Spin nematics in pyrochlore antiferromagnet with ferromagnetic next-nearest-neighbor interaction

The classical Heisenberg antiferromagnet on the pyrochlore lattice remains disordered down to zero temperature. A weak ferromagnetic interaction between second neighbors $J_2$ leads to a discontinuous ordering at a temperature $T_c\sim |J_2|$. Below the transition, a spin order with an extended unit cell containing as many as 1024 spins was found in Monte-Carlo simulations for $J_2 = -0.1 J_1$ [1]. Here we present the characterization of ordered states at a smaller $J_2 = -0.01 J_1$. This time the magnet shows a layered structure in the ordered phase: tetrahedra of the same layer develop a collinear N\'eel order with an in-plane wavevector ${\bf q}= 2\pi(1,1)$. At the mean-field level, each different layer has its own preferred spin direction. Thermal fluctuations, however, favor a collinear alignment of spins in different layers. There still remains a $Z_2$ symmetry for each layer: the N\'eel vector of a plane can be parallel or antiparallel to the common preferred direction, rendering the magnet a \textit{spin nematic,} possibly with an additional bond order. [1] D. Tsuneishi, M. Ioki, and H. Kawamura, J. Phys. Condens. Matter, to be published; cond-mat/0609655.