Nature of the Dirac gap modulation and surface magnetic interaction in axion antiferromagnetic topological insulator MnBi2Te4A

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na u e o he Di ac gap modula ion
and su ace magne ic in e ac ion
in axion an i e omagne ic
opological insula o
MnBi2
Te
4
A. M. Shikin1*, D. A. es yunin1, i. i. Klimo skikh1, S. o. ilno 1, e. . Schwie 2, S. Kuma 2,
K. Miyamo o2, . okuda2, A. Kimu a3, K. Ku oda4, K. Yaji4, S. Shin4, Y. akeda5, Y. Sai oh5,
Z. S. Alie 6,7, n. . Mamedo 7, i. R. Ami aslano 7,8, M. B. Babanly8,9, M. M. o oko 10,11,
S. V. e emee 1,12,13 & e. V. chulko 1,13,14,15
Modi ica ion o he gap a he Di ac poin (DP) in axion an i e omagne ic opological insula o
MnBi2
Te
4
and i s elec onic and spin s uc u e ha e been s udied by angle- and spin- esol ed
pho oemission spec oscopy (ARPES) unde lase exci a ion a a ious empe a u es (9–35 K), ligh
pola iza ions and pho on ene gies. We ha e dis inguished bo h la ge (60–70 meV) and educed
(
<20 meV
) gaps a he DP in he ARPES dispe sions, which emain open abo e he Neél empe a u e
(
TN
=
24.5 K
). We p opose ha he gap abo e
TN
emains open due o a sho - ange magne ic ield
gene a ed by chi al spin luc ua ions. Spin- esol ed ARPES, XMCD and ci cula dich oism ARPES
measu emen s show a su ace e omagne ic o de ing o he “la ge gap” sample and appa en ly
signi ican ly educed e ec i e magne ic momen o he “ educed gap” sample. These obse a ions
can be explained by a shi o he Di ac cone (DC) s a e localiza ion owa ds he second Mn laye due
o s uc u al dis u bance and su ace elaxa ion e ec s, whe e DC s a e is in luenced by compensa ed
opposi e magne ic momen s. As we ha e shown by means o ab-ini io calcula ions su ace s uc u al
modi ica ion can esul in a signi ican modula ion o he DP gap.
In e play be ween opology and magne ism plays a signi ican ole in gene a ion o a numbe o exo ic opological
quan um e ec s such as Quan um Anomalous Hall E ec (QAHE)1–4 and opological magne oelec ic e ec 1, 5, 6.
These e ec s, disco e ed in magne ic opological insula o s (TIs), a e e y impo an o bo h undamen al sci-
ence and u u e echnological applica ions, like dissipa ion-less opological elec onics and opological quan um
compu a ion. They a e accompanied by a p edic ed opening o a gap a he Di ac poin (DP) a ising as a esul
o he ime e e sal symme y (TRS) b eaking due o he induced magne ic o de ing. In u n, his magne ic
gap and i s magni ude can be good indica o s o he de eloped e ec s and hei modi ica ion unde di e en
condi ions. In insic magne ic TIs (see, o example, Re s.7–18) a e cu en ly iewed as he bes candida es o
implemen ing he a o emen ioned e ec s. Thus, hese compounds can be conside ed as a e y p omising pla o m
open
1Sain Pe e sbu g S a e Uni e si y, 198504 Sain Pe e sbu g, Russia. 2Hi oshima Synch o on Radia ion Cen e ,
Hi oshima Uni e si y, Hi oshima, Japan. 3Depa men o Physical Sciences, G adua e School o Science,
Hi oshima Uni e si y, Hi oshima, Japan. 4ISSP, Uni e si y o Tokyo, Kashiwa, Chiba 277-8581, Japan. 5Ma e ials
Sciences Resea ch Cen e , Japan A omic Ene gy Agency, Sayo, Hyogo 679-5148, Japan. 6Aze baijan S a e Oil
and Indus y Uni e si y, AZ1010 Baku, Aze baijan. 7Ins i u e o Physics, ANAS, AZ1143 Baku, Aze baijan. 8Baku
S a e Uni e si y, AZ1148 Baku, Aze baijan. 9Ins i u e o Ca alysis and Ino ganic Chemis y, ANAS, AZ1143 Baku,
Aze baijan. 10Cen o de Física de Ma e iales (CFM-MPC), Cen o Mix o CSIC-UPV/EHU, 20018 Donos ia-San
Sebas ián, Basque Coun y, Spain. 11IKERBASQUE, Basque Founda ion o Science, 48011 Bilbao, Basque Coun y,
Spain. 12Ins i u e o S eng h Physics and Ma e ials Science, 634055 Tomsk, Russia. 13Tomsk S a e Uni e si y,
634050 Tomsk, Russia. 14Donos ia In e na ional Physics Cen e (DIPC), 20018 Donos ia-San Sebas ián, Basque
Coun y, Spain. 15Depa amen o de Física de Ma e iales, Facul ad de Ciencias Químicas, UPV/EHU, Apdo. 1072,
20080 San Sebas ián, Spain. *email: [email p o ec ed]
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o ealizing o he in e es ing and exo ic e ec s, such as magne ic monopole and axion ield and hei possible
manipula ion1, 19–22.
Recen ly, an in insic an i e omagne ic (AFM) TI wi h
MnBi2Te4
s oichiome y has been success ully syn-
hesized, and i s elec onic s uc u e has been heo e ically and expe imen ally in es iga ed7–13. This compound
has laye ed c ys al s uc u e consis ing o sep uple laye s (SLs) wi h an de Waals ( dW) bonding be ween hem.
Each SL con ains Mn laye in he cen al plain wi h e omagne ic coupling be ween Mn magne ic momen s.
