Spin-orbit physics of iridates with Wien2kJan Kuneš

R. Arita (Univ. Tokyo)A. Kozhevnikov (ETH Zurich)A.G. Eguiluz (Univ. Tennessee)

M. Imada (Univ. Tokyo)P. Augustinský (IoP, Prague)

Outline

• Brief introduction to Sr2IrO4

• Spin-orbit in Wien2k

• PM - AFM transition in Sr2IrO4 (LDA+DMFT)

crystal structure:similar to that ofLa2CuO4, but withrotational distortionof IrO6

Kim et al., PRL, 2008

SO U

Introduction: Sr2IrO4

Spin-orbit assisted (driven) Mott insulator ?

d5

Sr

Resonance observedonly for L3 edge: J=1/2model is moreappropriate than S=1/2model

Kim et al., Science, 2009

Resonance observedonly for L3 edge: J=1/2model is moreappropriate than S=1/2model

Kim et al., Science, 2009

Sr2IrO4: resonant X-ray scattering

Non-relativistic Relativistic

Sr2IrO4: Mott insulator or Slater insulator ?

Temperature dependence of optical conductivityMoon et al., PRB, 2009

Sr2IrO4: Mott insulator or Slater insulator ?

Time-resolved optical studyHsieh et al., PRB, 2012

Fit the time-resolved reflectivitytransient ΔR/R to

Magnetic properties of Sr2IrO4 and Ba2IrO4

canting moment ~0.075 µB/Ircanting =10°~ rotation angle

TN ~ 240K

Sr2IrO4Sr2IrO4

Ba2IrO4Ba2IrO4

Small canting momentSmall rotation angle ?

TN ~ 240K

Kim et al., Science, 2009

Okabe et al., PRB, 2011

Purpose of the present study

Clarify whether Sr2IrO4 and Ba2IrO4 are

Mott insulator or Slater insulator by non-

empirical, parameter-free calculation

Clarify whether Sr2IrO4 and Ba2IrO4 are

Mott insulator or Slater insulator by non-

empirical, parameter-free calculation

LDA+DMFT

If Sr2IrO4 is a Slater insulator, can we make ita Mott insulator by increasing a ?If Sr2IrO4 is a Slater insulator, can we make ita Mott insulator by increasing a ?

We can increase a by replacing Sr with Ba

Spin-orbit interaction in Wien2k

Wien2k LAPW basis:orbital coordinates - chosen in each spherespin coordinates - global, only z-axis specified by user

Diagonalization of H+Hso : orbital coord. ≡ spin coord.

Wien2k unit cell:

Analysis and postprocessing (QTL, wien2wannier) : orbital coord. can be chosenarbitrarily - for example to put t2g states into the common form xy, yz, zx

CAUTION! only the z-spin-axis can be defined by user (case.inso)Currently one cannot automatically use the textbook form of the t2g relativistic orbitals.Solution. Put the z-spin-axis in the desired direction (e.g. along Ir-O bond) and workout the orbital in a z-rotates basis (‘only’ phase factors).

Spin-orbit interaction in Wien2k

Sr2IrO4

standard coord.

wien2k coord.

Na2IrO3

DOS

0

-1

-2

Ener

gy

[eV]

j=1/2

j=3/2

Wannier functions are constructed from the t2g bandsWannier functions are constructed from the t2g bands

Result: Downfolding

Ba2IrO4 (opt.)Sr2IrO4 (exp.)

j=1/2 Wannier orbital

Band width of J=1/2becomes narrower (~1.2eV)

by replacing Sr with Ba

Band width of J=1/2becomes narrower (~1.2eV)

by replacing Sr with BaJ=1/2 and 3/2 have asubstantial overlap

J=1/2 and 3/2 have asubstantial overlap

Result: projected DOS

Sr2IrO4 (exp.) Ba2IrO4 (opt.)

