Anisotropic magnetoresistance and magnetic field-tunable Weyl nodes in Weyl metal SrRuO$_{3}$ thin films

Abstract

Weyl semimetals are a unique class of topological materials, possessing Fermi-arc surface states and exhibiting the chiral anomaly effect. The chiral anomaly refers to non-equilibrium charge transfer within a Weyl-node pair of opposite chirality under the condition of aligned electric and magnetic fields ($\bf{E} \parallel \bf{B}$), leading to non-conserved chiral charges and thus enhanced electrical conductivity. In experiments, such an enhanced conductivity due to the chiral anomaly manifests as a negative longitudinal magnetoresistance (MR) when the external field $\bf{H}$ is applied along the bias current direction $\bf{I}$. In this work, we present rigorous $φ$- and $α$-dependent magnetotransport measurements to investigate such a negative longitudinal MR due to the chiral anomaly in a sunbeam-shaped device fabricated from an untwinned Weyl metal SrRuO$_{3}$ (SRO) thin film. Here, $φ$($α$) represents the angle between $\bf{I}$ and the in-plane $\bf{H}$(SRO monoclinic [001]$_{\rm o}$). Unusual $φ$ dependences of in-plane MR and Hall effects were uncovered at low temperatures, accompanied by the emergence of the fourfold-symmetric component in the in-plane MR. These results indicate that the chiral anomaly and resistivity anisotropy in SRO play important roles. In particular, the dramatic variation of Weyl nodes near the Fermi level through magnetic field manipulation of the magnetization orientation, as revealed by band structure calculations, is consistent with the observed in-plane MR and Hall effect.

Figures (5)