An o e all AFM o de ing in he compound is o med by he nea es neighbo ing Mn FM laye s coupled an i e -
omagne ically wi h each o he . As a esul , all magne ic momen s a e o de ed and aligned wi h he c-axis, i.e.
pe pendicula o he su ace (in he ou -o -plane di ec ion). The opological su ace s a e is o med a
MnBi2Te4
(0001) due o he in e ed Bi
pz
and Te
pz
bulk bands a he
Ŵ
-poin due o s ong spin-o bi coupling, which is
essen ially he same as o
Bi2Te3
7, 9–11. Despi e he ac ha due o AFM coupling, TRS (

) is b oken, he e a e
wo symme ies:
P2
and
S=�T
1
/2
(whe e
P2
is he in e sion ope a ion cen e ed be ween neighbo ing SLs, and
T
1
/2
is a la ice ansla ion), which p ese e he opological in a ian , and allow his compound o be AFM TI.
Theo e ical calcula ions p edic o AFM TI
MnBi2Te4
a magne ically-d i en ene gy gap a he DP o 88meV7.
Expe imen ally measu ed DP gap a ies om 50 o85meV depending on pho on ene gy and he measu e-
men s condi ions, see, o ins ance, Re s.7, 11, 12, 23. Mo eo e , i was ound ha he Di ac cone (DC) s a e emain
p ac ically empe a u e independen abo e and below he Neél empe a u e (
TN
), al hough ce ain empe a-
u e dependence o he pho oemission in ensi y and lineshape was also obse ed7. Simila esul s, which show
he gapped DC s a e a empe a u e abo e
TN
we e also epo ed o he Gd-doped TI17, 24 and o he kinds o
magne ically-doped TIs (see, o ins ance, Re s.6, 25–29). A he same ime, a se ies o wo ks14–16, 30 has appea ed
in li e a u e whe e a “gapless”-like ARPES dispe sion was obse ed o
MnBi2Te4
. Howe e , o hese measu e-
men s a small DP gap o abou 13meV can be also dis inguished, which also emains open abo e
TN
14, 30. The
educed gap o hese samples has been a ibu ed o he di e ence be ween he bulk and su ace magne ic
o de s, al hough i should be no ed ha only a weak empe a u e dependence o he spec a has been e ealed.
The signi ican di e ence in he gap wid h obse ed o di e en samples o
MnBi2Te4
and i s weak dependence
on he long- ange magne ic o de ansi ion ha e no been sa is ac o ily explained so a .
In he p esen wo k we ha e ca ied ou a de ailed analysis o he DP gap in
MnBi2Te4
based on he Spin and
Angle- esol ed Pho oemission Spec oscopy (spin-/ARPES) measu emen s pe o med bo h abo e and below
TN
(24.5K) wi h a ia ion o he pho on ene gy and pola iza ion. We show ha DP gap o his compound is sligh ly
educed, bu emains open abo e
TN
. We a ibu e i o he chi al-like spin luc ua ions which can be conside ed
as a local eme gen magne ic ield p ese ing he gap. We p esen and compa e he esul s o he ARPES meas-
u emen o di e en kinds o he
MnBi2Te4
samples (o di e en su ace a eas o one sample), demons a ing
a la ge (60–70
meV
) and educed (
<20 meV
) gap a he DP. Bo h kinds o he samples a e cha ac e ized by he
same pe ec X- ay di ac ion13. We ha e s udied hese samples by XMCD, CD and spin- esol ed ARPES and
ha e shown he possibili y o di e ences in he o med su ace magne ic momen , which a ec s he DC s a e
di e en ly, o he samples wi h di e en gap a he DP. These e ec s can be ela ed o a shi o he opological
DC s a e owa ds he second SL block, due o su ace s uc u al modi ica ion, whe e i senses simul aneously he
opposi e magne ic momen s o he i s and he second Mn laye s, as i is e ealed by ou ab-ini io simula ions.
Thus, his shi leads o a dec ease in he e ec i e magne ic momen , which ac s on he DC s a e.
Resul s
ARpeS dispe sion maps. Figu e1a,b-uppe ow show a compa ison be ween he ARPES dispe sion maps
measu ed o
MnBi2Te4
below and abo e
TN=24.5 K
7, 13 o samples o su ace a eas which he ea e we will
call as sample wi h a “la ge gap” a he DP (a) and sample wi h “ educed gap” a he DP (b), see de ails in he ex
below. In he bo om ow in panels (a, b) he co esponding ARPES maps in he
d2N/dE2
o m a e shown o
be e isualiza ion. Fo he measu emen s p esen ed in panels (a) and (b) we used he
µ
-Lase ARPES sys em
(
hν=6.3 eV
) a he Hi oshima Synch o on Radia ion Cen e 31 wi h imp o ed angle, ene gy and spa ial eso-
lu ions. F om he dispe sion maps a 9K (a,b) he posi ions o he edges o he conduc ion and alence bands
(CBandVB) a e loca ed a abou 0.22eV and 0.36eV binding ene gies (BEs), espec i ely. A empe a u e o
35K he CB and VB edges espec i ely shi o BEs o app oxima ely 0.19and0.38eV. This di e ence is due o
he exchange spli ing o he bulk s a es below
TN
leading o dec ease o a o al undamen al gap (see Re .23 o
mo e de ails and analysis o hese s a es and hei spli ing).
One can see om ARPES dispe sion in panel (a) ha he ene gy gap a he DP seems o be open bo h below
and abo e
TN
. Fo mo e quan i a i e es ima ion in Fig.1c we p esen spec al decomposi ion o Ene gy Dis i-
bu ion Cu es (EDCs) a he
Ŵ
-poin (
k�
=
0Å
−1
) a
T=9K
(blue cu es) and 35K ( ed cu es). A signi i-
can dip in pho oemission in ensi y is seen a 9K be ween uppe and lowe pa s o he DC (ma ked by black
lines) and i emains isible e en abo e
TN
. The i ing yields alue o he DP gap
∼70 meV
a 9K ha sligh ly
dec eases o 60meV a 35K. Conside ing he ull wid h a hal maximum o he spec al componen s he e o
in he es ima ions is abou 20meV. Al hough he es ima ion abo e
TN
becomes somewha less accu a e due o
educed in ensi y and sha pness o he DC componen s, such educ ion can be ea ed as impo an e idence o
he magne ism in luence on he elec onic s uc u e (Re s.7, 23).
