Table Of ContentSpin moment formation and reduced orbital polarization in LaNiO /LaAlO
3 3
superlattice: LDA+U study
Myung Joon Han and Michel van Veenendaal
Department of Physics, Northern Illinois University, De Kalb, Illinois 60115, USA and
Advanced Photon Source, Argonne National Laboratory,
9700 South Cass Avenue, Argonne, Illinois 60439, USA
(Dated: January 26, 2012)
DensityfunctionalbandcalculationshavebeenperformedtostudyLaNiO3/LaAlO3superlattices.
Motivated by recent experiments reporting the magnetic and metal-insulator phase transition as a
2 function ofLaNiO3 layerthickness,weexamined theelectronic structure,magnetic properties, and
1 orbitaloccupationdependingonthenumberofLaNiO3 layers. Calculationsshowthatthemagnetic
0 phase is stabler than the nonmagnetic for finite and positive U values. The orbital polarization is
2 significantlyreducedbyU eveninthemagneticregions. Theimplicationsoftheresultsarediscussed
in comparison to recent experimental and theoretical studies within thelimitations of theLDA+U
n
method.
a
J
PACSnumbers: 73.20.-r,75.70.-i,71.15.Mb
5
2
I. INTRODUCTION analysis for the electronic structure, magnetism, and or-
]
l bital polarization of LNO/LAO superlattice using the
e
LDA+U method [18–20]. Since previous calculations
- Understanding transition metal oxides is of perpetual
r were performed at the LDA [14] or DMFT level [12, 15]
t interestandimportanceincondensedmatterphysicsand
s and assumed the bulk-like PM phase, LDA+U calcula-
material science [1]. Recent advances in layer-by-layer
.
t growthtechniquesofheterostructuresoftransitionmetal tion can provide meaningful information especially re-
a
garding the magnetism in this system. Total energy cal-
m compounds have created particular interest due to their
culations showed that the LDA+U stabilizes ferromag-
great scientific and technological potential [2]. Exotic
- netic (FM) spin order along in-plane and out-of-plane
d materialphenomenathatareclearlydistinctive fromthe
n ‘normal’ phases include interface superconductivity [3], direction. This result may indicate the existence of an-
o magnetism [4, 5], charge [6, 7] and orbital reconstruc- other ground state configuration in between m ∼ 2 and
c m ∼ 4 superlattices. The orbital polarization is signif-
tion [8].
[ icantly reduced by U which is in contrast to the sim-
One of the most intriguing classes of materials may
1 be the nickelate superlattices [9–16]. A series of re- plified Hubbard-type model prediction [12], but consis-
v tent with the extended charge-transfer model DMFT
cent theoretical studies have created considerable inter-
9 calculation [15]. The calculated Ni-d valence based on
est, suggesting the heterostructuring-inducedorbital po-
6 LDA+U supports the recently suggested picture for the
3 larization and the possible high-Tc superconductivity in metal/insulator phase diagram based on the d-valency
5 LaNiO3 (LAO)/LaAlO3 (LAO) superlattice [12, 17]. In
[21], and demonstrates the importance of the double
. this picture, the two degenerate Ni e orbital states
1 g counting issue. These results are discussed in compar-
are split by a combination of translational symmetry
0 ison to the recent theoretical and experimental studies.
