Low-temperature magnetic properties of a two-dimensional spin nematic state

A mean-field theory of the low-temperature magnetic properties of a 2D spin nematic (SN) state, which is one of the possible states of the weakly interacting electron system with a half-filled band on a square lattice, is considered. Such a state can result from a spin-triplet anisotropic electron-hole pairing and is characterized by circulating local spin currents violating translational symmetry of the underlying lattice in the absence of the charge-density wave or spin-density wave structures. The existence of gapless quasiparticle excitations determines the peculiarities of the low-temperature behaviour of the 2D SN state. The 'relativistic' Landau quantization of the low-energy states in an external magnetic field results in anomalously strong diamagnetism, changing to paramagnetism on decreasing the angle between the field and the plane. The orientational effect of the magnetic field and spin-orbit interaction on the spin vector d of the order parameter is studied. Different possibilities for the equilibrium orientation of the d-vector are discussed.