magnetismin layeredruthenates oberseminar ws 2007/08...1. superconducting sr2ruo4 - unconventional...
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Universität zu Köln
17.12.2007
Markus Braden
Magnetism in layered RuthenatesOberseminar WS 2007/08
Sr2RuO4
Ca3Ru2O7 Sr3Ru2O7
Ca2RuO4
Ca Srlayered ruthenates
Ł Ruddlesdon-Popper : n = 1,2, .. 3, 4, ...
Outline1. superconducting Sr2RuO4
- unconventional pairing- magnetic fluctuations
2. insulating Ca2RuO4- antiferromagnetism- role of orbital degrees of freedom
3. the phase diagram of Ca2-xSrxRuO4- strongly enhanced magnetic fluctuations- metamagnetism
4. double-layer materials : Ca3-xSrxRu2O75. Conclusions
own work : collaboration withP. Steffens, O. Schumann, O. Friedt, M. Kriener, J. Baier, T. Lorenz . . .Y. Sidis, P. Bourges, A. Gukasov, . . . S. Nakatsuji & Y. Maeno
superconductivity in Sr2RuO4
a
a
c
Sr2RuO4
Tc~ 1.5 K
La2-xBaxCuO4
Tc~ 35 K
Sr
OO
RuLa/Ba
Cu
Y. Maeno et al., Nature 1994
Normal-State properties
• Anisotropic 3 dim. metal
• Γ=ρc/ρab∼450=const.
at low temperatures
• ρ(T)~T2 e- -e--scattering
Für T < 30 K:
• Pauli-Paramagnetism S=1
• c(T)=γT+βT3 γ=40mJ/(mol K2)
• Wilson-Ratio Rw=const.χ/γ=1.8
Fermi-liquid
Hussey et al., PRB 1998
Maeno et al., JPSJ 1997
impurity effect
Al~450ppm
Al~130ppm
Al<30ppm
l=900Å ~ξ
Tc extremely sensitive
• non-magnetic impurities
• defects Mao et al., PRB 1999
s-wave pairing
is unlikely
Mackenzie et al., PRL 1998
Verletzung der Zeit-Umkehr
Invarianz
µ+-Spin Relaxation:
Luke et al., Nature 1998
Spontanes internes Magnetfeld
für T<Tc
Verletzung der T Invarianz
Evidenz für p-Wellen Symmetrie
Lz=±1
17O Knight Shift in Sr2RuO4
Spin-Susceptibility
Singlet
Triplet
↑↓
↑↑
Ishida et al., Nature 1998
µ0H=0.65 T//[100]
Tc(H)
K1x
K1y
d-wave
Spin-Susceptibility KS=KN
Spin-Triplet pairing
Spin-Triplet Superconductivity
Rice & SigristSr2RuO4 electronic analogue with 3He
strong correlations SrRuO3
ferromagnet
Sr2RuO4: spin-triplet superconductor with
p-wave symmetry
Cooper-Paar wavefunction: ΨΨΨΨ(2,1)=)=)=)=−−−−Ψ(Ψ(Ψ(Ψ(1,2) antisymmetric for Fermions
Spin-part Orbital part
Singlet Sz=0 L=0,2,...(s,d,...wave)
S=0 antisymmetric symmetric,even parity
Triplet Sz=1 L=1,3,...(p,f,...wave)
S=1 0 antisymmetric, odd parity
-1 symmetric
↑↓
||2
1 ↓↑>−↑↓>
↑↑>|
||2
1 ↓↑>+↑↓>
↓↓>|
↑↑
Quantum interference devices
Science 306, 1151 (2004)
High resolution polar Kerr effect
Jing Xia et al., PRL 97, 167002 (2006)
A.P. Mackenzie and Y. Maeno, Rev. Mod. Phys. 75, 657 (2003).
⋅⋅±⋅⋅∆=1
0
0
)(ˆ0 yx kikzdr
Magnetism in Sr2RuO4 and inelasticneutron scattering
α,β-bands
Ru4+: 4d4
γ-band4d4 eg
t2g
crystal field
α
β
γ
xy
yz,zx
Dispersion E(k) Fermi surfaceOrbitals
(C.Bergemann. et al., (Adv. Phys. 2003)
dxydyz
dxz
α
β
γ
( )ωχ ,''~ qIr
( ) ∑ ++
++
+−−−
=jik iqjqk
jqkik
ji
qkk
Bi
ffMgq
,, ,),(
),(,,
)(;20 0
)]()([),(
ωεεεε
µωχh
dynamic suszeptibility (RPA)
)()(1
)()(
0
0
qqI
χχχ
−=
nesting : α/β-Fermi surface
magnetism in Sr2RuO4 / inelastic neutron scattering
Mazin and Singh , PRL (1999)
Inelastic neutron scattering
neutron sources
FRM-II, Garching,D ILL, Grenoble,F
U235+n → Mo95+La139+2n235x7.6 95x8.6 138x8.4MeVi.e. 200 MeV energy
6MeV kinetic energy of the neutron
- Scans at constant energy, E=6.2meV, along Q=(1.3 y 0) show a clear peak
- incommensurate fluctuations due to nesting inone-dimensional bands
)kt
hexp(1
),Q(''
)g(
)Q(F2r
dd
d2
B
22
0
2
ωωωω−−−−−−−−
ωωωωχχχχ⋅⋅⋅⋅µµµµππππ
⋅⋅⋅⋅====ωωωωΩΩΩΩ
σσσσ
Sidis et al., PRL 1999
Braden et al., PRB66, 064522 2002; PRL92, 097402, 2004.
