Dimensionality-strain phase diagram of strontium iridates

2.5 MB·

by  Bongjae Kim

Dimensionality-strain phase diagram of strontium iridates
Bongjae Kim1, Peitao Liu1,2, and Cesare Franchini1
1University of Vienna, Faculty of Physics and Center for Computational Materials Science, Vienna, Austria and
2Shenyang National Laboratory for Materials Science, Institute of Metal Research,
Chinese Academy of Sciences, Shenyang 110016, China
(Dated: February 24, 2017)
The competition between spin-orbit coupling, bandwidth (W) and electron-electron interaction
(U) makes iridates highly susceptible to small external perturbations, which can trigger the onset
of novel types of electronic and magnetic states. Here we employ first principles calculations based
on density functional theory and on the constrained random phase approximation to study how
dimensionalityandstrainaffectthestrengthofU andW in(SrIrO ) /(SrTiO )superlattices. The
3 m 3
7 result is a phase diagram explaining two different types of controllable magnetic and electronic
1 transitions, spin-flop and insulator-to-metal, connected with the disruption of the J =1/2 state
eff
0 which cannnot be understood within a simplified local picture.
2

b
e I. INTRODUCTION relativistic-Mott state, to the 3-dimensional (3D) limit
F (m = ∞, SrIrO ) which is nonmagnetic, (semi)metallic
3
and exhibits nontrivial topological features10,27,32. The
2 Manyinterestingphenomenafoundintransitionmetal
accepted picture is that with increasing m, also W in-
2 oxides are explained by the competition of intertwined
energy scales usually parameterized as electronic corre- creases and this leads to a progressive disruption of the

] lation (U), bandwidth (W), spin-orbit-coupling (SOC) Jeff=1/2phase22,31. Thefirstmagnetictransitionisob-
l
e and crystal field splitting. In 3d oxides, U typically served already at m=2, manifested by a spin-flop tran-
- sition from an in-plane (IP) to out-of-plane (OP) spin
r acts as a leading parameter and this sets the ground
st for a variety of interesting effects such as Mott-like orderingcausedbyinterlayerexchangecoupling33 (Fig.1
. insulator-to-metal transition (IMT), superconductivity, (b)). On the other hand, strain engineering uses the lat-
t
a and spin/orbital/charge orderings1. In the heavier 4d ticemismatchbetweenthestrontiumiridatesandagiven
m substrate,resultingincompressiveandtensilestrainusu-
and 5d transition metal oxides the Mott paradigm is
allyupto5%dependingonthetypeofsubstratematerial
- largely attenuated owing to the stronger SOC and the
d
broader spatial extension of the d orbitals (larger W):
n
U is not the dominant factor anymore and the com-
o
c peting balance between similar energy scales (U, W,
[ and SOC) promotes the onset of a novel and often ex-

otic physics2–5. Strontium-based iridates represent the
2
archetypal playground for these uncommon behaviors.
v
2 The most notable example is the relativistic-Mott insu-
4 latingJ =1/2stateassociatedwithacantedantiferro-
eff
9 magnetic planar ordering realized in Sr IrO 6–8.
2 4
8
Asthestrengthofthedifferentphysicalinteractionsat
0
play in the 5d oxides is similarly small (about 1 eV), the
.
