Ligh -D i en Topological and Magne ic Phase T ansi ions in Thin
Laye An i e omagne s
Ma in Rod iguez-Vega, Ze-Xun Lin, A i z Leona do, A hu E ns ,*Maia G. Ve gnio y,
and G ego y A. Fie e
Ci e This: J. Phys. Chem. Le . 2022, 13, 4152−4158
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sıSuppo ing In o ma ion
ABSTRACT: We heo e ically s udy he effec o low- equency ligh pulses in esonance wi h
phonons in he opological and magne ically o de ed wo-sep uple laye (2-SL) MnBi2Te4
(MBT) and MnSb2Te4(MST). These ma e ials sha e symme y p ope ies and an
an i e omagne ic g ound s a e in p is ine o m bu p esen diffe en magne ic exchange
in e ac ions. In bo h ma e ials, shea and b ea hing Raman phonons can be exci ed ia
nonlinea in e ac ions wi h pho oexci ed in a ed phonons using in ense lase pulses ha can be
a ained in he cu en expe imen al se ups. The ligh -induced ansien la ice dis o ions lead
o a change in he sign o he effec i e in e laye exchange in e ac ion and magne ic o de
accompanied by a opological band ansi ion. Fu he mo e, we show ha mode a e an isi e
diso de , ypically p esen in MBT and MST samples, can acili a e such an effec . The e o e,
ou wo k es ablishes 2-SL MBT and MST as candida e pla o ms o achie ing non-equilib ium
magne o- opological phase ansi ions.
An i e omagne ic opological insula o s (ATIs) can hos
exo ic phases o ma e such as he quan um anomalous
Hall (QAH) effec and axion insula o s.
1
The sea ch o hese
opological phases mo i a ed he addi ion o magne ic dopan s
in opological insula o s, which led o he obse a ion o a
QAH effec and candida es o axion insula o s a e y low
empe a u es.
2−4
Howe e , in insic ATIs p omise o mani es
hese phases a highe empe a u es, which a e desi able o
applica ions. Indeed, he ecen p edic ions, syn hesis, and
ex olia ion o he an de Waals ma e ials MnBi2Te4,
MnBi2nTe3n+1, and MnSb2Te4
5−12
allowed he de ec ion o
QAH s a es in odd sep uple laye s (SLs) and axion s a es in
e en SLs
13−17
and he obse a ion o an elec ic field-induced
laye Hall effec in six SL samples.
18
The in e wined na u e o he magne ic and opological
o de in ATIs offe s he possibili y o explo ing opological
ansi ions induced by changes in he magne ic o de and ice
e sa. Fo example, ecen expe imen s sugges ha inc easing
he dis ance be ween he magne ic planes in he MnBi2nTe3n+1
amily leads o e omagne ic o de .
8
On he con a y,
dec easing he dis ance in MnBi2Te4single c ys als ia
hyd os a ic p essu e leads o he supp ession o he AFM
o de .
19,20
In con as , in C I3, a low-dimensional magne ic
sys em wi h i ial opology, hyd os a ic p essu e induces an
an i e omagne (AFM) o e omagne (FM) ansi ion.
21
Howe e , a sui able mechanism o modi ying he magne ic
o de in ATIs wi hou applied ex e nal magne ic fields o
supe la ices emains elusi e.
To his end, non-equilib ium app oaches p o ide a possible
pa hway o achie ing magne o- opological ansi ions in
ATIs.
22−25
Mos no ably, nonlinea phononics,
22,26,27
a
ansien and con olled la ice dis o ion induced by pho o-
exci ed phonons, has been success ully used o ansien ly
enhance supe conduc i i y,
28−30
manipula e and induce e o-
elec ic s a es,
31,32
and induce dynamical e imagne ic
ansi ions.
33
Mo e ecen ly, S upakiewicz e al. induced
swi ching o magne iza ion in y ium i on ga ne (YIG) hin
films by pumping o phonon modes.
34
Mo e gene ally, ligh
has been shown o induce me as able cha ge-densi y-wa e
s a es
35
and inci e ansi ions in o hidden phases.
36
This
expe imen al e idence mo i a es he use o non-equilib ium
app oaches o manipula e magne o- opological o de in ATIs.
