Antiferromagnetic domain wall dynamics in magnetoelectric ${\mathrm{MnTiO}}_3$ studied by optical imaging

We study the dynamics of the antiferromagnetic domain wall in collinear antiferromagnet ${\mathrm{MnTiO}}_3$ by means of optical magnetochiral imaging. Antiphase domains are clearly visualized by exploiting the asymmetry in absorption coefficients between two distinct antiferromagnetic states with Néel vectors in opposite directions. Utilizing the coexistence of several types of magnetic multipoles, antiferromagnetic states in ${\mathrm{MnTiO}}_3$ are switched by longitudinal DC electric and magnetic fields applied along the propagation direction of incident light while imaging the domain pattern. The memory effect enables the imaging of millisecond dynamics with domain inversion. Detailed investigation of the domain-wall motion with varying temperature and external-field strength reveals the thermal effects on the mobility of the domain wall.

Figure 1

Schematic of antiferromagnetic domain imaging in ${\mathrm{MnTiO}}_3$. The red arrows represent $S$ = 5/2 spins of ${\mathrm{Mn}}^{2+}$. The antiferromagnetic domain pattern is mapped as the difference in the transmitted light intensity. Signs of the $c$ component of the toroidal moment and all the components of the ME tensor $\alpha$ are opposite between the two types of antiferromagnetic domains with $L_c$ of opposite signs. Exploiting the diagonal ME coupling ${\alpha }_{\parallel }$, $L_c$ is manipulated by external DC electric and magnetic fields parallel to the propagation direction of light.

Figure 2

(a) Difference image at 60.0 K. An image at 65.0 K is used as the reference. The exposure time is 2 s. (b) Temperature dependence of the relative difference $\mathrm{\Delta }{I}_{AB}$/$I_{AB}$ in the integrated intensity between square regions $A$ and $B$ indicated in (a) at 0 T. (c) Temperature dependence of the magnetic susceptibility $\chi$ along the easy axis. (d) Temperature dependence of the DC ME susceptibility ${\alpha }_t$ calculated using magnetic-field induced electric polarization in 6 T [see Eq. (1) in the text]. (e) Light-polarization dependence of difference images. Images at 65.0 K ($\phi =0^{\circ }$), 65.4 K ($\phi ={45}^{\circ }$), and 65.7 K ($\phi ={90}^{\circ }$) are used as the reference. The data for (d) are from Ref. [27].

Figure 3

(a) Change in the averaged transmitted light intensity $I$ with a sweeping electric field $E_c$ along the $c$ axis. (b)–(d) Difference $c$-plane images recorded at each electric field. The panels in (b), (c), and (d) were recorded during the first decrease, second increase, and second decrease in $E_c$. Images at $E_c$ = $-7.9$ MV/m in the first loop, $E_c$ = 7.9 MV/m at the end of the first loop, and $E_c$ = $-7.9$ MV/m in the second loop are used as the reference for (b), (c), and (d), respectively. The white scale bar in the left panel of (b) corresponds to 0.5 mm.

Figure 4

(a) Timing scheme of the experiment. Reference images were recorded in every poling process. All the measurements were performed under ${\mu }_0{H}_c$ = 0.1 T. The averaged transmitted light intensity (blue dotted line) takes the maximum value after poling with the negative voltage and decreases by $\mathrm{\Delta }I$ in response to the application of the positive pulsed electric field for $\mathrm{\Delta }t$. (b) The change in the transmitted light intensity $\mathrm{\Delta }I$ compared with each reference image at 64 K as a function of $\mathrm{\Delta }t$. (c)–(f) Difference images recorded after the application of a positive pulsed field of several pulse widths $\mathrm{\Delta }t$ [31]. The white bar in (c) corresponds to 0.5 mm.

Figure 5

(a) Timing scheme of the experiment to study the domain-wall dynamics. Each reference image was recorded in the poling process. (b) Comparison of difference images recorded after the application of positive and negative pulsed electric fields with amplitude $E_{\mathrm{pulse}}=7.1$ MV/m. Before the application of the pulsed field, a multidomain state was realized with a $t_{\mathrm{pre}}$ of 450 ms. The position of the domain wall is denoted by a red line. The white bar corresponds to 0.5 mm. (c) Relationship between the domain-wall velocity $v_{\mathrm{DW}}$ and the pulse height $E_{\mathrm{pulse}}$ of the driving electric field, $v_{\mathrm{DW}}\text{−}{E}_{\mathrm{pulse}}$, at 64.0 K. Measurements were performed for the same multidomain state as was realized for (b). (d) Temperature dependence of the mobility $\mu$ of the domain wall in the viscous regime. Measurements were performed for a multidomain state realized with a $t_{\mathrm{pre}}$ of 400 ms.