To in es iga e he e olu ion o he DP gap wi h empe a u e, we pe o med a se o measu emen s be ween
9and35K. In Fig.1d, he a ia ion o he DC componen s in ensi y is p esen ed, whe e he whi e dashed lines
app oxima ely show he posi ions o hei maxima. The DC componen s a e loca ed a BEs o abou 0.245eV
and 0.3eV a 9K and hey g adually shi owa ds lowe BEs while he empe a u e inc eases. As one can see,
he DP gap magni ude dec eases con inuously up o
TN
, bu emains almos cons an abo e i . Addi ionally,
Fig.1e demons a es a ia ion o he spec al weigh o he DC componen s wi h empe a u e (sepa a ely o
i s uppe and lowe pa s). One can clea ly see ha he in ensi ies g adually dec ease wi h empe a u e up o
TN
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353025201510
0.32
0.30
0.28
0.26
0.24
0.22
Binding ene gy (eV)
DP band gap
TN
kx (Å-1)
(a)
(c) (d) (e)
1.6
1.4
1.2
1.0
35
3025201510
Bo om Cone In
Top Cone In
0.32 0.28 0.24 0.20
T = 9 K
T = 35 K
0.32 0.28 0.24 0.20
EDC a he Г - poin , p-pol
T = 9 K
T = 35 K
d
2
NdE
2
353025201510
0.32
0.30
0.28
0.26
0.24
0.22
1.4
1.3
1.2
1.1
1.0
353025201510
Top + Bo om
Cone In
Tempe a u e (K)
Tempe a u e (K)
In ensi y (a b. u )s in
Binding ene gy (eV)
Binding ene gy (eV)
Binding ene gy (eV)
In ensi y (a b.
u )s in
In ensi y (a b. u )s in
In ensi y (a b.
u)s in
TN
(b)
kx (Å-1)
( ) (g) (h)
Binding ene gy (eV)
0.5
0.4
0.3
0.2
0.1
0.0
0.1-0.1 00.1-0.1 0
0.5
0.4
0.3
0.2
0.1
0.0
0.1-0.1 00.1-0.1 0
T = 9 KT =35 KT = 9
KT
=35 K
0.5
0.4
0.3
0.2
0.1
0.0
0.1-0.1 00.1-0.1 0
0.5
0.4
0.3
0.2
0.1
0.0
0.1-0.1 00.1-0.1 0
d2NdE2
d2NdE2
d2NdE2
d2NdE2
Figu e1. (a,b) uppe line—ARPES dispe sion maps measu ed o
MnBi2Te4
a pho on ene gy 6.3eV using
p-pola ized lase adia ion below (9K) and abo e
TN
(35K) o he sample wi h a la ge (a) and educed gap
(b). (a,b) lowe line— he same as in he uppe line bu in he
d2N/dE2
ep esen a ion. (c) EDCs cu a he
Ŵ
-poin (
k�
=
0Å
−1
) in ene gy egion a ound he DP o he “la ge gap” sample a 9K (blue cu es) and 35K
( ed cu es) wi h co esponding spec al decomposi ions. The modi ica ion o he DC s uc u e nea he DP
unde g adual inc ease o empe a u e be ween 9and35K shown as a se o EDCs a he
Ŵ
-poin (d) and as
in eg a ed in ensi y o co esponding EDCs in he ene gy in e als co esponding o he uppe (pink) and lowe
(g een) DC pa s (e). ( –h) The same as in panels (c–e) measu ed o sample wi h a “ educed gap”. No e ha no
dis inc ion be ween he uppe and lowe pa s o he DC is made in (h).
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a e which hey emain a an app oxima ely cons an le el. Thus, he p esen ed esul s con i m he opening o
a la ge DP gap which has sligh empe a u e a ia ion and is mi iga ed abo e
TN
.
Besides, we obse ed samples o ano he ype ha , al hough being measu ed a he same condi ions, dem-
ons a e signi ican ly educed DP gap. Figu e1b shows he ARPES dispe sion maps o his kind o samples,
measu ed a empe a u es below and abo e
TN
. A da ase ob ained wi h he same ea men as o discussed
abo e “la ge gap” sample is shown in panels ( -h) o he sample wi h “ educed gap”. Spec al decomposi ion o
EDCs (panel ( )) yields he DP gap size less han 20meV, independen ly on empe a u e, which is consis en
wi h he epo o Re .30. Figu e1g di ec ly demons a es he beha io o he DC componen s nea he DP upon
c ossing
TN
. All isible a ia ions o he line wid h a e ela ed o he in ensi y dec ease. In eg a ed in ensi y o
he DC componen s (panel (h)) beha es quali a i ely simila o he one obse ed o he sample wi h he “la ge
gap” (panel (e)). Mo eo e , he exchange spli ing o he CB s a e (a 
∼0.2 eV BE
23) o bo h samples below
TN
has almos he same alue (see
d2N/dE2
in (a) and (b)). Thus, one can expec he iden i y o he bulk magne ic
o de ing o bo h samples which hough demons a e signi ican ly di e en DP gap alues.
Resonan pho oemission measu emen s. In Re s.28, 32, 33 i was p oposed ha he DP gap in magne -
ically-doped TIs can ha e a non-magne ic o igin and appea s due o he a oided c ossing hyb idiza ion o he
DC wi h he impu i y le els o magne ic a oms nea he DP. Thus, o con i m possible magne ic-de i ed o igin o
he gap opening (i.e. absence o Mn-le els nea he DP) we pe o med esonan PE measu emen s. This me hod
allows one o enhance he con ibu ion o he Mn-de i ed s a es in PE spec a and o indica e he exac ene gy
ange o localiza ion o hese s a es.
