Magnetism and superconductivity at LAO/STO-interfaces: the role of Ti 3d interface electrons

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by  N. Pavlenko

Magnetism and superconductivity at LAO/STO-interfaces:
the role of Ti 3d interface electrons
N. Pavlenko1,2, T. Kopp2, E.Y. Tsymbal3, G.A. Sawatzky4, and J. Mannhart5
1Institute for Condensed Matter Physics, 79011 Lviv, Ukraine,
2 EKM and Institut fu¨r Physik, Universita¨t Augsburg, 86135 Augsburg, Germany
3 Department of Physics and Astronomy, Nebraska Center for Materials and Nanoscience,
University of Nebraska, Lincoln, Nebraska 68588-0299, USA
4Department of Physics and Astronomy, University of British Columbia, Vancouver,
Canada V6T1Z1 5Max Planck Institute for Solid State Research, 70569 Stuttgart, Germany
(Dated: January 20, 2013)
2
1 Ferromagnetism and superconductivity are in most cases adverse. However, recent experiments
0 revealthattheycoexist atinterfacesofLaAlO3 andSrTiO3. Weanalyzethemagneticstatewithin
2 density functional theory and provide evidence that magnetism is not an intrinsic property of the
two-dimensional electron liquid at the interface. We demonstrate that the robust ferromagnetic
n
a state is induced by the oxygen vacancies in SrTiO3- or in the LaAlO3-layer. This allows for the
J notion that areas with increased density of oxygen vacancies produce ferromagnetic puddles and
accountforthepreviousobservationofasuperparamagneticbehaviorinthesuperconductingstate.
1
1
PACSnumbers: 74.81.-g,74.78.-w,73.20.-r,73.20.Mf

]
l
e
The formation of a metallic state at the interface of perconductingstate. MagneticoxygensitesattheAlO -
- 2
r the bulk insulators LaAlO and SrTiO 1 has become a surface (cf. Ref.12) and the build-up of triplet coupling
3 3
t
s prototype for the reconstruction of electronic states in of Ti 3d states through the oxygen bonds (or possibily
t. systems with artificially reduced dimensionality. This vacancies) in the TiO2 interface plane (cf. Ref.13) have
a two-dimensional (2D) electronic system is affected by been proposed7 as scenarios for the formation of a mag-
m
sizable electronic correlationswhich allow characterizing netic state.
- the extended interface electronic states as an electron
d The interpretationof the experimental results opens a
n liquid2,3. The correlations not only induce a supercon- compelling question: can the Ti 3d orbitals that were
o ductingstate4 butalsosupportmagnetism5. Anovelyet identified in the previous band structure calculations
c unexplainedphenomenonisthecoexistenceofmagnetism (see, e.g., Refs.14–22) be responsible both for the metal-
[ and superconductivity6,7 in the 2D electron liquid.
lic and magnetic states coexisting at the same interface?

2 Recent measurements by Dikin et al.6 demonstrate a Inthispaper,wepresenttheresultsofdensityfunctional
v hysteretic behavior in the field-dependences of magne- studieswhichsupporttheexistenceofarobustferromag-
3
toresistance and critical temperature which suggests the neticstateattheLAO/STOinterfaceinducedbyoxygen
6
existenceofferromagnetisminthesuperconductingsam- vacancies. Wedemonstratethatboththemagnetismand
1
ples of LaAlO (LAO) grown on SrTiO (STO). More- conductivity occur involving the Ti 3d electrons but the
1 3 3
. over, Dikin et al. take the viewpoint that two distinct magnetism is due to rather confined electrons around O
5
electronic systems are associated with the antagonistic vacancies while the conductivity is a result of the 2D
0
superconducting and ferromagnetic properties: the elec- electron gas caused by electronic reconstruction. We ar-
1
1 trons that are generated by the polar catastrophe mech- gue that this behavioris a prerequisite of co-existenceof
: anism are suggested to be related with magnetism while magnetism and superconductivity which are observedat
v
superconductivity is associated with the charge carriers low temperatures.
