Transcript Anomalous excitation spectra of frustrated quantum

Anomalous excitation spectra of
frustrated quantum antiferromagnets
John Fjaerestad
University of Queensland
Work done in collaboration with:
Weihong Zheng, UNSW
Rajiv Singh, UC Davis
Ross McKenzie, UQ
Radu Coldea, Oxford (Bristol)
Reference: cond-mat/0506400 (Phys. Rev. Lett., in press)
Outline
Two-dimensional antiferromagnets
In systems with a magnetically ordered ground state,
semiclassical spin-wave theory has been believed to
give a good account of the ground state and excitations
Will show that in frustrated systems with magnetically
ordered ground state, the high-energy excitations can
show strong deviations from spin-wave theory
Will suggest a possible interpretation of the excitation
spectrum of the triangular antiferromagnet
Two-dimensional antiferromagnets
Important “minimal” model: Heisenberg model
Here we will focus on S=1/2
2D S=1/2 Heisenberg antiferromagnet on square lattice
Low-energy effective model for the cuprate superconductors
(stacked layers of 2D CuO2 planes) at zero doping
Ground state: Long-range magnetic (Neel)order
Excitations:
Dispersion for
S=1 magnons
Circles: Data points for Cu(DCOO)2 4D20 (Christensen et al (2004))
Full line: Linear spin-wave theory
Dashed line: Series expansion result (Singh & Gelfand (1995))
S=1/2 square lattice model: Ground state and excitations well described by
spin-wave theory (except for small deviations in high-energy spectra)
Spin-wave theory: semiclassical approach to magnetically
ordered systems
Spin waves: weak oscillations of the spins around their classical direction
Classical spins:
Consider quantity A(S) (energy, magnetization)
i.e. effects of quantum fluctuations enter as correction terms
to the classical result in powers of 1/S
What can be done to increase
the impact of quantum fluctuations?
?
Introduce frustration
Quantum fluctuations, enhanced by frustration, may lead to
a magnetically disordered ground state (spin liquid)
(Anderson 1973, Fazekas and Anderson 1974)
The fundamental excitations are spinons with S=1/2
(“fractionalized” compared to the S=1 of conventional magnons)
A less exotic, but still very interesting possibility:
Ground state is magnetically ordered, but magnon dispersion
shows large deviations from spin-wave theory
S = ½ Heisenberg antiferromagnet
on an anisotropic triangular lattice
Focus here:
J1/J2 = 0 : Square lattice model (old results)
J1/J2 < 0.7
J1/J2 = 1 : Triangular lattice model
J1/J2 = 3 : Cs2CuCl4
Frustrated Neel phase (0 < J1/J2 < 0.7)
Magnon dispersion for different values of J1/J2 (Zheng et al., cond-mat/0506400)
As J1/J2 is increased, the
local minimum at (p,0)
becomes more pronounced
and the energy difference
between (p,0) and (p/2,p/2)
increases
In contrast, linear spin-wave
theory predicts no energy
difference between (p,0)
and (p/2,p/2) (Merino et al., 1999)
(p/2,p/2)
Triangular lattice model
LSWT
(J1 = J2)
Ground state:
Magnetically
ordered
(120° pattern)
Series
A
B
C
O
A Q
Magnon dispersion
ky
Large deviations from linear
spin-wave theory (LSWT) at
high energies
kx
D
Cs2CuCl4 (J1 = 3J2)
With respect to the linear
spin-wave theory (LSWT)
curve, the dispersion is
strongly enhanced along
the strong (J1) bonds and
decreased perpendicular
to them
Nonlinear spin-wave theory is
also not able to account
quantitatively for this large
quantum renormalization
(Dominant continuum scattering indicative of
spin liquid physics at high energies
(Coldea et al, PRB 2003))
Exp
Series
LSWT
(Veillette et al., PRB 72, 134429 (2005)
Quantum fluctuations make the dispersion
look more one-dimensional
Main message so far:
In frustrated systems with magnetically ordered
ground state, high-energy excitations can show
strong deviations from spin-wave theory
In remaining part of the talk:
Present a possible interpretation of
the excitation spectra for the triangular
antiferromagnet (J1=J2)
Square lattice model (J1 = 0)
Excitations: Dispersion for S=1 magnons
Circles: Data points for Cu(DCOO)2 4D20 (Christensen et al, JMMM 272-276, 896 (2004))
Full line: Linear spin-wave theory
Dashed line: Series expansion result (Singh & Gelfand, Phys. Rev. B 52, 15695 (1995))
Local minimum in dispersion at (p,0): not captured by spin-wave theory
Interpreted as signature of RVB physics (Hsu, Phys. Rev. B 41, 11379 (1990);
Syljuasen and Ronnow, J. Phys. Condens. Matter 12, L405 (2000) , Ho et al, Phys. Rev. Lett. 86, 1626 (2001))
Description of resonating-valence-bond (RVB) states (Anderson)
The S=1/2 Heisenberg model is the U/t  limit of
the fermionic Hubbard model at half-filling
0
Ground state of a mean-field (i.e. quadratic) fermionic Hamiltonian
  PG 0
RVB state
Gutzwiller projection:
Projects onto space of
singly-occupied sites
p-flux phase:
Ground state of mean-field Hamiltonian
describing fermions hopping on a square
lattice with fictitious flux ± p threading
alternating plaquettes
p-flux phase spinon dispersion:
Gapless excitations at (± p/2,± p/2)
“p-flux state” RVB solution for square lattice model (J1=0)
(Affleck and Marston 1988, Kotliar 1988)
Ground state energies:
True ground state (Neel-ordered)
E = -0.3346 J/bond
Projected p-flux state:
E = -0.319 J/bond
S=1 magnon dispersion (Hsu, PRB 1990):
Magnon is bound state of two spinons
Deep minimum at (p,0)
Incorporate magnetic long-range order
into p-flux state (Hsu, PRB 1990):
E = -0.332 J/bond
(p/2,p/2) points where spinon dispersion of
p-flux phase has gapless excitations
(p,0) points where magnon dispersion
has local minima
Two-spinon (particle-hole) continuum also
has minima at (p,0) points: pushes down
magnon energy
Triangular lattice model
(J1 = J2)
LSWT
Magnon dispersion
Large deviations from linear
spin-wave theory (LSWT) at
high energies
Series
A
B
C
O
A Q
The two-spinon continuum
has local minima at the kvectors showing the largest
deviations from LSWT
ky
kx
Assumed locations of
minima of spinon dispersion
D
Conclusions
Deviations from LSWT at high energies increase with
frustration in Neel phase
Very strong deviations from LSWT in triangular-lattice
model leading to local minima and flat regions in dispersion
Interpreted in terms of two-spinon picture
Quantum fluctuations make Cs2CuCl4 dispersion look
more one-dimensional