aimed o analyze he magne iza ion p ocess o indi idual
magne osomes wi hin an in ac magne o ac ic bac e ium, we
selec ed a cell con aining a 15-magne osome chain. Figu e 2d
depic s he XAS image o he selec ed bac e ium o he
expe imen . The image has been ob ained by a e aging σ+and
σ−images ob ained a he Fe L3-edge esonance ene gy.
The space- esol ed STXM-XMCD signal was eco ded a E
= 709.3 eV (maximum XMCD signal) while cycling he
ex e nal magne ic field μ0Hxbe ween ±260 mT. As p e iously
men ioned, he e exis μ0Hy,zcomponen s associa ed wi h μ0Hx
(Figu e 2c). Figu e 3 (cen al panel) illus a es he dependence
o he no malized XMCD signal on μ0Hx.Figu e 3a−g shows
selec ed space- esol ed images o he XMCD a specific alues
o μ0Hx. A mo ie showing he field-dependen STXM-XMCD
image sequence o e e y single poin in he loop can be ound
in he Suppo ing In o ma ion.TheXMCDsignalis
p opo ional o he p ojec ion o he magne ic momen
along he p opaga ion di ec ion o he X- ay beam, so ha
ed o blue colo in he XMCD images indica es opposi e
di ec ion o he p ojec ion o he magne ic momen . Du ing
he p ocess, he colo o each magne osome is ei he
comple ely ed o blue (wi h some excep ions, a ibu ed o
he signal noise), confi ming ha magne osomes a e magne ic
single domains whose magne ic momen s o a e cohe en ly
Figu e 3. Magne iza ion p ocess o an in acellula magne osome chain. (Cen al panel) Hys e esis loop o he whole chain. (a−g) Space-
esol ed STXM-XMCD images o he 15-magne osome in acellula chain collec ed a he Fe L3-edge esonance ene gy (709.3 eV) a
selec ed alues o he applied magne ic field μ0Hx. Red and blue colo s ep esen he no malized XMCD signal a ying be ween ±1.
Opposi e colo indica es opposi e di ec ion o he p ojec ion o he magne ic momen . A mo ie showing he field-dependen STXM-XMCD
image sequence o he whole chain can be ound in he Suppo ing In o ma ion.
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owa d he applied field. The e o e, s a ing om a s a e o
magne ic sa u a ion (μ0Hx=+260 mT), all magne osomes a e
aligned showing a nega i e XMCD signal (all magne osomes
ed, panel a). As μ0Hxdec eases, he XMCD signal emains
almos cons an un il μ0Hxa ound −10 o −20 mT (panel c)
when he XMCD sign o le mos magne osomes changes sign,
and hence i s magne ic o ien a ion, as hei magne ic momen
eo ien s owa d he magne ic field di ec ion. A u he
dec ease o μ0Hxleads o a sequen ial o a ion o he es o
magne osomes which is comple ed a μ0Hx=−50 mT (all
magne osomes blue, panel e). Simila esul s we e ob ained
when amping he magne ic fields om μ0Hx=−260 mT o
+260 mT (panels e−g). Main panel o Figu e 4 shows he
space- esol ed 2D map o he coe ci e field (μ0Hc) compu ed
om he XMCD signal s μ0Hx(see Me hods). Acco dingly,
wi h he magne iza ion p ocess desc ibed, he e i can be seen
ha |μ0Hc|inc eases in magni ude om 17 o 25 mT o
magne osomes 1−5 and 9−10 h ough 30 mT o magne o-
somes 6−8 un il 45−50 mT o he igh mos magne osomes
(11−15). Acco ding o he S one −Wohl a h model, being
magne osomes wi h s able uniaxial magne ic single domains,
hese diffe ences in μ0Hcsugges diffe ences in he effec i e
magne ic aniso opy alues and/o o ien a ion o he magne o-
somes [111] easy axes wi h he applied field.
51
Indeed, he
hys e esis loops o he pa icles, shown in Figu e 4 o selec ed
magne osomes, display diffe en p ofiles, om squa e-shaped
such as ha o magne osome 15 o nea ly anhys e e ic as o
magne osome 1.
