Ferromagnetism in ruthenate perovskites Hung T. Dang 1 , Jernej Mravlje 2 , Andrew J. Millis 3 and Antoine Georges 4 1 Institute for Theoretical Solid State Physics, RWTH Aachen University, Germany 2 Department of Theoretical Physics, Jozef Stefan Institute, Ljubljana, Slovenia 3 Department of Physics, Columbia University, New York, USA 4 Centre 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
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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)
Hung T. Dang Ferromagnetism in ruthenate perovskites
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?
Hung T. Dang Ferromagnetism in ruthenate perovskites
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?
Hung T. Dang Ferromagnetism in ruthenate perovskites
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?
Hung T. Dang Ferromagnetism in ruthenate perovskites
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?
Hung T. Dang Ferromagnetism in ruthenate perovskites
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.
Hung T. Dang Ferromagnetism in ruthenate perovskites
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).
Hung T. Dang Ferromagnetism in ruthenate perovskites