1 electronic and magnetic ground state in these systems
0 is expected to be highly susceptible to small changes of
7
the interaction parameters 5,9–15. A realistic tuning of
1
these interactions can be achieved using external pertur-
:
v bations such as doping and strain or via a change of the
Xi structural stacking16–28. For iridates, apart from dop-
ing19–21, two approaches have been used often to tune
r
a the ground state properties: (i) variation of the degree
of dimensionality through a modification of the struc-
tural stacking intrinsic to the Ruddlesden-Popper (RP)
FIG. 1. (Color online) (a) Crystal structures of bilayer
series29 Sr Ir O (m = 1,2,···∞)22,23,30,31, and
m+1 m 3m+1 (Sr Ir O ,m=2)andof(SrIrO ) /(SrTiO )SLfordifferent
(ii) strain engineering14,15,24–27. In the RP series, the 3 2 7 3 m 3
m. IrO and TiO octahedra are depicted in gray and light
6 6
degree of dimensionality is controlled by the number
gray(blue),respectively. OandSratomsarenotshown. (b)
of IrO2 layers (m) interleaved in the layered perovskite Schematic description of the IP and OP magnetic orderings
structure (see Fig. 1 (a) for m = 2 case). As m in- for one single IrO layer. (c) 2D lattice parameters of typ-
2
creases, the system undergoes a dimensional crossover ical substrates and corresponding lattice mismatch between
from the 2-dimensional (2D) limit (m = 1, Sr2IrO4), SrTiO3 and RP strontium iridates
characterizedbytheaforementionedmagneticallycanted
2
(Fig. 1 (c)). Optical studies indicate that strain effects m=1 m=2 m=3
induce changes in U, W and SOC14,24, as well as modi- 1.0
0.5
fications of the strength of the magnetic interactions be-
0.0
ttwheeseensItrrasiitne-sin13d,1u5c,2e6d. cHhoawnegveesr,anaddetthaeiilredreepxeprlcaunsastioionnoonf Energy (eV)−−10..05
the J =1/2 state remains still elusive. −1.5
eff
Thepossibilitytocontrolinthesameexperimentboth −2.0
−2.5
dimensionalityandstrainrepresentsaviableroutetoen- G M X G G M X G G M X G
hance the spectrum of tuning opportunities. This has
becomefeasibleusingsuperlattice(SL)structuresthanks FIG. 2. (Color online) Thin (red) lines denote PBE band
structuresofSLswithnonmagneticsetup,fordifferentvalues
to the development of improved growing technique and
the diverse choice of available substrate materials34. A ofm. Wannier-interpolatedbandsareshownwithwiththick
(blue) lines. The shaded background (yellow) marks to the
first example in this direction is the research of Matsuno
t bandwidthsof thesystems. Substrate strainis setto0%.
et. al. in which the authors have modulated the num- 2g
ber of SrIrO layers within SLs of (SrIrO ) /(SrTiO )
3 3 m 3
and demonstrated that it is possible to guide a tailored
IMT from m = 1 to m = 4 by means of only structural
proximation by Perdew-Burke-Ernzerhof (PBE) with a
assembly11.
full treatment of relativistic effects (SOC) and including
In this work, we aim to perform a computational ex-
an on-site Hubbard U. We have used a plane-wave cut-
periment not yet realized in practice which consists in
off of 400 eV37,38. Benchmark calculations with a cutoff
considering simultaneously the effect of both dimension-
600 eV do not lead to significant differences. Regarding
ality and substrate strain in (SrIrO ) /(SrTiO ) SLs.
3 m 3 thestructureofthe(SrIrO ) /(SrTiO )superlattice,we
Wedothisfullyabinitiobycombiningdensityfunctional 3 m 3
took as reference in-plane lattice parameter the one of
theory(DFT)andtheconstraintrandomphaseapproxi-
SrTiO , and varied it up to 4% considering both tensile
mation (cRPA) calculations. The cRPA approach is em- 3
and compressive strain. Full atomic relaxation was per-
ployed to quantify the variation of U as a function of m
formed for all studied m at the corresponding IP lattice
and strain from a fully ab initio perspective. By means
parameter using U=2 eV. We found that the structure
of DFT+SOC+U, we scrutinize the detailed structural
is only marginally sensible on the specific value of U: by
changes as a function of m and strain (≤ 5%) and their
varying the U from 0 to 2 eV, the structural changes
impactonW andonthemomentordering. Theresultis are in the order of 10−3 ˚A. Monkhorst-Pack k-meshes of
adimensionality-strainquantumphasediagramofstron-
6×6×4, 6×6×2 and 6×6×3 are used for m = 1, m = 2,
tium iridates constructed from first principles with real-
and m = 3 superlattices, respectively. We note that for
istic values of strain, U and W. We show that U and W
the m = 2 system we have employed a twice larger su-
are largely dependent on dimension and strain and their
percell in order to allow for a−a−c+ type tilting of the
accurate estimation is crucial to achieve a comprehen-
octahedra network along the c-direction.