Quan i a i e in o ma ion on he magne ic aniso opy
cons an and o ien a ion o he magne ic easy axis o each
indi idual magne osome has been ga he ed om he
heo e ical modeling o he hys e esis loops. Acco ding o
he S one −Wohl a h model
51
o uniaxial magne ic single
domains, he equilib ium magne ic o ien a ion o each
magne osome’s magne ic momen can be de e mined by
minimizing he single dipole ene gy densi y, gi en by he sum
o an effec i e uniaxial aniso opy con ibu ion along he [111]
di ec ion and he Zeeman ene gy:
EKuuMHuu(, ) 1 ( ) ( )
111 m 2
0sHm
θφ μ=[− ·]− ·(1)
He e, ec o s a e e e ed o he xyz e e ence sys em shown in
Figu e 2a. Kis he effec i e uniaxial aniso opy cons an , umis
he magne ic momen uni ec o defined by he pola and
azimu hal angles θand φ, espec i ely, and u111 is he uni
ec o along he di ec ion o he effec i e magne ic easy axis,
namely, he [111] di ec ion defined by he pola and azimu hal
angles αand λ, espec i ely (Figu e 1d). He e we assume ha
he uniaxial shape aniso opy plays a dominan ole compa ed
o he weak cubic magne oc ys alline aniso opy o magne -
i e.
49,50
This is e idenced in he ze o-field ene gy su aces
cons uc ed conside ing bo h con ibu ions (see Figu e S3 in
he Suppo ing In o ma ion), whe e i is shown ha he o e all
aniso opy emains uniaxial along he [111] long axis
ega dless o he cubic con ibu ion. In addi ion, aking in o
accoun he cohe en o a ion o neighbo ing magne osomes’
magne ic momen s as sugges ed by he STXM imaging, he
magne ic in e ac ions be ween nea es neighbo s a e exp essed
in he same way as a uniaxial aniso opy ene gy,
60
hus he
effec i e aniso opy e m accoun s o he compe i ion be ween
bo h con ibu ions: shape aniso opy and dipola in e ac ions
be ween nea es neighbo s, and a mino con ibu ion om he
cubic magne oc ys alline aniso opy. Finally, in he Zeeman
Figu e 4. Hys e esis loops o indi idual magne osomes: expe imen s model. Cen e : Space- esol ed XAS image o he in acellula 15-
magne osome chain collec ed a he Fe L3-edge esonance ene gy (709.3 eV) displayed in Figu e 2. The colo map below co esponds o he
coe ci e field, |μ0Hc|map, ha is, he μ0Hx alue a which he in e pola ed dich oic signal o he fi s b anch o he hys e esis loop (μ0Hx
om 260 o −260 mT) becomes null. Figu es a ound he p e ious one ep esen he space- esol ed hys e esis loops ob ained o selec ed
magne osomes o he chain. Red sphe es co espond o he dec easing field b anch (+ o −) and black squa es o he inc easing field b anch
(− o + ). Con inuous lines co espond o he simula ed hys e esis loops conside ing he op imal alues ound o he aniso opy cons an
(K) and pola (α) and azimu hal (λ) angles shown in Figu e 5.
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e m, uH ep esen s he 3D applied magne ic field uni ec o
and Msis he spon aneous magne iza ion, se o ha o
magne i e Ms=48×104A/m. The analy ical exp ession used
o he field H
has been ob ained om he fi o he
expe imen al calib a ion poin s (Figu e 2c).
Fo a gi en unc ion E(θ,φ), hys e esis loops ha e been
simula ed assuming a dynamical app oach ha accoun s o he
he mal fluc ua ions o he magne iza ion, as desc ibed
elsewhe e.
52−54
Fo each magne osome, we ha e calcula ed a
collec ion o hys e esis loops conside ing combina ions o he
h ee a iables K,α, and λ, whe e K∈[10 kJ/m3, 30 kJ/m3], α
∈[44°, 136°], and λ∈[−90°,90°]. Fo each combina ion (K,
α,λ), he goodness o he fi is e alua ed by calcula ing he
oo -mean-squa e de ia ion (RMSD) be ween he expe imen-
al and calcula ed hys e esis loops ollowing he exp ession
shown in he Me hods. The bes ag eemen be ween he
expe imen al and calcula ed hys e esis loops co esponds o
he combina ion (K,α,λ) ha minimizes he RMSD (as e isks
in Figu e 5a−c).
