Topology and manipulation of multiferroic hybrid domains in ${\text{MnWO}}_4$

An investigation of the spatially resolved distribution of domains in the multiferroic phase of ${\text{MnWO}}_4$ by optical second harmonic generation reveals that characteristic features of magnetic and ferroelectric domains are inseparably entangled. Consequently, the concept of multiferroic hybrid domains is introduced for compounds in which ferroelectricity is induced by magnetic order. The three-dimensional structure of the domains is resolved. Annealing cycles reveal a topological memory effect that goes beyond previously reported memory effects and allows one to reconstruct the entire multiferroic multidomain structure subsequent to quenching it.

Figure 1

(Color online) (a) Magnetic phase transitions in ${\text{MnWO}}_4$. Below the Néel temperature $T_N$ the ${\text{Mn}}^{2+}$ moments display collinear incommensurate long-range order within the easy plane. At $T_2$ an additional transverse spin component orders which leads to an elliptical incommensurate arrangement of spins. In the magnetic ground state below $T_1$ commensurate antiferromagnetic ordering is obtained. The spin spiral in the AF2 phase induces a spontaneous electric polarization along the $y$ axis while the AF1 and AF3 phases are not multiferroic. [(b)–(d)] Spatially resolved SHG measurements in the AF1 to AF3 phases. A domain structure (with black lines revealing domain walls) is detected in the multiferroic AF2 phase only. $x$, $y$, and $z$ represent a Cartesian coordinate system, approximating the monoclinic unit cell with lattice parameters $a=4.83\text{Å}$, $b=5.76\text{Å}$, $c=4.99\text{Å}$, and $\beta =91.1°\approx 90°$.

Figure 2

(Color online) Spatially resolved SHG images reveal the hybrid nature of the multiferroic domains in ${\text{MnWO}}_4$. (a) Domain structure in the $xz$ plane. A pronounced elongation along the magnetic easy axis of the crystal (double arrow) and the bubble topology reflect the magnetic aspect of the domains. [(b) and (c)] Domain structure in electric fields of (b) 1.67 kV/cm and (c) 2.17 kV/cm applied along the $y$ axis. [(d) and (e)] Domain structure in magnetic fields of (d) 0 T and (e) 5 T applied along the $x$ axis. Only the electric field affects the distribution of the domains, thus reflecting their electric aspect.

Figure 3

(Color online) Three-dimensional distribution of the multiferroic domains. [(a)–(c)] Domains in the $xz$, $yz$, and $xy$ plane of ${\text{MnWO}}_4$ samples taken from the same batch. (d) Three-dimensional visualization of the multiferroic domain structure in (a)–(c).

Figure 4

Response of the multiferroic domains to a temperature annealing cycle through the paramagnetic phase. (a) Domain structure after initial zero-field cooling from room temperature to the multiferroic AF2 phase. (b) Domain structure after subsequent application of the annealing cycle.

Figure 5

(Color online) Response of the multiferroic domains to magnetic field $\left(H\right)$ and temperature $\left(T\right)$ annealing cycles through the AF1 phase. (a) Sketch of the $\left(H,T\right)$ phase diagram with arrows indicating the respective annealing procedure. [(b) and (d)] Domain structure after initial zero-field cooling from room temperature to the multiferroic AF2 phase. [(c) and (e)] Domain structure after application of the respective annealing cycle. (f) Temperature dependence of the SHG signal (${\chi }_{yxx}$ component at 1.95 eV) (Ref. 13) in a temperature decreasing run. Nonzero SHG yield in the AF1 phase points to a residual polar contribution in the AF1 phase as probable basis of the topological memory effect revealed in panels (b)–(e).