Magnetoelastic and magnetoelectric couplings across the antiferromagnetic transition in multiferroic ${\mathrm{BiFeO}}_3$

Clear anomalies in the lattice thermal expansion (deviation from linear variation) and elastic properties (softening of the sound velocity) at the antiferromagnetic-to-paramagnetic transition are observed in the prototypical multiferroic ${\mathrm{BiFeO}}_3$ using a combination of picosecond acoustic pump-probe and high-temperature x-ray-diffraction experiments. Similar anomalies are also evidenced using second-principles calculations supporting our experimental findings. Those calculations, in addition to a simple Landau-like model we also developed, allow us to understand the elastic softening and lattice change at $T_N$ as a result of magnetostriction combined with electrostrictive and magnetoelectric couplings, which renormalize the elastic constants of the high-temperature reference phase when the critical $T_N$ temperature is reached.

Figure 1

(a),(b) Temperature dependence of the $a$ (top panel) and $c$ (bottom panel) lattice constants of the conventional hexagonal cell. Inset: difference of the unit-cell parameters $a$ and $c$ arising below Néel temperature (vertical lines) from the deviation of the linear variation of the thermal expansion.

Figure 2

(a) Sketch of the pump-probe experiment conducted with a disoriented BFO grain permitting to emit both LA and TA coherent acoustic phonons [27, 31]. (b) Temperature dependence of the time resolved optical reflectivity in ${\mathrm{BiFeO}}_3$ for three selected temperatures. Note that the Néel temperature is about 650 K. (c) Corresponding fast Fourier transform (FFT) of the Brillouin components (TA and LA modes).

Figure 3

Temperature dependence of the Brillouin frequencies of the (a) TA and (b) LA modes. The inset in (b) shows the temperature evolution of normalized Brillouin frequencies.

Figure 4

Calculated independent elastic stiffness tensor components $C_{ij}$ in the conventional rhombohedral axes show anomalies at the Néel temperature (red curves). Results with the absence of the magnetoelastic coupling terms in the effective Hamiltonian $({\lambda }_L=0$, blue diamond curve), with the absence of magnetoelectric coupling terms $({\lambda }_{LP}=0$, green square curve) and the absence of both $({\lambda }_L,{\lambda }_{LP}=0$, purple triangle curve) are also shown for comparison.

Figure 5

Simulation of the temperature dependence of the LA (left columns) and TA (right columns) sound velocities for variable grain orientation angle $\theta$. The values are normalized to the value obtained at 5 K.