1. Interplay between spin, charge, lattice and orbital degrees of freedom Lecture notes Les Houches June 2006 lecture 3 George Sawatzky

2. 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)

5. Tpd(eg) = 2x Tpd(t2g)

6. Crystal and ligand field splittings Often about 0.5 eV In Oh symmetry Angular integrals Are different for t23g and eg

7. Eg-O2p hoping is 2 times as large as T2g-O-2p hoping Often about 1-2eV In Oxides

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

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

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

14. If the charge transfer energy gets small we have to Modify the superexchange theory Anderson 1961 New term

17. tij = t cos (Oij/2) Oij = angle between neighbouring spins Khomskii et al S S Comm.102,87, 1997

25. 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

28. YVO3 Pervoskite structure V(3+) 2 electrons in T2g Orbitals S=1. Note the tilted and Rotated octahedra Tsvetkov et al PRB 69, 075110 (2004)

29. YVO3 Perovskite V(d2 S=1) O not In inversion symmetry DM canting competing With staggered magnetic Anisotropy. See Aharoni’s lectures

30. After applying a high field Just above above trans On the downward tragectory Without the high field Applied in the downward trajectroy

31. All V have one electron in a dxy orbital O between the V ions are not in inversion center Tilted Octahedra D.SxS interactions compete With local staggered anisotropy

32. 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

33. Electronic reconstruction at surfaces and interfaces By moving 1 electr. Per O From 2- side to 2+ side the Potential becomes flat.

35. Example of two particles in U=  limit t t tt 11 2221 Triplet Singlet “+” for singlet; “-” for triplet Energy level diagram for holes (t>0) -2t -t t 2t Triplet Singlet

36. Balla et al One electron spectral function in a magnetically and orbitally Ordered system

39. Resonant soft x ray scattering

41. 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

42. Nature 431, 1078 (2004) Chains with model of spin singlets

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

45. Rushdy et al PRL in press

46. Models mentioned in White, Affleck and Scalapino PRB 65 165122 For 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

47. Pr 1-x Ca x MnO 3 Pr 0.6 Ca 0.4 MnO 3 CE type charge, orbital and magnetic order Goodenough (1955) Charge ordering below T CO ~ 240K Cooperative orbital ordering + oxygen distortion at T OO = T CO Magnetic ordering below T N ~ 170K K.J. Thomas et al NSLS/BNL Phys. Rev. Lett. 92, 237204 (2004)