Figure 5

Mathematically allowed magnetic states of a collinear two-sublattice antiferromagnet as a function of J, γ, D and B. (a) As magnetic field B increases from 0 to B_SFO (for a FO SFO transition) or to B_SFOB and B_SFOF (for a SO SFO transition) and then to B_SFI, the antiferromagnet transfers from an AFM ground state to a FO SFO transition 1 or a FO SFO transition 2 or a SO SFO transition, and then to a SFOD state, from where a SFI transition occurs until all spins are flipped by applied magnetic field. (b) When $D=-\frac{1}{2}\gamma$ and J>−γ, there exists an AFM easy plane. (c) When $D=-\frac{1}{2}\gamma$ and J=−γ, the SFID state has the same energy level as that of the AFM ground state. (d) Based on the above analysis of b, c, one can deduce that when J=D=γ=0, if magnetic field B>0 applied, all spins will directly go to the SFID state and point to the applied-field direction. This is the so-called superparamagnetism. (e) When J>0 and $D>-\frac{1}{2}\gamma$, the AFM easy axis is along the z direction, whereas when $D<-\frac{1}{2}\gamma$, the x axis becomes an AFM easy direction. (f) When J>0 and $J>\frac{1}{2}(2D-\gamma )$, the magnet houses an AFM state, whereas when $J<\frac{1}{2}(2D-\gamma )$, the spins are ferromagnetically arranged. (g) When J>0 and $J=\frac{1}{2}(2D-\gamma )$, it is reasonable to deduce that the AFM state coexists with the FM state.