Hall Effect of Spin-Chirality Origin in a Triangular-Lattice Helimagnet ${\mathrm{Fe}}_{1.3}\mathrm{Sb}$

We report on a topological Hall effect possibly induced by scalar spin chirality in a quasi-two-dimensional helimagnet ${\mathrm{Fe}}_{1+\delta }\mathrm{Sb}$. In the low-temperature region where the spins on interstitial-Fe (concentration $\delta \sim 0.3$) intervening the 120° spin-ordered triangular planes tend to freeze, a nontrivial component of Hall resistivity with opposite sign of the conventional anomalous Hall term is observed under magnetic field applied perpendicular to the triangular-lattice plane. The observed unconventional Hall effect is ascribed to the scalar spin chirality arising from the heptamer spin clusters around the interstitial-Fe sites, which can be induced by the spin modulation by the Dzyaloshinsky-Moriya interaction.

Figure 1

(a) Temperature dependence of the in-plane and out-of-plane resistivities, ${\rho }_{\Vert }$ and ${\rho }_{\perp }$, for ${\mathrm{Fe}}_{1.3}\mathrm{Sb}$. (b) $T$ dependence of the magnetization ($M$) in external magnetic-field ($H$) parallel or perpendicular to the $c$ axis. Two triangles indicate the ordering temperatures of the in-plane Fe(l) spins ($T_N$) and the interstitial-Fe(i) spins, respectively. The inset shows the magnified $M\mathrm{\text{−}}T$ curve around $T_N$ in $H\perp c$. (c) Schematic view of the crystal structure of ${\mathrm{Fe}}_{1+\delta }\mathrm{Sb}$. Fe(i) atoms, whose concentration is $\delta$, randomly occupy the sites shown by dotted circles. (d) Top view of the Fe(l) and Fe(i) sites where the (red) arrows indicate the directions of the Fe(l) spins in the 120°-spin structure below $T_N$.

Figure 2

Magnetic-field ($H$) dependence of (a) the in-plane resistivity (${\rho }_{\parallel }$), (b) the magnetization ($M$), and (c) the Hall resistivity ${\rho }_{yx}$ under $H\Vert c$ at several temperatures. Small hysteresis is observed in $M$ and ${\rho }_{yx}$ at 2 K, as seen as the difference between closed ($H$-decreasing run) and open ($H$-increasing run) circles, while hardly discernible in ${\rho }_{yx}$ above 4 T within the experimental accuracy.

Figure 3

(a)–(h) Fitting (solid lines) of the Hall resistivity ${\rho }_{yx}$ with the relation of ${\rho }_{yx}=R_0({\mu }_{0}H)+R_s^i{M}^i+R_s^l{M}^l$ below 120 K. Fitting parameters $R_0$, $R_s^i$, and $R_s^l$ are assumed to be $T$ independent (see text).

Figure 4

(a) Magnetic-field ($H$) dependence of the chirality-driven Hall resistivity, ${\rho }_{yx}^{\chi }$, estimated from Fig. 3. Inset shows temperature ($T$) dependence of ${\rho }_{yx}^{\chi }$ at 14 T. (b) Schematic views of two types of the heptamer spin clusters, $A$ and $B$, consisting of one Fe(i) spin and two Fe(l)-spin triads above and below it under $H\Vert c$ at low temperatures. Here the Fe(i) spins are assumed to be well $H$ polarized. Vectors normal to the faces as described by (green) open arrows denote directions of the scalar spin chirality from the respective triangle faces of the heptamer. The (yellow) arrows indicate directions of the DM vectors ${\mathit{D}}_{ij}$ on the nearest-neighbor Fe(l)-Fe(i) bonds. (c) Scalar spin chiralities ${\chi }_A$ and ${\chi }_B$ of the cluster $A$ and $B$, and their sum ${\chi }_A+{\chi }_B$ as functions of $D$ (normalized by the in-plane interaction $J_1$) obtained by a numerical calculation (see text).