i
X induced by the presence of oxygen vacancies. The con-
Toexplorewhetheraferromagneticstateisinducedat
r cept oftwo differenttypes ofchargecarrierswhich could theseinterfaces,weconsideroxygenvacanciesasamech-
a contribute to the interface electrical transport has been
anismresponsibleformagnetism. Wegenerateanumber
discussed also in8–11.
of supercells which consist of two symmetric LAO/STO
Very recently, Li et al.7 probed magnetism through parts,whereeachpartcontainsastackof4unit-cell(uc)
torquemagnetometrywhichallowsdetectingdirectlythe thick LAO layersdeposited onaSTO-slabofa thickness
magneticmomentoftheinterfaceinanexternalmagnetic varying between 1.5 uc and 6 uc. The interfacial config-
field H. They found a strong superparamagnetic torque urationisconsideredasTiO /LaO.TheLAO-STO-LAO
2
signal in the superconducting state. With the assump- partsare separatedby a 13˚A thick vacuumsheet. Oxy-
tion that the signal originates from the STO layer next gen vacancies are assumed to lie in the first interfacial
to the interface, they obtained the magnetic moment M TiO -layers or in one of the AlO -layers of the LAO-
2 2
of 0.3 0.4µ per unit cell and a collective magnetic film. Acellwith anoxygenvacancyinMO (M=Ti. Al)
B 2
−
moment of the superparamagnetic grains of the order of is sketched in Fig. 1(b). The vacancy is introduced by
1000µ . TheobservationofasuperparamagneticM(H) excluding the oxygen atom O(a/2, b/2) in the center of
B
indicates that ferromagnetic grains form even in the su- the M O -plaquette. The location of the vacancy at the
2 4
2
1
dxy 0.5 up
3
Ti 0
S
O -0.5 dn
D pure system
-1
1
dxy up
3
Ti 0
S
O with O-vacancy dn
D -1
3d
dxz,yz 0.3 3dxyzz up
3
Ti 0
S
DO -0.3 with O-vacancy dn
-1 0 1 2 3 4
Energy E-E (eV)
F
FIG. 2: Projected DOS (in eV−1) for 3d (t2g) states of the
interfacial Ti in the supercell containing 4 unit cell-thick
LaAlO3 layers and a 4-unit cells thick SrTiO3 layer. DOS in
thepuresystemandinthesystemwithoneO-vacancy(25%)
per supercell area in the interfacial TiO2-layer are shown for
comparison. Thevertical grey line denotes the Fermilevel.
FIG. 1: Schematic view of the SrTiO3/LaAlO3 heterostruc-
ture. The supercell contains a 4 unit cell thick LaAlO3 layer
depositedona2.5unitcellthickSrTiO3 slab. Thefullsuper- (2 2) planar unit cells have been structurally relaxed
×
cellconsists oftwosymmetricpartsof thedepictedstructure along the z-axis by a combination of the optimization
and avacuum layerof 13 ˚A.Thestructures on theright side procedures of the full potential WIEN2k-package and
show (a) a projection of the supercell of STO/LAO on the the pseudopotential QE package26,27. The in-plane
(x,y)-plane of TiO2, and (b) a M2O4 (M=Ti, Al)-plaquette lattice constants have been fixed to their bulk-STO
generated for thestudy of thesystem with O-vacancies. The cubic values (a = b = 3.905 ˚A). Similar to
STO STO
position of an O-vacancyis identified by a red dashed circle.
the previous calculations14–19, we find that a metallic
state is produced at the LAO/STO interface due to the
electronic reconstruction.
interface is motivated by the experimental evidence of Fig. 2 presents the projected Ti 3d densities of states
O-vacancies present in STO in samples grown at oxygen (DOS) for both spin directions in the system with su-
pressures below 10−5 mbar23,24. percells containing 4 LAO uc and 4 STO uc along the
Density functional calculations are performed using z-direction (the full supercell contains twice the number
the Generalized Gradient Approximation (GGA) of LAO unit cells). The difference in the spin-projected
in the Perdew-Burke-Ernzerhof pseudopotential DOS implies a non-zero spin polarization. For the pure
implementation25 in the Quantum Espresso (QE) systemwithout oxygenvacancies,the occupanciesof the
package26. We use a kinetic energy cutoff of 640 eV and spin-up and spin-down 3d states are almost identical.