In Figu e 4, we ha e included he bes fi cu es o en
selec ed magne osomes. The cu es ep oduce sa is ac o ily
he expe imen al hys e esis loops. Consis en ly, he coe ci e
field alues ob ained expe imen ally o he 260 o −260 mT
b anch (see Figu e 4) a e compa able o he ones ob ained
om he fi o ou model. No e, howe e , ha he hys e esis
loops a e no symme ic wi h espec o μ0Hx; see, o example,
loops co esponding o magne osomes 3 and 6. This is due o
he expe imen ally imposed axi-asymme ic magne ic field.
This cha ac e is ic applied magne ic field in oduces an
asymme y in he sys em which is essen ial o de e mine he
3D o ien a ion o he magne iza ion easy axis. A magne ic field
pu ely di ec ed h ough he xdi ec ion would no allow o
Figu e 5. Magne ic aniso opy cons an and o ien a ion o he magne ic easy axis o indi idual magne osomes. (a) Effec i e uniaxial
aniso opy cons an (K) and (b) pola (α) and (c) azimu hal (λ) angles ex ac ed om he fi o he STXM hys e esis loops o he uniaxial
aniso opy axis o he magne osomes. Blue as e isks ep esen he bes heo e ical-expe imen al ma ch (minimum oo -mean-squa e
de ia ion, RMSD) used o he simula ions in Figu e 4. Black squa es and ed sphe es ep esen he mean alue o he RMSD dis ibu ions
wi hin a confidence in e al o 5% and 10% wi h espec o RMSDmin. The e o ba s ep esen he s anda d de ia ions o he dis ibu ions.
(d) 3D dis ibu ion and con ou plo o he RMSD as a unc ion o αand λob ained o magne osome 2 conside ing an effec i e aniso opy
cons an alue K= 15 kJ/m3. (e) Accu acy o he fi ed a iables K,α,o λ o each o he magne osomes o a confidence limi o 5% ( ull
ba s) and 10% (dashed ba s) o he RMSD. ( ) Compa ison be ween expe imen al XMCD dependence on magne osome numbe ob ained a
Hx= 0 (blue do s) and he expec ed (compu ed) XMCD o an easy axis o ien ed along he di ec ion defined by he αand λ alues o panels
b and c conside ing a RMSD confidence o 5% (g een squa es). The XMCDexpe imen al has been ob ained om he da a depic ed in Figu e 4 by
a e aging he absolu e alue o he XMCD a Hx= 0 o he inc easing and dec easing field b anches. E o ba s o XMCDexpe imen al ha e
been se o ±0.1 based on he XMCD signal dispe sion measu ed expe imen ally. The e o ba s o XMCDcompu ed ha e been calcula ed om
he 5% RMSD epo ed e o s o αand λ.
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accu a ely de e mine he o ien a ion o he easy axis due o a
degene acy in he model which makes +λand −λ
indis inguishable (see Figu e S4 in he Suppo ing In o ma-
ion). This degene acy is emo ed wi h axi-asymme ic fields
(see he Suppo ing In o ma ion). Mo eo e , he field
asymme y educes he co ela ions be ween he h ee
adjus able pa ame e s, imp o ing he obus ness o he
simula ions. Likewise, he geome y imposed on he expe -
imen al sys em also a o s o disce n sligh changes in he
o ien a ion o he magne osomes (pa icula ly, α). Since he
dich oic signal eco ded by STXM is p opo ional o he
p ojec ion o he magne ic momen along he beam di ec ion,
and no o he di ec ion o he applied field, small changes o
±10°in αchange d as ically he p ofile o he hys e esis loops
(see he Suppo ing In o ma ion, Figu e S5). Such la ge
diffe ences simpli y he fi ing p ocess.
The bes -fi alues o he h ee adjus ed pa ame e s o each
one o he 15 magne osomes a e ma ked wi h blue as e isks in
Figu e 5a−c.
The alues ob ained o he effec i e uniaxial aniso opy
cons an ange om K= 12 kJ/m3(magne osome 5) o K=27
kJ/m3(magne osome 15) (Figu e 5a). As indica ed p e iously,
he effec i e aniso opy cons an includes he con ibu ions o
he pa icle shape aniso opy and he dipola in e ac ions
be ween pa icles plus a mino con ibu ion om he
magne oc ys alline aniso opy.
