Figure 4: Experimental result and calculation of magnetic field induced polarization, and magnetic field dependence of free energy.
From: Non-hysteretic colossal magnetoelectricity in a collinear antiferromagnet
(a,b) Experimental results and theoretical calculations for the magnetic field dependence of the electric polarization ΔP(H) at various temperatures, respectively. A black dashed line in a indicates linear fit to ΔP(H) curve for H>Hc and at T=47 K. (c–e) The dependence f(θ) of the free-energy density on the direction of the antiferromagnetic order parameter for different values of fourth-order anisotropy constant K4 in various magnetic fields. Free-energy minima are indicated by red dots. For K4=0 the barrier is absent and the switching occurs instantaneously in the bulk. For K4>0 there is a finite barrier and the transition should be of the first order with a hysteresis. If K4<0 the minimum of the free energy shifts continuously from θ=0 to θ=π/2 as the magnetic field increases. This case is consistent with our experimental observations.
