Low-temperature propertiesLow-temperature properties of the tof the t2g2g

1 1 Mott insulatorsMott insulators

Interatomic exchange-coupling constants Interatomic exchange-coupling constants by 2nd-order perturbation theory in by 2nd-order perturbation theory in tt

tt2g2g1 1 + + tt2g2g1 1 = = tt2g2g0 0 + + tt2g2g22

Orbital and Magnetic OrdersOrbital and Magnetic Orders

Superexchange: JAF ~ 4t2/U

tx=ty=99 meV

t z=10

5 m

eV

tx=ty=48 meV

t z=38

meV

3D AF3D AF FF

5.05.0 3.03.0 -0.7-0.7 -4.7-4.7JJsese

0 meV

0 meV

53 meV

80 meV

92 meV

207 meV

High-temperature orthorhombic phase

LaLaVVOO33 YYVVOO33

Mott transition and suppression of orbital fluctuations in Mott transition and suppression of orbital fluctuations in tt2g2g22 perovskites perovskites

LaVO3 YVO3

t2g2 770 K (orthorhombic PI phase)

Much stronger orbital fluctuations for the t2g2 La and Y vanadates than for the t2g

1 titanates because of 1) Hunds rule and 2) less AB(O) covalency

1 2 3

Empty crystal-field orbital, |3), in the monoclinic phase

Vanadate t2g2 conclusions

The missing piece in the SrThe missing piece in the Sr22RhORhO44 puzzle puzzle

SrSr22RhORhO44 is a K2NiF4-structured 4d (t2g)5 paramagnetic metal

Transition-metal oxides have interesting properties because they have many lattice and electronic (orbital, charge, and spin) degrees of freedom, coupled by effective interactions (electron-phonon, hopping t, Coulomb repulsion U, and Hunds-rule coupling J). When some of the interactions are of similar magnitude, competing phases may exist in the region of controllable compositions, fields, and temperatures.

The interactions tend to remove low-energy degrees of freedom, e.g. to reduce the metallicity

Guo-Qiang Liu, V.N. Antonov, O. Jepsen, and OKA, PRL 101, 026408 (2008)

Ca or Sr

o

RuRu 4d (t2g)4

(Ca1-xSrx)RuO4:

The relatively small size and strong covalency of Ca cause the RuO6 to rotate and tilt. For x increasing from 0 to 1 these distortions go away and the properties go from insulating to metallic and from magnetic (AF/F metamagn) to paramagnetic at low T. Sr2RuO4 is a 2D Fermi liquid whose Fermi surface agrees well with LDA and has a mass enhancement of 3. It becomes superconducting below 1K.

K2NiF4

From Haverkort et al. PRL 026406 (2008)

Ruddlesden-Popper (Ca,Sr)n+1RunO3n+1

where n=1, 2, 3,

Alternating rotation of octahedra and cell doubling in xy-plane gaps the broad, overlapping xyxy and xx22-y-y22 bands for a filling of 5 t2g electrons.

From Haverkort et al. PRL 026406 (08)

(t2g)4 (t2g)5

ARPESARPES

LDA

But still unusually bad agreement between

and

2-parameter fit2-parameter fit + + ζζeff eff / / εεFF

+ + εεFF

ζζeffeff

ζζeffeff = 2.15 = 2.15 ζζ why?

Since Sr2RhO4 is paramagnetic at low temperature,

HF mean field approximation

We had:

where the polarization, p, should be determined selfconsistently.

, leading to:

For each Bloch state,

so the polarization function is:

2-parameter fit2-parameter fit + + ζζeff eff / / εεFF

ζeff = 2.2 ζ, why?+ + εεFF

ζζeffeff

The missing piece:The missing piece: