ferromagnetism in ruthenate perovskites

Ferromagnetism in ruthenate perovskites

Hung T. Dang1, Jernej Mravlje2, Andrew J. Millis3

and Antoine Georges4

1Institute for Theoretical Solid State Physics, RWTH Aachen University, Germany

2Department of Theoretical Physics, Jozef Stefan Institute, Ljubljana, Slovenia

3Department of Physics, Columbia University, New York, USA

4Centre de Physique Theorique, CNRS, Ecole Polytechnique, 91128 Palaiseau, France

March 6, 2014

Supported by Grant No. DOE ER046169and the Columbia-Ecole Polytechnique Alliance program.

Hung T. Dang Ferromagnetism in ruthenate perovskites

Motivations: from experiments

Normally, strong correlation leads to magnetic order while weakcorrelation does not.

Not true for ruthenates: CaRuO3 (more correlated) is paramagneticwhile SrRuO3 (less correlated) is ferromagnetic at T < Tc = 160K .

FM ordering temp.

Curie-Weiss temp.

SrxCa1−xRuO3 (Cao 1997) Mass enhancement (Ahn 1999)

Our previous work

Vollhardt et. al, and then our previous study (PRB 87, 155127) showsthe conditions for ferromagnetism (FM) for less-than-half-filling

(1) (2) (3)

Curie temperature Tc1 > Tc2 > Tc3

d4 systems (ruthenates) are related to d2 by a particle-holetransformation.

In d2 systems, proximity to the Mott insulator also suppresses theferromagnetism (PRB 87, 155127).

Which condition is more significant to the ruthenates?

Our previous work

(1) (2) (3)

Our previous work

(1) (2) (3)

Our previous work

(1) (2) (3)

Model and methods

SrRuO3 (Pnma) CaRuO3 (Pnma)

Valence d shell Ru+4: [Kr]4d4 Ru+4: [Kr]4d4

M-O-M bond angle 163 (Jones 1989) 150 (Bensch 1990)metal/insulator FM metal PM metal

The model considers 3 t2g orbitals as correlatedbands: H = Hkin + Honsite .

Hkin: kinetic energy (lattice structure embedded)

Honsite : 3-orbital interaction

Honsite = U∑α

nα↑nα↓ + (U − 2J)∑α 6=β

nα↑nβ↓+

+ (U − 3J)∑α>β,σ

nασnβσ + J∑α 6=β

(c†α↑cβ↑c†β↓cα↓ + c†α↑cβ↑c

†α↓cβ↓).

Density Functional plus Dynamical Mean-Fieldmethod (DFT+DMFT) is used to solve the model.

Density functional (DFT) calculations

Maximally-localized Wannier function (MLWF) is used to obtain the t2g

subspace

1 Bandwidth of CaRuO3 is smaller than SrRuO3.

2 DOS peak of SrRuO3 is more concentrated (near the Fermi level).

Γ T Y X4

3(a) SrRuO3

Γ T Y X U

(b) CaRuO3

DFT bands

−3.0 −2.5 −2.0 −1.5 −1.0 −0.5 0.0 0.5 1.0energy (eV)

l densi

CaRuO3

SrRuO3DFT result

subspace

Γ T Y X4

3(a) SrRuO3

Γ T Y X U

(b) CaRuO3

DFT bands

MLWF bands

−3.0 −2.5 −2.0 −1.5 −1.0 −0.5 0.0 0.5 1.0energy (eV)

l densi

CaRuO3

SrRuO3DFT result

MLWF fitting

subspace

Γ T Y X4

3(a) SrRuO3

Γ T Y X U

(b) CaRuO3

DFT bands

MLWF bands

−3.0 −2.5 −2.0 −1.5 −1.0 −0.5 0.0 0.5 1.0energy (eV)

l densi

CaRuO3

SrRuO3DFT result

MLWF fitting

subspace

Determine the Curie temperature Tc and the magneticphase boundary

Tc is extrapolated from χ−1(T )curve.

Small J: both are paramagnetic

Intermediate J: SrRuO3 isferromagnetic, CaRuO3 isparamagnetic

Large J: both are ferromagneticbut T SRO

c > TCROc

SrRuO3 is more ferromagneticthan CaRuO3

J=0.25eV0

0.1 J=0.25eVzoom in

J=0.33eV

CaRuO3

SrRuO3

ity χ-1

(μ B2

0.1 J=0.33eVzoom in

J=0.4eV0

0.1 J=0.4eVzoom in

J=0.5eV0

temperature (eV)0 0.05 0.1 0.15 0.2

J=0.5eVzoom in

temperature (eV)0 0.020.04

The case U = 3eV

Ferromagnetic/paramagnetic phase diagrams

0.0 0.2 0.4 0.6 0.8J (eV)

5U (eV)

(a) SrRuO3

FM metal

PM metal

PM insulator

0.0 0.2 0.4 0.6 0.8 1.0J (eV)

(b) CaRuO3

U<3J region

MIT boundary

Ferromagnetic/paramagnetic phase diagrams for(a) SrRuO3 and (b) CaRuO3

0.0 0.2 0.4 0.6 0.8 1.0J (eV)

U (eV)

FM metal

PMmetal

PM insulator

U<3J regionCaRuO3

SrRuO3

MIT boundary

Two phase diagrams together.