An es ima ion o he shape aniso opy cons an can be
ga he ed om he calcula ion o he shape aniso opy ene gy
landscape o a unca ed hexa-oc ahed on mo phology using a
model based on fini e elemen me hod
61
(mo e de ails can be
ound in he Suppo ing In o ma ion). As expec ed, he model
confi ms ha o his geome y he e is only one absolu e
ene gy minimum along he elonga ed di ec ion pa allel o he
⟨111⟩c ys allog aphic axis. The ene gy ba ie be ween he
minima and maxima, and hence he shape aniso opy o he
hexa-oc ahed al magne osomes, depends on hei elonga ion
deg ee (wid h/leng h, W/L). Fo an a e age magne osome o
MV-1 wi h W/L= 0.72,
62
he model yields Kshape = 22 kJ/m3,
o he same o de as he alues ob ained om he fi s. The
diffe ences in Kobse ed among he magne osomes can hus
be asc ibed o ei he changes in he W/L a io and/o he
dipola in e ac ions be ween magne osomes.
Rega ding he o ien a ion o he magne ic easy axis ([111]
elonga ed di ec ion) o he magne osomes, Figu e 5b and c
shows he esul sob ained o αand λ o he 15
magne osomes.
The pola angle, α, is a pa ame e ha can be de e mined
wi h g ea accu acy, as la e e idenced by he small
inde e mina ion o he esul s. α, ha is, he inclina ion o
he easy axis wi h espec o he sample plane, is expec ed o be
close o 90°because he bac e ium lies on he subs a e plane
and so magne osomes a e also expec ed o es on his e y
same plane. Indeed, we ound ha he αdis ibu ion o all he
magne osomes is cen e ed a 90°albei wi h some dispe sion
o ±15.
On he o he hand, λ anges be ween ±90°. Fo ins ance, he
magne ic easy axis o magne osome 1 is mos ly pe pendicula
o he μ0Hxfield di ec ion, which ag ees wi h he anhys e e ic
hys e esis loop obse ed o his nanopa icle in Figu e 4.
Fo he sake o p o ing he accu acy o he alues ob ained
o he h ee a iables (K,α, and λ) by he minimiza ion o he
RMSD and o de e mining hei unce ain ies, we ha e
pe o med a s a is ical analysis o all fi ed cu es by assessing
he dispe sion and asymme y o he pa ame e space close o
he minima. To illus a e his, Figu e 5d shows an example o
he 3D ep esen a ion o he RMSD as a unc ion o he
a iables αand λ o magne osome 2, whe e he absolu e
minimum RMSDmin is well obse ed. We ha e calcula ed he
p obabili y dis ibu ion o each a iable by conside ing he
simula ions ha gi e a RMSD ha lies below a ce ain
confidence limi . He e we ha e conside ed wo confidence
limi s: 5% and 10% abo e RMSDmin; see he Suppo ing
In o ma ion (sec ion S6) o mo e de ails. The alues ob ained
om he fi (blue as e isks in Figu e 5a−c) a e conside ed o
be accu a e i hey a e simila o hose ob ained by a e aging
he alues om he s a is ical dis ibu ions wi hin hei
espec i e confidence limi s (black squa es and ed sphe es
o 5% and 10% confidence limi s, espec i ely). The s anda d
de ia ions o he dis ibu ions ha e been aken as a measu e o
he unce ain y o he co esponding a iable and a e
ep esen ed by black (5%) and ed (10%) e o ba s in Figu e
5a−c. As depic ed in panels (a)−(c) o Figu e 5, he alues
de e mined om he fi (blue as e isks) and hose de e mined
om he s a is ical analysis (black squa es and ed do s) a e
alike in mos o he cases. We ha e defined he accu acy on he
de e mina ion o a gi en a iable (K,α,o λ)asaccu acy = 100
×((1 −|V i −Vs a .|/ΔV) whe e V i and Vs a a e he alues o
ha a iable ob ained om he fi and om he s a is ical
analysis (confidence o 5% and 10%), espec i ely. ΔVis he
ange o e which he a iable has been explo ed (20 kJ/m3 o
K,92° o αand 180° o λ). As shown in Figu e 5e, while he
a e age accu acy o λis ≈92%, he accu acy on he
de e mina ion o bo h αand Kis e en highe and eaches
95% on a e age.