2 breaking and on-site Coulomb interaction, leading to a
1 cuprate-like band structure. Although this kind of the-
: oretical picture has been challenged by more recent dy-
v
II. COMPUTATIONAL DETAILS
namicalmean-fieldtheory(DMFT)calculationsbasedon
i
X a charge transfer model including oxygen states explic-
r itly [15], several experimental papers have found other For the band-structure calculations, we employed
a
interesting phenomena in this system. Boris and co- Troullier-Martins type norm-conserving pseudopotential
workers[10]reporteda metalto insulatortransitionas a [22] with a partial core correction and linear combina-
function of LNO layer thickness: Even though the bulk tionofthelocalizedpseudo-atomicorbitals(LCPAO)[23]
LNO is a paramagnetic(PM) metal, the heterostructure as a basis set. In this pseudo-potential generation, the
(LNO)m/(LAO)n becomes insulating and magnetic if m semi-core 3p electrons for transition metal atoms were
is small, m≤2, while it remains PM and metallic when included as valence electrons in order to take into ac-
m≥4[10]. Theinsulatingbehaviorwasalsoobservedby countthecontributionofthesemi-corestatestotheelec-
Freeland et al. [13]. However the detailed magnetic and tronic structure. We adopted the local density approxi-
electronic structure changes, as well as the other impor- mation(LDA)forexchange-correlationenergyfunctional
tantphysicalquantities suchas orbitalpolarizationhave asparametrizedbyPerdewandZunger[24],anduseden-
not yet been clearly understood as a function of layer ergy cutoff of 400 Ry and k-grid of 12×12×6 per unit
thickness, m. superlattice volume. The LDA+U functional is adapted
In this study, we performed a detailed first-principles from the formalism of Ref. 26 and Ref. 25 [27]. The
2
0.2 (a) AFM
V) 0.1 FM
e
y ( 0
erg -0.1 PM
n
E -0.2
-0.3
0.2 (b) AFM
V) 0.1 FM
e
y ( 0
erg -0.1 PM
n
E -0.2
-0.3
µ)B 12..50 (c) mm==21
nt ( 1.0
e
m
o 0.5
M
0
FIG. 2: (Color online) The suggested schematic phase dia-
2.4 (d) m=1 gram(basedonthepreviousexperimentandourcalculation)
e (e)g 2.3 m=2 aosftahefupnocstsiiobnleogfrmoun(sdeesttahteectoexntfi)g.urationof(LNO)m/(LAO)n
v
aN
2.2
(AFM) spins eventually converge to a PM solution, the
0 3 5 7
magnetic groundstates are stabilizedat the finite U. As
U (eV)
clearlyseeninFig.1(a),FMspinorderingisenergetically
FIG. 1: (Color online) (a) Calculated total energy of favoredwithintheLNOplane. Theenergydifferencebe-
(LNO)1/(LAO)1 with the in-plane spin ordering of FM and tween FM and AFM state is 3, 246, and 525 meV per
AFM as a function of U. (b) Calculated total energy (LNO)1/(LAO)1 for U=3,5,and7 eV, respectively. FM
of (LNO)2/(LAO)1 with the out-of-plane spin ordering of spinorderisalsofavoredalongtheout-of-planedirection
FM and AFM as a function of U where the in-plane spins as shown in Fig. 1(b) in which we present total energies
are set to be FM. (c) Calculated Ni magnetic moment for of (LNO)2/(LAO)1; the out-of-plane spin orderings are
(LNO)1/(LAO)1and(LNO)2/(LAO)1asafunctionofU (FM settobeFMorAFMwhilethein-planeorderisFM.The
order considered). (d) Average number of Ni-eg electrons in calculatedFM-AFMenergydifferenceis60,126,and201
(LNO)1/(LAO)1 and (LNO)2/(LAO)1 as a function of U.
meVper(LNO)2/(LAO)1 forU=3,5,7eV,respectively.
TheenergydifferencesbetweenFMandAFMspinstruc-
ture becomes larger as U increases in both cases of in-
geometry relaxation has been performed with the force
criterion of 10−3 Hartree/Bohr. During the relaxation planeandout-of-planeordering. Thatis,theon-sitecor-
relationsstabilize FM spin ordering,and asU decreases,
process,the in-plane lattice constant is fixed considering
the two magnetic solutions becomes more close in their
the substrate effect in the experimental situation. The
energies, and eventually converges to the PM phase at
orbital polarization P, defined as
U=0. The magnetic moment is also dependent on U.
nx2−y2 −n3z2−r2 Fig. 1(c) shows the calculated magnetic moment for FM
P = , (1)
nx2−y2 +n3z2−r2 case as a function of U. The moment increases as U in-
creasesasintheothertypicalcorrelatedtransitionmetal
can be calculated by integrating the projected density- oxide materials [18, 20, 25]. It is noted that, as soon as
of-states (DOS) up to Fermi level. All the calculations U is turned on, the Ni moment becomes ∼ 1 µ (U=3
B
were performed using the density functional theory code eV), and further increases to be 1.2 and 1.4 µ at U=5
B
OpenMX [28]. and 7 eV, respectively.