Acco ding o heo e ical calcula ions7, 9, 34 he Mn 3d s a es in
MnBi2Te4
a e ene ge ically sepa a ed om
he opological su ace s a e. Expe imen ally i is shown in Fig.2 by esonan PE measu emen s a ene gies o
Mn(
3p−3d
) adso p ion edge (
hν
= 48–50
eV
). One can clea ly see a esonan inc ease o he Mn 3d s a es a
abou 3.2eVBE (see panels (a), (e) and ( )) while he e is no isible in ensi y change in he DC egion (see panels
(b–d) and (g)). This p o es he absence o any no able con ibu ion o he Mn d s a es in he icini y o he DP
and shows he unlikeliness o an a oided-c ossing-scena io in
MnBi2Te4
. This is clea ly opposed o obse ed
o Mn-doped
Bi2Te3
35.
(b) h =50 eV (c) h =48 eV (d) (I
b
-I
c
)/(I
b
+I
c
)
-0.2 -0.1 0.00.10.2
0.6
0.4
0.2
0.0
-0.2 -0.1 0.00.10.2
0.6
0.4
0.2
0.0
-0.2 -0.1 0.00.10.2
0.6
0.4
0.2
0.0
Binding ene gy (eV)
Wa e ec o (A-1)Wa e ec o (A-1)Wa e ec o (A-1)
(a)
30 25 20 15 10 5 0
on- esonance
14 12 10 8 6 4 2 0
on- esonance
max min
In ensi y (a b. uni s)
Binding ene gy (eV)
0.60.40.2 0
on- esonance
-1.0 -0.5 0.00.51.
0
5
4
3
2
1
0
Wa e ec o (A-1)
(e) (I
b
-I
c
)/(I
b
+I
c
)
max min
0
( ) (g)
Figu e2. (a) Resonan Mn(
3p
−
3d
) PE spec a measu ed a on- esonance ene gy
hν=50 eV
(blue cu e)
and o - esonance ene gy
hν=48 eV
(o ange cu e). A zoom in o he egion up o he BE o 15eV is shown in
( ). (b,c) On- and o - esonance ARPES dispe sion maps measu ed in he egion o he DC wi h hei di e ence
shown in (d). (e) The same as in panel (d), bu up o highe BEs. (g) On- and o - esonance spec a in he DC
egion aken as EDCs in he icini y o he
Ŵ
-poin cu om panels (b) and (c).
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Panels (e,g) show some weak in ensi y g ow h on- esonance in he VB egion wi h 1eVBE and in he CB
egion ha poin s o p esence o some Mn-de i ed s a es he e. They migh be ela ed o he o ma ion o
he Mn(d)-Te(p) hyb id s a es34. Howe e , hese s a es a e unlikely o ha e signi ican con ibu ion o he DP
gap opening ia he a oided-c ossing hyb idiza ion mechanism. All measu ed samples demons a e analogous
beha io du ing he esonan pho oemission expe imen wi h a small a ia ion o he in ensi y o he Mn-de i ed
peak a 3.2eVBE.
in-plane and ou -o -plane spin ex u e o he gapped Di ac s a e. To analyze he spin s uc u e
o he DC s a e o med in
MnBi2Te4
we measu ed spin- esol ed ARPES dispe sion maps o he in-plane and
ou -o -plane spin componen s a empe a u es bo h below and abo e
TN
, which a e p esen ed in Fig.3. One can
see ha o he in-plane spin componen (Fig.3a,b) a helical spin s uc u e is obse ed wi h a p onounced spin
in e sion o opposi e b anches o he DC o all measu ed empe a u es. A he same ime, o he ou -o -plane
spin pola iza ion he spin- esol ed dispe sion maps (Fig.3c,d) demons a e no isible spin in e sion be ween
he uppe and lowe DCs. Al hough, o posi i e and nega i e
k
he magni ude o he spin pola iza ion is sha ply
changed in he BE egion be ween 0.2and0.3eV. This change occu s in he backg ound o he cons an -like con-
ibu ion o spin pola iza ion which may be ela ed o he PE-induced spin pola iza ion o he CB s a es hyb id-
ized wi h he Mn 3d s a es. This beha io o he ou -o -plane pola iza ion is obse ed bo h below and abo e
TN
wi h some change in he pola iza ion le el wi h empe a u e. The obse a ion o he ou -o -plane spin pola iza-
ion abo e
TN
is consis en wi h he assump ion abou he occu ence o spin luc ua ions, as in Re .7, wi h a
common spin ex u e, simila o ha in Re .36, which includes bo h in-plane and ou -o -plane spin componen s.
Besides, he spin pola iza ion o he Mn 3d s a es in he CB egion (see Fig.2) also may ha e a con ibu ion o
his spin-pola ized backg ound in he measu ed spin-ARPES dispe sion maps.
O e all, he spin s uc u e ha is shown in Fig.3 con i ms ha
MnBi2Te4
is cha ac e ized by he helical spin
ex u e o empe a u e below and abo e he
TN
. A he same ime, he measu ed ou -o -plane spin- esol ed
spec a show complex s uc u e, possibly due o he PE inal s a e e ec (as in Re .27) and he impac o he
Mn3d s a es.