sive interpretation of the electronic (IMT) and magnetic
To quantify U and J from ab initio, we performed
(spin-flop)transitionsdrivenbymandstrain. Moreover,
cRPA calculations, using an Ir t basis set constructed
the possibility to selectively control the leading interac- 2g
by means of Maximally localized Wannier functions ob-
tions in iridates allow for a direct assessment of the ro-
tained by the Wannier90 code39–41 at each value of m.
bustness and validity of the J =1/2 local picture.
eff We present the results obtained for m = 1 and m = 2
in Table I and II. For the DFT+SOC+U calculations,
we have employed an effective U = U¯ −J¯, where U¯
eff
II. CALCULATIONAL DETAILS and J¯are obtained by averaging the U and J matrix
ij ij
elements in Table I and II. In Figs. 2 and 3, the pro-
We performed ab initio electronic structure calcu- jectedWannier-interpolatedbandoft2g statesareshown
lations using the projector augmented wave method together with the PBE band structure as a function of
employing the Vienna ab initio simulation package m and strain. To quantify the bandwidth W we have
(VASP)35,36. We adopted the generalized gradient ap- taken the width of the t2g bands (denoted as shadow
TABLE I. Calculated on-site Coulomb (U ) and exchange TABLE II. Calculated on-site Coulomb (U ) and exchange
ij ij
(J )interactionvalues(ineV)withinIr-t orbitalsbasedon (J )interactionvalues(ineV)withinIr-t orbitalsbasedon
ij 2g ij 2g
the cRPA calculations for m=1 SL without any strain. the cRPA calculations for m=2 SL without any strain.
U xy xz yz J xy xz yz U xy xz yz J xy xz yz
ij ij ij ij
xy 2.43 1.79 1.63 xy - 0.25 0.24 xy 2.09 1.49 1.42 xy - 0.22 0.21
xz 1.79 2.43 1.63 xz 0.25 - 0.24 xz 1.49 2.09 1.42 xz 0.22 - 0.21
yz 1.63 1.63 2.05 yz 0.24 0.24 - yz 1.42 1.42 1.83 yz 0.21 0.21 -
3
−4% −2% 0% 2% 4%
1
V) 0
e
y (
erg−1
n
E
−2
G M X G G M X G G M X G G M X G G M X G
FIG. 3. (Color online) Same as Fig. 2 but for m=1 for different strains.
background in Figs. 2 and 3). For m = ∞, we used (a) (b) (c)
the cRPA value computed for the bulk phase SrIrO342. 2.8U (e0V%) WW U m=1 WW2 ((.8eeVV)) IP OP NM
The unscreened Coulomb parameters (Ubare and Jbare) 2.4 2.4 1
2.0 2.0
for each m are also listed in Table III.
1.6 1.6 Insulator
1.2 1.2
¥ . . . 3 2 1 −4 −2 0 2 4 m 2
(d) m strain (%) 3
III. RESULTS AND DISCUSSIONS U
m ... Metal
¥
A. Phase diagram W/2 comp. strain −4 −2 0 2 4
strain (%)
We start by inspecting the evolution of U as a func-
FIG. 4. (Color online) Variation of U and W as a function
tion of m and strain (Fig. 4(a)-(b)). For m = 1 SL of (a) dimensionality, m, with no strain and (b) strain (in
at the SrTiO3 (STO) lattice parameter the effective U %) for m = 1. (c) Electronic and magnetic phase diagram
for Ir is 1.59 eV, almost unchanged with respect to the of (SrIrO ) /(SrTiO ) SLs. IP and OP magnetic orderings
3 m 3
corresponding value of bulk Sr IrO 13. As the system are denoted with filled squares (red) and filled circle (blue),
2 4
evolves from 2D (m = 1) to 3D (m = ∞), U undergoes respectively, whereas the nonmagnetic phase is labelled with
a significant change from 1.59 eV (m = 1) to 0.95 eV filled triangles (green). The insulating and metallic phases
arehighlightedwiththegrayandwhitebackgroundarea. The
(m=∞) (Fig. 4(a)). Concomitantly W, defined here as
arrowstracetheIMTdrivenbydimensionalityandstrain. For
the width of the full t in the nonmagnetic state, goes
2g m = ∞ (SrIrO ) the system remains a non-magnetic metal
through a huge change from 1.9 eV (m = 1) to 2.8 eV 3
at any strain14,25. (d) Schematic band diagram showing the
(m=3). Such a large reduction of U (∼40%) has been
role of U and W in the IMT.
