Evolution of Spin-Orbital-Lattice Coupling in RVO3 Perovskites

1
Evolution of Spin-Orbital-Lattice Coupling in
RVO3 Perovskites

• Peter Horsch (MPI-FKF Stuttgart)
• Lou-Fe Feiner (UtrechtEindhoven)
• Giniyat Khaliullin (Stuttgart)
• Andrzej M. Oles (Cracow)

Entanglement in Spin Orbital Systems Cracow,
Poland, June 18-22, 2008
2
Outline

• Introduction
• Spin and orbital model for cubic vanadates
• High anisotropy of magnetic and optical
  properties
• Orbital-Peierls dimerization in YVO3
• Phase diagram of RVO3 Interplay of
  superexchange orbital-lattice I.

3
Manganites Vanadates eg vs. t2g systems
robust vs. soft orbital order
Manganites

• Eg-orbitals point to intermediate O-ions leading
  to strong Jahn-Teller orbital lattice coupling.

LaMnO3

• Significant hole-doping is required to destroy
  orbital order.
• In t2g systems soft orbital order ist expected
  in the undoped Mott insulator.

4
Cubic vanadates RVO3 t2g-system
Expectation Jahn-Teller couplings crystal
fields much smaller than in manganites Hence Orbit
al fluctuations not completely quenched
5
Temperature-induced magnetization reversal in
YVO3 crystals

• - C-type Antiferromagnet below
• TN 116 K
• - G-type below structural transition
• Ts 77 K
• - Magnetization reversal near 100 K
• upon heating (cooling) in a weak magnetic
  field !
• - Magnetization due to canting
• - Memory effect when switching on and off a
  strong magnetic field !

Y. Ren et al., Nature 396, 441 (1998), Y. Ren et
al. PRB 62, 6577 (00)
6
Phase diagram of cubic vanadates RVO3
S. Miyasaka et al. (2003), T. Yasue et al. (2008)
Control GdFeO3 distortion
Control Jahn-Teller distortion
C-type SO G-type OO
G-type SO C-type OO
7
Superexchange in cubic Vanadates Interplay of
spins orbitalsKugel-Khomskii type spin-orbital
model

• Transitions across Hubbard gap determine
  magnetism.
• Two t2g electrons in ground state V3
• 1 electron in xy, 2nd electron in xz or yz
• Spin 1 due to Hund interaction JH
• Only electrons in xz and yz orbitals can hop
  along c-direction. (active orbitals xz yz)
• Exchange of a (xy,yz) into (yz,xy) pair leads to
  strong orbital fluctuation along c-axis.

C-Spin (G-Orbital) favored by superexchange !!
G.Khaliullin, P.H., A.M.Oles, PRL 86, 3879 (2001).
Occupied xy-orbital not shown!
8
G-C phase transition in YVO3
Orbital lattice coupling JT GdFeO3 distortion

• Superexchange favors C-phase
• Vc favors low T G-phase !

• 1st order transition entropy controlled
• Smaller excitation energy in high-T C-phase

Spin orbital waves LSWT
G-phase (Low T)

• Free energy Vc1.3 J, Va0.65 J, hJH/U

C-phase
G. Khaliullin et al., PRL 86, 3879 (01)
A.M. Oles et al., PRB 75, 184434 (07)
9
Magnons Evidence for Orbital Peierls State in
YVO3
Neutron scattering C. Ulrich et al., PRL 91,
257202 (2003)

• Low-T phase G-type antiferromagnetism
• Jc5.7 meV, Jab5.7 meV
• C-Phase Splitting of magnon in acustic and optic
  branch
• Orbital Peierls dimerization!
• No evidence for significant dimerization of the
  lattice !
• Yet symmetry group (Raman) consistent with
  dimerization (Tsvetkov et al 2004)
• Strong ferro-coupling along c!
• Jab2.6 meV, Jc1-2.2 meV, Jc2-4 meV

10
Two Ground States
Shen, Xie, Zhang, PRL 88, 027201 (2002) Oles,
P.H., Khaliullin, Acta Phys. Pol. B34, 857 (02)
Khaliullin, P.H., Oles, PRL 86, 3879 (2001).
11
Orbital-Peierls Dimerization in C-Phase at finite
temperature

• Nearest neighbor spin- and orbital-correlation
  functions are dimerized at finite temperature in
  the C-phase
• Dimerization of FM chain only possible at finite
  T by simultaneous formation of orbital singlet
  pairs
• Magnetic structure factor S(q,w)
• Magnons at qp/2 (along c) are split as result of
  the orbital dimerization.
• High-energy structure due to orbital excitations.