Besides he ac ha he ob ained fi a iables all wi hin
expec a ion and possess s a is ical significance, we can u he
asses he obus ness o he p oposed me hod by compa ing he
ou come o he fi s wi h he expe imen al da a. By making use
o he αand λfi ed a iables, defining he [111] magne ic easy
axis o each magne osome, and by aking in o accoun he
geome y o he expe imen (see Me hods) we can compu e
he expec ed XMCD a H= 0. Indeed, in he absence o any
ex e nal magne ic field, he magne iza ion di ec ion o each
nanomagne is expec ed o lay along i s own magne ic easy
axis. The compu ed XMCD ( o H= 0) is depic ed in Figu e
5 by g een squa es. Fo he sake o compa ison we show wi h
blue do s he XMCD measu ed expe imen ally a Hx=0.We
conside ha he yand zcomponen s ( o Hx= 0) a e no
s ong enough o significan ly d ag he magne iza ion away
om i s easy axis di ec ion. We also no e ha he fi s leading o
he K,α, and λ alues epo ed in Figu e 5a−c assigned he
same weigh o all XMCD da a poin s (see Figu e 4) ob ained
o diffe en magne ic fields. Tha is, he XMCD measu ed a
Hx= 0 has no special influence in he ou come o he fi .
Al hough e iden , his in o ma ion is ele an because i
ensu es ha we can compa e he ou come o he fi , ha is, he
fi ed [111] di ec ion o he magne ic easy axis, wi h an specific
XMCD image which signal is de e mined by he o ien a ion o
he expe imen al [111] magne ic easy axis. As shown in Figu e
5 , he e is e y good ag eemen be ween he expe imen al and
compu ed XMCDs. We no e ha his esemblance is no jus
es ic ed o a compa ison be ween compu ed and expe -
imen al da a on a magne osome by magne osome basis. The
compu ed cu e does also ep oduce he a ia ion o XMCD in
be ween magne osomes. Such a diffe ence, solely due o he
diffe en o ien a ions o hei [111] magne ic axes, is ully
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ep oduced by he compu ed cu e. This p o es, no only ha
he αand λfi a iables ( esul ing om 15 independen fi s)
a e wi hin expe imen al e o simila o he expe imen al ones,
bu also ha he me hod he e p oposed is sel -consis en and
yields eliable esul s capable o cap u ing he physics o he
sys em.
CONCLUSIONS
In summa y, he e we ha e demons a ed he po en ial o a
combined expe imen al− heo e ical app oach o ob ain
ele an quan i a i e magne ic in o ma ion on nanomagne s.
Selec ing he p ope magne ic imaging echnique allows using
his app oach e en o encapsula ed sys ems, in pa icula i is
sui able o nanopa icles embedded in biological en i ies. The
me hod has been applied o magne o ac ic bac e ium M.
blakemo ei s ain MV-1. Fi s , space- esol ed magne ic
hys e esis loops wi h nanome ic esolu ion a e ob ained by
means o axi-asymme ic STXM-XMCD. Subsequen ly, he
expe imen al magne ic hys e esis loops a e fi ed by means o a
S one −Wohl a h-based app oach allowing ob aining ele an
quan i a i e magne ic in o ma ion in e ms o he magne ic
aniso opy cons an and o ien a ion o he magne ic easy axis.
The asymme y o he applied field allows an accu a e
heo e ical modeling o he expe imen al hys e esis loops
emo ing degene acies inhe en o symme ic magne ic field
configu a ions.
In conclusion, we p esen an expe imen al and heo e ical
app oach o explo e in an elemen -specific way he magne ic
p ope ies o aniso opic magne ic nanos uc u es. We show
ha his me hod can be applied o nanomagne s embedded in
biological en i ies including sys ems based on isola ed
magne ic nanopa icles o biomedical applica ions. Al hough
i is ue ha he applica ion o he p esen ed me hod equi es
access o a la ge scale acili y, ecen p og ess in lase -d i en X-
ay sou ces sugges s ha his migh change. Indeed, hese so-
called be a on- ype plasma X- ay sou ces, wi h dimensions
o de s o magni ude smalle han hose o synch o on
adia ion acili ies, can deli e X- ay adia ion wi h unable
pola iza ion, high spa ial cohe ence, and a peak b igh ness
simila o ha o hi d-gene a ion synch o ons.
63−66
Hence, i
is no un easonable o expec ha , in a no oo dis an u u e,
compac lase -d i en plasma X- ay sou ces will allow he he e
p esen ed me hod o become a s anda d labo a o y echnique.
