1. Spin-Orbital-Charge Coupled Dynamics in t2g-electron Systems
Yoshi Tokura
Dept of Appl Phys, Univ Tokyo
ERATO Multiferroics Project, JST
and
Cross-Correlation Materials Research Group (CMRG), RIKEN
Orbitally-active t2g2 systems with Mott criticality:
Orbital order and dynamics in (hole-doped) perovskite RVO3
Diffuse charge dynamics on frustrated double-exchange system R2Mo2O7
Collaborators
Univ. Tokyo
S.Iguchi, J. Fujioka, T. Yasue, K. Sano, S. Kumakura
N. Hanasaki Okayama Univ), S. Univ)
Univ. Budapest
RIKEN- CMRG
AIST-CERC
I. Kezsmarki, S. Bordacs
Y. Taguchi, C. Terakura
N. Takeshita

2. Interplay of charge, spin and orbital degree of freedomzx xy yz
3z2-r2
x2-y2
3d orbital
Orbital
Superconductivity
Colossal magnetoresistance (CMR)
Charge and orbital ordering
Non-Fermi liquid
In the strongly correlated electron system, the strong electron-electron interaction often induces the localization of electron to specific site. In such systems, spin, charge and orbital degree of freedom play important role for drastic change of electronic structure such as SC, MIT, CMR and so on.
One prototypical example is CMR. In this case, the spin degree of freedom is controled by external magnetic field and drastic change of the charge dynamics is induced. However, recent studies reveal the importance of the orbital degree of freedom
Role of orbital degree of freedom on versatile phase

3. t2g oribtal eg orbital (a) LaVO3 (b) YVO3 (d) BiMnO3 (c) LaMnO3
spin C-type
orbital G-type
spin G-type
orbital C-type
eg orbital

4. Electronic phase in CMR manganites
eg orbital system
Too>>Tso
Strong Jahn-Teller interaction
Charge dynamics coupled with
lattice degree of freedom
t2g orbital system
Too~Tso
Jahn-Teller interaction
orbital exchange interaction
This is the electronic phase diagram in CMR manganites.
The holizontal zxis is the hole concentration and vertical one is the bandwidth.
Variety of the electronic phases show up with the control of the band-fillng that is hole doping.
One prominent feature in CMR manganites is strong Jahn-Teller interaction, that is, the orbital and lattice interaction.
spin-orbit interaction
Comparable
Y. Tokura, Rep. Prog. Phys. 69, (2006) 797
spin-orbital coupled phenomena

5. Electronic structure in perovskite LaVO3
Perovskite structure
V3+ (3d 2)
LaVO3 V O V O La
dxy
dzx
dyz eg eg
One prototypical example for t2g orbital system is LaVo3.
This is the schematic view of the orthorhombic perovskite structure.
The vanadium ion has two valence electrons and they occupy the triply degenerate t2g level in the cubic symmetry crystal field.
Actually, the orthorhombic distortion as shown here lifts the degeneracy of t2g levels and one electron occupies higher lying dyz, dzx levels and another one does lower lying dxy level.
In the low T region dyz and dzx orbital orders.
In this system, since the energy scale of Jahn-Teller interaction is comparable to that of orbital exchange interaction and spin-orbit interaction, the versatile spin and orbital ordering can be observed.
t2g
dxy1dyz1/ dxy1dzx1
Orbital ordering in dyz and dzx orbitals

6. Spin and orbital ordering in LaVO3
E || c
E ⊥ c
G-type OO
C-type SO
TOO=141K
TSO=143K T
Orbital
Spin
Quasi-one-dimensional (1D) electronic structure along c-axis originating from the C-type SO and G-type OO　
In this system, the C-type SO appear at 143K and G-type OO appear 141K.
Here in the G-type phase, orbitals stagger in all direction and C-type SO state, spins align ferromagnetically along c-axis and stagger in ab plane.
Reflecting the spin and orbital ordering, the ansisotropic electronic structure can be observed.
This is the temperature dependece optical conductivity spectra in LaVO3 for E parallel to c axis and E perpendicular to c axis.
The E || c spectra show a prominent peak structure corresponding to the Mott gap excitation around 2eV in the low-T region.
The spectral weight appears to increase rapidly around TSO and TOO.
By contrast, the E perp spectra show minimal T dependence.
According to theoretical calculation, these feature is explained by the quasi-1D orbital exchange interaction along c-axis.
Y. Motome et al., Phys. Rev.Lett, 90,146602(2003)
Quasi-1D orbital exchange interaction
S. Miyasaka et al, J. Phys. Soc Jpn, 71, 2086(2002)