Inelastic neutron scattering
Energy-Temperature-
dependency
- ‘(q0,0) and and FWHMvary as function of T- all indicate a close instability !
22)0,('),(''
ωωωωωωωωχχχχωωωωχχχχ
++++ΓΓΓΓ⋅⋅⋅⋅ΓΓΓΓ⋅⋅⋅⋅==== ii qq
Braden et al., PRB 2002
neutron diffraction in Ti-doped Sr2RuO4
- static peaks at the incommensurate positions- coherence ~40Å
Sr2Ru1-xTixO4x=0.09
Braden et al., PRL 88, 2002
- Sr2RuO4 is close to a QCP !
Pairing : Where is the problem ?
- assume : coupling via magnetic excitationsand weak coupling
(Fay & Appel; Monthoux & Lonzarich)
- application to Sr2RuO4: Mazin&Singh (1999)nesting response ŁŁŁŁ d-wave SCferromagnetic response ŁŁŁŁ p-wave SC
(Rice &Sigrist)
HOWEVERdx2-y2 -wave SC inconsistent with experiment also dxy-band should be active !!!
full spectrum ŁŁŁŁ superconducting order parameter
( ) ( ) ( )( ) ( )qqI
qqIkkqV
20
20
2
1'
χχ
−=−=
)()(1
)()(
0
0
qqI
χχχ
−=
ferromagnetic fluctuations in Sr2RuO4
polarized neutron scattering
T=1.6K
Diagonal
There is a weak FM component
model : χ‘(q)
χ‘(µ
B2 /
eV) ca. ×10
Γ = 15.5 ± 1.4 meV
W = 0.53 ± 0.04 r.l.u.
quantitative agreement:
- NMR- specific heat γ- suszeptibility (q=0)
ferromagnetic fluctuations in Sr2RuO4
Ca2-xSrxRuO4 Sr2RuO4
Ca3Ru2O7 Sr3Ru2O7
Ca2RuO4
Ca Sr
Ca2-xSrxRuO4 Structural properties
r = 1.31Å
Sr2+
r = 1.18Å
Ca2+Isovalent substitutionrCa < rSr
complex phase diagram
Nakatsuji et al. PRL 84 2666 (2000), Friedt et al. PRB 63, 174432 (2001), Braden et al. PRB 58, 847 (1998)
rotation around c-axis
tilt|| edges
flattening „K2NiF4“(undistorted)
Structural distortions in Ca2-xSrxRuO4
Tilt distortion
x=0.2
a
b
tiltaxis(|| b)
Space group Pbca
x=0.22
• tilt stacking sequencealways one c !
x=0.2
Stacking sequence : rotation
I41/acdc=25Å
Bbcmc=12.5Å
+Tilt: (S,L-) Pbca (D-) Pbca
2 / 4 – foldSymmetry at Ru-site
Different ground State (orbital order)
Ca2-xSrxRuO4 Structural properties
r = 1.31Å
Sr2+
r = 1.18Å
Ca2+Isovalent substitutionrCa < rSr
complex phase diagram
Nakatsuji et al. PRL 84 2666 (2000), Friedt et al. PRB 63, 174432 (2001), Braden et al. PRB 58, 847 (1998)
T
Alexander et al., PRB 2000 Nakatsuji et al., PRB 2001PRL 2000
symmetry in metallic AND in insulating phasesPbca : one-c tilt plus one-c rotation
Metal-insulator-transition in Ca2RuO4
Friedt et al. PRB 63, 174432 (2001), Braden et al. PRB 58, 847 (1998)
• two magnetic ordering schemes in a nearly stoichiometric powder• best crystals only A-centering TN~110K• excess oxygen or Sr-substitution : B-centering TN~150K
Antiferromagnetic order in Ca2RuO4
MI-transition : orbital effects
Insulating:Flat octahedrone- àààà dxy-band
Metallic:Elongated octahedron
Ca2RuO4
a
b
Friedt et al. PRB 63, 174432 (2001), Braden et al. PRB 58, 847 (1998)Steffens et al. PRB 72,094104 (2005).
