Tuning the Multiferroic Properties of ${\mathrm{BiFeO}}_3$ under Uniaxial Strain

More than twenty years ago, multiferroic compounds combining in particular magnetism and ferroelectricity were rediscovered. Since then, ${\mathrm{BiFeO}}_3$ has emerged as the most outstanding multiferroic by combining at room temperature almost all the fundamental or applicative properties that may be desired: electroactive spin wave excitations called electromagnons, conductive domain walls, or a low band gap of interest for magnonic devices. All these properties have so far only been discontinuously strain engineered in thin films according to the lattice parameter imposed by the substrate. Here we explore the ferroelectricity and the dynamic magnetic response of ${\mathrm{BiFeO}}_3$ bulk under continuously tunable uniaxial strain. Using elasto-Raman spectroscopy, we show that the ferroelectric soft mode is strongly enhanced under tensile strain and driven by the volume preserving deformation at low strain. The magnonic response is entirely modified with low energy magnon modes being suppressed for tensile strain above pointing out a transition from a cycloid to an homogeneous magnetic state. Effective Hamiltonian calculations show that the ferroelectric and the antiferrodistortive modes compete in the tensile regime. In addition, the homogeneous antiferromagnetic state becomes more stable compared to the cycloidal state above a $+2\%$ tensile strain close to the experimental value. Finally, we reveal the ferroelectric and magnetic orders of ${\mathrm{BiFeO}}_3$ under uniaxial strain and how the tensile strain allows us to unlock and to modify in a differentiated way the polarization and the magnetic structure.

Figure 1

(a) Schematic of the uniaxial strain application system seen from below (piezoelectric stack) as well as an enlarged picture of the strain setup and a schematic of a cross section showing how the sample is fixed ([2]). (b) Phonon spectra measured for several compressive and tensile strains inside the pressure cell. (c) Raman shift of the phonon modes at 70 and $75{\mathrm{cm}}^{-1}$ [13]. The dashed lines are a quadratic guide for the eye.

Figure 2

(a) Low energy part of Raman spectra showing the spin excitations under the applied strain. (b) Magnon mode frequencies and 2D color map of the Raman intensity (color scale) as a function of the deformation ${\epsilon }_{[100]}$. (c) Comparison of the strain dependence between the integrated Raman intensity of the ${\psi }_1^{+}$ magnon mode and of the phonon mode at $75{\mathrm{cm}}^{-1}$.

Figure 3

(a) Evolution of the polarization and AFD mode components along [100], [010], and [001] directions under [100] oriented tensile and compressive strain. The AFD components along the $x$, $y$, and $z$ direction represent the antiphase tilts in radians about the $x$, $y$, and $z$ axes. The inset shows the polarization and AFD tilt magnitudes. (b) Energy comparison of relaxed bulk BFO with two magnetic spin configuration: type I spin cycloid state with propagation vector along [1-10] and homogeneous G-type AFM state.