7. The orbital excitation (two-orbiton)
1.96eV excitation c c k
pseudospinon
orbital -G
Another prominent feature is the one dimensional orbital excitation.
This is the schematic view of the exchange process of the orbital excitation called two orbiton.
Theoretically, this is described as a excitation of the pseudospinon.
The two-orbiton bands is observed in the Raman spectra for the polarization configuration (z,z) in C-type SO and G-type OO state.
Raman shift and peak width of two-orbiton band depend on the magnitude of the orbital exchange interaction and the Jahn-teller gap
One-dimensionality
Orbital exchange interaction and the Jahn-Teller
energy
S. Miyasaka, et al., Phys. Rev. Lett, 94, (2005)

8. Van Hove singularity of spinon band
H.Suzuura, H.Yasuhara, A.Furusaki, N.Nagaosa, and Y.Tokura , PRL(96).
c.f.　J.Lorenzana and R.Eder, PRB(97).
Spin-phonon coupling (Lorezana-Sawatzky)
Heisen. XY
accurate estimate of J
spinon interband trasnitions
(two-magnon band)
showing up as the sideband of phonon
J~0.26eV
optical phonon

9. Optical (Raman) probe for quantum orbital chains
S.Onoda-N.Nagaosa
ECJT/J=0.15
EDJT dynamical Jahn-Teller
ECJT classical Jahn-Teller
pseudo spion (orbital version of spinon)
gapping due to Jahn-Teller distortion
 /2 

10. Orbital excitations in NdVO3 as probed by Raman spectra

11. Filling-Control Metal-Insulator Transition
antiferromagnetic metal phase (AFM)
(no oribtal order)
decrease of carrier density
mass enhancement
cf. γ~ 40mJ/K2V-unit in V2-δO3
Miyasaka et al. PRL (2001).

12. Doping variation of the electronic structure in La1-xSrxVO3
C-type SO
G-type OO
Lightly doped region
Doped hole occupies dyz/dzx
orbital and forms a self-trapped
state accompanying the
modification in lattice, spin, and
orbital sector
Anisotropic hole dynamics,
reflecting the one-dimensionality
of the orbital exchange interaction
On the verge of insulator-
metal transition
doped holes nearly equivalently
occupy dxy, dyz and dzx orbital c

13. Electronic structure in the lightly doped systems
C-type SO
G-type OO
dyz, dzx c
The E||c spectra show a large temperature dependence as in the case of x=0.
To see the contributions from the Mott gap excitation and the mid-IR peak, the spectra were fitted with the Lorentz oscillator. Here, we showed the calculated effective number of electrons of each component.
The green line corresponds to the Mott gap excitation and the red and black ones correspond to the mid-IR peak for E para c and E perp c, respectively.
The N effective for the mid-IR peak in E || c spectra increases in the low T region. But that for E perpendicular to c spectra shows minimal T dependence.
Thus, It is expected that the doped holes predominantly occupy the dyz or dzx orbital and have large kinetic energy along c-axis, reflecting the 1D orbital exchange interaction.
Now, I would like to focus on the energy scale of the hole dynamics.
Large T dependence of the mid-IR peak in E || c spectra.
Minimal T dependence of the E⊥c spectra.
The doped holes predominantly occupy the dyz or dzx orbital
large kinetic energy along c-axis, reflecting one-dimensional orbital exchange interaction.

14. Spin-orbital phase diagram for RVO3( R=rare-earth ion )
YVO3
SO : Spin Ordering
OO : Orbital Ordering
G-type OO
1.15
1.2
1.25
1.3
1.35
100
200 r R
(Å) T SO , OO
(K)
G-type OO
C-type SO
G-type SO
C-type OO Nd Sm Gd Tb Dy Y
OO1
SO1
SO2 =
OO2 Er Yb Lu Ho Eu Pr La
(c) VO 3
C-type SO
G-type OO
G-type SO
C-type OO c a b
This is the spin-orbital phase diagram for RVO3.
For La and Ce, the G-type OO occurs below the C-type SO transition T. Here in C-type means that spins or orbital align ferromagnetically along c-axis and stagger in ab-plane. The G-type means that spins or orbitals stagger in all direction.
From Pr to Lu, the sequence of the magnetic and orbital transition is reversed.
In addition, from Dy to Lu another phase, that is, G-type SO and C-type OO phase appears in the low-T region.
Since the spin and orbital ordering modifies the charge transport property, anisotropic conductivity spectra can be observed
In the spin and orbital ordered phase.
Control of the orthorhombic lattice distortion by changing R ion
Variation of the spin and orbital ordered phase

