Ferromagnetism in ruthenate perovskites

Ferromagnetism in ruthenate perovskites
Hung T. Dang1 , Jernej Mravlje2 , Andrew J. Millis3
and Antoine Georges4
1 Institute
for Theoretical Solid State Physics, RWTH Aachen University, Germany
2 Department
of Theoretical Physics, Jozef Stefan Institute, Ljubljana, Slovenia
3 Department
4 Centre
of Physics, Columbia University, New York, USA
´
de Physique Th´
eorique, CNRS, Ecole
Polytechnique, 91128 Palaiseau, France
March 6, 2014
Supported by Grant No. DOE ER046169
and the Columbia-Ecole Polytechnique Alliance program.
Hung T. Dang
Ferromagnetism in ruthenate perovskites
Motivations: from experiments
Normally, strong correlation leads to magnetic order while weak
correlation does not.
Not true for ruthenates: CaRuO3 (more correlated) is paramagnetic
while SrRuO3 (less correlated) is ferromagnetic at T < Tc = 160K .
FM ordering temp.
Curie-Weiss temp.
Srx Ca1−x RuO3 (Cao 1997)
Hung T. Dang
Mass enhancement (Ahn 1999)
Ferromagnetism in ruthenate perovskites
Our previous work
Vollhardt et. al, and then our previous study (PRB 87, 155127) shows
the conditions for ferromagnetism (FM) for less-than-half-filling
(1)
(2)
(3)
Curie temperature Tc1 > Tc2 > Tc3
Hung T. Dang
Ferromagnetism in ruthenate perovskites
Our previous work
Vollhardt et. al, and then our previous study (PRB 87, 155127) shows
the conditions for ferromagnetism (FM) for less-than-half-filling
(1)
(2)
(3)
Curie temperature Tc1 > Tc2 > Tc3
d 4 systems (ruthenates) are related to d 2 by a particle-hole
transformation.
Hung T. Dang
Ferromagnetism in ruthenate perovskites
Our previous work
Vollhardt et. al, and then our previous study (PRB 87, 155127) shows
the conditions for ferromagnetism (FM) for less-than-half-filling
(1)
(2)
(3)
Curie temperature Tc1 > Tc2 > Tc3
d 4 systems (ruthenates) are related to d 2 by a particle-hole
transformation.
In d 2 systems, proximity to the Mott insulator also suppresses the
ferromagnetism (PRB 87, 155127).
Hung T. Dang
Ferromagnetism in ruthenate perovskites
Our previous work
Vollhardt et. al, and then our previous study (PRB 87, 155127) shows
the conditions for ferromagnetism (FM) for less-than-half-filling
(1)
(2)
(3)
Curie temperature Tc1 > Tc2 > Tc3
d 4 systems (ruthenates) are related to d 2 by a particle-hole
transformation.
In d 2 systems, proximity to the Mott insulator also suppresses the
ferromagnetism (PRB 87, 155127).
Which condition is more significant to the ruthenates?
Hung T. Dang
Ferromagnetism in ruthenate perovskites
Model and methods
Valence d shell
M-O-M bond angle
metal/insulator
SrRuO3 (Pnma)
Ru+4 : [Kr]4d 4
163◦ (Jones 1989)
FM metal
CaRuO3 (Pnma)
Ru+4 : [Kr]4d 4
150◦ (Bensch 1990)
PM metal
The model considers 3 t2g orbitals as correlated
bands: H = Hkin + Honsite .
Hkin : kinetic energy (lattice structure embedded)
Honsite : 3-orbital interaction
Honsite = U
X
nα↑ nα↓ + (U − 2J)
α
+ (U − 3J)
X
α>β,σ
X
nα↑ nβ↓ +
α6=β
nασ nβσ + J
X
†
†
†
†
(cα↑
cβ↑ cβ↓
cα↓ + cα↑
cβ↑ cα↓
cβ↓ ).
α6=β
Density Functional plus Dynamical Mean-Field
method (DFT+DMFT) is used to solve the model.
