Observation and Coupling of Domains in a Spin-Spiral Multiferroic

The coexistence, coupling, and manipulation of magnetic spiral domains and magnetically induced ferroelectric domains are spatially resolved by optical second harmonic generation in multiferroic ${\mathrm{MnWO}}_4$. Eight types of magnetic domains couple to two ferroelectric domains. An electric field uniquely creates a magnetic single-domain state. A magnetic field quenches the spontaneous polarization while retaining its magnetic origin so that the ferroelectric domains are concealed instead of destroyed.

Figure 1

Optical SHG on ${\mathrm{MnWO}}_4(100)$. The spectrum shows the SHG intensity $I_{\mathrm{SHG}}$ for the nonlinear susceptibilities ${\chi }_{yzz}$ and ${\chi }_{\mathrm{mix}}$ (see text). Insets show the temperature dependence of $\sqrt{I_{\mathrm{SHG}}}$. The black solid line shows the spontaneous polarization adopted from Ref. 12.

Figure 2

Coexistence of FEL and AFM domains in zero-field-cooled ${\mathrm{MnWO}}_4(100)$. Images were obtained at 8 K with SHG at (a, c) 2.75 eV from (${\chi }_{yzz}+{\chi }_{\mathrm{para}}$), and (b, d) 2.15 eV from (${\chi }_{\mathrm{AFM}}+{\chi }_{\mathrm{para}}$). FEL and AFM domains are denoted by $\mathcal{P}$ and $\ell$, respectively. Sets (a, b) and (c, d) were obtained in consecutive cooling cycles.

Figure 3

Control of AFM domain structures by electric fields. (a, b) Intensity of “electric” and “magnetic” SHG in electric-field cycles with $\mathcal{E}||y$. Bars denote the end points of the hysteresis. (c) FEL hysteresis derived from (a) on the basis of Eq. (2). Images: FEL and AFM domain structures with SHG from (${\chi }_{yzz}+{\chi }_{\mathrm{para}}$) and (${\chi }_{\mathrm{AFM}}+{\chi }_{\mathrm{para}}$), respectively, taken at 10 K after zero-field cooling (ZFC) and after subsequent poling in an electric field of $350\mathrm{kV}/\mathrm{m}$.

Figure 4

Control of FEL domain structures by magnetic fields. (a) FEL domain structure of ${\mathrm{MnWO}}_4(100)$ sample after zero-field cooling. (b) Application of a magnetic field $H_y>H_c$ with $H_c=4.3\mathrm{T}$ at 12 K quenches the magnetic spiral and, thus, the FEL order. SHG stems from ${\chi }_{\mathrm{para}}$ only. (c) By returning to $H=0$ the FEL order of (a) reemerges because the propagation vector as the source of the FEL polarization was not affected by the magnetic field. Sketches exemplify how the components $k_{x,z}$ of the magnetic propagation vector determine the FEL polarization $P_y$ in (a) to (c). SHG images were taken with light from (${\chi }_{\mathrm{FEL}}+{\chi }_{\mathrm{para}}$).