Anomalous Hall effect and rich magnetic phase diagram of Mn$_{100-x}$Rh$_{x}$ epitaxial films

TL;DR

This work maps how Mn100-xRhx ($20 \le x \le 50$) epitaxial thin films on MgO transition between ferromagnetic and antiferromagnetic orders as Rh content is varied, revealing three distinct magnetic regimes with $T_C$ and $T_N$ terminating at different compositions. Using magnetization, resistivity, and Hall measurements, the authors show that all magnetically ordered states exhibit a pronounced anomalous Hall effect, predominantly governed by intrinsic Berry-curvature mechanisms in the good-metal regime. A dome-like dependence of AHE on Rh content, peaking near $x \approx 35$, correlates with magnetic properties and carrier density, suggesting a strong interplay between magnetism and electronic topology. The results position Mn100-xRhx films as a promising platform for manipulating anomalous transport through Berry curvature and for exploring AFM spintronics applications.

Abstract

A series of Mn$_{100-x}$Rh$_x$ ($20 \le x \le 50$) thin films were epitaxially grown on the MgO substrate using magnetron sputtering technique, and were systematically investigated by magnetization, longitudinal electrical resistivity, and transverse Hall resistivity. After optimizing the growth conditions, phase-pure Mn$_{100-x}$Rh$_x$ films with a cubic CsCl-type structure were obtained, and their magnetic phase diagram was built. The manipulation of Rh content leads to a rich magnetic phase diagram, where three different regimes can be identified: for $x < 40$, Mn$_{100-x}$Rh$_x$ films undergo a ferromagnetic (FM) transition below $T_\mathrm{C} \approx$ 330-350 K; for $40 \le x \le 45$, in addition to the FM transition at $T_\mathrm{C} \approx$ 200 K, Mn$_{100-x}$Rh$_x$ films undergo a FM-to-antiferromagnetic (AFM) transition at $T_\mathrm{N} \approx$ 120 K; finally for $x > 45$, only one AFM transition at $T_\mathrm{N} \approx$ 150 K can be tracked. All the Mn$_{100-x}$Rh$_x$ films exhibit distinct anomalous Hall effect in their magnetically ordered state, which is most likely due to the intrinsic Berry-curvature mechanism. In addition, all the anomalous Hall transport properties, including the resistivity, conductivity, and angle exhibit a strong correlation with the magnetic properties of Mn$_{100-x}$Rh$_x$ films, which become most evident for $x$ = 35. Our systematic investigations suggest a strong correlation between magnetic properties and electronic band topology in Mn$_{100-x}$Rh$_x$ films, highlighting their great potential for AFM spintronics.

Figures (7)

• Figure 1: (a) Representative room-temperature HRXRD patterns for Mn$_{100-x}$Rh$_x$ epitaxial thin films with $x$ = 20, 40, and 50. The intensity is shown on a logarithmic scale. (b) The $\mathrm{\Phi}$-scan patterns for $x$ = 40 film and MgO substrate. In-plane rotation of 45$^\circ$ for the epitaxial growth can be clearly identified. (c) The XRR pattern for $x$ = 40 film. Solid line through the data represents a fitting curve. (d) The estimated out-of-plane (i.e., $c$-axis) lattice constant of Mn$_{100-x}$Rh$_x$ films ($20 \le x \le 50$) versus Rh-content $x$. The standard deviations are within the symbols. Inset shows the cubic CsCl-type crystal structure of Mn$_{100-x}$Rh$_x$ films.
• Figure 2: Temperature-dependent magnetization $M(T)$ (a) and electrical resistivity $\rho_\mathrm{xx}(T)$ (b) for Mn$_{100-x}$Rh$_x$ film with $x$ = 20. The analogous results for $x$ = 40 and 50 are shown in panels (c)-(d) and (e)-(f), respectively. For $M(T)$ measurements, the magnetization was collected by applying a field of $\mu_0$$H$ = 0.1 T within the film plane using both field-cooled (FC) and zero-field-cooled (ZFC) protocols. The results for $x$ = 30, 35, and 45 are presented in Fig. S2 in the Supplementary Materials Supple. Field-dependent magnetization $M(H)$ for $x$ = 20 (g), 40 (h), and 50 (i), respectively. The $M(H)$ data were collected at 5 K and 300 K by applying the magnetic field also within the film plane. The MgO substrate contributions (Fig. S3 in the Supplementary Materials Supple) were subtracted for the $M(H)$ data. The derivatives of electrical resistivity d$\rho_\mathrm{xx}$/d$T$ and FC-magnetization d$M$/d$T$ with respect to temperature are shown in Fig. S4 in the Supplementary Materials Supple, where the magnetic transition temperatures can be clearly identified.
• Figure 3: Temperature-dependent magnetization for Mn$_{100-x}$Rh$_x$ films ($20 \le x \le 50$), collected in the absence of external magnetic field upon heating the films. The finite magnetization indicates the presence of spontaneous magnetization in Mn$_{100-x}$Rh$_x$ films.
• Figure 4: (a) Field-dependent Hall resistivity $\rho_\mathrm{xy}(H)$ and (b) anomalous Hall resistivity $\rho^\mathrm{A}_\mathrm{xy}(H)$ at various temperatures between 50 and 300 K for Mn$_{100-x}$Rh$_x$ films with $x$ = 20. The analogous results for $x$ = 40 and 50 are shown in panels (c)-(d) and (e)-(f), respectively. The $\rho^\mathrm{A}_\mathrm{xy}(H)$ at other temperatures are shown in Fig. S5 in the Supplementary Materials Supple. The magnetic field was applied along the normal direction of the thin film, i.e., $H \parallel c$. The results for $x$ = 30, 35, and 45 are presented in Fig. S6 in the Supplementary Materials Supple.
• Figure 5: Temperature-dependent carrier density $n$ (a) and magnetoresistance MR (b) for Mn$_{100-x}$Rh$_x$ films ($20 \le x \le 50$). The inset in panel (a) shows carrier density at 5 K and 300 K as a function of Rh content. (c) MR versus the Rh content at $T$ = 5 and 300 K. The MR was calculated according to MR = [$\rho_\mathrm{xx}$(5 T) – $\rho_\mathrm{xx}(0)$]/$\rho_\mathrm{xx}(0)$, where $\rho_\mathrm{xx}$(5 T) and $\rho_\mathrm{xx}(0)$ are the resistivity in a field of 5 T and 0 T, respectively.