Our calculation results may seem to suggest that the
magnetic moment formed in the thin-LNO superlattice
III. RESULT AND DISCUSSION
[10]isorderedferromagnetically. Sincethespinpolarized
oxide heterostructure could be useful for the device ap-
One natural and evidently important question raised plications, there has been active research for finding the
from experimental studies on the magnetic moment for- structurethatproducesFMspinorder[29–31]. Therefore
mation in this heterostructure [10] is about the ground our result of a FM ground state in LNO/LAO may have
state spin structure and its moment size. Fig. 1 sum- a positive implication for such an application. However
marizes our results. Fig. 1(a) shows the calculated total it should be noted that the muon spin rotation (µSR)
energy of (LNO)1/(LAO)1 superlattice as a function of experiment by Boris et al. [10] is not well interpreted in
U. While at U=0 eV both FM and antiferromagnetic thelongrangeFMorderingpictureeventhoughtheµSR
3
s/eV) 01..80 (a) x2-y2 es/eV) 00..36 (a) m=1
S (State 00..46 S (Stat -00..03
O 0.2 O -0.6
D D
0.0
S (States/eV) 000...468 (b) 3z2-r2 S (States/eV) -0000....0363 (b) m=2
O 0.2 O -0.6
D D
0.0
ates/eV) 00..68 (c) ates/eV) 000...036 (b) m=3
St 0.4 St
S ( S ( -0.3
O 0.2 O -0.6
D D
0.0
OS (States/eV) 0000....2468 (d) S (States/eV) -0000....0363 (c) m=4 3xz22--yr22
D 0.0 O -0.6
-8 -6 -4 -2 0 2 4 D
Energy (eV) -8 -6 -4 -2 0 2 4
Energy (eV)
FIG.3: (Coloronline)Ni-eg DOSof(LNO)m/(LAO)1 super-
latticegeometrywithPMspin(U=0): (a)m=1,(b)m=2, FIG. 4: (Color online) Ni-eg DOS of (LNO)m/(LAO)1 su-
(c) m = 3, and (d) m = 4. Solid (red) and dotted (blue) perlattice geometry with FM spin (U=5 eV): (a) m=1, (b)
lines correspond to dx2−y2 and d3z2−r2 states, respectively, m = 2, (c) m = 3, and (d) m = 4. Up/down panels repre-
and Fermi level is set to be 0. sent the up/down spin states, respectively. Solid (red) and
dotted (blue) lines correspond to dx2−y2 and d3z2−r2 states,
respectively, and theFermi level is set to be0.
is basically a local probe and that the origin of metal-
insulator phase transition in the nickelate series are not
clearly understood yet. Especially regarding the charge dynamical mean field theory (DMFT) calculations with
disproportion or ordering in nickelates, the conventional charge self-consistency [36, 37], and compare the total
LDA+U has a clearlimitation to describe such phenom- energy for PM, FM and AFM configurations as we did
ena [32, 33]. Moreover Fig. 1(a) and (b) indicate the in this study within LDA+U scheme.
