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

qq

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

qq

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