0.0 0.2 0.4 0.6 0.8 1.0J (eV)

U (eV)

FM metal

PMmetal

PM insulator

U<3J regionCaRuO3

SrRuO3

MIT boundary

0.0 0.2 0.4 0.6 0.8 1.0J (eV)

U (eV)

FM metal

PMmetal

PM insulator

U<3J region

MIT boundary

Bandwidth of SrRuO3 is rescaled tobe the same as CaRuO3.

0.0 0.2 0.4 0.6 0.8 1.0J (eV)

U (eV)

FM metal

PMmetal

PM insulator

U<3J regionCaRuO3

SrRuO3

MIT boundary

0.0 0.2 0.4 0.6 0.8 1.0J (eV)

U (eV)

Hund's coupling region

Mott insulating region

MIT boundary

Classify into 2 regions offerromagnetism

Locate materials on the phase diagrams

J: should be the same.0.3 < J < 0.5eV so as CaRuO3 is PM.Choose J = 0.4eV .

U: 1 < U < 3.5eV so as two materialsare metallic.

Possibilities of U values:I Whether SrRuO3 and CaRuO3 share

the same U or notI If U ∼ 2eV : Hund’s coupling effectI If U ∼ 3eV : effect from the proximity

to Mott insulating phase

0.0 0.2 0.4 0.6 0.8 1.0J (eV)

FM metal

PMmetal

PM insulator

U<3J regionCaRuO3

SrRuO3

0.0 0.2 0.4 0.6 0.8 1.0J (eV)

FM metal

PMmetal

PM insulator

U<3J regionCaRuO3

SrRuO3

0.0 0.2 0.4 0.6 0.8 1.0J (eV)

FM metal

PMmetal

PM insulator

U<3J regionCaRuO3

SrRuO3

0.0 0.2 0.4 0.6 0.8 1.0J (eV)

FM metal

PMmetal

PM insulator

U<3J regionCaRuO3

SrRuO3

The U values (work in progress)

Based on optical conductivity sum rule:

1/π∫Reσ(ω)dω (unit Ω−1cm−1eV ) with 0 < ω < 0.12eV

U(eV ) J(eV ) T (K) Opt. sum rule

CaRuO3 SrRuO3

2.3 0.4 116 463 444

3 0.4 290 349 375

experiment at T = 200K 325 390

Exp. data: Kostic et.al (PRL 81, 2498), Lee et.al (PRB 66, 041104).

I The sum rule suggests CaRuO3 and SrRuO3 have the same U.I Sum rules at U = 3eV are closer to experimental data.

Based on the mass enhancement m∗/m: (exp. SRO=3.5, CRO=8 - Ahn (1999))

I At U = 3eV , m∗/m of two materials are similar - not goodI Another possibility: CaRuO3 has U ∼ 3eV ,

SrRuO3 has smaller U (e.g. ∼ 2eV )

Other conditions, such as low temperature resitivity or spectral functions, need tobe considered.

CaRuO3 SrRuO3

2.3 0.4 116 463 444

3 0.4 290 349 375

CaRuO3 SrRuO3

2.3 0.4 116 463 444

3 0.4 290 349 375

Conclusions

The ferromagnetism in SrRuO3 andparamagnetism in CaRuO3 comes from

1 DOS peak position (or lattice distortion)2 Proximity to the Mott insulating phase

U ≈ 3eV divides two regions that controlsthe ferromagnetism

Further study is in progress for determiningthe U values of the two materials

0.0 0.2 0.4 0.6 0.8 1.0J (eV)

FM m etal

PMm etal

PM insulator

U< 3J regionCaRuO3

SrRuO3

MIT boundary

Acknowledgements

Center for Nanophase Materials Sciences, Oak Ridge NationalLaboratory

Extreme Science and Engineering Discovery Environment (XSEDE)

High Performance Computing, RWTH Aachen University

TRIQS project (http://ipht.cea.fr/triqs)

Quantum Espresso package (http://www.quantum-espresso.org)

Supported by Grant No. DOE ER046169 and the Columbia-EcolePolytechnique Alliance program.

Thank you for your attention.

ferromagnetism in ruthenate perovskites

Documents