METHODS
Bac e ial S ain and G ow h Condi ions. Magne o ib io
blakemo ei s ain MV-1 (DSM 18854) was g own anae obically a
30 °C in liquid medium con aining pe li e o a ificial seawa e
(ASW): 41.8 mM sodium succina e and 2.4 mM sodium ace a e as
ca bon sou ces, 0.33% (w / ol) casamino acids, 33.4 mL modified
Wol e’s mine al solu ion and i on quina e (100 μM) as i on sou ce o
enhance magne osome o ma ion. The medium was dis ibu ed in o
Hunga e ubes and fluxed wi h ni ous oxide (N2O) o 20 min p io
o au ocla ing (15 min, 121 °C). Finally, a e he media was cooled
o oom empe a u e, 0.58 mM cys eine was added.
67
A e 144 h o
incuba ion, when well- o med magne osomes we e obse ed, he cells
we e ha es ed by cen i uga ion, washed h ee imes in mQ wa e ,
and fixed in 2% glu a aldehyde.
Subsequen measu emen s we e pe o med on uns ained cells
adso bed on o 300 mesh ca bon-coa ed coppe g ids. A 5 μL d op o
MV-1 in concen a ion 109cell/mL was deposi ed on o Cu g ids. To
ob ain homogeneous samples, in a ed adia ion was used du ing he
deposi ion aimed a accele a ing he d ying and minimizing he
su ace ension.
T ansmission Elec on Mic oscopy. TEM images we e acqui ed
wi h a PHILIPS EM208S elec on mic oscope a an accele a ing
ol age o 120 kV.
X- ay Magne ic Ci cula Dich oism (XMCD). Room empe -
a u e XMCD expe imen s we e ca ied ou using ALICE s a ion
68,69
a he PM3 beamline o synch o on BESSY II in Be lin, Ge many.
Da a acquisi ion was done in ansmission mode. X- ay adia ion
(ci cula ly pola ized, igh helici y, beam size 100 ×200 μm2)
impinged he sample su ace a no mal incidence. X- ay abso p ion
spec a (XAS) we e ob ained ac oss he Fe L3-edge wi h a s ep size o
0.2 eV wi h an applied magne ic field pa allel o he X- ay beam o
+0.35 T (σ+) and −0.35 T (σ−). Six spec a we e acqui ed and
a e aged o imp o e he signal- o-noise a io. XMCD, defined as σ−−
σ+, is p opo ional o he p ojec ion o he magne iza ion along he
beam p opaga ion di ec ion. Unde he desc ibed expe imen al
condi ions, he no malized XMCD would only depend on he
magne ic o ien a ion o he magne iza ion o each magne osome
(defined by αand λ, see Figu e 1) so ha XMCD = c (sin 30 sin α
cos λ+ cos 30 cos α), whe e c is a cons an common o all
magne osomes.
Scanning T ansmission X- ay Mic oscopy (STXM). Magne ic
imaging o indi idual magne osome chains wi hin M. blakemo ei was
pe o med a oom empe a u e by means o scanning ansmission
elec on mic oscopy (STXM) using X- ay magne ic ci cula dich oism
(XMCD) as a magne ic con as mechanism. Measu emen s we e
ca ied ou a he MAXYMUS end s a ion a HZB BESSY II, Be lin.
The Cu g id, wi h he sample deposi ed on i , defines he xy-plane.
The beam impinged he sample su ace a 30° om i s no mal, a
s anda d configu a ion o he STXM sys em allowing a nonze o
p ojec ion o he magne iza ion o in-plane magne ized sys ems along
he beam p opaga ion di ec ion. A sys em based on ou o a able
pe manen magne s
31
p oduces an axi-asymme ic magne ic field
whe e he in ensi y and di ec ion o he yand zcomponen s depend
on he μ0Hx( anging be ween ±260 mT); see Figu e 2.
Magne ic imaging was pe o med as a unc ion o μ0Hxwhich was
cycled om +260 mT o −260 mT and ice e sa. The 110 ×45 pixel
images co espond o a field o iew o 1100 ×450 nm2. The space-
esol ed ansmission was eco ded by scanning he beam posi ion in
10 nm s eps. A each magne ic field poin we ob ained images a he
Fe L3 esonance (709.3 eV) o incoming ci cula ly pola ized
adia ion wi h σ+and σ−helici y, espec i ely. The in eg a ion ime
was se o 20 ms. Each image was no malized o a b igh field image
and d i co ec ed o a e e ence image. The XMCD images we e
compu ed as σ−−σ+. This p ocess was epea ed wice o imp o e
signal- o-noise a io. Magne ic hys e esis loops o indi idual magne o-
somes displayed in Figu e 4 we e ob ained by in eg a ing he XMCD
signal o e hei posi ion as a unc ion o μ0Hx. The hys e esis loop
displayed in Figu e 3 has been ob ained by a e aging he XMCD o e
he whole magne osome chain.
