Unpinning the skyrmion lattice in MnSi: Effect of substitutional disorder

By employing magnetization and small angle neutron scattering measurements, we have investigated the behavior of the skyrmion lattice (SKL) and the helical order in $\mathrm{MnS}{\mathrm{i}}_{0.992}\mathrm{G}{\mathrm{a}}_{0.008}$ Our results indicate that the order of the SKL is sensitive to the orientation of an applied magnetic field with respect to the crystal lattice and to variations in the sequence of small temperature and applied magnetic field changes. The disorder caused by the substitution of the heavier element Ga for Si is sufficient to reduce the pinning of the SKL to the underlying crystalline lattice, reducing the propensity for the SKL to be aligned with the crystal lattice. This tendency is most evident when the applied field is not well oriented with respect to the high symmetry axes of the crystal resulting in disorder in the long range SKL while maintaining sharp short range (radial) order. We have also investigated the effect of substituting heavier elements into MnSi on the reorientation process of the helical domains with field cycling in $\mathrm{MnS}{\mathrm{i}}_{0.992}\mathrm{G}{\mathrm{a}}_{0.008}$ and $\mathrm{M}{\mathrm{n}}_{0.985}\mathrm{I}{\mathrm{r}}_{0.015}\mathrm{Si}$ A comparison of the reorientation process in these materials with field reduction indicates that the substitution of heavier elements on either Mn or Si sites creates a higher energy barrier for the reorientation of the helical order and for the formation of domains.

Figure 1

ac and dc magnetization of $\mathrm{MnS}{\mathrm{i}}_{0.992}\mathrm{G}{\mathrm{a}}_{0.008}$ (a) Temperature, T, dependence of the magnetization, M divided by the field, H, M/H, for MnSi and $\mathrm{MnS}{\mathrm{i}}_{0.992}\mathrm{G}{\mathrm{a}}_{0.008}$ measured at $H=1\mathrm{kOe}$. Inset: pyramid-shaped crystals grown using Ga flux. (b) Real part of the ac susceptibility, χ′, as function of magnetic field, H, and T. (c) Frequency, $f$, dependence of χ′ and the imaginary part of the ac susceptibility, χ″, at 32.5 K. (d) Orientation and field dependence of χ′ and χ″ at 32.5 K. A driving ac field of 2 Oe amplitude was applied during the ac susceptibility measurements.

Figure 2

Small angle neutron scattering (SANS) patterns from $\mathrm{MnS}{\mathrm{i}}_{0.992}\mathrm{G}{\mathrm{a}}_{0.008}$. (a) Scattering in zero magnetic field, $H=0$, such that the sample is in the helical state. Lines indicate several high symmetry crystallographic directions lying in the detector plane. (b) Summary of H and temperature, T, sequences for frames (c)–(j) which present the resulting scattering patterns. (k) Intensity scale. (l) Summary of H and T sequences for frames (m)–(p), which present the resulting scattering patterns. (q) Summary of H and T sequences for frames (r)–(v) which present the resulting scattering patterns. In (b) a constant field of 1.4 kOe was applied and T was increased from 31 to 34 K. In (l) $H=1.4\mathrm{kOe}$ was applied at each T and returned to $H=0$ after each measurement. T was then increased by 0.5 K and H ramped back to 1.4 kOe. In (q) a field of 1.4 kOe was applied and the sample cooled from 34 to 31 K.

Figure 3

Results of SANS measurement: (a) Variation of full width at half maximum (FWHM) of the radial scans with magnetic field, H. The dashed line is the instrumental resolution $(\sim 0.0035{\AA }^{-1})$ (b) Variation of wave vector Q with magnetic field, H. For 0 < H < 1 kOe, $\mathrm{MnS}{\mathrm{i}}_{0.992}\mathrm{G}{\mathrm{a}}_{0.008}$ has a conical magnetic order resulting in a loss of scattering intensity on the detector for our experimental geometry. (a) and (b) share the same symbols.