overlooked in previous studies where the dimensionality-
induced (i.e. increasing m) IMT was interpreted solely
in terms of a gradual increase of W11,22. However, opti-
cal conductivity measurements of the RP strontium iri-
calculations (Table III), the dimensionality-induced re-
dates series suggest a cooperative interplay of both W
duction of U is primarily due to an enhancement of the
and U across the IMT, manifested by an overall broad-
screening. This is the result of the increased coordina-
ening of the lower and upper Hubbard bands (larger W)
tion of each Ir site with increasing m that provides fur-
and by a shift of the characteristic α-peak towards lower
ther hopping channels (see Fig.1(a)). For the m = 1
energy (smaller U) for progressively larger m22. This
quasi-2Dlimit U andW have asimilarstrength, compa-
interpretation is consistent with our cRPA calculations
rabletotheSOCenergy(about0.5eV/Ir),andthisgives
which clearly indicate an active role of both W and U in
rise to the wealth of intricate phenomena observed in
the observed IMT. Since the unscreened (bare) Coulomb
Sr IrO 7,8,16,19,21,24; however, for larger m, W becomes
interaction remains almost unchanged for all m in our 2 4
the leading energy scale and pushes the systems towards
ametallicandnonmagneticregime,asrepresentedinthe
phase diagram of Fig.4(c).
TABLE III. Calculated unscreened (bare) on-site Coulomb Now we turn to the role of epitaxial strain. Follow-
(Ubare) and exchange (Jbare) interaction values (in eV) for ing the experimental setup of Matsuno and coworkers11
0% strain case with different m.
we have chosen STO as the reference substrate (strain
m=1 m=2 m=3 = 0%), which guarantees a minimal lattice mismatch
Ubare 8.70 8.70 8.51 with the known members of the RP series (Fig. 1(c)).
Jbare 0.25 0.25 0.24 We have considered realistic substrate-induced compres-
4
sive and tensile strain up to ± 4% with respect to the (a) (c)
m=1 15
SsuTbOstrsautbess,traastei,ndtihcuastedsiminulFatigin.g1(tch).e TeffheectchoafngdeiffseorfenUt (°)P 1146 mm==23 10OPa dIP a IP dOP a OP
and W upon strain for m = 1, reported in Fig. 4 (b), aI 5 (°)
12
are more modest than those caused by varying m: the
0
value of W for the most compressive case (-4%) is about (b) (d) 0
3tthi7ae%llyclhauarnngceghreacniongmeUdpaiinrsetdohnteloysttahrabeion4u%rta1nte0gn%es-il4ae%nsd-t0rra%eimn(saceainesseF,eiwgs.she4inl)e-. d/dOPIP11..0005 mmm===123 action (meV) −−−642000J2 JJ12
sTthraeinre,ausonnlikfeormth,isdomeosdneroattemcohdainfygethofeUnuamndbeWr oifshthoapt- 0.95 −4 −2 0 2 4 inter −80 −4 J−12 0 2 4
ping channels within the SL. Rather, the effect of strain strain (%) strain (%)
is manifested by a change of the structural distortions
within the octahedra network, specifically on the planar FIG. 5. (Color online) (a) Change of rotation/tilting angle
(IP) and apical (OP) Ir-O-Ir angles (α ) and Ir-O upon strain. Solid/Dotted lines refer to IP/OP cases. Note
IP/OP
that α is nonzero only for m = 3 case (right axis). (b)
bondlength (d ), as shown in Fig. 5 (a)-(c). Like OP
IP/OP
Change of the d /d ratio upon strain. (c) Schematic de-
many other perovskite-type oxides, upon tensile strain IP OP
scriptionoftheIr-O-IrbondangleandIr-Obondlengthboth
d (d ) increases (decreases), whereas the octahedral
IP OP in the ab plane (α , d ) and in the out-of-plane (α ,
rotationangleα (α )decreases(increases)(Fig.5(a) IP IP OP
IP OP d ) direction. (d) Change of J and J as a function of
OP 1 2
and (b)). We predict that the continuous application of
strain. (Inset) Schematic structure of the Ir sublattice for
compressive strain guides the system to a IMT, which m=2, showing the IP and OP exchange interactions J and
1
is caused by an increment of W. The small increase of J , respectively43.