In his wo k, we show heo e ically ha an AFM o FM
magne ic ansi ion accompanied by a opological ansi ion
can be induced in 2-SL MXT (X = Bi o Sb) samples wi h
in ense, expe imen ally accessible e ahe z lase pulses in
esonance wi h he phonons. In e es ingly, he mode a e
an isi e diso de ypically p esen in hese ma e ials educes
he lase in ensi y h eshold o induce he ansi ion.
In MXT ma e ials, he cons i uen SLs (see Figu e 1a) a e
held oge he ia an de Waals o ces, which allows ex olia ion
in hin samples.
37,38
We will ocus on sys ems wi h wo SLs,
because hey co espond o he minimal sys em ha can
Recei ed: Janua y 10, 2022
Accep ed: Ap il 19, 2022
Published: May 4, 2022
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accommoda e in e laye AFM o de . Wi hin each laye , he
magne ic momen s a e aligned e omagne ically, bu opposi e
laye s possess opposi e magne ic momen di ec ions. Fo 2-SL
MBT, he c i ical empe a u e is app oxima ely 20 K.
39
Fo
bulk MST, a c i ical empe a u e o 19 K has been epo ed.
40
Howe e , depending on he syn hesis condi ions, bulk MST
can possess a e omagne ic g ound s a e.
41,42
2-SL MBT and 2-SL MST p esen space g oup P3m1 (No.
164) wi h poin g oup D3din hei pa amagne ic phase. The
uni cell con ains N= 14 a oms wi h Te a oms loca ed in
Wyckoffposi ions 2d(1/3,2/3,z) and 2c(0, 0, z), Mn a oms a
posi ion 2d, and X = Bi and Sb a oms a posi ions 2cand 2d.
The la ice ib a ion ep esen a ion is gi en by he equa ion
Γ ib =7A1g⊕7A2u⊕7Eg⊕7Eu, which co esponds o se en
nondegene a e (A1g) and se en double-degene a e (Eg) Raman
modes, wi h equal numbe s o hei in a ed coun e pa s,
including he h ee acous ic modes (Eu⊕A2u). The cha ac e
able o D3dis shown in he Suppo ing In o ma ion.
Employing g oup heo y and p ojec ion ope a o s, we de i e
he se o eal-space displacemen s ha b ing he dynamical
ma ix in o block-diagonal o m, acco ding o hei i educible
ep esen a ions (see he me hods in he Suppo ing
In o ma ion o de ails). We find ha he shea mode whe e
one SL shi s in he [100] di ec ion and he opposi e SL in he
[100] di ec ion belongs o he Egi ep. I s pa ne co esponds
o an o hogonal in-plane displacemen . The b ea hing mode
consis s o he SLs mo ing away om and owa d each o he in
he di ec ion no mal o he plane ([001] and [001],
espec i ely) and belongs o he A1g ep esen a ion. Figu e
1b shows ep esen a ions o hese modes. Fo a de ailed g oup
heo y s udy o ew-SL MBT, see e 43.
Now ha we ha e es ablished ha he shea and b ea hing
modes a e allowed by symme y and de e mined hei i eps,
we calcula e he phonon equencies a he Γpoin . We
conside ed pa amagne ic, FM, and AFM configu a ions
wi hou spin−o bi coupling and ound only negligible
diffe ences among he co esponding phonon equencies.
The esul s o bo h 2-SL MBT and MST a e summa ized in
Figu e 2. Panels a and b show he Γpoin phonon equencies
wi h hei co esponding i educible ep esen a ion indica ed
by he shape o he ma ke . In bo h ma e ials, he shea and
b ea hing modes p esen he smalles equency among he
op ical modes (indica ed by downwa d g ay a ows), and hei
equency is smalle by a ac o o 2 compa ed wi h ha o he
nex op ical phonon.
Ha ing cha ac e ized he p ope ies o he phonons in he
ha monic egime, we nex conside he symme y aspec s o
hei nonlinea in e ac ions and hei lase exci a ion. A lase
pulse inciden on o a sample can couple di ec ly wi h in a ed
(IR) modes, depending on he lase equency and elec ic field
di ec ion. In u n, such an IR mode can couple nonlinea ly
wi h some Raman modes, p o ided hei i eps sa is y he
condi ion [ΓIR ⊗ΓIR]⊗ΓR⊃A1g.
27
This mechanism is
e med nonlinea phononics
26,27,44
and has allowed expe -
imen al
22,28−30,32,44,45
and heo e ical manipula ions o co e-
la ed s a es o ma e .
