Exchange interaction Model Hamiltonian for Strongly ...

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Paramagnetism Ferromagnetism Antiferromagnetism Exchange interaction Introduction to Magnetism Hamiltonian in Magnetic Substances H =-2JΣ ij S i S j 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 - 2JΣ ij S i S Coulomb repulsion Transferred integral (6-2) In order to improve the HL wave function; We incorporate the following states, using φ a (1) φ a (2) and φ (1) φ (2) Then, the improved trial wave function is expressed by Φ =c 1 Φ HL +c 2 Φ. Show how to get the following relation and solve an eigen energy for this state If U 0 U 1 > >| t | is valid for Mott insulator, show that the eigen energy is given as the follow;

Transcript of Exchange interaction Model Hamiltonian for Strongly ...

Page 1: Exchange interaction Model Hamiltonian for Strongly ...

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;

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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

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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)

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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

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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

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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

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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

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

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Electric-field control of ferromagnetism

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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.