2
U at the most tensile limits should be attributed to the
narrowing of the t orbitals (smaller W), which is un-
2g
derstandable in terms of a reduction of the hopping am-
plitude. Having a more itinerant character, the m = 2 tronic and magnetic properties of strontium iridates SLs
and3structuresareexpectedtobelesssensitivetostrain as a function of dimensionality and strain we have built
effects. Thedifferentwaysinwhichmandstraininduces a comprehensive dimensionality-strain phase diagram,
the IMT in strontium iridates is schematically shown in shown in Fig. 4 (c). To this purpose we have used
Fig.4(d): forcompressivestraintheleadingfactoristhe the cRPA values of U at zero strain 1.6 eV (m = 1)
increase of W at almost constant U; on the other hand, and 1.4 eV (m = 2,3) and considered IP, OP and non-
the tuning of m affects both W and U since the change magnetic (NM) ordering. The phase diagram indicates
of dimensionality alters not only the structure but also that strain and dimensionality represent two workable
the electronic connectivity between the octahedra. means to induce two type of transitions: (i) IMT and
(ii)spin-flop. TheIMTcanbeinducedeitherbyincreas-
Dimensionality and strain have a strong effect also on
ingm(up→down)orbycompressivestrain(right→left),
the magnetic properties of strontium iridates. For the
andinvolvesthetwofundamentallydifferentmechanisms
single layer system (m = 1), the magnetic exchange
sketchedinFig.4(d): cooperativeU/W drivenIMT(m)
interactions are purely 2D as in the corresponding RP
and W-driven IMT (strain); the spin-flop transition, on
compoundSr IrO , andthe IParrangementremainsthe
2 4
the other hand, is always explained as a reduction of the
most favorable one at any strain (see Fig. 4 (c)). For
intra-layer exchange interaction J which can be tuned
multilayer systems (m = 2 and 3), however, the mag- 2
byareductionoftheintralyerdistanced (strain)orby
netic ordering is subjected to a spin-flop transition from OP
OP-to-IPorderingforcompressivestrainlargerthan3%.
This transition can be explained by the dependence of
U=1eV U=2eV U=3eV
the effective intra- and interlayer interaction parameters
1 NM
J and J , that we have computed assuming a classi-
1 2 IP
Insulator
cal Heisenberg-type spin Hamiltonian. The results are OP
m 2
shown in Fig. 5 (d). For strain larger than -3%, J be- NC
1 3
comes the dominant magnetic interaction, as in the case ... Metal
¥
ofsinglelayersystem, causingareorientationofthespin
−4 −2 0 2 4 −4 −2 0 2 4 −4 −2 0 2 4
from OP to IP. J is much more susceptible to strain strain (%) strain (%) strain (%)
2
thanJ owingtotheassociatedstructuralchanges(Fig.5
1 FIG.6. (Coloronline)PhasediagramforfixedU parameters
(a) and (b)): for m = 2, α is always zero regard-
OP of 1 eV, 2 eV, and 3 eV. Due to the delicate balance of the
less of strain but the apical Ir-O distance d decreases
OP U with other energy scales, the overall metallicity depends
monotonicallywithprogressiveexpansion; conversely,J
1 highly on U parameters. U=1 eV and U=3 eV give metal-
changesverylittleasaresultofthebalancebetweendIP lic and insulating phase for all m values and strain ranges,
and αIP that follows an opposite trend upon strain. respectively.
