Evolution of magnetic bubble domains in the uniaxial ferromagnet CeRu$_2$Ga$_2$B inferred from the Hall effect and ac magnetic susceptibility

TL;DR

This paper demonstrates a finite topological Hall effect $\rho_{xy}^T$ in the uniaxial, centrosymmetric ferromagnet CeRu$_2$Ga$_2$B within the ordered phase, correlated with field-driven evolution of magnetic bubble textures. By decomposing the Hall signal into ordinary, anomalous, and topological contributions using $\rho_{xy}^A = S_H \rho^2 M$, the authors extract $\rho_{xy}^T(H)$ and relate it to bubble-area changes observed via magnetic force microscopy (MFM). The ac magnetic susceptibility $\chi_{\rm ac}$ shows a broad peak in $d\chi_{\rm ac}/dH$ at $H_P$, indicating a wide distribution of onset fields for topology across bubbles, while MFM reveals largely field-stable bubble areas up to $H_T$ followed by collapse as spin polarization sets in. The results suggest a crossover where bubbles evolve from topologically trivial to non-trivial textures under field, enabled by the uniaxial anisotropy, and they establish signatures that can guide the search for and tailoring of topological spin textures in DMI-free magnets for spintronic applications.

Abstract

We study the Hall effect, AC magnetic susceptibility ($χ_{\rm ac}$), and magnetic force microscopy of the uniaxial ferromagnet CeRu$_2$Ga$_2$B with a centrosymmetric crystal structure. We observe a finite topological Hall effect (THE) within the ordered phase before the magnetization is polarized by applied field. By comparing the field dependences of the area fraction of the magnetic bubbles, the derivative of $χ_{\rm ac}$, and the THE signal, we deduce that the magnetic bubbles of CeRu$_2$Ga$_2$B evolve from the trivial to topological spin texture with field. Our findings will be utilized to expand the search for magnetic materials hosting the topological spin textures to ones with uniaxial anisotropy, and open a new possibility to tailor the topological spin texture.

Figures (7)

• Figure 1: (a) Magnetization as a function of applied magnetic field $H$ in $\mathbf H\parallel c$ at different temperatures. The saturation of $M(H)$ at $H_S$ is indicated for each temperature (black arrow) and $H_S$ decreases as $T$ approaches $T_C=15.5$ K. The magnitude of $M$ for $\mathbf H\parallel ab$ is minuscule (dotted line), compared to $\mathbf H\parallel c$. (b) The fractional MR at various temperatures is shown as a function of $H$. Below $T_C$, MR changes little in $H<H_S$. The inset shows the zero field resistivity, where $T_C$ is clearly marked (arrow) by the rapid drop in resistivity with decreasing temperature.
• Figure 2: (a) $\rho_{xy}(H)$ measured at $T= 2, 5, 8, 11, 13, 15$ and 20 K. (b-e) Separating out the THE ($\rho_{xy}^T$) from $\rho_{xy}' = \rho_{xy} - \mu_0R_HH$ for (b) $T = 2$ K, (c) 8 K, (d) 11 K, and (e) 13 K. $\rho_{xy}^T(H)$ (darker, bold lines) is determined by subtracting $\rho_{xy}^A(H) = S_H\rho^2M$ (dotted lines) from $\rho_{xy}^{'}$ in each panel. See text for details.
• Figure 3: Temperature dependence of the maximum magnitude of $|\rho_{xy}^T(H)|$ (left $y$-axis) and $S_H$ (right $y$-axis). The sign of $S_H$ changes from negative to positive between 5 and 8 K, while that of $\rho_{xy}^T$ remains negative.
• Figure 4: (a)$\chi_{\rm ac}$ plotted as a function of $H$. Note that $\chi_{\rm ac} (H)$ at $T=15$ K is scaled by 1/10 in order to fit within the same range. (b) Derivative of $\chi_{\rm ac}$ as a function of $H$, normalized by the maximum value at each $T$. Vertical arrows mark the location of the peak in $\frac{d\chi_{\rm ac}}{dH}$, $H_P$. (c) $T$ dependence of $\chi_{\rm ac}$ at fixed $H$. Each curve is displayed with an offset for clarity.
• Figure 5: MFM images at $\mu_0H=40$ (left) and 100 mT (right) at $T= 4.2$ K(a,b) and at $T=13$ K (c,d) with the scan area $14\times14$$\mu$m$^2$. All images were taken with initially field-cooled at $\mu_0H=10$ mT. Scale bar corresponds to 5 $\mu$m. The colorbar indicates the linear scale between the minimum and maximum frequency shifts of the cantilever at each $T$. (e) $\rho_{xy}^T (H)$ (solid line, left $y$-axis) at $T=5$ K and area fraction of the bubble-like domains (gray circles, right $y$-axis) at $T=4.2$ K as a function of $H$ and (f) at 13 K. Dotted lines are a guide for the eyes for $\rho_{xy}^T$. $H_P$ and $H_T$ are marked with the vertical dashed lines, where the maximum of $\frac{d\chi_{\rm ac}}{dH}$ and $\rho_{xy}^T (H)$ are found, respectively.