Spinelektronik
Chapter 8
Colossal Magnetoresistance & Metal-Insulator Transition
http://www.fz-juelich.de/iff/staff/Schneider_C_M/Lectures/Vorlesungen_WS_2005.html
Winter 05/06 Spinelektronik
Magnetoresistance in complex systems
•
NaCl structure•
solid solution•
large effect of magnetic order on charge mobility2
EuSe: ferromag. insulator continuous solid solution GdSe: antiferromagnetic metal
Eu
0.99Gd
0.01Se
•
Increasing magnetic field reduces the resistivity•
induced magnetic order?•
effect of magnetic order on electrical transport?magn.
field H
Perovskites
•
doped perovskite•
ferromagnetic behavior•
large MR at room temperature•
structural changes upon annealingWinter 05/06 Spinelektronik
Parent compound LaMnO
3•
parent compound LaMnO3•
orthorhombic structure (slightly distorted cubic)•
Mn3+ in octahedral coordination with O2-•
transition metal oxide•
insulator•
antiferromagnetic5
Mn
3+O
2-Mn
3+Winter 05/06 Spinelektronik
Cubic perovskites
•
type CaTiO36
TM ions: crystal field splitting
•
splitting of degenerate d-levels of the ion due to the cubic symmetry of the electrostatic potential of the crystal lattice (lower than spherical symmetry)10Dq=Δ
CFcrystal field splitting of isolated ion
d
e
g(d
x2–y2, d
z2)
t
2g(d
xy, d
xz, d
yz)
3
/
5Δ
CF2
/
5Δ
CFTM ions: wave functions
•
eg wave functions oriented towards O ions•
t2g wave functions in betweene
g(d
x2–y2, d
z2)
t
2g(d
xy, d
xz, d
yz)
Winter 05/06 Spinelektronik
TM ions: p-d hybridization
•
eg wave functions have strong overlap with O- p states ➠ strong hybridization and formation of σ-orbitals•
t2g wave functions have less overlap ➠ weak hybridization and formation of π-orbitals•
filling of the orbitals according to Hund’s rules•
Mn3+ high spin state9
Δ
CFhybridization between TM d- and O p- states
d
e
gt
2gp Δ
Winter 05/06 Spinelektronik
Hybridization
10
e
g– p hybridization
t
2g– p hybridization
TM ions: Jahn-Teller distortion
•
Jahn-Teller effect leads to a ordering and orientation of the wave functions•
this symmetry reduction by means of the orientation leads to a splitting of the degenerate levels and a reduced total energy•
ground state is characterized by orbital orderingif the system can reduce its energy by lifting the degeneracy of levels, it will develop a symmetry-breaking mechanism, for example, a lattice distortion
Exchange interaction in TMO
•
electrons cannot move freely (itinerant ➠ Stoner model), but hop between lattice sites•
Exchange cannot take place directly between d-orbitals•
Two-step process via Oxygen p-states•
superexchange modelWinter 05/06 Spinelektronik
Superexchange
•
Exchange through virtual hopping of electrons between the lattice sites•
governed by Coulomb repulsion and Pauli principle•
integer number of d-states – no mixed valency13 Winter 05/06 Spinelektronik
Goodenough-Kanamori-Anderson rules 2
•
90°-exchange involves different d and p orbitals•
ferromagnetic and weak14
Goodenough-Kanamori-Anderson rules 3
•
Virtual hopping between occupied and empty TM orbitals•
Governed by Hund’s rules•
Parallel alignment in intermediate state reduces energy by JHExchange interactions
•
Layered (topological) antiferromagnetism on the Mn sublattice•
Simultaneous spin and orbital orderingWinter 05/06 Spinelektronik
Manganites (doped LMO)
17
•
substitution of La by Ba•
doping with electrons•
transition from insulator to metal, from AFM to FMAFM 300 FMM 200 100
transitiontemperatureT,T CN 0
Barium content x
0.2 0.4
La1-xBaxMnO3
Winter 05/06 Spinelektronik
Mixed valency
•
LaMnO3 ➠ La1-xSrxMnO3•
6s25d1 ➠ 5s2•
hole doping•
Mn3+ ➠ {Mn3+, Mn4+}18
