Topological and Planar Hall Effect in Monoclinic van der Waals Ferromagnet NbFeTe$_2$

TL;DR

This study addresses the emergence of topological and planar Hall signals in monoclinic NbFeTe2, a layered van der Waals ferromagnet. Through comprehensive magnetization, magnetotransport, and structural characterization, it reveals FM order below ~80 K with out-of-plane anisotropy, a topological Hall effect persisting up to 45 K, and a robust planar Hall effect persisting well above Tc. The data show negative longitudinal MR, a carrier-type reversal near 65 K, and a linear scaling of anomalous Hall conductivity with longitudinal conductivity, indicating a mixed intrinsic/extrinsic AHE and a nontrivial electronic structure underpinning the observed topology. These findings position NbFeTe2 as a versatile platform for exploring noncoplanar spin textures and Berry-curvature–driven transport in 2D vdW ferromagnets with potential spintronic and topological applications.

Abstract

Two-dimensional (2D) van der Waals (vdW) ferromagnets have emerged as a critical class of quantum materials for next-generation, low-dimensional spintronic devices. In this study, we report a comprehensive study of the transport properties of the layered soft ferromagnet $\text{NbFeTe}_2$. We report the first observation of the topological Hall effect (THE) and the planar Hall effect (PHE) in metallic $\text{NbFeTe}_2$. THE signatures persist up to 45 K, while PHE remains evident well above Curie temperature ($T_C$). The observed negative longitudinal magnetoresistance, along with the PHE, provides strong evidence for a nontrivial electronic band structure. The coexistence of perpendicular magnetic anisotropy and a substantial THE: two key properties that are highly desirable for future spintronics applications, makes monoclinic vdW ferromagnetic $\text{NbFeTe}_2$ a promising platform to advance spintronics applications.

Figures (4)

• Figure 1: (a) (Upper panel) Crystal structure of monoclinic NbFeTe$_2$, where the sky, green, and violet spheres define the Nb, Fe, and Te atoms, respectively. (Left of the lower panel) The high-resolution transmission electron microscopy (HRTEM) image of the as-grown crystal. (Right of the lower panel) SAED pattern obtained from a single grain with HRTEM measurement. (b) Typical X-ray diffraction pattern obtained from the cleaved plane of NbFeTe$_2$ single crystal at room temperature exhibits exclusively (h00) Bragg reflections. The optical image of the as-grown single crystal is shown in the inset. Temperature dependence of the dc magnetization measured in zero-field-cooled and field-cooled conditions for applied magnetic field in the range 200 Oe to 3 T for (c) $H$$||$$a$ and (d) $H$$||$$bc$. The inset of (c) and the upper inset of (d) show the first derivative of the $M$-$T$ curve under FC condition for $H$$||$$a$ and $H$$||$$bc$ directions, respectively. Lower inset of (d) shows isothermal magnetization for both $H$$||$$a$ axis and $H$$||$$bc$ plane at $T =$ 2 K. (e) The in-phase component of AC magnetic susceptibility $\chi'(T)$ measured at different frequencies ranging from 10 Hz to 1 kHz using 2.5 Oe ac field. The zoomed view of frequency dependence is shown in the upper inset. The temperature dependence of the out-of-phase component of AC magnetic susceptibility $\chi"(T)$ with varying frequencies is shown in the lower inset. (f) Temperature-dependence of the anisotropy constant $K_u$. The temperature variations of $M_s$ and $H_s$ are shown in the upper and lower insets, respectively.
• Figure 2: (a) Temperature dependence of the normalized longitudinal resistivity ($\rho_{yy}$) curves at zero-field and 3 T. Here, the current is applied along the in-plane direction. Theoretical fits to the temperature dependence of resistivity data at different temperature ranges are indicated with red, green, blue, and cyan colors. The inset shows the temperature derivative of resistivity. The magnetic field dependence of (b) LMR and (c) TMR at several representative temperatures up to 120 K. The inset of (b) shows the comparison between LMR (%) and TMR (%) at 5 K and 15 K. The measurement configuration for magnetoresistance is shown schematically in the inset of (c).
• Figure 3: (a) Magnetic field dependence of magnetization ($M$) at different temperatures with field perpendicular to the $bc$-plane of the crystal. (b) Magnetic field dependence of Hall resistivity ($\rho_{yz}$) measured in the temperature range from 5 K to 90 K, with current in $bc$-plane and magnetic field along the $a$-axis of the crystal. (c) Field dependence of topological Hall resistance at different temperatures. The inset shows the total Hall resistivity $\rho_{yz}^{total}(H)$ and the sum of the ordinary Hall resistivity $\rho_{yz}^0(H)$ and anomalous Hall resistivity $\rho_{yz}^A(H)$ at 5 K. (d) Temperature dependence of the ordinary Hall coefficient ($R_0$). The upper inset shows the obtained carrier density as a function of temperature. The lower inset shows the temperature variation of the anomalous Hall coefficient $R_s$. (e) Scaling behavior of anomalous Hall conductivity $\sigma_{yz}^A$ vs longitudinal conductivity $\sigma_{yy}$ following a linear relation. (f) Temperature dependence of $\sigma_{yz}^A$ and anomalous Hall angle $\Theta^A$, both decrease with increasing temperature.
• Figure 4: (a) The planar Hall resistivity ($\rho_{yz}^{\mathrm{PHE}}$) as a function of angle at 9 T for different temperatures. The inset schematic shows the experimental configuration or measurement set-up. (b) The $\rho_{yz}^{\mathrm{PHE}}$ for NbFeTe$_2$ as a function of angle at 5K for several magnetic fields. (c) The planar resistivity ($\rho_{yy}^{\mathrm{planar}}$) as a function of angle for different temperatures at 9T. (d) Global fittings of representative data for $\rho_{yz}^{\mathrm{PHE}}$ and $\rho_{yy}^{\mathrm{planar}}$ at 5 K and 9 T. (e) The extracted resistivity anomaly $\Delta\rho$ at 9 T as a function of temperature. Inset: The $\Delta\rho$ at 5 K as a function of magnetic field. (f) The extracted transverse resistivity $\rho_{\perp}$ as a function of temperature at 9T.