possibilityofAFMgroundstateinthenegativeU region To understand metal-insulator phase transition as a
which is more or less related to the reported charge dis- function of LNO thickness [10], we examined Ni e DOS
g
orders in the nickelate systems [32, 33]. Therefore one dependingonthethickness,m. Thed-bandwidthchange
needs to be careful in the interpretation of our LDA+U asafunctionofmmaybe anusefulinformationasU/W
results on the FM spin ground state as an indication of playsanimportantroleinthemetal-insulatorphasetran-
long range ordered ground state as one may see in the sition of rare-earth nickelate [38]. Fig. 3 shows DOS of
actinide systems for example [34, 35]. the PM case with U = 0. Even if the bulk LNO locates
Our results have another interesting implication re- at the vicinity of metal-insulator phase boundary and
gardingthephasediagram. Sincethethin-LNOsuperlat- exhibits the correlated electron behaviors, the electronic
tice, (LNO)m≤2/(LAO)n, can have either FM insulating structureofPMLNOhasbeenreasonablywelldescribed
(FM-I) ground state as predicted by LDA+U calcula- within LDA (or GGA) as shown in the previous studies
tions, or, AFM insulating (AFM-I) one which is more [14, 38, 39]. Fig. 3(a)-(d) presents the evolution of e
g
consistent with the µSR experiment, the system would DOS as a function of m. It is noted that the d3z2−r2
have FM metallic (FM-M) or AFM metallic (AFM-M) band width notably changes, whereas the dx2−y2 width
region in between the thin-LNO limit (m ≤ 2), and the remains almost same across m=2–4. The m = 2 case
bulk-likethick-LNOlimit(m≥4;PMandmetallic,PM- (Fig. 3(b)), which was reported to be magnetic and in-
M) [10]. One may also expect the PM insulating (PM-I) sulating [10], the right edge of the d3z2−r2 state is fairly
phase stabilized in the same region of m; the intermedi- similartothatofdx2−y2 whereastheleft-edgeisreduced.
ate regime,2≤m≤4 (see, Fig.2). As LDA+U method It is not certain howeverthat such a relatively small dif-
is unable to describe correlated PM solutions properly ferenceintermsoftheeffectivebandwidthisresponsible
[36, 37], the further pursue along this line is beyond the for the metal-insulator phase transition between m = 2
scopeofourstudy. Forthatpurpose,one mayresortthe and 4 as reported in experiment [10].
4
U=0 (PM) N , that is, the critical value of d-valency of transition
0.1 U=3 (FM) c
U=5 (FM) metal; the system is metallic if Nd ≥ Nc and insulat-
0.08 ing if N ≤ N . For nickelates, Neg ≈ 1.3. That is,
n d c c
o
ati for the parameters (implicitly including double-counting
z 0.06
olari correction), which result in Nd ≥ Nc, the system re-
e P 0.04 mains metallic even for the very large U. This conclu-
ag sion suggests Nd as the critical variable for understand-
ver 0.02 ing charge-transfer systems [21]. Now it might be in-
A
structive to analyze our LDA+U results within this new
0
picture of Ref. 21. Even if LDA+U is a lower level ap-
-0.02 proximationcomparedtoDMFT,abigmeritofLDA+U
1 2 3 4
is that it can be performed with the whole charge self-
Number of LNO Layers
consistency and take magnetism into account while the
FIG.5: (Coloronline) Theaveraged orbitalpolarization asa previous DMFT calculations have dealt with the PM
functionofLNOlayerthickness. Dotted(blue,doublecross), phase [12, 15]. Fig. 1(d) presents N for PM (U=0)
d
double-dotted(black,circle),andsolid(red,square)linesrep- and FM (U=3, 5, 7) calculations of (LNO)m=1/(LAO)1
resent U=0 (PM), U=3 (FM), and U=5 (FM), respectively. and (LNO)m=2/(LAO)1. While Nd decreases as U in-
creases, the difference is not significant; ∆N ≈ 0.15.
d
Therefore the current implementation of LDA+U and
the charge self-consistency roughly follow the constant
Acomplementarypicture canbe providedby LDA+U N line. Now we note that the value of Neg ≥2.2 is far
calculations for the magnetic phase. Fig. 4(a)-(d) shows d d
from the N ≈ 1.3 predicted by DMFT. Therefore it is
the evolution of e DOS as a function of m for the FM c
g consistent with the metallic ground state and supports
(LNO)1/(LAO)1. Onceagainthenotablechangeisfound
the conclusion of Ref. 21.