15. Optical conductivity spectra for YVO3
TOO1=200K
TSO1=115K
TSO2, TOO2=77K
C-type SO
G-type SO
disorder
G-type OO
C-type OO
Orbital
Spin T
This is the spin-orbital phase diagram.
As mentioned previously, with lowering temperature, the G-type OO, C-type SO show up and finally,
The Gso, Coo phase appear around 77K.
These are the optical conductivity spectra at disordred phase, Cso, Goo phase, and Gso, Coo phase, respectively.
In the disordered phase, the Mott-gap excitation is nearly isotropic, indicating the nearly isotropic electronic structure.
In the Cso, Goo phase, anisotropic electronic structure reflecting the one-dimensional orbital exchange interaction is observed.
But, in the Gso, Coo phase at low temperatures, the spectra are again isotropic.
This isotropic feature at low temperature phase is consistent with the nearly isotropic orbital exchange interaction in magnitude.
Next, we show the doping variation of the electronic structure.
G-type SO, C-type OO
C-type SO, G-type OO
Spin-orbital disordering
Nearly isotropic orbital
exchange interaction
in magnitude
1D-orbital exchange
interaction
Nearly isotropic charge
dynamics

16. Spin-orbital phase diagram for RVO3( R=rare-earth ion )
SO : Spin Ordering
OO : Orbital Ordering
G-type OO
1.15
1.2
1.25
1.3
1.35
100
200 r R
(Å) T SO , OO
(K)
G-type OO
C-type SO
G-type SO
C-type OO Nd Sm Gd Tb Dy Y
OO1
SO1
SO2 =
OO2 Er Yb Lu Ho Eu Pr La
(c) VO 3
C-type SO
G-type OO
G-type SO
C-type OO c a b
This is the spin-orbital phase diagram for RVO3.
For La and Ce, the G-type OO occurs below the C-type SO transition T. Here in C-type means that spins or orbital align ferromagnetically along c-axis and stagger in ab-plane. The G-type means that spins or orbitals stagger in all direction.
From Pr to Lu, the sequence of the magnetic and orbital transition is reversed.
In addition, from Dy to Lu another phase, that is, G-type SO and C-type OO phase appears in the low-T region.
Since the spin and orbital ordering modifies the charge transport property, anisotropic conductivity spectra can be observed
In the spin and orbital ordered phase.
Control of the orthorhombic lattice distortion by changing R ion
Variation of the spin and orbital ordered phase

17. Reentrant orbital ordering transitions in DyMnO3
R=Dy x z y
Miyasaka et al. PRL(2007)

18. Magnetic field induced orbital-state switching in DyMnO3
Coincident with metamagetic trasnsition of Dy Ising moments
contribution from Gd f moments via the f-d exchange interaction
G-type OO
G-type OO C-type SO
C-type OO G-type SO
hysteresis region
H//a
H//b

19. Spin-orbital phase diagrams of hole-doped RVO3
C-type SO
G-type OO
G-type SO
C-type OO
Insulator-metal transition point dependent on W
paramagnetic G-type OO phase
Change of band-filling
Quenched disorder
G-type SO, C-type OO state is extremely fragile against doping W
Summary of this chapter is as follows.
The critical doping level for insulator-metal transition is scale to the one-electron bandwidth.
However, the PM. G-type OO phase disappears before the IMT and is fragile against not only the change of the band-filling but also the quenched disorder
In the lattice sector.
When we plot the critical doping level for the melting of OO, one notice that
Fujioka et al. PRB (2006).

20. Optical conductivity spectra in Y1-xCaxVO3
1D M-H gap
inner-gap exc.
x>0.02 :
Anisotropic Mott-gap excitation reflecting the quasi-1D orbital exchange interaction
Nearly isotropic hole dynamics
These are the optical conductivity spectra at 10K at various doping level.
At x=0.02, the ground state is Cso, Goo and spectra are anisotropic, reflecting the one-dimensional orbital exchange interaction.
With the increase of doping level, the anisotropic feature is gradually suppressed.
On the other hand, the mid-IR peak looks nearly isotropic and the intensity of it also seems to be small.
To compare these feature with that for LSVO which is nearly cubic system, we fitted the spectra with Lorentz oscillator and calculated the spectral weight of the MIR peak.