Ou -o -plane
-40 -20 0 20 40
0.0
0.1
0.2
0.3
0.4
T = 9 K
Binding ene gy
)Ve(
-40 -20 0 20 40
0.0
0.1
0.2
0.3
0.4
T = 35 K
Binding ene gy (eV)
-40-20 0 20 40
0.0
0.1
0.2
0.3
0.4
-40 -20 0 20 40
0.0
0.1
0.2
0.3
0.4
In-plane
T = 9 K T = 35 K
Binding ene gy
)Ve(
k
x
(x10-3 Å
-1
)
Binding ene gy (eV)
-0.5
0.0
0.5
0.40.30.20.10.0
Binding ene gy (eV)
-0.5
0.0
0.5
Spin pola iza ion
-0.5
0.0
0.5
k
II
= - 0.03 Å
-1
k
II
= 0 Å
-1
k
II
= 0.03 Å
-1
-0.5
0.0
0.5
0.40.30.20.10.0
Binding ene gy (eV)
-0.5
0.0
0.5
Spin pola iza ion
-0.5
0.0
0.5
k
II
= - 0.03 Å
-1
k
II
= 0 Å
-1
k
II
= 0.03 Å
-1
-0.5
0.0
0.5
0.40.30.20.10.0
Binding ene gy (eV)
-0.5
0.0
0.5
Spin pola iza ion
-0.5
0.0
0.5
k
II
= - 0.03 Å
-1
k
II
= 0 Å
-1
k
II
= 0.03 Å
-1
-0.5
0.0
0.5
0.40.30.20.10.0
Binding ene gy (eV)
-0.5
0.0
0.5
Spin pola iza ion
-0.5
0.0
0.5
k
II
= - 0.03 Å
-1
k
II
= 0 Å
-1
k
II
= 0.03 Å
-1
(a) (b)
(c) (d)
k
x
(x10-3 Å
-1
)
k
x
(x10
-3
Å
-1
)k
x
(x10
-3
Å
-1
)
Figu e3. (a,b) Le pa s: in-plane spin- esol ed ARPES dispe sion maps measu ed o
MnBi2Te4
along he
ŴM
di ec ion using s-pola ized LR (
hν=7 eV
) a a empe a u e o 9and35K, espec i ely. (a,b) Righ pa s:
he co esponding in-plane pola iza ions measu ed a he
Ŵ
-poin and a
k=±0.03 Å−1
. (c,d) The same as in
panels (a,b) bu o he ou -o -plane spin- esol ed ARPES dispe sion maps and co esponding ou -o -plane
pola iza ion.

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pho on ene gy dependence o he ou -o -plane pola iza ion o he Dc s a e. In o de o s udy
he ou -o -plane spin pola iza ion in e sion be ween he uppe and lowe pa s o he DC in he icini y o he
Ŵ
-poin and i s possible a ia ion on he pho on ene gy we measu ed he pho on ene gy dependence o he
ou -o -plane spin componen in he spin- esol ed PE spec a unde pho oexci a ion by SR (Fig.4a) and LR
(Fig.4b). In panel (a) one can see ha spec a measu ed a pho on ene gies o 15,25and28eV show in e sion
o he spin pola iza ion o he uppe and lowe pa s o he DC which con i ms hedgehog-like spin s uc u e o
he DC a he
Ŵ
-poin , see, o ins ance25. Mo eo e , one can see ha he spec um measu ed wi h
hν=28 eV
and
T=40 K
also shows an e idence o in e sion o he spin pola iza ion a he
Ŵ
-poin . This also suppo s
ou assump ion o he magne ic gap opening a empe a u es highe han
TN
. Fu he mo e, he dependence o
he pola iza ion on he pho on ene gy has an oscilla ing cha ac e . The pola iza ion changes i s sign be ween
25and28eV (i.e. he BEs o he Bi
5d
3
/2
and
5d
5
/2
le els) and hen oscilla es wi h pho on ene gy in magni ude
and sign. The e o e, he a ia ion o he ou -o -plane pola iza ion wi h pho on ene gy has a he oscilla ing
cha ac e (Fig.4c) which is consis en wi h calcula ions shown in Re s.26, 27, 37, 38.
A he same ime, one can see ha he spin- esol ed spec um measu ed a
hν=7.0 eV
(panel (b)) demon-
s a es an addi ional ou -o -plane pola iza ion con ibu ion in he egion o he CB s a es, almos independen
on he BE. We ela e i o he ou -o -plane pola iza ion o he CB s a es hyb idized wi h he Mn3d s a es34 which
become mo e p onounced a he pho on ene gies be ween 6and15eV. Thei enhancemen is well isible in
Fig.2 .
Thus, he p esen ed spin- esol ed spec a demons a e a p onounced in e sion o he ou -o -plane spin
pola iza ion be ween he uppe and lowe pa s o he DC a he
Ŵ
-poin . The alue and he sign o he spin pola i-
za ion oscilla e wi h pho on ene gy in PE spec a due o he inal s a e e ec s. The obse ed ou -o -plane spin
pola iza ion con i ms a magne ic-de i ed o igin o he DP gap. The spin- esol ed spec a aken a
hν=28 eV
and
T=20
and40K demons a e a sligh dec ease in he DC spin pola iza ion abo e
TN
.
Howe e , in he p esen ed measu emen s pe o med using he SR we did no dis inguish be ween he sam-
ples (o su ace a eas) cha ac e ized by la ge o educed gap. In o de o es ima e he di e ence in he DC spin
s uc u e o he samples wi h he “la ge gap” and he “ educed gap” we used ci cula dich oism (CD) ARPES
me hod a
µ
-ARPES Lase s a ion whe e hese wo kinds o samples we e cha ac e ized p e iously (Fig.1). CD
ARPES is a use ul echnique o ob ain in o ma ion abou a ia ion o he o al o bi al momen um o s a es which
in case o he TI’s DC may e lec he DC spin ex u e.
0.60.0
0.40.2
h = 20eV
0.60.00.40.2
h = 15eV
0.60.00.40.2
h = 13eV
-10
-5
0
5
10
25201510
Lowe cone
Uppe cone
Fi by pol. unc.