in d3z2−r2 band; for m = 1, the up-spin d3z2−r2 state
(upper panel)formsafairlylocalizedDOSaroundFermi Relative orbital occupation in the two e orbitals is
g
level. Thisstatebecomesmoreandmoredelocalizedasm a central quantity in understanding LNO/LAO systems
increases as seen in Fig. 4(b)-(d). Once again, however, [9, 12, 14, 15]. The orbital polarization can be non-zero
theamountoftheeffectivebandwidthchangedepending due to the translation symmetry breaking induced by
onmdoesnotseemtobeenoughtomakemetal-insulator heterostructuring while the bulk polarization is 0. Ac-
phase transition across m=2–4. Other origins than the cording to the previous calculations, highly polarized
simple U/W change may be more relevant to the transi- P can possibly drives the system to be high-T super-
c
tion [21, 32]. conductor [12, 17]. On the other hand, a more recent
An interesting point observed in Fig. 4 is that even in DMFT calculation based on the realistic model hamil-
LDA+U calculation,thesystemsdonotbecomeaperfect tonian including oxygen orbitals predicted that the po-
insulator, but have finite number of states aroundFermi larization is actually reduced by the on-site correlation
level [40]. It may partly be attributed to the strong co- [15]. Since both of the previous DMFT calculations as-
valency between Ni-d and O-p states. As O-p is much sumed PM phase and did not consider the full charge
less affected by U, the small amount of DOS is not re- self-consistency, LDA+U calculation can give a compli-
movedperfectly. Anotherimportantfactoristhedouble- mentary information for the magnetic solution in spite
counting energy correction for which several functional ofitslimitationindescribingcorrelationeffectcompared
formshavebeensuggested[18–20,25,26],butthereisno to DMFT. The result is presented in Fig. 5. It is noted
welldefinedsolutionstillyet[21]: Asthedouble-counting that the inclusion of U reduces the polarization signif-
energy is typically represented by 1UN (N − 1), the icantly. There is a large separation between U=0 and
2 d d
LDA+U charge self-consistency adjusts N (or, the ef- U=3 results, while the differences between U=3 and 5
d
fective d-level energy and therefore the charge transfer results are small. Importantly the calculated polariza-
energy, ǫ −ǫ ), depending on U. According to the re- tions for finite U are order-of-magnitudesame compared
p d
centDMFTstudy,whichtunesthedouble-countingterm withtherecentDMFTresults[15]. Thereforeitsupports
as a parameter, the system eventually becomes insulat- the conclusionofthe recentDMFT calculation[15]. The
ingatlargeU [15,41]. Thereforethesmallstatesaround smallpolarizationatthefiniteU canalsobeseeninDOS
theFermilevelobtainedbyLDA+U canbeattributedto presented in Fig. 4 where no big difference can be found
the double-counting error that is hardly handled within between the two e orbital occupations. We note that
g
the current formalism of LDA+U. the reduced orbital polarization by U can be compati-
An interesting recent finding on (3-dimensional) nick- ble with the ferromagnetic spin order. For cuprates, for
elatesisthatthe metal-insulatortransitionoccursatthe example,the fullypolarizedx2−y2 orbitalisdirectlyre-
very narrow region of N and the same holds for the lated to the in-plane AFM spin order. In the nickelates,
d
cuprates [21]. From the single-site DMFT calculations wehaveonemoreorbitaldegreeoffreedomavailableand
with a double-countingenergyas anothertuning param- the spin can align ferromagnetically. And actually it is
eter, Wang et al. [21]showedthat there is a welldefined foundthat the enhancedferromagnetictrend by increas-
5
ing U corresponds to the reduced orbital polarization as be responsible for the metal-insulator transition. The
shown in Fig. 5. calculatedorbitalpolarizationis significantlyreducedby
U,stronglysupportingthe conclusionofarecentDMFT
calculations andindicating the absence of high tempera-
IV. SUMMARY ture superconductivity in this system.
Using the band structure calculations based on
V. ACKNOWLEDGMENTS
LDA+U, we examined the magnetic moment, electronic
structure, d-valence, and orbital polarization as a func-
tionofU andm(LNOthickness). Thecalculatedresults This work was supported by the U.S. Department
clearlyshowedthe formationofmagnetic momentatthe of Energy (DOE), DE-FG02-03ER46097, and NIUs In-
finite U region being consistent with a recent µSR, but stitute for Nanoscience, Engineering, and Technology.
the long range ordering pattern is not so clear consid- WorkatArgonneNationalLaboratorywassupportedby
ering the experiment. While d3z2−r2 band width is re- the U.S. DOE, Office of Science, Office of Basic Energy
duced as m approaches to 1, it may not be enough to Sciences, under Contract No. DE-AC02-06CH11357.
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