theBrillouinzoneofthe106-to166-atomsupercellssam- The maximal magnetic moments of the interface Ti are
pled with 5 5 1 to 9 9 1 k-point grids. An increase about 0.005µB and the polarization from the more dis-
of the k-poi×nt×mesh fro×m×(5x5x1) to (7x7x1) leads to a tant TiO2 planes is negligible. The calculated magnetic
negligibly small change of the total energy by 0.005Ry moment per (1 1) unit cell of LAO/STO interface is
×
and to an increase of the Ti magnetic moments by small 0.03µB whichoriginatesmostlyfromthe surfaceoxygen
values of about 0.05 µ in the presence of O-vacancies. sites. This polarization is too small to support a robust
B
The difference between the Ti magnetic moments for ferromagneticstatesuggestingthatmagnetismisnotdue
the two different (2nx2nx1) and (nx2nx1) k-meshes for to the pure interface electron gas.
n=4 is about 0.02 µ , which is a negligibly small value. ThesituationwithO-vacanciesisdifferent. Anoxygen
B
In our calculations we account for a local Coulomb vacancy adds two extra electrons at the interface to pre-
repulsion of Ti 3d electrons by employing a GGA+U servechargeneutrality. Thetwoelectronsaremostlikely
approach with U = 2 eV2. First, we consider pure localized in the vicinity of the O-vacancy as found for
Ti
stoichiometric TiO /LaO-interfaces as reference for the CaO by Elfimov et al.12. As shown below, this enhances
2
oxygen doped interfaces. The supercells which contain the charge density and increases the exchange splitting
3
puddles, as wasrecently observedby Bertet.al.28. Their
)Β 0.4
µ respective collective magnetic moments are a likely can-
nt ( Ti (0,0) didate for the source of the superparamagnetic behav-
me Ti (0.5,0.5) ior observed by Li et al.7. As compared to the ferro-
o
m
c 0.2 magnetically ordered structure, the total energy of the
eti (2 1)-configuration with antiferromagnetically ordered
agn int×erface increases by 0.36 eV/u.c. which implies a high
m
Ti 0 stability of the ferromagnetic state.
The ferromagnetic ordering can be examined in the
1 2 3 4
frameworkofthe Stonermodelforferromagnetism. This
TiO layer index
2 model treats the stabilization of the ferromagnetic state
as a result of the difference between the reduction of the
FIG. 3: Magnetic moments of Ti atoms in different TiO2
Coulomb interaction for the 3d electrons with parallel
layers in the (4 uc)SrTiO3/(4 uc)LaAlO3 structures for the
spins of neighbouring Ti ions and the increase of the ki-
structure with one O-vacancy in the interfacial TiO2 layer.
The black up and red down triangles correspond to the two netic energy caused by the widening of the 3d-bands for
Tiatomswiththeplanarcoordinates(0,0)and(0.5a,0.5a)in the electrons of the same spin21. The condition for the
a doubled unit cell of SrTiO3. The TiO2 layer 4 is the layer appearanceofferromagnetismisbasedontheStonercri-
next to theinterface. terion Iρ(ε ) > 1. The interaction I = ∆/m parame-
F
terizes the exchange splitting ∆, and m is the magnetic
momentofTi inthe ferromagneticstate (per µ ); ρ(ε )
B F
ofthe spinbands;consequentlyO-vacanciesstabilizethe is the paramagnetic density of states at the Fermi level.
