Finite-Temperature Properties of Multiferroic ${\mathrm{BiFeO}}_3$

An effective Hamiltonian scheme is developed to study finite-temperature properties of multiferroic ${\mathrm{BiFeO}}_3$. This approach reproduces very well (i) the symmetry of the ground state, (ii) the Néel and Curie temperatures, and (iii) the intrinsic magnetoelectric coefficients (that are very weak). This scheme also predicts (a) an overlooked phase above $T_C\simeq 1100\mathrm{K}$ that is associated with antiferrodistortive motions, as consistent with our additional x-ray diffractions, (b) improperlike dielectric features above $T_C$, and (c) that the ferroelectric transition is of first order with no group-subgroup relation between the paraelectric and polar phases.

Figure 1

Supercell average $⟨\mathbf{u}⟩$ of the local mode vectors (a), AFD-related $⟨\omega {⟩}_R$ quantity (b), magnetic moments (c), and dielectric constant (d), as a function of temperature in ${\mathrm{BiFeO}}_3$ and as predicted by the presently proposed method with the parameters of Eq. (1) having been reduced by 25% with respect to their values computed within the $\mathrm{LSDA}+U$ technique—in which $U$ is equal to 3.8 eV. The displayed dielectric constant is computed as one-third of the trace of the dielectric tensor. The inset of Fig. 1d emphasizes the kink of the dielectric constant around the Néel temperature.

Figure 2

Room-temperature polarization (a) and dielectric constant (b) of ${\mathrm{BiFeO}}_3$, as a function of magnetic field and as predicted by the presently proposed method with the parameters of Eq. (1) having been reduced by 25% with respect to their values computed within the $\mathrm{LSDA}+U$ technique—in which $U$ is equal to 3.8 eV. The displayed dielectric constant is computed as one-third of the trace of the dielectric tensor. The solid lines in (a) and (b) display quadratic and linear fits, respectively.

Figure 3

The experimental x-ray spectra at 1110 K. The star symbols indicate the weaker, but important, peaks.