Figure 4

Field orientation dependence of the skyrmion lattice. SANS data taken as the $\mathrm{MnS}{\mathrm{i}}_{0.992}\mathrm{G}{\mathrm{a}}_{0.008}$ crystal was rotated about its [-1-11] axis taken at $T=32.2\mathrm{K}$. (a) Intensity scale and schematic of experimental configuration. The red cylinder represents the crystal with three perpendicular axes identified. The crystal was rotated about the vertical axis which was parallel to the crystalline [-1-11] axis. (b)–(e) data taken in zero field, $H=0$. (f) Schematic showing the field and rotation angle, ϕ, sequence for the measurements presented in frames (g)–(j). H was ramped to zero during the rotation and energized prior to each measurement. (g)–(j) ϕ dependence of the scattering with $H=1.4\mathrm{kOe}$, within the A phase of $\mathrm{MnS}{\mathrm{i}}_{0.992}\mathrm{G}{\mathrm{a}}_{0.008}$. ϕ corresponds to the angle measured from the condition that the crystal [-110] direction was aligned parallel to the beam direction and to H. In all cases H was parallel to the incident beam and the [-1-11] direction of the crystal was vertical. The [001], [110] and [111] directions lie in the detector plane in frames (b) and (g). Data at a larger number of angles is presented in the sequence of images presented in the Supplemental Material [28].

Figure 5

Comparison of Q-integrated intensities for (a) zero magnetic field, H (helical state) and (b) $H=1.4\mathrm{kOe}$ (A phase) for different rotation angles, ϕ, of the crystal with respect to the neutron beam. ${\chi }_{az}$ is the azimuthal angle in the detector plane. The intensities in both frames are normalized to the same standard monitor count.

Figure 6

Comparison of SANS data for $\mathrm{MnS}{\mathrm{i}}_{0.992}\mathrm{G}{\mathrm{a}}_{0.008}\left(T_C=33.5\mathrm{K}\right)$ and $\mathrm{M}{\mathrm{n}}_{0.985}\mathrm{I}{\mathrm{r}}_{0.015}\mathrm{Si}\left(T_C=23\mathrm{K}\right)$. Intensity pattern observed in the helical state ($T=4\mathrm{K}$, $H=0$) after zero-field cooling, ZFC, (a) for $\mathrm{M}{\mathrm{n}}_{0.985}\mathrm{I}{\mathrm{r}}_{0.015}\mathrm{Si}$ and (b) for $\mathrm{MnS}{\mathrm{i}}_{0.992}\mathrm{G}{\mathrm{a}}_{0.008}$. Intensity pattern observed at $T=4\mathrm{K}$, $H=0$ after field cooling, FC, (c) for $\mathrm{M}{\mathrm{n}}_{0.985}\mathrm{I}{\mathrm{r}}_{0.015}\mathrm{Si}$ and (d) for $\mathrm{MnS}{\mathrm{i}}_{0.992}\mathrm{G}{\mathrm{a}}_{0.008}$. Intensity pattern in the SKL state (e) for $\mathrm{M}{\mathrm{n}}_{0.985}\mathrm{I}{\mathrm{r}}_{0.015}\mathrm{Si}$ and (f) for $\mathrm{MnS}{\mathrm{i}}_{0.992}\mathrm{G}{\mathrm{a}}_{0.008}$. Intensity scales are displayed in (c) and (d).

Figure 7

Variation of $H_{C1}$ for $\mathrm{M}{\mathrm{n}}_{1-\mathrm{x}}\mathrm{I}{\mathrm{r}}_{\mathrm{x}}\mathrm{Si}$ (blue) and $\mathrm{MnS}{\mathrm{i}}_{1-\mathrm{x}}\mathrm{G}{\mathrm{a}}_{\mathrm{x}}$ (red) at 4 K.