Thermodynamic properties of the fully unconstrained noncollinear magnetisms

The fully unconstrained noncollinear magnetisms, in which the magnetization density is a continuous vector variable of position, have been investigated in terms of the Heisenberg models by algebraic method. According to the different exchange interactions, several typical physical topics are discussed in the paper. It is shown that the Heisenberg models provide an adequate description of the magnetizations at low temperature. Temperature dependence of the specific heat of these models in the vicinity of the midpoint at the rising magnetization (M) shows remarkable double-peak structure due to the ferromagnetic (FM) gapless and antiferromagnetic (AFM) gap excitation of the spin system. The magnetization curves have several clear plateaus and their numbers change with the different ratios of J1/J2. Also, the susceptibilities exhibit typical FM and AFM ground-state features at different models, which are well consistent with the PAW method's result.