Figure 4

Three-dimensional (J, γ and D; up panel a–f) and two-dimensional (γ and D; down panel) phase diagrams of a collinear two-sublattice antiferromagnet. (a) When D>±0.5γ and $J>\frac{1}{2}(2D-\gamma )$, a FO SFO transition 1 occurs. (b) When 0⩽D⩽0.5γ, a FO SFO transition 2 occurs. It is pointed out that here γ and D cannot be zero simultaneously. (c) When $-\frac{1}{2}\gamma <D<0$, a SO SFO transition occurs. (d) When $D=-\frac{1}{2}\gamma$ and J>−γ, there is no SFO transition occurring at all. In this case, the antiferromagnet in question goes directly to a SFI transition from the AFM state, and the xz plane becomes an AFM easy plane. (e) When $D<-\frac{1}{2}\gamma$, the AFM easy axis changes automatically from the z to the x direction. (f) When D>±0.5γ and $0<J<\frac{1}{2}(2D-\gamma )$, the magnet hosts a FM state albeit with an AFM magnetic exchange.