Field-induced topological Hall effect in the noncoplanar triangular antiferromagnetic geometry of ${\mathrm{Mn}}_3\mathrm{Sn}$

Noncollinear triangular antiferromagnets with a coplanar spin arrangement and vanishing net magnetic moment can exhibit a large anomalous Hall effect owing to their nonvanishing momentum space Berry curvature. Here we show the existence of a large field-induced topological Hall effect in the noncoplanar triangular antiferromagnetic geometry of ${\mathrm{Mn}}_3\mathrm{Sn}$. A detailed magnetic and Hall effect measurements demonstrate the presence of three distinct Hall contributions: a high-temperature anomalous Hall effect, a low-temperature topological Hall effect, and an intermediate-temperature region with coexistence of both the effects. The origin of the observed topological Hall effect is attributed to the scalar spin chirality induced real-space Berry curvature that appears when the system goes from a trivial noncoplanar triangular spin alignment to a topologically protected nontrivial spin texture like skyrmions by application of magnetic field at low temperatures.

Figure 1

Atomic arrangement of Mn (blue balls) and Sn (yellow balls) in a single $c$ plane of the hexagonal crystal structure of ${\mathrm{Mn}}_3\mathrm{Sn}$. The magnetic moments of Mn atoms are represented by cylindrical arrows. (a) The ${120}^{\circ }$ triangular antiferromagnetic spin alignment of the Mn atoms where all the Mn moments lie in the $c$ plane. (b) All-out configuration, a slight tilting of the whole spin triangle along the $c$ axis. (c) Two-out-one-in configuration, two Mn moments of the spin triangle tilt along the positive $c$ axis, whereas one Mn-moment tilts towards the negative $c$ direction. In all cases a single spin triangle is shown inside a dashed box. Field dependence of Hall resistivity (${\rho }_{xy}$, left axis) and magnetization ($M$, right axis) measured at (d) 200 K and (e) 2 K. (f) Temperature dependence of magnetization measured in a field of 0.1 T in zero field cooled (ZFC) and field cooled (FC) modes. The inset shows the first derivative of the FC curve.

Figure 2

Field dependence of Hall resistivity $\left[{\rho }_{xy}\left(H\right)\right]$ measured at different temperatures. The filled circles represent ${\rho }_{xy}$ data measured from $+5$ T to $-5$ T, whereas, ${\rho }_{xy}$ data from $-5$ to $+5$ T are plotted with filled squares. The calculated ${\rho }_{xy}$ curves for $T=2–15$ K are represented by open circles and squares. The inset of (a) represents the virgin curve of ${\rho }_{xy}\left(H\right)$ at 2 K.

Figure 3

(a) Field dependence of magnetization $\left[M\right(H\left)\right]$ loops measured at different temperatures. (b) Variation of coercive field ($H_C$, left $Y$ axis) and $\mathrm{\Delta }M$ ($M_{FC}-M_{ZFC}$, right $Y$ axis) with temperatures. The inset shows the temperature dependence of spontaneous magnetization ($M_S$) derived from the $M\left(H\right)$ isotherms.

Figure 4

(a) Field dependence of topological Hall resistivity ${\rho }_{xy}^T$ at different temperatures. The closed and open symbols represent ${\rho }_{xy}$ from $+5$ T to $-5$ T and $-5$ T to $+5$ T, respectively. (b) Maximum value of different components of ${\rho }_{xy}$ with temperature. ${\rho }_{xy}^M$ and ${\rho }_{xy}^S$ are saturated anomalous Hall resistivity scaling with magnetization and spontaneous anomalous Hall resistivity from the coplanar triangular antiferromagnetic structure, respectively.

Figure 5

$H-T$ phase diagram showing contribution from different Hall effects. For the present purpose the ${\rho }_{xy}$ measurements with feld sweep from $+5$ T to $-5$ T is utilized. Color code represents the magnitude of ${\rho }_{xy}$ as depicted by scale bar on the right margin. The boundary between different phases are shown by dotted lines. The shaded region marked with ${\mathrm{Skx}}^{★}$ represents the possible skyrmion phase.