46−49
Fo he 2-SL MXT’s poin g oup,
d i ing a A2umode can ec i y o ally symme ic modes, such
as he b ea hing modes, because A2u⊗A2u=A1g. Thus, he
shea modes (Egi ep) a e no affec ed. On he con a y,
d i ing an Eumode allows coupling wi h he low- equency
shea modes in conjunc ion wi h he b ea hing mode, because
Eu⊗Eu=A1g⊕A2g⊕Eg.
Once an IR mode has been d i en wi h a sufficien ly s ong
lase pulse, coupling o all Raman modes wi h compa ible
i eps is allowed by symme y. Howe e , in ou case, because
he solu ion o he dynamical equa ions scales wi h he in e se
squa e o he Raman equency (∼ΩR−2), we can simpli y he
calcula ion and es ic he nonlinea in e ac ions o only he
low- equency shea and b ea hing modes.
27,48
We now
conside a lase pulse op imized o couple wi h he highes -
equency IR modes, wi h i ep A2u. This mode p esen s he
s onges coupling wi h he lase as shown by he la ges Bo n
effec i e cha ge Z*
50,51
(see he Suppo ing In o ma ion). In
his case, he nonlinea po en ial o 2-SL MBT akes he o m
γβ
[ ]=Ω +Ω
+++*·ΩZE
VQ Q Q Q
QQ Q F Q
,,1
2
1
2
1
3sin( ) ( )
0
IR R(3) IR
2
IR
2
R(3)
2
R(3)
2
3IR
2
R(3) 3 R(3)
3
IR
(1)
whe e γ3and β3a e nonlinea coefficien s de e mined om
DFT calcula ions ( o he p ocedu e and nume ical alues, see
he Suppo ing In o ma ion), E0is he elec ic field ampli ude
wi h he Gaussian p ofile F( ) = exp[− 2/(2τ2)], and Ωis he
lase equency, which we choose in esonance wi h he IR
Figu e 1. (a) 2-SL MXT la ice s uc u e and magne ic o de
(momen s shown as g ay a ows). Bi and Sb (X) a oms a e colo ed
pink, Te a oms yellow, and Mn a oms pu ple. (b) Low- equency
shea and b ea hing modes cha ac e is ic o ew-laye ma e ials. The
b ea hing mode p ese es all o he c ys al symme ies.
Figu e 2. Phonon equencies o (a) 2-SL MBT and (b) 2-SL MST
ob ained wi h fi s -p inciples calcula ions. The g ay a ows indica e
he phonons illus a ed below. (c and d) Real-space la ice
displacemen s wi h hei co esponding equencies. Red a ows
indica e he displacemen s.
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mode Ω=ΩIR = 4.69 THz. No e ha he d i en A2unonlinea
po en ial is much simple han ha o d i en Eumodes. This is
because he A2uphonons do no couple o Egmodes up o
cubic-o de in e ac ions.
Fo 2-SL MST, he e a e wo IR modes wi h A2ui eps,
simila Bo n effec i e cha ges, and simila equencies.
The e o e, we need o conside he simul aneous exci a ion
o he wo A2uIR modes, which leads o he po en ial
∑
γγ
γβ
[{ } ] = Ω
+Ω + +
++
+[ *+*]· Ω
=
ZZE
VQ Q Q
QQQQQ
QQQ Q
QQ F
,, 1
2
1
2
1
3
sin( ) ( )
i
i
ii
0
IR( ) R(3)
1
2
IR( )
2
IR( )
2
R(3)
2
R(3)
2
1,3 IR(1)
2
R(3) 2,3 IR(2)
2
R(3)
1,2,3 IR(1) IR(2) R(3) 3 R(3)
3
1IR(1) 2IR(2)
(2)
Fo 2-SL MST, we conside he lase equency Ω=[ΩIR(1)
+ΩIR(2)]/2 THz. The phonon dynamics a e de e mined by he
equa ions o mo ion ∂ 2QR=−∂QRV[QIR(i),QR] and ∂ 2QIR(i)=
−∂QIR(i)V[QIR(i),QR], whe e i uns o e he d i en IR modes.
We sol e he diffe en ial equa ions nume ically. In his wo k,
we do no conside he phonon li e ime. Recen Raman
measu emen s ha e shown ha he li e ime o he b ea hing
mode is app oxima ely 13.3 ps,
52
which is sufficien ly long o
he elec onic deg ees o eedom o espond.