ferromagnetic order. Theparametersappearinginthe Stonercriterionarede-
First, we assume that the oxygen vacancy lies within rived from the results of the GGA+U-calculations and
the TiO plane at the interface. In the oxygen-deficient presented in Table I. The Stoner condition is satisfied
2
system, we find sizable Ti magnetic moments at the in- irrespective of the thickness of the STO-layer,which im-
terfacial TiO -plane (see Fig. 3). The magnetic moment plies that the ferromagnatic state is favourable in these
2
of the Ti atoms next to the O-vacancy is 0.33µ and systems although the magnetic moment and exchange
B
that of the more distant Ti(0,0) atoms at∼the interfacial splittingslightlydecreasewithincreasingSTOthickness,
planeis 0.34µ . MagneticmomentsonTiatomsaway consistent with Ref. 21. The excess 3d charge in the
B
from the∼interface are negligible (Fig. 3). We also find vacancy-doped supercells leads to a substantial increase
a sizable magnetic moment on the AlO2 surface plane ofρ(εF) upto 1.5 1.8eV−1 as comparedto the pure
omfoambeonutto−f0t.h1e8iµnBteraflaigceneTdiaanttoimpasr.alNleeledtolestshetomsaagyn,etthiec sρy(εstFe)mcsonwtirtihbuρ∼t(eεsFt)o−≈the0.s5tr−on0g.7inecVre−a1s.e oTfhteheenThiamncaegd-
concentrationofO-vacanciesinthesemodelstructuresis netic monents in the oxygen-deficient systems.
farhigherthantheaveragedensityintheexperimentally O-vacanciesstrongly influence the electronic structure
investigated heterostructures. Nevertheless, it is evident oftheTi3dstates: theexcesschargeoriginatingfromthe
that a triplet coupling is induced between the nearest- eliminated O atom in the interfacialTiO2 plane leads to
neighbor Ti sites and that ferromagnetism is enhanced a redistribution in the occupancy of the five 3d orbitals.
in O-vacancy rich regions of the interfacial plane. The contribution of the 3d eg orbitals to the magnetic
moment formation is rather insignificant. In contrast, a
The elimination of the central oxygen in the (2 1)
× substantialamountoftheexcesselectronchargeistrans-
configuration results in the formation of stripes of O-
ferredtothet spin-uporbitals(Fig.2). Ina(2 1)-unit
vacancies along the y-direction characterized by two va- 2g
×
cell, the location of the O-vacancy along the y-direction
cancies near Ti(0.5a, 0) and no vacancies near Ti(0,0)
between the two Ti-atoms (see Fig. 1(b)) leads to sym-
atom. To test the stability of such an “inhomoge-
metry breaking, splitting the two t (3d and 3d )
neous” distribution of O-vacancies, we have also per- 2g yz xz
orbitals. Due to the random distribution of O-vacancies
formed GGA+U calculations of a supercell with an or-
dered ‘homogeneous” arrangement of the vacancies cor-
responding to exactly one vacancy per each Ti atom.
This can be obtained by elimination of one oxygen in TABLE I: Calculated magnetic moments of interface Ti
the square (√2 √2)-supercell shown in Fig. 1(a). The ions nearest to the O-vacancy, the exchange splitting
comparison of t×he calculated total energy with the en- (∆) and the parameter Iρ(εF) of the Stoner criterion for
ergy for that of the (2 1)-supercell (Fig. 1(b)), both (LaAlO3)4/(SrTiO3)n heterostructures with different n.
×
containinga 4u.c.thick-STO layer,givesanenergygain
ofabout0.25eVperinterfaceu.c. whichindicatesaten- n mTi(µB) ∆(eV) Iρ(εF)
dency towards an inhomogeneous spatial distribution of 1.5 0.31 1.15 3.89
oxygen vacancies in LAO/STO.
2.5 0.33 0.82 1.26
It is expected that areas with an increased density of
3.5 0.34 0.98 1.64
oxygenvacanciesallowfortheformationofferromagnetic
4
0.4 layer with the O-vacancy (Fig. 4(a)), similarly to that
(a)
µ)Β 0.3 obtained when the O-vacancy is placed in the interfa-
nt ( 0.2 cial TiO layer. This magnetic moment is due to the
e 2
m 0.1
o exchangesplittingofthenotfullyoccupiedlocaloxygen-
m
c 0 vacancy-centeredstateofamixedAls–p-characterwhich
gneti -0.1 Ti (0.5,0) producesquasi-one-dimensionalelectronicbandsandfer-
Ma -0.2 AlO2 romagnetic moments in the AlO -layer antiparallel to
2
V) 4 (b) that of the interface Ti atom30.
