Detection of antiskyrmions by topological Hall effect in Heusler compounds

Heusler compounds having $D_{2d}$ crystal symmetry gained much attention recently due to the stabilization of a vortexlike spin texture called antiskyrmions in thin lamellae of $\mathrm{M}{\mathrm{n}}_{1.4}\mathrm{P}{\mathrm{t}}_{0.9}\mathrm{P}{\mathrm{d}}_{0.1}\mathrm{Sn}$ as reported in the work of Nayak et al. [Nature (London) 548, 561 (2017)]. Here we show that bulk $\mathrm{M}{\mathrm{n}}_{1.4}\mathrm{P}{\mathrm{t}}_{0.9}\mathrm{P}{\mathrm{d}}_{0.1}\mathrm{Sn}$ undergoes a spin-reorientation transition from a collinear ferromagnetic to a noncollinear configuration of Mn moments below 135 K, which is accompanied by the emergence of a topological Hall effect. We tune the topological Hall effect in Pd and Rh substituted $\mathrm{M}{\mathrm{n}}_{1.4}\mathrm{PtSn}$ Heusler compounds by changing the intrinsic magnetic properties and spin textures. A unique feature of the present system is the observation of a zero-field topological Hall resistivity with a sign change which indicates the robust formation of antiskyrmions.

Figure 1

Lattice constants (a and c), $c/a$ ratio and cell volume V of $\mathrm{M}{\mathrm{n}}_{1.4}\mathrm{P}{\mathrm{t}}_{1-x}\mathrm{P}{\mathrm{d}}_x\mathrm{Sn}$ and $\mathrm{M}{\mathrm{n}}_{1.4}\mathrm{P}{\mathrm{t}}_{1-y}\mathrm{R}{\mathrm{h}}_y\mathrm{Sn}$. The size of the error bars is less than the symbol size.

Figure 2

Results of the Rietveld refinements of the neutron-powder-diffraction data of $\mathrm{M}{\mathrm{n}}_{1.4}\mathrm{P}{\mathrm{t}}_{0.9}\mathrm{P}{\mathrm{d}}_{0.1}\mathrm{Sn}$ collected with $\lambda =2.43\AA$ at (a) 449, (b) 203, and (c) 2.4 K, respectively. The crystal structure was refined in the tetragonal space group $I\overline{4}2d$. At 203 K the strongest magnetic intensity appears at the positions of the reflections 112, 200, 211, 220, and 204 (marked in red), indicating a ferromagnetic spin alignment of the Mn atoms. At 2.4 K the reflections 101 and 004 show additional magnetic intensities indicating a spin-reorientation transition. The calculated patterns (crystal structure in green, crystal and magnetic structure in red) are compared with the observed ones (black circles). The difference patterns (blue) as well as the positions (black bars) of the Bragg reflections are shown. In (d), (e), and (f) the temperature dependence of the total magnetic moment ${\mu }_{\mathrm{tot}}$ and the magnetic moment components ${\mu }_x$ and ${\mu }_z$ of the Mn atoms, the lattice parameters $a$ and $c$, and the $c/a$ ratio and the unit-cell volume V in $\mathrm{M}{\mathrm{n}}_{1.4}\mathrm{P}{\mathrm{t}}_{0.9}\mathrm{P}{\mathrm{d}}_{0.1}\mathrm{Sn}$ are depicted, respectively. The size of the error bars of $a$, c, and V is less than the symbol size. Ferromagnetic ordering sets in at the Curie temperature $T_{\mathrm{C}}=390\left(4\right)\mathrm{K}$. Below $T_{\mathrm{SR}}=135\left(3\right)\mathrm{K}$ the $x$ components of the Mn1 and Mn2 moments show a ferrimagnetic spin alignment. The dotted vertical lines are a guide for the eye.

Figure 3

Magnetic structure of $\mathrm{M}{\mathrm{n}}_{1.4}\mathrm{P}{\mathrm{t}}_{0.9}\mathrm{P}{\mathrm{d}}_{0.1}\mathrm{Sn}$ at 2.4 and 203 K, and the variation of the angle between Mn1 and Mn2 moments as a function of temperature.

Figure 4

(a) Curie temperature and (b) magnetization at 7 T and 2 K of $\mathrm{M}{\mathrm{n}}_{1.4}\mathrm{P}{\mathrm{t}}_{1-x}\mathrm{P}{\mathrm{d}}_x\mathrm{Sn}$ and $\mathrm{M}{\mathrm{n}}_{1.4}\mathrm{P}{\mathrm{t}}_{1-y}\mathrm{R}{\mathrm{h}}_y\mathrm{Sn}$.

Figure 5

(a) Hall resistivity (left axis) and magnetization (right axis) of $\mathrm{M}{\mathrm{n}}_{1.4}\mathrm{P}{\mathrm{t}}_{0.9}\mathrm{P}{\mathrm{d}}_{0.1}\mathrm{Sn}$ between 0 and 1.5 T. Decreasing and increasing field-sweep directions in ${\rho }_{yx}$ (red and green lines, respectively) are indicated by arrows. The inset shows full hysteresis loops between −5 and +5 T. (b) Topological Hall resistivity at 2, 120, and 150 K. (c) Temperature dependence of maximum and zero-field value and coercivity of the topological Hall resistivity.

Figure 6

(a) Corrected Hall resistivity ${\rho }_{yx}-R_0{\mu }_{0}H$ (left axis, red and green lines) and the calculated anomalous Hall resistivity ${\rho }^{\mathrm{A}}\left(=b{\rho }_{xx}^{2}M\right)$ (right axis, black lines) at 2 K of $\mathrm{M}{\mathrm{n}}_{1.4}\mathrm{P}{\mathrm{t}}_{1-y}\mathrm{R}{\mathrm{h}}_y\mathrm{Sn}$. The black arrows detail the magnetization hysteresis around zero fields with the down (up) arrow for the decreasing (increasing) field sweep. The red (green) arrow shows the position of the Hall resistivity for decreasing (increasing) field sweep around zero fields with respect to the magnetization. (b) Topological Hall resistivity at 2 K and (c) the temperature-dependent parameters characterizing ${\rho }^{\mathrm{T}}$.

Figure 7

(a) Coercive field of topological Hall resistivity (left axis) and magnetization (right axis) and (b) topological Hall resistivity of $\mathrm{M}{\mathrm{n}}_{1.4}\mathrm{P}{\mathrm{t}}_{1-x}\mathrm{P}{\mathrm{d}}_x\mathrm{Sn}$ and $\mathrm{M}{\mathrm{n}}_{1.4}\mathrm{P}{\mathrm{t}}_{1-y}\mathrm{R}{\mathrm{h}}_y\mathrm{Sn}$ at 2 K. The compounds are classified in three composition ranges corresponding to the aSK phase, NCP spin structure, and FiM configuration which are indicated by blue, green, and yellow colors.