Fo he sake o enhancing he magne ic con as , and hus he
isualiza ion o he XMCD, Figu e 3 shows XMCD images ob ained
a e mul iplica ion o he o iginal XMCD signal by he X- ay
abso p ion image (XAS = σ−+σ+) a e backg ound sub ac ion.
The 2D map o |μ0Hc|displayed in Figu e 4 was ob ained by
smoo hing and in e pola ing he XMCD s μ0Hxsignal ob ained o
he posi i e b anch ( om +260 o −260 mT) a each pixel o he
image. The local coe ci e field was defined o be ha co esponding
o he μ0Hx alue o which XMCD c ossed ze o.
Hys e esis Loop Simula ion and Fi ing P ocedu e. Fo a
gi en unc ion E(θ,φ), he hys e esis loops ha e been modeled
assuming a dynamical app oach desc ibed elsewhe e.
52−54
A
collec ion o mo e han 85 500 hys e esis loops we e simula ed
conside ing diffe en alues o K,α, and λ.Kwas a ied om 10 o 30
kJ/m3in s eps o 1 kJ/m3,αwas anged be ween 44°and 136°on
s eps o 2°, and λwas a ied be ween −90°and 90°in s eps o 2°.
The hys e esis loops ha e been compu ed by conside ing he axi-
asymme ic magne ic field and he geome y used o he expe imen s.
No e ha ollowing he geome y o he expe imen , desc ibed in
Figu e 2, he yaxis o he simula ed hys e esis loop co esponds o he
p ojec ion o he magne iza ion ec o along he beam di ec ion, ha
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is, 120°off he xy sample plane. I explains ha a sa u a ing posi i e
field gi es a nega i e magne iza ion and ice e sa.
Each simula ion was compa ed wi h he expe imen al hys e esis
loops ob ained o each indi idual magne osome aiming o find he
bes fi . Thus, he h ee a iable pa ame e s associa ed wi h he
magne ic aniso opy cons an and he o ien a ion o he magne ic easy
axes (K,α, and λ) ha e been adjus ed o minimize o each
magne osome he oo -mean-squa e de ia ion (RMSD):
d
RMSD (exp sim )
iii
2
=∑−
(2)
whe e i ep esen s he numbe o expe imen al poin s acqui ed in he
expe imen , 28 in ou case, and dis he numbe o deg ees o eedom
defined as he numbe o expe imen al da a minus he numbe o
pa ame e s compu ed, h ee in his pa icula p oblem: K,α, and λ.
In o de o double check he goodness o he fi , we ha e ca ied
ou a s a is ical analysis by analyzing he RMSD dis ibu ion ob ained
o each single magne osome. Thus, conside ing an in e al o
confidence o 5% and 10%, we ep esen he p obabili y dis ibu ion
o K,α, and λwhose RMSD alues a e wi hin he defined in e al
(RMSDmin and RMSDmin + 5/10% RMSDmin). In his way, K,α, and λ
a e defined as he mean alue o he p obabili y dis ibu ion while i s
associa ed e o is ob ained as he s anda d de ia ion o he ob ained
dis ibu ion.
ASSOCIATED CONTENT
*
sıSuppo ing In o ma ion
The Suppo ing In o ma ion is a ailable ee o cha ge a
h ps://pubs.acs.o g/doi/10.1021/acsnano.1c09559.
STXM-XAS as a unc ion o ene gy (MOV)
Magne iza ion p ocess o an in acellula magne osome
chain (MOV)
Mac o- and mic oscopic XAS and XMCD spec oscopy,
analy ical exp ession o he axi-asymme ic magne ic
field, calcula ion o he shape magne ic aniso opy using
fini e elemen s me hod, influence o he cubic magne o-
c ys alline aniso opy o magne i e in he ene gy o he
sys em, influence o he axi-asymme ic magne ic field
and geome y o he expe imen al sys em on he p ofile
o he hys e esis loops, s a is ical analysis o he RMSD
dis ibu ion (PDF)
AUTHOR INFORMATION
Co esponding Au ho s
Lou des Ma cano −Helmhol z-Zen um Be lin u
Ma e ialien und Ene gie, 12489 Be lin, Ge many; Dp o.
