### Magnetization plateau in triangular lattice antiferromagnet

Phase diagram of Cs_{2}CuBr_{4} in magnetic field is remarkably different
from that of isostructural Cs_{2}CuCl_{4}: it has magnetization plateau at
M= M_{sat}/3 (and another one, possibly, at M= 2 M_{sat}/3). Here M_{sat}
is the magnetization of the fully polarized state.

Experimental data by T. Ono et al. Phys.Rev.B **67**, 104431 (2003), J.Phys.:Condens. Matter
**16**, S773 (2004), Prog. Theor. Phys. Suppl. **159**, 217 (2005). See also
H. Tsuji et al., Phys.Rev.B **76**, 060406 (2007).

These as well as NMR measurements (Y. Fujii et al., Physica B **346-347**, 45 (2004),
JMMM **272-276**, 861 (2004),
J.Phys.:Condens. Matter **19**, 145237 (2007)) indicate collinear
UP-UP-DOWN (**UUD**) state,
predicted by interacting spin wave calculations of A.V. Chubukov and D.I. Golosov,
J.Phys.:Condens. Matter **3**, 69 (1991). Closely related classical entropic mechanism
has been analyzed by H. Kawamura and S. Miyashita, J. Phys. Soc. Jpn. **54**, 4530 (1985).

One of the problems with this explanation is that its key element, **UUD state**,
becomes classically unstable for arbitrary small spatial anisotropy in
the exchange, that is when J'/J < 1. It is believed
that Cs_{2}CuBr_{4} has J'/J = 0.75 while Cs_{2}CuCl_{4} has
J'/J = 0.34.

The resolution is that quantum fluctuations can stabilize classical unstable state.
This type of phenomena is known as "order-by-disorder". In our problem one needs to work
with **interacting** spin waves from the very beginning, and treat spatial anisotropy
(J - J') as a perturbation to the isotropic **UUD state** which is described by
interacting spin waves. It turns out that the competition between classical and quantum
effects can be parametrized by a single dimensionless parameter
δ=(40/3) S (J - J')^{2}/J^{2}. The plateau is locally stable for
0 < δ < 4. However, it is a global minimum only for 0 < δ < 2.
(It is interesting to note that δ=0.6 for Cs_{2}CuBr_{4} while
Cs_{2}CuCl_{4} has δ=2.9.) This, and numerous
BEC transitions out of the UUD state, are described in Quantum stabilization of the
1/3-magnetization plateau in Cs_{2}CuBr_{4},
Jason Alicea, Andrey V. Chubukov, and Oleg A. Starykh, Phys. Rev. Lett. **102**, 137201 (2009).