• Figure 1: Resistivity anisotropy in the SRO thin film. (a) An illustration of the crystal structure of the monoclinic SRO thin film. The black dotted lines and light blue solid lines correspond to the unit cells for the monoclinic and pseudocubic structures, respectively. (b) shows an optical image of a sunbeam-shaped SRO device. The green and blue arrows indicate the two principal axes of [001]$_{\rm o}$ and [11̄0]$_{\rm o}$, respectively. The lower left inset is a blowup view of the red box, where the black dashed lines enclose the SRO Hall-bar regions after the argon-ion milling. The upper and lower panels of (c) show the field-dependent $\rho_{\rm xx}$ and $\rho_{\rm yx}$, respectively, at $T$ = 2 K, where different line colors correspond to data acquired at different $\alpha$ values. The resulting $\alpha$-dependences of $\rho_{\rm xx}$ and $\rho_{\rm yx}$ at different field strengths are plotted in the upper and lower panels of (d), respectively. Different symbols correspond to various field strengths applied along the film out-of-plane direction ([110]$_{\rm o}$), and the red lines are simulated curves based on a resistivity anisotropy model.
• Figure 2: In-plane MR and Hall effect in the SRO thin film at $T$ = 2 K. (a) A minimum model of a WSM and the chiral anomaly, showing non-conserving chiral charges under the condition of $\bf{B} \parallel \bf{E}$. As illustrated in (b), $\alpha$ is the angle between the $\bf{I}$ and [001]$_{\rm o}$, and $\phi$ is the angle between the in-plane $\bf{H}$ and $\bf{I}$. (c) The upper (lower) panel shows the field-dependent $\rho_{\rm xx}$ and $\rho_{\rm yx}$ for the $\alpha$ = 0$^{\rm o}$ (90$^{\rm o}$) Hall-bar device. The red and green curves correspond to data acquired with an in-plane $\bf{H}$ at $\phi$ = 0$^{\rm o}$ and 90$^{\rm o}$, respectively. The black curves are MR and Hall data with an out-of-plane $\bf{H}$ along [110]$_{\rm o}$ for comparison. The corresponding magnetoconductivity ($\sigma(H)$) for the $\alpha$ = 0$^{\rm o}$ (90$^{\rm o}$) Hall-bar device is shown in the upper (lower) panel of (d). The blue dashed lines are fitting curves calculated using the same $\beta$ parameter in the formula of $\sigma_{\rm chiral} = \beta (\mu_{\rm 0}H)^2$, representing the enhanced conductivity arising from the chiral anomaly.
• Figure 3: In-plane MR and Hall data in the SRO thin film for four Hall-bar devices. Data are shown for $\alpha$ = 0$^{\rm o}$, 22.5$^{\rm o}$, 45$^{\rm o}$, and 90$^{\rm o}$ from left to right. The upper and lower panels show the $\phi$-dependent $\Delta\rho_{\rm xx}/\rho_{\rm xx}$(0 T) and $\Delta\rho_{\rm yx}/\rho_{\rm xx}$(0 T), respectively. The solid and dashed lines are the experimental data and simulated noncrystalline AMR curves, respectively. The color code corresponds to different $T$s of 2, 5, 50, 100, and 180 K. For $T \geq$ 5 K, the data are vertically shifted for clarity. The black arrows indicate the $\phi$ values for $\bf{H}$ along the principal axes of [001]$_{\rm o}$ and [11̄0]$_{\rm o}$. An apparent fourfold-symmetric component appears in the $\phi$-dependent $\Delta\rho_{\rm xx}$ at low $T$s.
• Figure 4: $T$-dependent in-plane MR and extracted AMR parameters in the SRO thin film. (a) The upper panel shows the experimental MR at 14 T ($\Delta\rho_{\rm xx}$(14 T)/$\rho_{\rm xx}$(0 T)) for four different sets of ($\phi$, $\alpha$). For $T \leq$ 25 K, indicated by a gray-shaded regime, rapid drops in the MR were observed for $\phi$ = 90$^{\rm o}$. The corresponding $\Delta$MR for $\alpha$ = 0$^{\rm o}$ and 90$^{\rm o}$ is shown in the lower panel of (a), indicating a growing NLMR at low temperatures that is consistent with the enhanced conductivity due to the chiral anomaly in a WSM. (b) and (c) show the $T$-dependent AMR parameters ($C_{2\phi,\rm L}$, $C_{2\phi,\rm T}$, $C_{4\phi}$, $\phi_{0,\rm L}$, and $\phi_{0,\rm T}$) for $\alpha$ = 0$^{\rm o}$ and 45$^{\rm o}$, respectively, based on the phenomenological AMR formula, where the subscript L(T) refers to the in-plane MR(Hall) signals. For all $\alpha$ values, a sizable $C_{4\phi}$ value appears only in the in-plane MR at low $T$s. An unusual $T$-dependent phase difference between $\phi_{0,\rm L}$ and $\phi_{0,\rm T}$ is observed for $\alpha$ = 45$^{\rm o}$.
• Figure 5: Calculated Weyl-node distribution for various $\bf{M}$ orientations. (a) The black solid and red dashed lines are the calculated electronic band structures for $\alpha_{\rm M}$ = 0$^{\rm o}$ and 45$^{\rm o}$, respectively. The angle $\alpha_{\rm M}$ is defined as the angle between $\bf{M}$ and [001]$_{\rm o}$ as illustrated in the upper left inset. The calculated Weyl-node locations for $\alpha_{\rm M}$ = 0$^{\rm o}$ and 45$^{\rm o}$ are shown in (b) and (c), respectively. The different symbols correspond to Weyl nodes from different pairs of bands, and the symbol colors of red and blue represent the chiral charges of +1 and -1, respectively. The $W_{\rm I}^1$($\pm$1) pair is located within the blue shaded region in (a), which is the closest Weyl-node pair to the Fermi surface for $\alpha_{\rm M}$ = 0$^{\rm o}$. (d) plots the Weyl-node energy ($\varepsilon-\varepsilon_{\rm F}$) versus $\alpha_{\rm M}$. The corresponding band dispersions for $W_{\rm I}^1$($\pm$1) projected on two orthogonal planes cutting across the Weyl nodes are shown in (e) and (f).