Revisiting spin cycloids in multiferroic ${\mathrm{BiFeO}}_3$

We revisit the inverse spin current model that has been previously used to explain the existence of magnetic cycloids in bulk multiferroic ${\mathrm{BiFeO}}_3$. Using a first-principles-based effective Hamiltonian method, and in combination with Monte Carlo simulations, we predict a magnetic phase diagram as a function of first- and second-nearest-neighbor interaction strength in the spin current model and show that, in contrast with previous understanding, both first and second nearest neighbors have to be taken into account to be in accordance with experimental findings, including the existence of type-1 and type-2 cycloids with, respectively, $\left[1\overline{1}0\right]$ and $\left[11\overline{2}\right]$ propagation directions, and the cycloid-to-antiferromagnetic transition under magnetic field. Other previously unknown magnetic arrangements are found in this phase diagram. The microscopic origins of all its magnetic phases are further explained in terms of the coexistence of single solutions of the spin current model having different weights (in magnitude and even sign).

Figure 1

Predicted magnetic structures at various $C_1$ and $C_2$ values for bulk BFO. (a) Calculated phase diagram as functions of $C_1$ and $C_2$ [33]. For the $\langle 1\overline{1}0\rangle$ cycloid, the blue cross symbols are the $C_1$ value converted from Ref. [20] (with $C_2=0)$; circles are the $C_2$ values in Ref. [19] (with $C_1=0)$; the blue triangle symbols are calculated by density functional theory [39]. The black lines are determined by considering the critical magnetic field of 18 T changing the $\left[1\overline{1}0\right]$ cycloid to AFM. (b) Illustration of the propagation directions of the five types of cycloids. For each type, equivalent cycloids of different propagation directions are shown in red, blue, and green colors.