21. Pyrochlore-type structure : R2 Mo2 O7
Mo-sublattice, composed of corner-sharing teterahedra.
(111)-plane is Kagome lattice. R Mo
Double-excange int. + frsturation 4d
a1g
eg’ eg
t2g Oh
D3d
(111) Mo
O2-

22. Electronic band structure based on DFT
a1g
eg’ eg
D3d
I.V. Solovyev PRB (2003)
t2g manifold
(conduction electron)
a1g local spin
nearly half-metallic EF EF EF
up-spin
t2g- band

23. Metal-insulator phomena dependent on R-ion size

24. randomness vs. frustration in double-exchange systems
bandwidth
Perovskite Mn AF FM
Pyrochlore Mo
phase competition
(d)
Y. Tomioka　et al.
Randomness Spin glass
Spin frustration Spin glass
(on frustrated lattice)
(size mismatch of RE and AE ions)

25. Importance of electron correlation4d
a1g eg
t2g Oh
D3d
orbital dependent Mott transition
conduction/localized electron
local spin
Mo-Mo distance
P (hydrostatic pressure)
a1g bandwidth
(JAF)
eg’ bandwidth (W/U)
Mo-O-Mo bond angle
rA (chemical pressure)

26. Y2Mo2O7 Sm2Mo2O7 EF Mott-Hubbard type (as opposed to CT type)
Optical conductivity spectra for Mott gap and CT exitation
・large enegy scale (=1 eV) over which electronic structure is reconstructed.
O 2p
Mo 4d EF
Sm2Mo2O7
Y2Mo2O7
Eg～0.1 eV
O2p →Mo4d UH
Mott-Hubbard type (as opposed to CT type)
Taguchi-YT PRB (2002)

27. Mott gap variation in R2Mo2O7
Drude
Kezsmarki et al.PRL (2004)

28. Drude component near the Mott criticality
Kezsmarki et al.PRL (2004)

29. Optical phase diagram in R2Mo2O7
Drude weight
charge gap
incoherent metal
low-energy
spectral weight around ωM
Kezsmarki et al.PRL (2004)

30. scrutinizing phase boundary・・・
mass enhancement (~×3） in FM
state (orbital fluctuation?)
Curie-Weiss temperature
ferromagnetic(eg’mediated) vs.
antiferromagnetic(a1g mediated)
ferromagnetic fluctuation
spin flipping time of spin glass
from atomic to cluster-like
Hanasaki et al. PRL (2007).

31. Effect of Pressures 4d t2g eg a1g Oh D3d
orbital dependent Mott transition
conduction/localized electron
local spin
rA (chemical pressure)
P (hydrostatic pressure)
eg’ bandwidth (W/U)
a1g bandwidth
(JAF)

32. Pressure effects Nd2Mo2O7 FM SGI metallic & ferromagnetic
-> metallic & spin glassy
-> metallic & paramagnetic
SGI FM
3kHz
Ferromag.
Spin glass
anomalously T-independent
bad conductivity
Paramag.

33. Pressure effects Sm2Mo2O7 FM SGI metallic & ferromagnetic
-> metallic & spin glass
-> metallic & paramagnetic
SGI FM
Sm2Mo2O7
Ferromag.
Spin glass
anomalously T-independent
bad conductivity
Paramag.

34. Spin　glass to paramagnetic metal transition in pressurized Gd2Mo2O7FM
SGI
anomalously T-independent
bad conductivity in paramagnetic metal state

35. Phase diagram multicritical feature (b)
incoherent (non Fermi Liquid?) metal
conduction electrons interacting with
glassy or flctuating local spins
on the frustrated lattice
(b)

36. DE model on frustrated lattice?
a1g eg
t2g Oh
D3d
(d)
W,U
JAF
<<JH
paramag.
metal
(non-FL?)
spin-glass
insulator
JAF
ambient pressure
ferromag. metal
W/U
large finite scattering rate in T=0 limit

37. DE model on frustrated lattice?
a1g eg
t2g Oh
D3d
(d)
W,U
JAF
<<JH
paramag.
metal
(non-FL?)
spin-glass
insulator
JAF
ambient pressure
ferromag. metal
W/U

38. minute spin anisotropy leads to non-Fermi-liquid behavior
α=0,0.3,0.5,0.7,1

39. Rich electric phases in t2g –electron frustrated systems
all close to the metal-insulator transition (Mott, charge/orbital order)
LiTi2O4
supercond. (Tc=14K)
d0.5
pyrochlore lattice
ferromag. Mott ins.
(orbital order)
Lu2V2O7 d1
d1.5
LiV2O4
heavy electron
Mott transition
spin chirality
(anomalous Hall) d2
Nd2Mo2O7
Y2Mo2O7
entanglement in spin & orbital sectors
Kugel-Khomskii type and spin-orbit interactions
scalar spin chirality Si・(Sj×Sk),vector spin chilarity Si×Sj, spin current, orbital current?