Hung T. Dang
Ferromagnetism in ruthenate perovskites
Density functional (DFT) calculations
Hung T. Dang
Ferromagnetism in ruthenate perovskites
Density functional (DFT) calculations
(a) SrRuO3
(b) CaRuO3
40
1
0
20
10
0
−10
1
−20
2
−30
3
4Γ
CaRuO3
30
DFT bands
2
total density of states
3
T
Y
X
Γ
Hung T. Dang
T
Y
X
U
DFT result
SrRuO3
−40
−3.0 −2.5 −2.0 −1.5 −1.0 −0.5
energy (eV)
Ferromagnetism in ruthenate perovskites
0.0
0.5
1.0
Density functional (DFT) calculations
(a) SrRuO3
(b) CaRuO3
40
1
0
20
10
0
−10
1
−20
2
−30
3
4Γ
CaRuO3
30
DFT bands
MLWF bands
2
total density of states
3
T
Y
X
Γ
T
Y
X
U
DFT result
MLWF fitting
SrRuO3
−40
−3.0 −2.5 −2.0 −1.5 −1.0 −0.5
energy (eV)
0.0
0.5
1.0
Maximally-localized Wannier function (MLWF) is used to obtain the t2g
subspace
Hung T. Dang
Ferromagnetism in ruthenate perovskites
Density functional (DFT) calculations
(a) SrRuO3
(b) CaRuO3
40
1
CaRuO3
30
DFT bands
MLWF bands
2
total density of states
3
0
20
10
0
−10
1
−20
2
−30
3
4Γ
T
Y
X
Γ
T
Y
X
U
DFT result
MLWF fitting
SrRuO3
−40
−3.0 −2.5 −2.0 −1.5 −1.0 −0.5
energy (eV)
0.0
0.5
1.0
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).
Hung T. Dang
Ferromagnetism in ruthenate perovskites
Determine the Curie temperature Tc and the magnetic
phase boundary
0.1
Small J: both are paramagnetic
Intermediate J: SrRuO3 is
ferromagnetic, CaRuO3 is
paramagnetic
Large J: both are ferromagnetic
but TcSRO > TcCRO
SrRuO3 is more ferromagnetic
than CaRuO3
0.05
inverse susceptibility χ-1 (μ2B/eV)
Tc is extrapolated from χ−1 (T )
curve.
J=0.25eV
zoom in
0
0.1
0.05
J=0.25eV
J=0.33eV
zoom in
CaRuO3
SrRuO3
J=0.33eV
0
0.1
J=0.4eV
zoom in
0.05
J=0.4eV
0
0.1
J=0.5eV
zoom in
0.05
J=0.5eV
0
0 0.05 0.1 0.15 0.2
temperature (eV)
0 0.020.04
temperature (eV)
The case U = 3eV
Hung T. Dang
Ferromagnetism in ruthenate perovskites
Ferromagnetic/paramagnetic phase diagrams
5
U (eV)
4
(a) SrRuO3
3 PM
5
(b) CaRuO3
FM
PM
4
FM
2
3
2
FM metal
PM metal
PM insulator
1
0
0.0 0.2 0.4 0.6 0.8
J (eV)
U<3J region 1
MIT boundary
0.0 0.2 0.4 0.6 0.8 1.0
J (eV)
Ferromagnetic/paramagnetic phase diagrams for
(a) SrRuO3 and (b) CaRuO3
Hung T. Dang
Ferromagnetism in ruthenate perovskites
0
Ferromagnetic/paramagnetic phase diagrams
5
U (eV)
4
PM insulator
FM metal
3
2
1
PM
metal
U<3J 3region
CaRuO
SrRuO3
MIT boundary
0
0.0 0.2 0.4 0.6 0.8 1.0
J (eV)
Two phase diagrams together.
Hung T. Dang
Ferromagnetism in ruthenate perovskites
Ferromagnetic/paramagnetic phase diagrams
5
PM insulator
FM metal
3
2
1
4
U (eV)
U (eV)
4
5
PM
metal
U<3J 3region
CaRuO
SrRuO3
MIT boundary
0
0.0 0.2 0.4 0.6 0.8 1.0
J (eV)
Two phase diagrams together.
Hung T. Dang
PM insulator
FM metal
3
2
1
PM
metal
U<3J region
MIT boundary
0
0.0 0.2 0.4 0.6 0.8 1.0
J (eV)
Bandwidth of SrRuO3 is rescaled to
be the same as CaRuO3 .
Ferromagnetism in ruthenate perovskites
Ferromagnetic/paramagnetic phase diagrams
U (eV)
4
5
PM insulator
FM metal
3
2
1
PM
metal
U<3J 3region
CaRuO
SrRuO3
MIT boundary
0
0.0 0.2 0.4 0.6 0.8 1.0
J (eV)
Two phase diagrams together.
