We figure out that the ground state of a multiple-spin exchange model applicable to thin films of solid 3He possesses an octahedral spin nematic order. In the presence of magnetic field, it is deformed into an antiferro-quadrupolar order in the perpendicular spin plane, in which lattice Z3 rotational symmetry is also broken. Furthermore, this system shows a narrow magnetization plateau at half, m/m_{sat}=1/2, which resembles recent magnetization measurement [H. Nema et al., Phys. Rev. Lett. 102, 075301 (2009)].
@article{arxiv.1111.6668,
title = {Spin nematic order in multiple-spin exchange models on the triangular lattice},
author = {Tsutomu Momoi and Philippe Sindzingre and Kenn Kubo},
journal= {arXiv preprint arXiv:1111.6668},
year = {2012}
}