The phonon dynamics o a gene al lase in ensi y and pulse
du a ion can be ob ained by sol ing he equa ions o mo ion
nume ically. In Figu e 3a, we show a ske ch o a lase -i adia ed
2-SL MBT sample. The incoming ligh wi h equency Ω=ΩIR
= 4.69 THz couples di ec ly o he co esponding esonan IR
mode. As we show in Figu e 3b, his mode oscilla es a ound i s
equilib ium posi ion. Anha monic coupling induces dynamics
in he Raman b ea hing mode, e en hough i does no couple
di ec ly o he lase . The nonlinea na u e o he in e ac ion
(γ3QRQIR2) leads o oscilla ions abou a posi ion shi ed wi h
espec o he equilib ium posi ion. Figu e 3c shows such
oscilla ions o a lase wi h peak elec ic field E0= 0.6 and pulse
du a ion τ= 0.6 ps. Simila esponses we e ob ained in 2-SL
MST, whe e he main diffe ence is he p esence o wo A2uIR
modes, ins ead o one. No ice ha wi h ligh , we can ob ain
only ⟨QR(3)⟩≥0, which co esponds o an effec i e inc ease in
he Mn−Mn laye sepa a ion. This is a consequence o he sign
o he nonlinea coefficien s (γ3 o MBT and γ1,3 and γ2,3 o
MST), which is in insic o he ma e ials.
The complemen a y p ocess o b inging he Mn planes
close o each o he could be achie ed by applying uniaxial
p essu e. Theo e ically, e 53 p edic s ha bulk MBT
unde goes a opological quan um phase ansi ion unde
2.12% comp essi e s ain.
In Figu e 3d, we plo he ime a e age o he shea modes as
a unc ion o E0 o τ= 3 ps. Expe imen ally, fields o ≤100
MV cm−1ha e been epo ed in he ange o 15−50 THz,
54,55
bu limi a ions a e imposed by he ampli ude o he
co esponding la ice dis o ion. Fo 2-SL MBT (2-SL
MST), ⟨QR(3)⟩=5Å/amu co esponds o a 1.68%
(1.88%) inc ease in he Mn−Mn plane in e laye dis ance.
Fo 2-SL MST, he dynamical equa ions become uns able o
E0≳2 MV/cm. Howe e , he ange o s abili y is la ge enough
o ob ain a magne ic ansi ion.
Inelas ic neu on sca e ing measu emen s
56
sugges ha he
magne ic o de in bulk MBT is desc ibed by he local-momen
Hamil onian (S=5/2)
/
//=+
in a in e
,whe e he
in alaye Hamil onian can be w i en as
/
=−
∑·− ∑
JDSSS ()
ij ij ij ii
z
in a
2wi h exchange in e ac ion
Jij (up o ou h-neighbo in e ac ions a e needed o fi he da a
co ec ly wi h SJ1= 0.3 meV, SJ2=−0.083 meV, and SJ4=
0.023 meV), and SD = 0.12 meV is a single-ion aniso opy.
Thus, he effec i e in alaye coupling is posi i e and leads o
he e omagne ic o de in each Mn laye . The in e laye
Hamil onian is gi en by
/
=− ∑·
⟨⟩
JSS
ij i
j
in e c, whe e expe i-
men s sugges a nea es -neighbo AFM in e laye in e ac ion
SJc=−0.055 meV.
56
We ob ain he spin Hamil onian om
fi s -p inciples calcula ions, employing a G een’s unc ion
app oach and he magne ic o ce heo em.
57,58
The calcu-
la ions we e pe o med using a GGA+U app oxima ion, which
desc ibes adequa ely localized Mn 3d s a es wi h Ue =U−J=
5.3 eV.
5,41
Fo he in e laye in e ac ions, he Hamil onian
akes he mo e gene al o m
/
=−∑·JSS
ij c,ij ijin e , whe e
longe - ange in e ac ions a e ele an . In p is ine MXT
compounds, he in e laye coupling go e ns he an i e omag-
ne ic o de in he g ound s a e, which is mainly media ed by a
long- ange double-exchangein e ac ion iaTeions.
5,41
Howe e , na u al la ice de ec s such as an isi e Mn−Bi o
Mn−Sb diso de o Mn excess in Bi (Sb) laye s can lead o
e omagne ic o de in hese sys ems.