• orbital occupation changes : at MI-transition & in insulating phase
Orbital effects in Ca2RuO41. Orbital-Selective Mass Enhancements in Multiband Ca2-xSrxRuO4 Systems Analyzed by the Extended Drude Model
J. S. Lee et al. , Phys. Rev. Lett. 96, 057401 (2006)2. Strong Orbital-Dependent d-Band Hybridization and Fermi-Surface Reconstruction in Metallic Ca2-xSrxRuO4
Eunjung Ko et al., Phys. Rev. Lett. 98, 226401 (2007)3. Subband Filling and Mott Transition in Ca2-xSrxRuO4 A. Liebsch et al. Phys. Rev. Lett. 98, 216403 (2007)4. Orbital Ordering Transition in Ca2RuO4 Observed with Resonant X-Ray Diffraction I. Zegkinoglou et al., PR.L. 95,136401 (2005)5. Ferro-Type Orbital State in the Mott Transition System Ca2-xSrxRuO4 Studied by the Resonant X-Ray Scattering Interference
Technique M. Kubota et al., Phys. Rev. Lett. 95, 026401 (2005)
6. Lattice dynamics and the electron-phonon interaction in Ca2RuO4 H. Rho et al., Phys. Rev. B 71, 245121 (2005)7. Orbital-Selective Mott Transitions in the Degenerate Hubbard Model Akihisa Koga et al., Phys. Rev. Lett. 92, 216402 (2004)8. Correlation effects in Sr2RuO4 and Ca2RuO4 : Valence-band photoemission spectra and self-energy calculations
T. T. Tran et al., Phys. Rev. B 70, 153106 (2004)9. Orbital-dependent phase control in Ca2-xSrxRuO4 (0<~x<~0.5) Zhong Fang et al., Phys. Rev. B 69, 045116 (2004)10. Orbital state and metal-insulator transition in Ca2-xSrxRuO4 (x=0.0 and 0.09) studied by x-ray absorption spectroscopy
T. Mizokawa et al. , Phys. Rev. B 69, 132410 (2004)11. Raman scattering studies of spin, charge, and lattice dynamics in Ca2-xSrxRuO4 (0<~x<0.2) H. Rho et al., PRB 68, 100404 (2003)12. Change of Electronic Structure in Ca2RuO4 Induced by Orbital Ordering J. H. Jung et al., Phys. Rev. Lett. 91, 056403 (2003)13. Electron and Orbital Correlations in Ca2-xSrxRuO4 Probed by Optical Spectroscopy J. S. Lee et al, PRL. 89, 257402 (2002)14. Orbital state and metal-insulator transition in Ca2-xSrxRuO4 studied by model Hartree-Fock calculations
M. Kurokawa et al. Phys. Rev. B 66, 024434 (2002)15. Pressure-Tuned Collapse of the Mott-Like State in Can+1RunO3n+1 (n=1,2): Raman Spectroscopic Studies
C. S. Snow et al., Phys. Rev. Lett. 89, 226401 (2002)16. Prediction of Orbital Ordering in Single-Layered Ruthenates Takashi Hotta and Elbio Dagotto Phys. Rev. Lett. 88, 017201 (2002)17. From Mott insulator to ferromagnetic metal: A pressure study of Ca2RuO4 Fumihiko Nakamura et al., PRB 65, 220402 (2002)18. Spin-Orbit Coupling in the Mott Insulator Ca2RuO4 T. Mizokawa et al. Phys. Rev. Lett. 87, 077202 (2001)19. Magnetic phase diagram of Ca2-xSrxRuO4 governed by structural distortions Z. Fang Phys. Rev. B 64, 020509 (2001)20. Quasi-Two-Dimensional Mott Transition System Ca2-xSrxRuO4 S. Nakatsuji et al. Phys. Rev. Lett. 84, 2666 (2000)21. Electronic structure of Ca2RuO4: A comparison with the electronic structures of other ruthenates L. M. Woods PRB 62, 7833
(2000)22. Ground-state instability of the Mott insulator Ca2RuO4: Impact of slight La doping on the metal-insulator transition and
magnetic ordering G. Cao et al., Phys. Rev. B 61, R5053 (2000)23. Destruction of the Mott insulating ground state of Ca2RuO4 by a structural transition C. S. Alexander et al., PRB 60, R8422 (1999)24. Layered Ruthenium Oxides: From Band Metal to Mott Insulator A. V. Puchkov et al., Phys. Rev. Lett. 81, 2747 (1998)
metal-insulator-transition as function of doping
metallic compounds are all very similar :small tilt & elongated & small RuO-volume
one-c period two-c period no rotation
no tiltone-c tilt
anomalous metals close to MI transition
Braden et al., PRB 1998, Friedt et al., PRB 2001, Nakatsuji PRB 2000, PRL 200, JPSJ 1997.
magneto-elastic coupling : 0.2<x<1.5
S. Nakatsuji and Y. Maeno
PRB, PRL (2000)
critical pointof the structural transition
Tilt distortion Rotational distortion
O. Friedt et al., PRB 63, 174432 (2001)
Ca1.5Sr0.5RuO4 x=0.5
• large susceptibility200 · ( Sr2RuO4)
• large Cp/T-ratio
250 mJ/mol ·K2
S. Nakatsuji and Y. Maeno
PRB, PRL (2000)
critical pointof the structural transition
Tilt distortion Rotational distortion
S. Nakatsuji, et al., PRL 2003.
metamagnetism !