By collecting all data on the evolution of the elec-
5
controllingthenumberofIrO layers(m). Wewouldlike
2
to underline the importance of an accurate evaluation of
U in the construction of the phase diagram: employing
the same U for different m, as commonly done, not only
fails to describe the experimentally observed IMT from
m = 2 to m = 311, but also leads to the stabilization of
the wrong magnetic structure. This is shown in Fig. 6,
where we show the dimensionality-strain phase diagram
obtained for U=1, 2, and 3 eV. The phase diagrams are
very different to the optimum one shown in Fig. 4(c).
Inparticular,U=1eVandU=3eVgiveasinglemetallic
andinsulatingphase,respectively,withoutanyelectronic
transition. For the weak U=1 eV regime, the reduction
of electronic localization produces a strong tendency to-
wards nonmagnetic solutions. In the strong U=3 eV FIG. 7. (Color online) (a) µ /µ and (b) δ as a function of
O S
limit, on the contrary, the systems does not exhibit any epitaxialstrainform=1SL43. Redandbluecrossmarksare
nonmagnetic phase. In the intermediate limit, U=2 eV, for the value for bulk Sr2IrO4 and Sr3Ir2O7 systems in their
the phase diagram appears overall correct, but it fails IPlatticeparameterpositions. (c)and(d)arethesamefora
local model. Inset in (c) describes the structure used for the
indescribingsomekeyfeaturesobservedexperimentally:
localmodel. Theδ=0andtheµ /µ =2pointsaremarked
(i) IMT from m=2 to m=3 is not reproduced. (ii) In O S
by arrows.
them=∞,thesystemshowsanonvanishingmagnetism
characterizedbyanoncollinear(NC)magneticstructure,
in disagreement with observation and with the optimum
phasediagram. Thisisknowntoemergewhentoostrong
B. Validity of the local picture
correlation is employed10.
Basedontheaboveanalysis,wecannowstudytheevo-
lution of the J =1/2 and assess the validity of what is
eff
Overall,ourpredictionsattheoptimumU valuesagree conventionally called local picture7,9. One way to iden-
well with previous experiments on (SrIrO ) /(SrTiO )
3 m 3 tifytheJ =1/2-nessofasystemistheratioµ /µ be-
eff O S
SLs,specificallyonthedimensionality-inducedIMTfrom tweentheorbital(µ )andspin(µ )magneticmoment50.
O S
m = 2 to m = 311. However, no sign of spin-flop transi-
In a purely local picture the ideal J =1/2 phase as-
eff
tion was measured experimentally for SLs with m>111.
sociated with a cubic symmetry exhibits an isotropic
As the magnetic properties of iridates are highly sensi- µ /µ =27,9. However, in the presence of a tetragonal
O S
tive to growth conditions44, oxygen vacancies are easily
distortion, the deviation from the cubic symmetry lifts
developed which could gives magnetic response different
the degeneracy of the t manifold, results in a energy
2g
from the ordered pattern15, we ask for exact probe, such
splitting (δ=(cid:15)(d )−(cid:15)(d )) and alters µ /µ . In-
xy xz/yz O S
as x-ray diffraction, to resolve this issue.
deed we find that within the SL geometry tensile strain
induces a decrease of δ and a spin-dependent anisotropic
bifurcation of the µ /µ curve (Fig. 4(a) and (b)).
O S
ItisalsoworthwhiletocomparetheSLswiththebulk Our findings on the evolution of µ /µ and δ with
O S
RP counterparts. The observed red-shift of the char- strain conflicts with the local picture since the isotropic
acteristic α-peak for SL compared to the bulk RP sys- limit(µ /µ =2)foundat-2%strain(arrowinFig.7(a))
O S
tem45 suggests a reduced degree of electronic correlation does not coincide with the cubic limit, associated with
in the SL. This agrees well with our cRPA results: The d = d (Fig. 5 (b)) and δ ≈ 0 (arrow in Fig. 7(b)),
IP OP
U undergoes a sizable reduction from the bulk Sr IrO which is instead established at about 0% strain. To in-
2 4
(1.99 eV) to m = 1 SL (1.59 eV)42,46,47. Note that the spectthevalidityofthepurelylocalpicturewehavecom-
unscreened Ubare for bulk Sr IrO is 8.81 eV, similar to paredtherealisticSLm=1situationwithanideallocal
2 4
thecorrespondingm=1SLvalue(TableIII),indicating structural setup constructed by isolated IrO octahedra
6
that the origin of the reduced strength of the electronic surrounded by TiO octahedra as depicted in Fig. 7(c).