41,59
We now s udy he effec o lase -induced ansien la ice
dis o ions on he magne ic o de . Unde a ime-dependen
la ice de o ma ion, small compa ed wi h he equilib ium
in e a omic dis ances, he spin exchange in e ac ion can be
app oxima ed as
60
6δδ[]=+·+[]J J J uuu() () ()
02
(3)
whe e u( ) is he eal-space la ice displacemen , J0is he
equilib ium in e ac ion, and δJis he coupling cons an
be ween he phonon and he spins. The connec ion wi h
Figu e 3. (a) Ske ch o a ligh -induced la ice dis o ion. (b) Time
dependence o he in a ed phonon mode di ec ly exci ed by he
inciden lase pulse in 2-SL MBT. (c) Nonlinea ly exci ed b ea hing
mode, which oscilla es abou a new shi ed posi ion. The lase
pa ame e s used in panels b and c a e τ= 0.6 ps and E0= 0.6 MV/cm.
(d) A e age displacemen o he nonlinea ly pho oexci ed b ea hing
mode QR(3) o MBT (black) and MST ( ed) o τ= 0.3 ps and lase
equency Ω=ΩIR(1) o 2-SL MBT and Ω=[ΩIR(1) +ΩIR(2)]/2 o
2-SL MST.
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phonon ampli ude Qis gi en by =
κκ
κ
Qmue/, whe e mκis
he mass o a om κand eκis he no malized dynamical ma ix
eigen ec o s.
Nex , we define he effec i e spin in e ac ion employing
Floque heo y. The exchange in e ac ions se he ele an
ene gy scale, wi h ≲1 meV. Because he in a ed phonon
equency (ΩIR ≈4.95 and 4.69 THz) used is la ge han he
exchange ene gy, we can define an effec i e ime-a e aged
exchange in e ac ion Je =J0+δJδ·⟨uR⟩, whe e ⟨···⟩indica es
he ime a e age. Thus, when he phonons oscilla e abou hei
equilib ium posi ions (ha monic phonons), such ha ⟨u⟩=0,
he exchange in e ac ions a e no modified in he pic u e
discussed he e. The non-ze o a e age shi , howe e , can
eno malize he in e ac ions leading o diffe en magne ic
configu a ions compa ed wi h he equilib ium coun e pa s.
We compu e he ligh -induced effec i e exchange in e -
ac ions as a unc ion o phonon ampli ude QR(3). Ou esul s
a e summa ized in Figu e 4. We plo he a e age in e laye
exchange in e ac ion
5
=∑
JJ1/
ij c,i
j
e
as a unc ion o QR(3).
We used a supe cell, which consis s o se en SLs o MBT
(MST) and h ee SLs o acuum simula ed by emp y sphe es.
Je ep esen s an a e age exchange in e ac ion, and
5
is he
numbe o in e ac ing magne ic momen s aken o he
a e age. Fo p is ine 2-SL MBT (2-SL MST), we find a sign
change in he in e laye exchange in e ac ion a QR(3) ≈2.4 Å
amu [QR(3) ≈0.7 Å amu]. These phonon ampli udes can
be ob ained wi h a lase pulse wi h an E0o ≈1.7 MV/cm and a
τo 0.3 ps (E0≈1.5 MV/cm, and τ= 0.3 ps), as we show in
Figu e 3. Gene ally, inc easing he e ical dis ance be ween
he Mn magne ic momen s weakens he an i e omagne ic
coupling and a o s e omagne ic o de in hese sys ems. The
ime scale o he spin eo ien a ion ollowing he sign change
in Je depends on pa ame e s such as he Gilbe damping
ac o ,
61
he exac spin aniso opy o 2-SL MBT and MST,
and he lase -induced Je bu is wi hin he limi s o he effec
we p edic o occu .
Because MXT samples a e p one o an isi e diso -
de ,
41,59,62−65
wi h diso de pe cen ages depending on he
sample ab ica ion p ocess, we also discuss he ole o diso de
in he ligh -induced magne ic ansi ion. Depending on he
concen a ion pe cen age, Mn−Sb an isi e diso de can une
he in e laye magne ic in e ac ion in o e omagne ic s a es.
63
He e, we s udy heo e ically he ole o an isi e diso de in he
ligh -induced magne ic ansi ion discussed p e iously.
Fi s , we will assume ha he an isi e diso de has a
negligible effec on he phonon equencies. This assump ion is
suppo ed by ecen Raman measu emen s in 2-SL MBT
samples wi h inhe en an isi e diso de , because he measu ed
phonon equencies a e in ag eemen wi h densi y unc ional
calcula ions o p is ine samples.