Summ. Pola iza ion (%)
Ene gy o pho oexi a ion (eV)
Binding ene gy (eV)Binding ene gy (eV)Binding ene gy (eV)
Pola iza ion (%)
-4
-2
0
2
4
Binding ene gy (eV)Binding ene gy (eV)
0.60.00.40.2
Binding ene gy (eV)
0.60.00.40.2
0.60.00.40.2
-30
-20
-10
0
10
20
h = 28 eV
T = 20 K
h = 25 eV h = 28 eV
T = 40 K
Pola iza ion (%)
T = 20 K
0.40.2 0.0
-40
-20
0
20
40
h = 7 eV
T = 13 K
Pola iza ion (%)
Spin up
Spin dn
Binding ene gy (eV)
(a) (b)
(c)
In (a b. uni s)
In (a b. uni s)In (a b. uni s)
Figu e4. (a) Pho on ene gy dependence (
hν=13 −28 eV
,SR) o he ou -o -plane spin esol ed spec a
measu ed a
k�
=
0Å
−1
below (20K) and abo e (40K)
TN
. Uppe pa s o each panel show he spin-up and
spin-down componen s, while he lowe pa s demons a e co esponding ou -o -plane pola iza ion. (b) The
same as in (a) bu acqui ed wi h a
hν=7.0 eV
(LR) and
T=13 K
. (c) Pho on ene gy dependen a ia ion o
he ou -o -plane pola iza ion o he uppe and lowe DC s a e.
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La ge and small gaps a di e en pola iza ions o LR and empe a u e. In Fig.5 we compa e he
ARPES dispe sion maps o samples wi h la ge (panels a,b) and educed (panelsc,d) gap, measu ed a di e en
empe a u es and pola iza ions o LR. In Fig.5a1–d1 he ARPES dispe sion maps, measu ed using p-pola ized
LR a
hν=6.3 eV
a e p esen ed in he
d2N/dE2
o m. Fig.5a2–d2 show he co esponding EDCs measu ed a
he
Ŵ
-poin a di e en pola iza ions o LR and empe a u es o 9and35K. The maxima o he peaks’ in ensi y,
co esponding o he edges o he DP gap, a e ma ked by e ical black dashed lines. One can see ha o he
sample wi h la ge gap (panels a,b) he pho oemission signal s ongly depends on he pola iza ion o LR. The
mos impo an obse a ion is a p onounced modi ica ion o he in ensi y o he uppe and lowe DC s a es a
opposi e ci cula pola iza ions. Fo posi i e ci cula pola iza ion, he in ensi y o he uppe DC is enhanced.
In con as , o nega i e ci cula pola iza ion an enhancemen o he lowe DC in ensi y is obse ed. Redis i-
bu ion be ween he uppe and lowe DC s a es unde ci cula pola iza ion o LR is seen o bo h 9and35K,
while o he la e he in ensi y o he DC s a es is educed. Panels a3,b3 and a4,b4 show his edis ibu ion in
de ails. In panels a3,b3 he ci cula dich oism (CD) ARPES dispe sion maps a e shown, which we e de i ed by
sub ac ing he spec a measu ed a opposi e ci cula LR pola iza ions. Figu e5(a4 and b4, uppe panels) com-
pa e he EDCs measu ed a opposi e ci cula pola iza ions in he egion close o he DC gap. The lowe panels
demons a e he co esponding CD signal ob ained by sub ac ion o he EDCs p esen ed in uppe panels wi h
no maliza ion on hei sum.
Fo he case o la ge gap a he DP a empe a u e below
TN
(panels a3,a4), he CD-signal demons a es a
p onounced in e sion be ween he uppe and lowe DC s a es. The change o he sign o CD signal co ela es
o some ex en wi h he change o he spin pola iza ion o he gapped DC s a e (see Re .39). To con i m such a
co ela ion, he spec a a e p esen ed in he egion including also he Te-de i ed exchange-spli s a es a he edge
o CB loca ed in he ene gy egion 0.14–0.22 eV (see o compa ison Re .23). We ha e o no e he p esence o
spin-pola ized Mn-de i ed s a es weigh in his ene gy egion (see Fig.2), which may con ibu e o CD signal.
Thus, he CD signal sign in e sion is no p onounced o CB s a es, ha can be explained by he opposi e spin-
pola iza ion o he Mn- and he Te-de i ed exchange-spli s a es.
Abo e
TN
, when he long- ange magne ic o de ing is des oyed, he ene gy spli ing be ween he edge CB
s a es collapses, and no sign in e sion is obse ed o hese s a es in he CD signal (panel b4). A he same ime,
he sign in e sion in he CD signal be ween he uppe and lowe DC s a es emains isible abo e
TN
. The same
in e sion can be dis inguished in he ARPES dispe sion map (panel b3). This may indica e he p ese a ion o a
magne ic o igin o he gap abo e
TN
, possibly due o sho - ange o de e ec s. The pe sis ence o he gap abo e
TN
had been explained by p esence o s ongly aniso opic spin luc ua ions in he wide empe a u e ange, see
Re .7. While he exac mechanism o spin luc ua ions equi es u he s udies, we would like o no e he e he
ollowing poin s. Owing o he s ong ou -o -plane aniso opy i is highly expec able ha Mn magne ic momen s
p e e ou -o -plane di ec ion e en abo e
TN
. Taking in o accoun ela i ely la ge de ec s concen a ion ( om
3 o 17.5% o
MnBi
and
BiMn
an isi e de ec s as well as Mn acancies40–42) one can assume ha Mn a oms in Bi
laye also possess ou -o -plane momen s. These magne ic momen s may induce he chi al spin ex u e in he
su ounding media (simila o Re .36) ha can a ec he magne ic s a e o he c ys al. On he o he hand, com-
pe ing magne ic in e ac ions in
MnBi2Te4
can induce a numbe o a ious magne ic phases, including sky mion
ones (see Re .43). We specula e ha he o ma ion o he sky mion-like spin ex u es can be gene a ed a ele a ed
empe a u es in he Mn-Te bilaye s inside SLs, like as i is in he e os uc u es MnTe/TI44.