6
correlation should be attributed to an increased screen- The results shown in Fig. 7(c) and (d) indicate that in-
ing. Regarding the response upon the epitaxial strain, deed within an ideal local picture both J =1/2 con-
eff
therehasbeenpreviousopticalandtransportstudiesfor ditions, δ=0 and µ /µ ≈ 2 for both IP and OP align-
O S
theRPseries14,24,48,49,whichareareconsistentwithour ments,arerealizedaroundzerostrain. Thisisincontrast
data on the SL system. Finally, our previous study on with the results obtained for the SL system, implying
bilayer Sr Ir O , shows a spin-flop transition upon com- that the application of a local picture for realistic situ-
3 2 7
pressive strain similar to the one observed in the m = 2 ations is deceptive and could lead to an incorrect anal-
SL 15, suggestive of a similar response to the epitaxial ysis. Further support for this conclusion is provided by
strain. the larger degree of hybridization in the SL system com-
6
paredtotheartificiallocalmodel. InFig.8,weshowthe thebulklatticeparametersasindicatedbycrossedmarks
charge density plot for SL m = 1 and the local model. in Fig.6(a). This implies that not only hybridization ef-
OnecanclearlyseethestrongerhybridizationbetweenIr fects but also spin arrangement have important implica-
and O for the SL case compared to the local case. This tions on the degree of J =1/2-ness of the system: the
eff
indicates that hybridization effects are crucial to achieve IP-to-OP spin-flopping perturbs strongly the J =1/2
eff
a proper account of the bonding picture51. phase as manifested by the largely reduced µ /µ ratio
O S
of 1.24 in OP-ordered Sr Ir O and SL-m = 1 in com-
3 2 7
parison with the IP-ordered case15,31,52.
IV. CONCLUSION
Insummary,wehavepresentedadimensionality-strain
phase diagram of (SrIrO ) /(SrTiO ) superlattices that
3 m 3
showsthetunabilityoftheelectronicandmagneticprop-
erties of the system as notably illustrated by a spin-
flop and insulator-to-metal transition. Mismatch of
FIG. 8. Charge density plot in the IrO2 plane for (a) SL the isotropic Jeff=1/2 phase with tetragonal distortion
m=1 case and (b) local structure. Both plots are obtained shows the incompleteness of the local model for this sys-
from the 0% epitaxial strain.
tem. As we have shown, the accurate quantification of
the effective U, typically employed as adjustable param-
eter in DFT calculations, is of vital importance to inter-
Finally, we note that the values of µ /µ for the bulk pret the intricate coupling between the various degree of
O S
Sr IrO and Sr Ir O phases, 2.25 and 1.2415,20, are al- freedom in action in weakly correlated relativistic oxides
2 4 3 2 7
most identical to the SL values for the corresponding andtoprovideacrediblepredictionoftheroleofexternal
mostfavorablespinordering(IPandOP,respectively)at perturbations.
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ACKNOWLEDGMENTS
(1998).
39 N. Marzari and D. Vanderbilt, Phys. Rev. B 56, 12847
(1997). B.K. thanks J. Matsuno and V. V. Shankar for fruit-
40 A.A.Mostofi,J.R.Yates,Y.-S.Lee,I.Souza,D.Vander- ful discussions. This work was supported by the joint
bilt, andN.Marzari,ComputerPhysicsCommunications Austrian Science Fund (FWF) and Indian Department
178, 685 (2008). ofScienceandTechnology(DST)projectINDOX(I1490-
N19). P.L. is grateful to the China Scholarship Council
(CSC)-FWF Scholarship Program. Computing time at
the Vienna Scientific Cluster is greatly acknowledged.