52
Nex , we in oduce diso de in o ou calcula ions o he
exchange in e ac ions. The an isi e diso de is assumed o be
an in e change o Mn wi h Bi(Sb) elemen s be ween he Mn
laye and Bi(Sb) laye s. This is consis en wi h ecen
expe imen s.
41
An isi e diso de effec s we e ound o ha e a
quan i a i ely impo an effec on he exchange in e ac ion in
hese ma e ials. Diso de effec s a e ea ed using a cohe en
po en ial app oxima ion (CPA) as i is implemen ed wi hin
mul iple sca e ing heo y.
66
We show ou esul s in Figu e 4,
whe e we conside 5% an isi e diso de , which is a ealis ic
concen a ion in mos o he known MXT samples.
5,41,63
In
gene al, an isi e diso de a o s a e omagne ic in e laye
coupling. The main eason o his is ha Mn momen s in
Bi(Sb) laye s a o a long- ange e omagne ic coupling
be ween he sep uple laye s.
67
Also, he educ ion o magne ic
momen s in Mn laye s diminishes he ex en o an i e omag-
ne ic coupling. A ze o displacemen , a fini e amoun o
diso de can weaken he effec i e exchange in e ac ion, leading
o weake elec ic fields ha a e necessa y o d i e he
ansi ion. In Figu e 4, he concen a ion we conside leads o a
diso de -induced e omagne ic g ound s a e.
We es ablished heo e ically he possibili y o uning he
in e laye magne ic o de om an i e omagne ic o e omag-
ne ic in 2-SL MXT samples using ligh in esonance wi h he
phonons. Now we demons a e ha a opological ansi ion
accompanies such a ligh -induced magne ic ansi ion.
The opology in MBT is ich. In bulk MBT, he magne ic
s uc u e is in a ian wi h espec o ime e e sal and hal -
la ice ansla ion symme ies. This leads o a
2
opological
classifica ion, wi h =
1
2
.
5
In he hin-film limi , he opology
depends in he numbe o SLs.
68
Fo example, 1-SL MBT is
p edic ed o be a FM i ial insula o , wi h Che n numbe C=
0. 2-SL, 4-SL, and 6-SL MBT p esen a ze o pla eau QAH,
wi h C= 0 in he AFM phase and |C|= 1 in he FM phase.
Odd laye (3-, 5-, and 7-SL) MBT is p edic ed o be in a |C|=
1 QAH insula ing s a e. Expe imen ally, he QAH s a e has
been obse ed in 5-SL MBT a 1.4 K
37
and a ze o Hall pla eau,
cha ac e is ic o an axion insula ing s a e, in 6-SL MBT.
38
We s udy he opology o 2-SL MBT as a unc ion o he
la ice displacemen s by examining he elec onic band
s uc u e and he p ojec ion o he p X = Bi, Sb, and Te
s a es. The band in e sion se es as an indica o o he
opological na u e o he ma e ial wi hin opological band
heo y.
69
Ou esul s a e summa ized in Figu e 5.In he
equilib ium configu a ion (le panels wi h Q= 0) wi h FM
o de , bo h 2-SL MBT and 2-SL MST exhibi he expec ed
band in e sion.
5,41
Fo he ou -o -equilib ium dis o ed
s uc u es ( igh panels), FM o de is p e e ed as we showed
be o e. We find ha he band in e sion is p esen , which
indica es he opological na u e o he new lase -induced
s uc u es.
Figu e 4. Effec i e a e aged in e laye exchange in e ac ion as a
unc ion o a e age b ea hing mode ⟨QR(3)⟩ o (a) 2-SL MBT and
(b) 2-SL MST. The pu ple ci cles co espond o p is ine samples,
while squa es co espond o 5% an isi e diso de (ASD).