Magneto-elastic coupling : x ~ 0.2
O. Friedt et al., PRB 63, 174432 (2001)
Magnetization density
Polarized neutrons (5C1)Maximum Entropy method (MEM)
x=0.2
Ru
O
RuO
x=0.5
Spin-density: dxy-characterGukasov et al. PRL 89 (2002)
dxy
structural anomalies in Ca1.8Sr0.2RuO4
• temperature dependencies indicate crossover
Susceptibility
resistivity
M. Kriener et al., PRL 95, 267403 (2005).
- low temperature anomaly- strongest for x=0.2
M. Kriener et al., PRL 95, 267403 (2005).
J. Baier et al., condmat0610769.
• field dependencies
metamagnetism in Ca1.8Sr0.2RuO4
S. Nakatsuji, et al., PRL 2003.
Electronic transition in Ca2-xSrxRuO4
- zero field : lattice flattening - high field : lattice elongation
neutron-powder-diffraction at high field GEM (ISIS)
• zero field : octahedron flattening • high field : octahedron elongation
(GEM ISIS & Fullprof )
Electronic transition in Ca2-xSrxRuO4
M. Kriener et al.,
PRL 95, 267403 (2005).
Tuning of orbital occupation
- zero field : electrons move into the γγγγ-band upon cooling- high field : electrons leave γγγγ-band
strong effects in tilted phase (x~0.2)
α and β FS (1dim.)γ FS (2 dim.)
cooling
field
e-
- nearly localized electrons (close to the Mott transition)ŁŁŁŁ high electronic Grüneisen-parameter
Incommensurate scattering aroundCa1.5Sr0.5RuO4
O. Friedt et al., PRL 93, 147404 (2004).
Ca1.38Sr0.62RuO4
scattering near (0.2,0,0)
X~0.5
-0.1eV
+0.025eV
0 eV
+0.05eV
+0.06eV
+0.07eV
+0.1eV
+0.085eV
+0.15eV
-0.05eV
γ-Fermi surface
Magnetism of dxy-band
-0.4 -0.2 0.0 0.2 0.4
0
20
40
60
80
Q = (H, 0, 1.6)
counts
1.5 K
E = 0.4 meV
10 K
32 K
( ) ( )22
0,',''ω
ωχωχ+Γ
Γ⋅= qq
mol
emu
eV
B 32
1023.3100 −⋅=µ
0 20 40 60 80 1000
200
400
600
800
1000
0 20 40 60 80 100
hω = 1 meV
χχχχ'' ( QFM
, ωωωω )
χ', χ''
(µµµµΒΒΒΒ
2222/eV)
hω = 0.4 meV
χab makroskop.
χ' ( QFM
, ωωωω = 0 )
Temperatur (K)
(S. Nakatsuji)
Magnetic fluctuations & metamagnetism
Ca1.8Sr0.2RuO4
- paramagnons at 10K- they get suppressed at low T
P. Steffens et al., PRL 2007
x=0.2
-0.4 -0.2 0.0 0.2 0.4
10
20
30
40
10
20
30
40
-0.4 -0.2 0.0 0.2 0.410
20
30
40
counts
8 T
6 T
4 T
3 T
2 T
Qh, 0, 1.6
0 T
Qh, 0, 1.6
T=1.5K E=0.5 THz
Mag
net
icfield
Magnetic field Ł
FM paramagnons
Ca1.8Sr0.2RuO4: Magnetic fluctuations
= 2meV
S. Nakatsuji, et al.,PRL 2003.
x=0.2
-0.5 0 0.5
H
AFM
FM
Conclusions
Interplay betweencharge, orbital and magnetic
degrees of freedom in layered-ruthenates.
- pure Sr2RuO4 : unconventional superconductorstrong nesting-type fluctuationsbut also broad quasi-FM fluctuations
- metal-insulator transition in Ca2RuO4
driven through orbital rearrangement„continuous“ aspects
- metamagnetism in Ca2-xSrxRuO4
very flat bands close to the MI transition (heavy QP)orbital occupation importantcompetition of at least two magnetic instabilitiesfield-induced FM paramagnons
RuO