Figu e5c1,d1 and c2,d2, show he ARPES dispe sion maps and he co esponding EDCs o he sample wi h
educed gap, measu ed a empe a u es below and abo e
TN
, espec i ely. Fi s o all, i can be clea ly seen in
Fig.5c2,d2 ha he gap wid h does no depend on pola iza ion o LR bo h below and abo e
TN
. I is in e es ing
ha bo h CD ARPES dispe sion map (panel c3) and co esponding EDC (panel c4) measu ed o he Te- de i ed
CB edge s a es below
TN
demons a e he p onounced in e sion o he CD signal. A he same ime, he in e sion
o he CD sign o uppe and lowe DC s a es is p ac ically no obse ed. Whe eas, some edis ibu ion in he
CD-signal be ween he uppe and lowe DC s a es can be dis inguished in he CD ARPES dispe sion maps. We
associa e his obse a ion wi h a educed e ec i e magne ic momen de eloped o his kind o sample in he
a ea o he opological DC s a e localiza ion (see below). On he o he hand, he exchange spli ing o he CB
s a es collapses abo e
TN
(panel d4), ha es i ies a he o a de eloped FM magne ic coupling in he p obing
su ace-con ibu ed a ea. I means ha despi e he FM magne ic o de ing p obed by he exchange-spli CB s a es,
he DC s a es a e a ec ed by a signi ican ly educed e ec i e ou -o -plane magne ic momen . On he con a y,
acco ding o he heo e ical modelling pe o med in Re .14 he “gapless”-like DC can a ise in
MnBi2Te4
due
o he su ace magne ic econs uc ion esul ing in o ma ion o a ze o ou -o -plane magne ic momen in he
Mn-laye inside he su ace SL. This may be due o (1) o ma ion o he in alaye 2D AFM coupling (ins ead
he 2D FM one), (2) in-plane a angemen o he magne ic momen s in he su ace SL and (3) o ma ion o he
su ace spin-diso de ed pa amagne ic-like laye . Howe e , he p esen ed expe imen al CD measu emen s (wi h
spin- esol ed da a) likely demons a e main aining o he su ace FM o de ing. An al e na i e explana ion o
he gapless-like dispe sion in such a case can be a possibili y o opological su ace s a e weigh edis ibu ion
and gap dec ease owing o he an-de -Waals space enla gemen (see below).
XMCD wi h a ied applied ou -o -plane magne ic ield. To s udy he su ace magne ic o de ing, we
ha e ca ied ou measu emen s o X- ay Magne ic Ci cula Dich oism (XMCD) which a e mo e su ace sensi-
i e in compa ison o SQUID measu emen s. XMCD signal is p opo ional o he sample magne iza ion ei he
in insic o induced unde applied magne ic ield. Figu e6a shows he X- ay Abso p ion Spec a (XAS) and
XMCD signal. One can see p onounce XMCD signal o Mn
L2,3
e en in ze o magne ic ield. Thus, hese esul s
may indica e an FM magne ic o de ing.
8
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In . (a b. uni s)
Pola iza ion (%)
Binding ene gy (eV)
-15
-10
-5
0
5
10
15
0.30 0.25 0.20 0.15
-30
-20
-10
0
10
20
30
0.30 0.25 0.20 0.15
-40
-20
0
20
40
0.30 0.25 0.20 0.15
-20
-10
0
10
20
0.30 0.25 0.20 0.15
In . (a b. uni s)
Pola iza ion (%)
In . (a b. uni s)
Pola iza ion (%)
In . (a b. uni s)
Pola iza ion (%)
Binding ene gy (eV)k
x
(Å
-1
)
-40 0 40
0.30
0.25
0.20
0.15
-40 0 40
0.30
0.25
0.20
0.15
0.30 0.25 0.20 0.15
p-pol
s-pol
cw-pol
ccw-pol
In ensi y (a b. uni s)
0.30 0.25 0.20 0.15
p-pol
s-pol
cw-pol
ccw-pol
0.30 0.25 0.20 0.15
p-pol
s-pol
cw-pol
ccw-pol
0.30 0.25 0.20 0.15
p-pol
s-pol
cw-pol
ccw-pol
In ensi y (a b. uni s)
In ensi y (a b. uni s) In ensi y (a b. uni s)
-400 40
0.30
0.25
0.20
0.15
-400 40
0.30
0.25
0.20
0.15
Binding ene gy (eV)
Binding ene gy (eV)
Binding ene gy (eV) Binding ene gy (eV)
Binding ene gy (eV)k
x
(Å
-1
)
(a)
(b)
(c)
(d)
(1) (2) (3) (4)
-40 -200 20 40
0.30
0.25
0.20
0.15
Binding ene gy (eV)
-40 -200 20 40
0.30
0.25
0.20
0.15
Binding ene gy (eV)
-40 -200 20 40
0.30
0.25
0.20
0.15
Binding ene gy (eV)
-40 -200 20 40
0.30
0.25
0.20
0.15
35 К
35 К
9 К
9 К
Figu e5. (a1–d1) ARPES dispe sion maps measu ed o he cases o a la ge (a1,b1) and educed (c1,d1)
gap a he DP a empe a u es o 9K(a1,c1) and 35K(b1,d1) using p-pola ized LR (wi h
hν=6.3 eV
). The
spec a a e shown in he egion close o he DP in he
d2N/dE2
p esen a ion o be e isualiza ion o he DP
gap. (a2–d2) he co esponding EDCs measu ed a he DP a
k�
=
0Å
−1
using di e en pola iza ion o LR a
empe a u e 9and35K, espec i ely. CW and CCW deno e ci cula ly pola ized lase adia ion wi h clockwise
and coun e clockwise pola iza ions. (a3–d3) The CD ARPES dispe sion maps ob ained by sub ac ion o he
PE signal o opposi e ci cula pola iza ion. (a4–d4) A compa ison be ween he co esponding CD EDCs in
he egion close o he DP (uppe panels) wi h p esen a ion o he sub ac ed PE signal measu ed a opposi e
ci cula pola iza ions (bo om panels).
