Interplay between spin, charge, lattice and orbital degrees of

freedom

Lecture notes Les Houches June 2006 lecture 3

George Sawatzky

Need multiband models to describe TM compounds

However numerous studies have shown that this can sometimes be reduced to an effective

single band Hubbard model at least for highTc’s BUT ONLY FOR LOW ENERGY

EXCITATIONS E<0.5eV

Macridin et al Phys. Rev. B 71, 134527 (2005)

Tpd(eg) = 2x Tpd(t2g)

Crystal and ligand field splittings

Often about 0.5 eVIn Oh symmetry

Angular integrals Are different for t23g and eg

Eg-O2p hoping is 2 times as large as T2g-O-2p hoping

Often about 1-2eVIn Oxides

High Spin – Low Spin transition very common inCo(3+)(d6), as in LaCoO3, not so common in Fe(2+)(d6)Because of the smaller hybridization with O(2p)

Mixed valent system could lead to strange effects Such as spin blockade for charge transport and high thermoelectric powers

What would happen if 2Jh <10Dq<3JhIf we remove one electron from d6 we would go fromS=0 in d6 to S=5/2 in d5. The “hole “ would carry a spinOf 5/2 as it moves in the d6 lattice.

If the charge transfer energy gets small we have to Modify the superexchange theory

Anderson 1961

New term

tij = t cos (Oij/2)

Oij = angle between neighbouring spins

Khomskii et al S S Comm.102,87, 1997

dxy

dxz

dyz

Pen et al PRL 78,1323

This orbital ordering yields a large internal Antiferromagnetic exchange and a weak external ferromagnetic exchange .

Orbital ordering removes frustration

YVO3 Pervoskite structureV(3+) 2 electrons in T2g Orbitals S=1.Note the tilted and Rotated octahedra

Tsvetkov et alPRB 69, 075110 (2004)

YVO3 PerovskiteV(d2 S=1) O not In inversion symmetryDM canting competingWith staggered magneticAnisotropy . See Aharoni’s lectures

After applying a high fieldJust above above transOn the downward tragectory

Without the high fieldApplied in the downwardtrajectroy

All V have one electron in a dxy orbital

O between the V ions are not in inversion centerTilted Octahedra D.SxS interactions compete With local staggered anisotropy

Three ways to get ferromagnets with High Tc without using 3d’s or 4f’s

1. Use electronic reconstruction of polar surfaces

2. Use defects and topology and symmetry

3. Use doping and large Hund’s rule coupling of O,N

Electronic reconstruction at surfaces and interfaces

By moving 1 electr. Per O From 2- side to 2+ side the Potential becomes flat.

LSDA Band Structure of CaO (111) Slab

-10

-5

0

5

10

Γ K M Γ A L H A

Ener

gy (e

V)

-10

-5

0

5

10

Γ K M Γ A L H A

Spin Up Spin Down

12

-4

-2

0

2

4

6

8

10

L X W L K

Ener

gy (e

V)Note:

Bulk material(no surface)

is an insulator

But surface is metallic!

Ca 4s

O 2p

Example of two particles in U= limit

t t

t

1 1

2 2 2 1

00

0

tttttt

H

),(),( 2121 ss mmxx

212

1

),( 21 ss mmTriplet

Singlet

“+” for singlet; “-” for triplet

Energy level diagram for holes (t>0)

-2t-t

t2t

Triplet

Singlet

Balla et al

One electron spectral function in a magnetically and orbitally Ordered system

Hopping :

abplane c axis

Interactions :

( Jab> 0 and Jc>0 )c

b

a

Resonant soft x ray scattering

Doped holes in cuprate

C. T. Chen et al. PRL 66, 104 (1991)

Cu2+ d9 S=1/2

O 2- full shell

La2-xSrxCuO4 Sr ---doped holes

Nature 431, 1078 (2004)

Chains with model of spin singlets

CDW with Q=0.2 is 5 cl modulation along the ladder

 

Rushdy et al PRL in press

Models mentioned in White , Affleck and Scalapino PRB 65 165122For ¼ modulation

RXS shows that ¼ does not exist but 1/3 and 1/5 do and more recent Results show the model with paired holes along the rungs is most likely Correct. This could be of great importance for the understanding of High Tc’s

NOTE WE DON’T SEE A 4 FOLD MODULATION

Pr1-xCaxMnO3

Pr0.6Ca0.4MnO3 CE type charge, orbital and magnetic order

Goodenough (1955)

• Charge ordering below TCO ~ 240K

• Cooperative orbital ordering + oxygen distortion at TOO = TCO

• Magnetic ordering below TN ~ 170K

K.J. Thomas et al NSLS/BNL

Phys. Rev. Lett. 92, 237204 (2004)