Figure 1

(a) Multiferroic phase diagram of YSm (adapted from Ref. 9); numbered paths indicate the thermomagnetic trajectories used in experiments. (b) Temperature dependence of the polarization after different cooling processes. Inset: Dependence of the polarization ${\mathbf{P}}_{\mathbf{a}}^{+}$ at 5 K on the poling field ${\mathbf{E}}_{\mathbf{a}}$. (c) Dependence of the measured polarization on magnetic field applied along the $c$ axis. In (b) and (c) the numbers on curves indicate paths as in (a). Inset: Dependence of the polarization at 5 K, 9 T on the number of magnetic cycles (one loop corresponds to a decrease and increase in the magnetic field once). (d) Sketch of the polar domain structure after the ${\mathbf{E}}_{\mathbf{a}}$-poled cooling process and ${\mathbf{E}}_{\mathbf{a}}$ zeroing, after successive $H$ cycles. Labels in sketches A, B, and C indicate the same states as in (c). Vertical arrows represent $P_a^{\pm }$ domains, and horizontal arrows represent $P_c^{\pm }$ domains. Sketches do not intend to reproduce the actual population of domains. Domain walls (DW) are indicated.Reuse & Permissions

Figure 2

(a) Polarization vs temperature (measured upon heating from 5 K) as a function of the temperature $T_R$ at which the sample has been heated prior to measurement, without any $E$ poling. The initial low-temperature state is defined by cooling the samples under ${\mathbf{E}}_{\mathbf{a}}^{+}=625$ V/cm and ${\mu }_0\mathbf{H}\parallel c$. See the text for experimental details. (b) Left axis: Dependence of the polarization at 5 K on $T_R$ (solid symbols). Right axis: The solid line is the dielectric permittivity recorded upon heating. (c) Sketch of the initial (5 K) polarization state of the sample (red arrows) after heating to $T_R$ (green arrows) and after subsequent cooling to 5 K without any $E$ bias (blue arrows). Saturation polarization ($P_S$) corresponds to the measured polarization after $E$-field poling. Panels (i), (ii), and (iii) correspond to the same temperature regions as in (b).Reuse & Permissions

Figure 3

Inset: Temperature dependence of the real component of the magnetic susceptibility (${\mu }_0{h}_{\mathrm{ac}}\parallel c\mathrm{axis}$; $H$ $=$ 0). Field dependence (μ${}_{0}H$ from 0 to 9 T and to 0 T) of the real component of the magnetic susceptibility at 8 K. Solid symbols (squares and circles) correspond to data collected by increasing or reducing $H$, respectively; the arrows indicate the sense of variation of $H$. Triangle symbols (open) are susceptibility data measured, at 8 K, at some particular values of $H$ back from $H$ $=$ 0. Open rhombuses correspond to data collected after heating the crystal to above $T_N$, cooled down to 8 K under zero field, and $H$ increased again.Reuse & Permissions