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In o de o s udy his peculia esul , we measu ed dependence o sys em magne iza ion (ampli ude o XMCD
signal) on applied magne ic ield M(H), see Fig.6b. P esen ed M(H) cu e demons a es a p onounced hys e esis
loop also wi h FM-like beha io in an applied magne ic ield below 2T (abo e − 2T). I di e s om he M(H)
cu e, measu ed by bulk-sensi i e SQUID me hod, which demons a es well-known AFM cha ac e wi hou
hys e esis loops be ween a ield o − 3.5 and 3.5 T (see Fig.2e in Re .7). Mo eo e , an unusual de ia ion o
FM-like M(H) cu e is obse ed in he egion be ween 2and3.5T whe e i demons a es e e sed di ec ion
o he “main” loop. Appea ance o hese addi ional hys e esis loops can be obse ed in case o A- ype AFM (as
in
MnBi2Te4
) due o ollowing easons. The XMCD me hod is su ace sensi i e so he signal apidly dec eases
wi h a dep h and is mainly p o ided by he con ibu ion o he se e al op SLs. In case o A- ype AFM each SL
has FM o de ing wi h opposi e o ien a ion o i s neighbo s. The e o e, opmos SL deli e s FM beha io wi h
maximum con ibu ion in he signal which is schema ically shown by magen a M(H) cu e in Fig.6c. Unde ly-
ing SLs almos compensa e each o he hough gi e some esidual XMCD signal due o hei inequi alen dep h
which can be p esen ed as M(H) cu e (cyan) wi h opposi e di ec ion. Besides he ampli udes, M(H) cu es
o he opmos SL and unde lying SLs migh show di e en magne ic coe ci i y. This can be caused by change
in su ounding on he su ace o /and possible s uc u al elaxa ions. As seen om bo om pa o panel (c)
a ia ion o coe ci i y is c ucial o appea ance o addi ional hys e esis loops. Resul ing modeled XMCD signal
(magne iza ion) quali a i ely ep oduce expe imen al obse a ion in panel (b).
Thus, ou magne ic measu emen s indica e an ou -o -plane FM o de ing wi h an XMCD signal coming mos ly
om he opmos SL. A he same ime, XMCD measu emen s can be consis en wi h he A- ype AFM o de ing
inhe en o
MnBi2Te4
. Also, ou esul s demons a e ha in se e al cases a conside a ion o he magne iza ion
con ibu ion om he second and ollowing SLs can be impo an . As we show in he ollowing, hei e ec on
he DP gap migh be d ama ic when he opological su ace s a e pa ially eloca es o he second SL due o he
inc ease o he dW spacing.
S uc u al e ec on su ace elec onic s uc u e o
MnBi2
Te
4
. The al e a ion o he opological
su ace s a e localiza ion is possible due o s uc u e modi ica ion caused by na u al una oidable de ec s. I
was e ealed ha
MnBi2Te4
usually con ains om 3 o 17.5% o
MnBi
and
BiMn
an isi e de ec s as well as Mn
acancies40–42. Due o he ac ha Mn and Bi a oms ha e no iceably di e en size i is e iden ha p esence o a
numbe o
BiMn
de ec s in he Mn laye should expand a e age in e laye Te-Mn-Te dis ances in he middle o
SL, and ice e sa, he p esence o
MnBi
in he Bi laye s should lead o a dec ease in he Bi-Te a e age in e laye
dis ances. Indeed, he s uc u al pa ame e s p esen ed in Re s.40, 42 show ha Mn-Te and ou e Te-Bi in e laye
spacings a e espec i ely by 3–3.5% expanded and con ac ed as compa ed o ou calcula ed equilib ium in e -
laye dis ances whe eas he second, Bi-Te, dis ance di e s only wi hin one pe cen om he heo e ical alue.
A he same ime hese da a o de ec con aining samples also show ha dW spacing be ween neighbo ing
SLs is o
∼
8–10% la ge wi h espec o he calcula ed
MnBi2Te4
s uc u e. Ano he s uc u al e ec ea lie
discussed25 o TIs wi h weak an de Waals coupling be ween building mul ilaye ed blocks is a b oadening o
dW spacing nea he su ace caused by he mechanical clea age o ex olia ion implied o he su ace p epa a-
ion o ARPES and STM expe imen s. Fo ab-ini io simula ion o he s uc u al e ec s we apply an app oach
ha p e iously showed i s e iciency in explaining he expe imen ally obse ed ea u es in laye ed TIs spec a
and which is based on conside a ion o changes in in e laye spacings wi hin o be ween building blocks o
TI45–47. In ou simula ion we es ic he s uc u al changes only in he su ace SL and in he i s dW gap, since
i is known ha he opological su ace s a e is almos comple ely localized in his a ea. Fi s we conside he
12
10
8
6
4
2
0
-2 660655650645640635630
2.6
2.4
2.2
2.0
1.8
-80
-60
-40
-20
0
20
40
60
80
-6 -4 -2 0 2 4 6
Magne ic ield (T)Pho on ene gy (eV)
XAS (a b. uni s)
XMCD
(
x
10
-3
a b. uni s)
XMCD in ensi y
(
x
10-3 a b. uni s)
M
H
1s SL
M
H
(a) (b) (c)
Unde lying SL
s
Figu e6. (a, uppe panel) X- ay Abso p ion Spec a (XAS), wi h blue and ed cu es co esponding o he
opposi e ci cula pola iza ions o SR and (a, bo om panel) XMCD spec um, i.e. he di e ence o he wo XAS.
The measu emen s ha e been made in he o al elec on yield mode a Mn
L2,3
edge (630–660 eV) a 15K in
ze o magne ic ield. (b) XMCD ampli udes a he Mn
L2,3
edge plo ed as a unc ion o applied ou -o -plane
magne ic ield (linea backg ound is sub ac ed). A ows show di ec ion o he cu e mo ing om − 6 o 6T
( ed) and back (blue). (c) Schema ic p esen a ion o con ibu ions om opmos SL (magen a) and unde lying
SLs wi h e ec i e opposi e magne iza ion (cyan) o he XMCD signal as well as he esul ing cu e (g een).