The Jou nal o Physical Chemis y Le e s pubs.acs.o g/JPCL Le e
h ps://doi.o g/10.1021/acs.jpcle .2c00070
J. Phys. Chem. Le . 2022, 13, 4152−4158
4155
This wo k s udied he effec o e ahe z ligh pulses in
esonance wi h in a ed phonons in he magne ic and
opological o de o 2-SL MXT samples heo e ically. We
ound ha mode a e lase in ensi ies, which can be a ained in
cu en expe imen al se ups, can induce nonlinea dynamics in
he Raman b ea hing mode. The ime a e age o hese
dynamics leads o effec i e la ice dis o ions ha sepa a e he
SLs, effec i ely inc easing he dis ance be ween magne ic a om
planes. Using fi s -p inciples me hods, we ound ha he new
non-equilib ium la ice configu a ion can a o e omagne ic
o de . Fu he mo e, he ansi ion be ween an i e omagne ic
and magne ic o de can be uned ia an isi e diso de . We
showed ha he magne ic change is accompanied by a
opological ansi ion, as diagnosed by a band in e sion as a
unc ion o phonon ampli ude. Thus, ou heo e ical wo k
demons a es he possibili y o achie ing a sough -a e
magne ic opological ansi ionin2-SLMXTsamples
expe imen ally. Such a ansi ion in bo h 2-SL MBT and
MST es ablishes a b oade end in ma e ials, which could be
applied o o he an de Waals magne ic opological ma e ials.
■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/acs.jpcle .2c00070.
Addi ional de ails abou he g oup heo y phonon
symme y analysis, cha ac e able o he c ys al poin
g oup, phonon fi s -p inciples calcula ions, and a
discussion o he single-pa icle exci a ion spec um
(PDF)
T anspa en Pee Re iew epo a ailable (PDF)
■AUTHOR INFORMATION
Co esponding Au ho
A hu E ns −Ins i u u Theo e ische Physik, Johannes
Keple Uni e si ä , A 4040 Linz, Aus ia; Max-Planck-
Ins i u u Mik os uk u physik, D-06120 Halle, Ge many;
o cid.o g/0000-0003-4005-6781; Email: A hu .E ns @
jku.a
Au ho s
Ma in Rod iguez-Vega −Theo e ical Di ision, Los Alamos
Na ional Labo a o y, Los Alamos, New Mexico 87545,
Uni ed S a es; o cid.o g/0000-0001-8929-6546
Ze-Xun Lin −Depa men o Physics, The Uni e si y o Texas
a Aus in, Aus in, Texas 78712, Uni ed S a es; Depa men
o Physics, No heas e n Uni e si y, Bos on, Massachuse s
02115, Uni ed S a es
A i z Leona do −Donos ia In e na ional Physics Cen e ,
20018 San Sebas ian, Spain; EHU Quan um Cen e ,
Uni e si y o he Basque Coun y UPV/EHU, 48940 Leioa,
Spain
Maia G. Ve gnio y −Donos ia In e na ional Physics Cen e ,
20018 San Sebas ian, Spain; Max Planck Ins i u e o
Chemical Physics o Solids, D esden D-01187, Ge many
G ego y A. Fie e −Depa men o Physics, No heas e n
Uni e si y, Bos on, Massachuse s 02115, Uni ed S a es;
Depa men o Physics, Massachuse s Ins i u e o Technology,
Camb idge, Massachuse s 02139, Uni ed S a es
Comple e con ac in o ma ion is a ailable a :
h ps://pubs.acs.o g/10.1021/acs.jpcle .2c00070
No es
The au ho s decla e no compe ing financial in e es .
■ACKNOWLEDGMENTS
The au ho s hank Michael Vogl o use ul discussions. This
esea ch was p ima ily suppo ed by he Na ional Science
Founda ion (NSF) h ough he Cen e o Dynamics and
Con ol o Ma e ials: an NSF MRSEC unde Coope a i e
Ag eemen DMR-1720595, wi h addi ional suppo om NSF
G an s DMR-1949701 and DMR-2114825. This wo k was
pe o med in pa a he Aspen Cen e o Physics, which is
suppo ed by NSF G an PHY-1607611. A.L. acknowledges
suppo om he unding g an : PID2019-105488GB-I00.
M.R.-V. was suppo ed by he LANL LDRD P og am and he
U.S. Depa men o Ene gy, Office o Science, Basic Ene gy
Sciences, Ma e ials Sciences and Enginee ing Di ision,
Condensed Ma e Theo y P og am. M.G.V. is hank ul o
he suppo om he Spanish Minis y o Science and
Inno a ion (G an PID2019-109905GB-C21) and Deu sche
Fo schungsgemeinscha (DFG, Ge man Resea ch Founda-
ion, GA 3314/1-1-FOR 5249) (QUAST). A.E. acknowledges
unding by Fonds zu Fö de ung de wissenscha lichen
Fo schung (FWF) g an I 5384. Pa o he calcula ions we e
pe o med a Rechenzen um Ga ching o he Max Planck
Socie y (Ge many).
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