Introduction of many-body terms

Ab initio estimate of interaction parametersAb initio estimate of interaction parameters

Result: cRPA

t2g Uij matrix for Ba2IrO4

1.89 1.43 1.43 1.43 1.94 1.55 1.43 1.55 1.94

UJ=1/2 = 1.62 eV

t2g Uij matrix for Sr2IrO4

2.35 1.78 1.78 1.78 2.21 1.74 1.78 1.74 2.21

UJ=1/2=1.96 eV

Replacement of Sr with Ba• Smaller crystal field splitting t2g and eg

• More efficient screening• Smaller U• W/U does not change so drastically

Uc~2.3 > UcRPA=1.96 Uc~1.7 > UcRPA=1.6

Paramagnetic LDA+DMFT

Insulating solution not obtained for cRPA interaction parameters.Insulating solution not obtained for cRPA interaction parameters.

The ground state is magnetic J=1/2 insulatorSimilar TN for Sr2IrO4 and Ba2IrO4AF long-range order is essential

The ground state is magnetic J=1/2 insulatorSimilar TN for Sr2IrO4 and Ba2IrO4AF long-range order is essential

AF LDA+DMFT

U=1.96

U=1.6

Sr2IrO4 AFM ordering

quasi-particle energyquasi-particle energy

εσ* = ε0 + Re Σσ (εσ

* )

Re Σσ = Frequency independent term (Hartree)+ Frequency dependent term

Re Σ+ − ReΣ−

Bands 1p - DoS Selfenergy for j=1/2 orbitals

Sr2IrO4 AFM ordering

quasi-particle energyquasi-particle energy

εσ* = ε0 + Re Σσ (εσ

* )

Re Σσ = Frequency independent term (Hartree)+ Frequency dependent term

Re Σ+ − ReΣ−

Bands (zoomed) 1p - DoS Selfenergy for j=1/2 orbitals

Comparison of LDA+DMFT results

Γ M X Γ

Γ N X Γ

PM insulator AFM insulator(PM metal)

AFM insulator(PM metal)

Zhang et al., 2013 Arita et al., PRL, 2012Martins et al., PRL, 2011

Conclusion

• When constructing spinor orbitals in Wien2k keep in mind that spin and orbital coordinate systems may not be aligned

• Sr2IrO4 is a material close to metal-insulator transition - the presents study puts in on the metallic side - the charge gap opens due to AFM correlation (long range order)

• Ba2IrO4 and Sr2IrO4 have different U and W, but similar U/W ratio

U/W: large enough to have a magnetic ground state

U/W: not large enough to be a Mott insulator

Energy scale of U, W: half of cuprates

J=1/2 states are not isolated from J=3/2

Is iridate a promising candidate for high Tc SC?

There are several families of high Tc cuprates :

Motivation: Why Sr2IrO4 ?

Nd2CuO4La2CuO4 YBa2Cu3O7

Are there any other transition-metal oxides satisfying these conditions?

Key words to describe electrons in CuO2 layers:2D, single orbital system,

nearly half-filling (mother compound = Mott insulator)

Key words to describe electrons in CuO2 layers:2D, single orbital system,

nearly half-filling (mother compound = Mott insulator)

Result: Structure Optimization

Sr2IrO4 = 153° (optimized), 159° (exp.)Ba2IrO4 = 164° (optimized)Not yet determined experimentally, but ~170° ?

Ir-O-Ir angle

Evaluation of interaction parameters: Constrained RPA

Occupied (O 2p, …)

Virtual (Ir eg, …)

Target (Ir t2g)

Full RPA polarizability:

target target

Screening by Occupied/Virtual states

target

Aryasetiawan et al, PRB 70, 195104 (2004)Solovyev-Imada, PRB 71, 045103 (2005)

Constrained RPA method

E nergy

Sr2IrO4: Mott insulator or Slater insulator ?

“The resistivity data in the wholetemperature range could not be fittedto a single model.”

Kini et al., J. Phys. CM, 2006

For T>200K,but not Arrhenius-type behavior

cf) Cao et al., PRB, 98

Sr

Ir-O-Ir angle < 160°

increase a by 4% andsuppress rotationaldistortion of the IrO6:more analogous to La2CuO4

Introduction: Ba2IrO4

Ba

Okabe et al., PRB, 2011

Ground state: J=1/2 Mott insulator ?

Kim et al., PRL, 2008

Sr2IrO4: optical conductivity