e 3
E(1) (tot2 twRoedcieffnetresntutdtiyepseosfotfhechLaArgOe/cSaTrrOierinstienrftaecremssdiosftitnhgeuiisnh-
E-tot1 terfacial localized Ti 3d electrons and the mobile 3dxy
0
1(AlO) 2(AlO) 3(AlO) 4(AlO) 5(TiO) electrons of several distant Ti layers10, or they relate
2 O-vac2ancy position (X2O layer) 2 2
2 magnetism to the interfacial electrons produced by the
electronic reconstruction and associate superconductiv-
FIG. 4: (a) Magnetic momentsof theinterface Ti and AlO2- ity to the charge carriers induced by O-vacancies6. Our
layer (per u.c.) in (2STO)/(4LAO)-supercells with a change
findings open a new perspective: both the magnetism
of the position of the O-vacancy along the (001)-direction
and the superconductivity are due to the interfacial Ti
between thetop AlO2-layer (left) and interface TiO2 (right).
(b)VariationofthetotalenergyEtot−Etot(1)withthechange 3d electrons. The magnetism, however, is a result of the
of the position of the O-vacancy along the (001)-direction. spin splitting of the populated electronic states induced
Here Etot(1) is the total energy for the system with an O- by O-vacancies, while the metallic behavior of the inter-
vacancy located in the top AlO2 surface. face results from the 2D electron liquid caused by the
electronic reconstruction. The metallic state has been
related to a superconducting state below 300 mK and
along the x- and y-directions in LAO/STO samples, the the predicted scenario suggests that the corresponding
electron chargeis assumed to occupy both, the 3dyz and charge carriers move in regions of small or vanishing O-
the 3dxz state—yet the dominant contribution to the vacancy concentrations.
magnetic moment has to be ascribed to the 3d spin-
xy Note added during revision: After the submission of
up occupancy.
the manuscript we were informed that Bert et. al.28
Oxygen vacancies may appear not only at the interfa-
in fact observed submicrometer puddles of ferromag-
cial TiO layer but also on the surface and in the bulk
2 netisminthepresenceofthesuperconductingstateatthe
of the LAO layer. Consistent with the previous calcula-
LaAlO /SrTiO interface. An alternative scenario has
tions 29 we find that the lowest total energy is achieved 3 3
recently been proposedby K.Michaeli et. al.31 who sug-
with the vacancy located in the top AlO -surface layer
2 gest a homogeneously polarized interface layer which is
(Fig. 4(b)), with an energy gainof about 1.5 eV as com-
magnetically coupled to a second superconducting layer.
paredtoavacancyintheinterfaceTiO -layer. The25%-
2
concentrationofsurfacevacanciesproducestwoelectrons The authors acknowledge helpful discussions with
per (2 1)-unit cell, with one electron transferred to the R. Ashoori, I.S. Elfimov, S.S. Jaswal, Lu Li, L. Klein,
×
interfaceandanotheronehybridizedattheAlO surface I.V. Stasyuk, and S. Seri. This work was supported by
2
close to a central O vacancy, similarly to12. Our calcu- theDFG(TRR80),the EC(oxIDes),NebraskaMRSEC
lations show that the placement of an O-vacancy in the (NSFDMR-0820521),NSF-EPSCoR(EPS-1010674),the
AlO -planes of the LAO-layer still induces a significant A. von Humboldt Foundation and the Ministry of Edu-
2
magnetic moment on the interface Ti atoms (Fig. 4(a)). cationandScienceofUkraine(GrantNo.0110U001091).
This magnetic moment originates from the spin polar- Financial support from the CFI, NSERC, CRC, and
ization of the occupied Ti-3d states due to the electron the Max Planck-UBCCentrefor QuantumMaterialsare
charge transferred from the O-vacancy site. Interest- gratefully acknowledged. Grants of computer time from
ingly, when the O-vacancy lies close to the surface of theLeibniz-RechenzentrumMu¨nchenthroughtheHLRB
LAO we find a sizable magnetic moment in the AlO - project h1181 are thankfully acknowledged.
2
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