Electric Current Control of Helimagnetic Chirality from a Multidomain State in the Helimagnet MnAu$_2$

Abstract

In this paper, we study the domain wall dynamics under electric current in the helimagnet MnAu$_2$. We have found that the threshold electric current of the transition from a multidomain state to a single-chiral domain state in a magnetic field is much lower than that of chirality reversal from a single-chiral domain within certain ranges of temperature and magnetic field. The chirality after the transition depends on whether the magnetic field and electric current were parallel or antiparallel. Numerical calculations based on the Landau-Lifshitz-Gilbert equation reproduced the experimental observations. These results indicate that the domain walls are highly mobile in the helimagnet.

Figures (4)

• Figure 1: (a), (b) Schematic illustrations of helimagnetic single-domain states with (a) $-$Chirality and (b) $+$Chirality. (c) Schematic illustration of a helimagnetic multidomain state with a domain wall. (d) Second-harmonic resistivity $\rho^{2\omega}$ as a function of magnetic field at 250 K. Before the measurements, $+$Chiral, $-$Chiral, and multidomain states were prepared by the magnetic field sweep from $+$5 T to 0 T with applying the electric currents $+8.0\times 10^9$ A/m$^2$, $-8.0\times 10^9$ A/m$^2$, and 0 A/m$^2$, respectively. The data in the positive magnetic field region was obtained by increasing the magnetic field from the controlled initial states at 0 T, whereas the data in the negative magnetic field region was obtained by decreasing the magnetic field from the separately prepared initial states. (e) The field-antisymmetric component of second-harmonic resistivity $\rho^{2\omega}_\mathrm{anti}=(\rho^{2\omega}(+H)-\rho^{2\omega}(-H))/2$. (f) The field-symmetric component of second-harmonic resistivity $\rho^{2\omega}_\mathrm{sym}=(\rho^{2\omega}(+H)-\rho^{2\omega}(-H))/2$.
• Figure 2: Second-harmonic resistivity $\rho^{2\omega}$ measured after the application of an electric current pulse $j_\mathrm{p}$ with a duration of 1 second at 250 K. The magnetic field was $+$0.1 T in (a) and (b), and $-$0.1 T in (c) and (d). The initial $+$Chiral, $-$Chiral, and multidomain states were prepared similarly to the case of Fig. 1. The electric current pulses were repeatedly applied while changing their magnitude and polarity, as indicated by dotted arrows, and $\rho^{2\omega}$ was measured after each pulse application. The electric current was first decreased from 0 A/m$^2$ in (a) and (c), and increased from 0 A/m$^2$ in (b) and (d).
• Figure 3: Second-harmonic resistivity $\rho^{2\omega}$ measured after the application of an electric current pulse $j_\mathrm{p}$ at various magnetic fields at 250 K. The electric current pulses were repeatedly applied while changing the magnitude, as indicated by dotted arrows. For each field, two subfigures are shown in this figure: in the left subfigure, the electric current was decreased from 0 A/m$^2$ to $-22\times 10^9$ A/m$^2$ and then increased back to 0 A/m$^2$; in the right subfigure, it was increased from 0 A/m$^2$ to $+22\times 10^9$ A/m$^2$ and subsequently decreased back to 0 A/m$^2$. The initial $+$Chiral, $-$Chiral, and multidomain states were prepared similarly to the case of Figs. 1 and 2. Note that the range of the vertical axis is larger at 1.5 T.
• Figure 4: Numerical calculation of chirality variation under electric current for a $1000\times10$ two-dimensional helimagnetic model. (a) Variation of the averaged chirality under electric current at 0 K, 100 K, 200 K, and 300 K. (b)-(f) Spatial variation of the chirality at 100 K under electric currents of (b) 0 A/m$^2$, (c) $-3.9\times10^{11}$A/m$^2$, (d) $-10.1\times10^{11}$A/m$^2$, (e) $6.2\times10^{11}$A/m$^2$, and (f) $9.9\times10^{11}$A/m$^2$. The methodological details are described in the main text and ref. ohe_ChiralityControl.