P.H., G. Khaliullin, A.M. Oles, PRL 91, 257203
(2003) TMRG J. Sirker G. Khaliullin, PRB
67, 100408 (2003)
12
Effective spin model
Coupling constants determined by orbital
correlations
Magnons in C-Phase of YVO3 (T85 K) Linear
spin-wave theory.
Exp. Ulrich et al. (2007)
A.M.Oles et al PRB 75, 184434 (07)
13
IntermezzoWhat can be learned from optics about
magnetism?
14
Optical spectra of LaVO3
High anisotropy! Ec strong T-dependence
Schematicd-d Multiplet Transitions
U2.1 eV vs. 3.8 eV
Spectral weight of LaVO3
Miyasaka, Okimoto, Tokura (2002)
Controlled by magnetism !
15
Partial optical sum rules from superexchange
Optical spectral weights for different multiplet
transitions n1,2 3

Partial sum rules at finite JH follow from the
individual multiplet contributions

• Virtual transitions across the Hubbard gap
  determine magnetism.
• Same d-d transitions appear in optics.
• Strength of absorption into different multiplet
  states linked to the magnetic order.

Jt2/U, hJH/U, R1/(1-3h), r1/(12h)
16
Comparison of optical weights and superexchange
energy LaVO3

• Optical weights for c-polarization
• At low temperature all weight in high-spin
  transition n1
• Kinetic energy K(c) amplified by orbital
  fluctuations along c.
• Exp. Points Miyasaka et al. (2002)
• Strong variation at TN143 K
• J40 meV from kinetic energy in high-spin
  multiplet transition.
• Optical weights for a(b) polarization
• High anisotropy

G.Khaliullin, P.H., A.M. Oles, Phys. Rev. B 70,
195103 (2004)
17
Phase diagram of cubic vanadates dependence on
cation radius
18
Phase Diagram of Vanadates Spin-Orbital Model

• Orbital-lattice couplings
• Ez GdFeO3 distortion, Q(p,p,0)
• Vab Vc Jahn-Teller GdFeO3 distortion
• Ez Vc favor orbital-C structure competes
  with superexchange interaction.
• Hu orthorhombic distortion u(b-a)/a (NEW)

V-O-V angle
GdFeO3-distortion versus R-ion radius rR r0- a
sin2(2J) r01.5 A, a0.95 A assume jJ/2
PH, Oles, Khaliullin Feiner, PRL (08)
19
GdFeO3 distortion and crystal field
Crystal field splitting of xz and yz orbitals
from point charge model
20
Orthorhombic distortion u(b-a)/a
Sm
Y Sm La
Transverse field favors
M.H.Sage et al. PRL 96 ,036401 (06) PRB
76,195102 (07) G.R. Blake et al, PRL 87, 245501
(01) Y. Ren et al. PRB 67, 014107 (03) M.
Reehuis et al. PRB 73, 094440 (06) P. Bordet et
al. J.Sol.St.Chem. 106, 253 (93) P. Munoz et al.
J. Mater. Chem. 13, 1234 (03)
21
Order parameter vs. Temperature
SmVO3
Too
TN1

• La TOTN1 fixed by choice of Vc
• At TO no discontinuity of lttxgt for Sm
• Decrease of lttxgt below TN1

M.H.Sage et al. PRL 96 ,036401 (06)
22
Variation of coupling constants orthorhombicity
u(J)
Result confirms our assumption that g and K are
independent of J, i.e.,

1. Relation 0.03 geffu(J) yields g 30 J
2. Relation 15lttxgt3 geff/J yields c(T)0.2/J
3. Given K8 eV/A2 (SrTiO3) the orbital contribution
   is about 5

23
Conclusions

• Phase-diagram controlled by interplay of
  superexchange orbital-lattice couplings (JT,
  GdFeO3, orthorhombic distortion competes with xz
  yz order
• ? nonmonotonous Too)
• Extreme anisotropy of magnetic C-phase due to
  quasi-1D orbital fluctuations.
• Temperature dependence of partial optical sum
  rules can be obtained from spin-orbital model.
• Orbital and spin degrees of freedom usually
  cannot be factorized! (entanglement,
  orbital-Peierls) Cluster mean-field theory (ED)

24
Spin-orbit coupling Orientation of spins

• Orbital moments are quenched except for
  contribution from degenerate xz, yz orbitals
  which contribute to Lz.

P.H., Khaliullin, Oles, PRL 91, 257203 (2003)
25
Goodenough-Kanamori rules
JAF 4 t2/U
JF -4 t2/U (JH/U) Usually FM interactions
smaller by factor JH/U
Conjecture for C-phase Strong 1D (singlet)
orbital fluctuations along c-axis support
and amplify
ferromagnetism along c!!
G.Khaliullin, P.H., A.M.Oles, PRL 86, 3879 (2001).