Hung T. Dang
4
U (eV)
5
3
2
Mott insulating region
Hund's coupling region
1
MIT boundary
00.0 0.2 0.4 0.6 0.8 1.0
J (eV)
Classify into 2 regions of
ferromagnetism
Ferromagnetism in ruthenate perovskites
Locate materials on the phase diagrams
5
PM insulator
U (eV)
4
FM metal
3
2
1
PM
metal
0
0.0
Hung T. Dang
U<3J region
0.2
Ferromagnetism in ruthenate perovskites
0.4
0.6
J (eV)
CaRuO3
SrRuO3
0.8
1.0
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 .
5
PM insulator
U (eV)
4
FM metal
3
2
1
PM
metal
0
0.0
Hung T. Dang
U<3J region
0.2
Ferromagnetism in ruthenate perovskites
0.4
0.6
J (eV)
CaRuO3
SrRuO3
0.8
1.0
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 .
PM ins ula tor
4
U (e V)
U: 1 < U < 3.5eV so as two materials
are metallic.
5
FM m e ta l
3
2
1
PM
m e ta l
U<3J re g ion
0
0.0
Hung T. Dang
0.2
Ferromagnetism in ruthenate perovskites
0.4
0.6
J (e V)
Ca RuO 3
SrRuO 3
0.8
1.0
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 .
I
I
I
Whether SrRuO3 and CaRuO3 share
the same U or not
If U ∼ 2eV : Hund’s coupling effect
If U ∼ 3eV : effect from the proximity
to Mott insulating phase
Hung T. Dang
PM ins ula tor
4
U (e V)
U: 1 < U < 3.5eV so as two materials
are metallic.
Possibilities of U values:
5
FM m e ta l
3
2
1
PM
m e ta l
U<3J re g ion
0
0.0
0.2
Ferromagnetism in ruthenate perovskites
0.4
0.6
J (e V)
Ca RuO 3
SrRuO 3
0.8
1.0
The U values (work in progress)
Based on optical conductivity sum rule:
R
1/π Reσ(ω)dω (unit Ω−1 cm−1 eV ) 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
I
The sum rule suggests CaRuO3 and SrRuO3 have the same U.
Sum rules at U = 3eV are closer to experimental data.
Hung T. Dang
Ferromagnetism in ruthenate perovskites
The U values (work in progress)
Based on optical conductivity sum rule:
R
1/π Reσ(ω)dω (unit Ω−1 cm−1 eV ) 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
I
The sum rule suggests CaRuO3 and SrRuO3 have the same U.
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
I
At U = 3eV , m∗ /m of two materials are similar - not good
Another possibility: CaRuO3 has U ∼ 3eV ,
SrRuO3 has smaller U (e.g. ∼ 2eV )
Hung T. Dang
Ferromagnetism in ruthenate perovskites
The U values (work in progress)
Based on optical conductivity sum rule:
R
1/π Reσ(ω)dω (unit Ω−1 cm−1 eV ) 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
I
The sum rule suggests CaRuO3 and SrRuO3 have the same U.
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
I
At U = 3eV , m∗ /m of two materials are similar - not good
Another possibility: CaRuO3 has U ∼ 3eV ,
SrRuO3 has smaller U (e.g. ∼ 2eV )
Other conditions, such as low temperature resitivity or spectral functions, need to
be considered.
Hung T. Dang
Ferromagnetism in ruthenate perovskites
Conclusions
5
PM insulat or
The ferromagnetism in SrRuO3 and
paramagnetism in CaRuO3 comes from
2
DOS peak position (or lattice distortion)
Proximity to the Mott insulating phase
U ≈ 3eV divides two regions that controls
the ferromagnetism
Further study is in progress for determining
the U values of the two materials
Hung T. Dang
U (eV)
1
4
FM m et al
3
2
1
PM
m et al
U< 3J3region
CaRuO
SrRuO3
MIT boundary
0
0.0
Ferromagnetism in ruthenate perovskites
0.2
0.4
0.6
J (eV)
0.8
1.0
Acknowledgements
Center for Nanophase Materials Sciences, Oak Ridge National
Laboratory
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-Ecole
Polytechnique Alliance program.
Thank you for your attention.
Hung T. Dang
Ferromagnetism in ruthenate perovskites

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