Double-exchange Interaction and Orbital Ordering
-
Upload
dhanapal-pal -
Category
Documents
-
view
228 -
download
1
description
Transcript of Double-exchange Interaction and Orbital Ordering
-
Some interesting physics in transition metal oxides: charge ordering, orbital ordering and spin-charge separationC. D. HuDepartment of physics National Taiwan University1. Introduction to double-exchange interaction (DE) 2. Introduction to charge ordering 3. Introduction to orbital ordering and orbital dynamics4. Interplay between double-exchange interaction, charge ordering, and orbital ordering
-
Double-exchange interaction
La1-xDxMnO3 D: divalent elements 3-dLan(1-x)Sr1+nxMnnO3n+1 n = # of layers. 2-d
-
Phase diagram
OOI
-
CMR: Temperature DependenceThe electrical resistance depends strongly on applied magnetic field. As the temperature is increased through the ferromagnetic Curie temperature Tc, the MR ration rises sharply.
-
Manganites Structure
LaMnO3 La+3 Mn+3 O-23
Mn+3 3d4 xy, yz, zx orbitals form t2g band, localized spin 3/2 x2-y2, 3z2-r2 form eg band, mobile spin 1/2 S=3/2+1/2 -------doping-----
La1-xCaxMnO3 La+3 Ca+2 Mn+4 O+23Mn+3 3d4 xy, yz, zx orbitals form t2g band, localized spin 3/2 S=3/2.
-
atomCrystalfield eg t2gJahn-Tellerdistortionx2-y23z2-r2xyxz, yz MnYT
-
Zener, Anderson, Hasegawa: Double-Exchange interaction
-
Mean field picture
-
Recent Development (PRB 64,054406(2001))
From the point of view of the total spin on a site.|S=3/2,m> and |1/2,+1/2> |S=2,m+1/2>|S=3/2,m> and |1/2,-1/2> |S=2,m-1/2>
-
Slave fermionSchwinger bosonsFinallycombine or with the localized spin.
-
Similar to one-magnon process.
-
Saito, et. al., PRB 62,1039 (2000).
Experimental results II: ARPES shape of Fermi edge (1) Different from that of Gold (metal).(2) Temperature sensitive
-
f
ffffffff
-
Charge orderingMany compoundscuperatesmanganitesmagnetites
-
Nd doped La2-xSrxCuO4 (Niemoller et. al.)ac-plane, Stripe in b-directuion
-
Charge-ordered stripes seen in La0.33Ca0.67MnO3 by Uehara, Mori, Chen and Cheong, Nature399, 560 (1999).
-
DV2O4 D: divalent elementsNew J. Phys. 7, 53. RadaelliPRL 93 157206. Tchernyshyov
-
cubic to monoclinicMiles, et. al.Rev. Mod. Phys. 29, 279 Orbital ordering Fe3O4 Verway transition
-
Fe3O4 Verway transition O O-2 O A-type: 1/3 Fe+2 O B-type: 1/3 Fe+2 O B-type: 1/3 Fe+3
-
Orbital ordering
Manganite, Spinel (AB2X4, MgTi2O4, FeSc2S4), R1-xAxTiO3, TiOX (X=Cl,BR), V2O3, LiNiO2, NaTiO2, Ca3Ru2O7, KCuF3, Fe3O4,
-
Fe3O4PRL 93, 156403. Jen, Guo, Huang PRB 66, 214422. Wright, Attfield, Radaelli
-
z-directiontzx, y-directiontx(y)(PR. 93, 1498. Slater, Koster)simple cubic latticeInterplay between DE and OO
-
La0.5Ca0.5MnO3
La0.5Sr1.5MnO4PR 100, 545. Wollen, Koehler PR 100, 564. Goodenough: Mn4+, : spin, lobes: orbitals of Mn3+
-
Summary
1. A lot of interesting phenomena.2. Orbital dynamics is simple.3. With the new form of DE, the system seems to be managable.
-
PRL. 88 167204Kim et. al.
-
PRL. 81, 1517x=0.3
Feathures:Drude peak and broad peak
-
polaron?small polaronlarge polaron
-
orbital?PRB. 58, 11841Kilian and KhaliulinJ. Phys. Soc. Jpn. Shiba et. al.
-
Probing the orbital ordering
Resonant x-ray scattering (RXS) :An Incident photon excites an electron to a higher level. The Electron emits a photon and falls to a lower state.
-
La0.5Sr1.5MnO4 1s4p (PRL 80, 1932. Murakami et. al.)
1. The energy of 4p state is affected by the electrons at 3d state.2. The energies of 4p state of Mn3+ and Mn4+ are different.3. Intensity varies with the direction of polarization due to the Aj coupling.4. Incident photon: polarization. z-axis: b direction. orbitals: y2-z2 and x2-z2.