Contents - Max-Planck-Institut für Physik komplexer Systeme

Here fij = e iK(ri+rj)/2 fK(r) is the wave-function
of the lowest energy pairs and ∆ is the complex
amplitude of the condensate. The state (5) is a
bosonic equivalent of the BCS pairing wave-function
for fermions and represents a variational ansatz for the
exact ground-state wave-function.
Energy
2−magnon
Hc Hs1 Hs2 spin−cone spin−nematic
1−magnon
Field
Figure 2: Energy-field diagram for a frustrated quantum magnet
close to the saturation field. Dot-dashed lines represent lowest oneand
two-magnon states. Solid lines illustrate the field dependence
of the ground state energy for the one-magnon and the two-magnon
condensate.
In the bosonic language the wave-function (5) has no
single-particle condensate, 〈aq〉 = 0, while superfluidity
is present in the two-particle channel:
〈a K/2+qa K/2−q〉 =
∆fK(q)
1 − |∆| 2f2 . (6)
K (q)
The anomalous average (6) is reminiscent of that for a
superconductor in the FFLO state. The phase of the
order parameter ∆ determines the orientation of the
nematic-director in the plane perpendicular to the applied
magnetic field.
Knowledge of various bosonic correlators allows to
compute spin-spin correlators and the ground-state energy.
In particular, the transverse spin correlations are
expressed as
〈S −
i S+ j
〉 ≈ |∆|2
l
f ∗ ilflj
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(7)
and exhibit an exponential decay with distance. With
decreasing magnetic field, the bound magnon pairs
overlap more and more appreciably and at a certain
point give way to a conventional one-particle condensate,
as illustrated in Fig. 2. The corresponding transition
field can be calculated explicitly for a given set of
exchange parameters. Breaking of a bound pair corresponds
to an energy loss ∼ EB. Hence, the excitation
spectrum observed in the inelastic neutron-scattering
experiments remains gapped in the nematic phase. The
gapless collective branch related to motion of the nematic
director can be observed only in higher-order
spin correlators.
Frustrated chain material LiCuVO4 Let us briefly
discuss the probable experimental realization of the
spin nematic state in LiCuVO4. This material consists
of planar arrays of spin-1/2 copper chains with a ferromagnetic
nearest-neighbor exchange J1 = −1.6 meV
and an antiferromagnetic second-neighbor coupling
J=3.8 meV [9]. The chains are coupled by a weaker
exchange J3 = −0.4 meV. For the above set of coupling
constants our theory predicts the following values for
critical fields: Hs1 = 46.2 T and Hs2 = 47 T. The spinnematic
phases remain stable down to Hc ≈ 44 T.
The pulsed magnetic field magnetization experiments
performed in response to our prediction has indeed
observed a new phase in LiCuVO4 in the field range
40–44 T [4], which is in quite good correspondence
with the predicted theoretical values. In addition, there
is good quantitative agreement between the slope of
the magnetization curve in the nematic phase and the
measured value of dM/dH. Thus, LiCuVO4 provides
the first experimental observation of the exotic spinnematic
order in magnetism.
In summary, competing ferro- and antiferromagnetic
interactions may lead to formation of bound magnon
pairs in quantum magnets. Condensation of magnon
pairs leads to formation of a spin nematic state in high
magnetic fields. The spin-nematic state is predicted to
exist in the chain compound LiCuVO4 at high fields.
Another promising candidate is a frustrated planar material
BaCdVO(PO4)2, which was recently studied at
MPI-CPfS [10].
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[10] R. Nath, A. A. Tsirlin, H. Rosner, and C. Geibel, Phys. Rev. B 78, (2008) 064422.
2.25. Magnon Pairing in a Quantum Spin Nematic 91