exchange interaction model hamiltonian for strongly
TRANSCRIPT
Paramagnetism Ferromagnetism Antiferromagnetism
Exchange interaction
Introduction to MagnetismHamiltonian in Magnetic Substances
H = -2JΣij Si・Sj
J < 0 (in case of wave functions mixed )
:Antiferromagnetism
J > 0 (in case of wave functions being orthgonalized )
:Ferromagnetism
Model Hamiltonian for Strongly Correlated Electrons Systems
- 2JΣij Si ・Sj
Coulomb repulsion
Transferred integral
(6-2) In order to improve the HL wave function;
We incorporate the following states, using φa (1) φa (2) and φb(1) φb (2)
Then, the improved trial wave function is expressed by Φ =c1ΦHL +c2Φ’ .
Show how to get the following relation and solve an eigen energy for this state
If U0ーU1 > >| t | is valid for Mott insulator, show that the eigenenergy is given as the follow;
Charge
OrbitalSpin
Electric fieldPhoto Irradiation
External StrainMagnetic Field
Pressure Induced Metal-Insulator Transition
Magnetic fieldinduced structural phase transition
Magnetic Field Induced Metal-Insulator Transition
Giant Change in Resistance by Magnetic Field
Strongly Correlated Materials
Magnetic field Electric field Strength of photon
Photo irradiationElectric FieldMagnetic Field
ConductivityMagnetization
MagnetizationConductivity
Giant Response to magnetic and electric fields due to the multi-criticality
3d遷移磁性元素
4f希土類磁性元素
Mn2+ Fe2+ Co Ni2+ Cu2+
Ti3+ V3+ Cr3+ Mn3+ Fe3+ Co3+ Ni3+ Cu3+
V4+ Cr4+ Mn4+ Fe4+
eg
t2g
S= 1/2 S=1 S=2S=3/2 S=5/2 S=1
d1 d4
d5 d6 d8 d7
d2 d3
d9
S=0
S=1 S=2
S=1/2S=1/2
Hunds’ rule and Crystal Electric Field Effect
Electron Configuration in Transition Metal Ions
Perovskite
Transition metal Elements
Oxygen
Rare earthions
Layered Perovskite
eg orbitals
t2g
zx yz xy
x2-y23z2-r2
y
xz
3d orbitals3d orbitals
orbitals
eg
t2g
x2-y2 3z2-r2
Mn4+ Mn3+
(d3, S=3/2) (d4, S=2)
3d orbital10Dq JH>0
Mn
O
x
y
z
MnO6 Octahedron
xy yz zx
Hund’s Coupling JH > CEF splitting 10Dq
Electronic Structure of Manganese oxides When J is negative due to the overlap of wave functions among nearest neighbor atomic sites, Spins are anti-parallel. On the other hand, if the wave function is orthogonalized, J is always positive and hence ferromagnetism is realized
Proof:
1 / r is expanded in a Fourier series as
J = -2St + J’ = J’ (because of S=0)
強いスピン-電荷結合 伝導電子
フント結合
局在スピン
Strong coupling of spin and charge degrees of freedom
Hund’s coupling
Conduction electrons
Localized spins
AntiferromagneticInsulator
Ferromagnetic Metal
Resistivity
Temperature (K)
When carriers doped, metallic state is stabilized
(Nd,Sm)0.5Sr0.5MnO3CMR effectCMR effect
ColossalMagnetoResistanceMagnetization
Resistance
Magnetic field
Competition between Ferromagnetic Metallic and charge ordered insulating phases
eg orbits
t2g orbitslocal spins Magnetic field
Conductivity controlled by Magnetic filed → local spins → mobile electrons
Magnetic Field Control of Magnetic and Transport Properties in Pr1-xCaxMnO3
Conduction electron
Hund’s rule
Magnetic field (T)
Resistance Photo-induced insulator –metal transition
0.1 0.5 1
0
1
ΔR
/R
0
0.25
0.5
Ref
lect
ivity
0.75
Photon Energy [eV]
Ni
BrNC
b
Ni 3d(LH)
Ni 3d(UH)
Br 4p
CT
U
0.1ps
1ps
2ps
10ps
~5 psInsulatorMetal
Photo-excitation
One dimensional Mott Insulator(Halogen Ni chrage transfer salts)
Drude contribution in reflectivity Observed in metal
Increase of reflectivity due to photo induced carriers
Ultra-fast Switching Phenomenon in Strongly Correlated One Dimensional Mott Insulators - Photo Induced Carrier Doping -
Photo-excitation
Perovskite
Transition metal Elements
Oxygen
Rare earthions
Layered Perovskite
eg
t2g
x2-y2 3z2-r2
Mn4+ Mn3+
(d3, S=3/2) (d4, S=2)
3d orbital10Dq JH>0
Mn
O
x
y
z
MnO6 Octahedron
xy yz zx
Hund’s Coupling JH > CEF splitting 10Dq
Electronic Structure of Manganese oxides
Competition between Ferromagnetic Metallic and charge ordered insulating phases
eg orbits
t2g orbitslocal spins Magnetic field
Conductivity controlled by Magnetic filed → local spins → mobile electrons
Magnetic Field Control of Magnetic and Transport Properties in Pr1-xCaxMnO3
Conduction electron
Hund’s rule
(Nd,Sm)0.5Sr0.5MnO3CMR effectCMR effect
ColossalMagnetoResistanceMagnetization
Resistance
Magnetic field
TMR = =ρAF-ρF
ρF
2PAPB1-PAPB
(PA: spin polarization ofmetal A)
Parallel spin
・If PA=PB=1, then TMR → ∞
FM metal A FM metal B
barrier
Spin polarization and Tunnel Magneto-Resistance(TMR)
barrier
Antiparallel spin
FM metal A
FM metal B
Junction resisrance
Magnetic field
Magnetic field
Magnetization
4.5eV
0.6eV
2.5eV
1.5eV
Ni La1-xSrxMnO3
PNi = 11% PLSMO = 100%
Half metallic state
Density of states
Energy
Spin Polarization
EF
EF
Strong coupling of spin and charge degrees of freedom
Magnetic field (Gauss)-200 -100 0 100 200
250K
275K
300K
310K
320K
330K
1%
TMR
RH
RL
トン
ネル
磁気
抵抗
[(R H
–R
L)/R
H×
100]
(%)
Tunnel Magneto-Resistance(TMR) at room temparatueTunnel Magneto-Resistance(TMR) at room temparatue
LSMO/STO/LSMO Junction
charge
orbitalspin
Sz= +1/2 , -1/2
Q= -e
Tz=+1/2, -1/2
Rich electron phases due to three degrees of freedom instrongly correlated matters
eg orbital degeneracy
Electric-field control of ferromagnetism
Read the reference;
H. Ohno, D. Chiba, F. Matsukura, T. Omiya, E. Abe, T. Dietl, Y. Ohno,
and K. Ohtani, “Electric-field control of ferromagnetism”,
Nature 408, 944 (2000).
1. Describe the origin of ferromagnetism in Mn-doped semiconductors.
Magnetism on Report (deal line: 11/11)
2. Consider why the decrease (increase) of the hole concentration by the application of electric field results in a reduction (an increase) of hole-mediated ferromagnetic exchange interaction among localized Mn spins.