Elec icidad y Elec ónica, Uni e sidad del País Vasco -
UPV/EHU, 48940 Leioa, Spain; o cid.o g/0000-0001-
9397-6122; Email: [email p o ec ed]
M. Luisa Fdez-Gubieda −Dp o. Elec icidad y Elec ónica,
Uni e sidad del País Vasco - UPV/EHU, 48940 Leioa,
Spain; BCMa e ials, 48940 Leioa, Spain; o cid.o g/
0000-0001-6076-7738; Email: [email p o ec ed]
Se gio Valencia −Helmhol z-Zen um Be lin u Ma e ialien
und Ene gie, 12489 Be lin, Ge many; o cid.o g/0000-
0002-3912-5797; Email: se gio. alencia@helmhol z-
be lin.de
Au ho s
Inaki O ue −SGIke , Uni e sidad del País Vasco - UPV/
EHU, 48940 Leioa, Spain
Da id Gandia −BCMa e ials, 48940 Leioa, Spain
Lucía Ganda ias −Dp o. Inmunología, Mic obiologíay
Pa asi ología, Uni e sidad del País Vasco - UPV/EHU,
48940 Leioa, Spain
Ma kus Weigand −Helmhol z-Zen um Be lin u
Ma e ialien und Ene gie, 12489 Be lin, Ge many
Radu Ma ius Ab udan −Helmhol z-Zen um Be lin u
Ma e ialien und Ene gie, 12489 Be lin, Ge many
Ana Ga cía-P ie o −Dp o. Física Aplicada, Uni e sidad del
País Vasco - UPV/EHU, 48013 Bilbao, Spain
Al edo Ga cía-A ibas −Dp o. Elec icidad y Elec ónica,
Uni e sidad del País Vasco - UPV/EHU, 48940 Leioa,
Spain; BCMa e ials, 48940 Leioa, Spain; o cid.o g/
0000-0003-1580-0302
Alicia Muela −Dp o. Inmunología, Mic obiologíay
Pa asi ología, Uni e sidad del País Vasco - UPV/EHU,
48940 Leioa, Spain
Comple e con ac in o ma ion is a ailable a :
h ps://pubs.acs.o g/10.1021/acsnano.1c09559
Au ho Con ibu ions
S.V., M.L.F., L.M, A.G.P., A.M., and A.G.A. concei ed and
designed he esea ch. L.G. cul i a ed Magne o ib io blakemo ei
cells and p epa ed he samples. L.M., L.G., D.G., and A.G.P.
collec ed he XMCD da a wi h he help o R.A., M.W., and S.V.
The XMCD da a we e analyzed by L.M., D.G., and S.V. L.M.
and I.O. adap ed he S one −Wohl a h model o he
expe imen al se up. I.O. was in cha ge o he heo e ical
modeling and so wa e de elopmen . L.M. compa ed expe -
imen al esul s wi h heo e ical modeling. D.G. was in cha ge
o fini e elemen calcula ions. L.M., A.G.P., S.V., M.L.F., and
I.O. w o e he manusc ip wi h con ibu ions o all au ho s.
No es
The au ho s decla e no compe ing financial in e es .
ACKNOWLEDGMENTS
L.M. acknowledges he financial suppo p o ided h ough a
pos doc o al ellowship om he Basque Go e nmen (POS-
2019-2-0017). Funding om he Spanish Go e nmen (g an
PID2020-115704RB-C31 unded by MCIN/AEI/10.13039/
501100011033) and om he Basque Go e nmen (p ojec s
IT-1245-19 and KK-2021/00040) is acknowledged. We
acknowledge he echnical and human suppo p o ided by
SGIke (UPV/EHU). We hank he HZB o he alloca ion o
synch o on adia ion beam ime and unding unde he p ojec
CALIPSOplus (G an Ag eemen 730872) om he EU
F amewo k P og amme o Resea ch and Inno a ion HORI-
ZON2020.
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ACS Nano www.acsnano.o g A icle
h ps://doi.o g/10.1021/acsnano.1c09559
ACS Nano 2022, 16, 7398−7408
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