Increasing skyrmion stability in ${\mathrm{Cu}}_2{\mathrm{OSeO}}_3$ by chemical substitution

The cubic chiral helimagnets with the $P{2}_{1}3$ space group represent a group of compounds in which the stable skyrmion-lattice state is experimentally observed. The key parameter that controls the energy landscape of such systems and determines the emergence of a topologically nontrivial magnetic structure is the Dzyaloshinskii-Moriya interaction (DMI). Chemical substitution is recognized as a convenient instrument to tune the DMI in real materials and has been successfully utilized in studies of a number of chiral magnets, such as MnSi, FeGe, MnGe, and others. In our study, we applied small-angle neutron scattering to investigate how chemical substitution influences the skyrmionic properties of an insulating helimagnet ${\mathrm{Cu}}_2{\mathrm{OSeO}}_3$ when Cu ions are replaced by either Zn or Ni. Our results demonstrate that the DMI is enhanced in the Ni-substituted compounds $(\mathrm{Cu},{\mathrm{Ni})}_2{\mathrm{OSeO}}_3$, but weakened in $(\mathrm{Cu},{\mathrm{Zn})}_2{\mathrm{OSeO}}_3$. The observed changes in the DMI strength are reflected in the magnitude of the spin-spiral propagation vector and the temperature stability of the skyrmion phase.

Figure 1

The SkL in polycrystalline ${\mathrm{Cu}}_2{\mathrm{OSeO}}_3$ at 57 K. (a1)–(a5) SANS patterns collected at the SANS-1 instrument. Different values of the applied magnetic field are indicated at the detector images. The magnetic field is applied perpendicular to the neutron beam. (b1)–(b5) The corresponding normalized SANS intensity as a function of the momentum transfer along and perpendicular to the field direction. (c) The normalized azimuthal intensity profiles at different magnetic fields extracted from the SANS patterns. The radial integration range of (0.005–0.015) ${\AA }^{-1}$ was applied. The solid lines are a guide to the eye. (d) The integral intensity of the Bragg peaks as a function of the field. The integration areas are shown by the white boxes in (a1)–(a5). The solid lines are a guide to the eye. The SkL phase is highlighted by the shaded area. A measurement at 65 K ($T>T_{\text{C}}$) was used for a background subtraction for all the data shown.

Figure 2

The helimagnetic structure of (Cu,${\mathrm{Ni})}_2{\mathrm{OSeO}}_3$ and (Cu,${\mathrm{Zn})}_2{\mathrm{OSeO}}_3$. (a1)–(a5) SANS patterns collected from the compounds with different substitution levels of Zn and Ni. The detector images in (a1) and (a4) were taken in measurements on the SANS-1 instrument, (a2), (a3), and (a5) represent data from PA20. The masked horizontal line in (a5) is due to an inactive detector tube. The background subtraction was applied to all the diffraction patterns. (b1)–(b5) The corresponding intensity profiles without the background subtraction. The solid and dashed lines show the results of the fit as described in the legend of (b1). The vertical bars show the extracted Bragg positions. The horizontal bar in (b3) shows an estimated instrumental resolution (see the text).

Figure 3

Integral intensity of the helical Bragg peak $I$ as a function of magnetic field at different temperatures just below $T_{\text{C}}$ in (Cu,${\mathrm{Ni})}_2{\mathrm{OSeO}}_3$ and (Cu,${\mathrm{Zn})}_2{\mathrm{OSeO}}_3$. (a) The $I\left(H\right)$ curves showing the SkL phase observed in the pure ${\mathrm{Cu}}_2{\mathrm{OSeO}}_3$ compound. The black arrows denote the boundaries of the SkL phases $H_{\text{a}1}$ and $H_{\text{a}2}$. The gray arrows point to the critical fields $H_{\text{c}1}$ of the transition from the multidomain helical to the monodomain conical phase. (b) $I\left(H\right)$ at $T=T_{\text{C}}-2.6$ K measured in samples with different substitution. (c) The $I\left(H\right)$ curves of the Ni-4% doped compound. The data were offset for clarity as indicated by the dashed lines. The error bars are smaller than the symbol size, the solid lines are a guide to the eye. (d) The first derivative of the data presented in (c). The SkL phase is highlighted by the shaded area. The calculated derivative at each temperature was smoothed by a cubic B-spline function with the same smoothing factor for clarity.

Figure 4

The magnetic phase diagrams of ${\mathrm{Cu}}_2{\mathrm{OSeO}}_3$ with different chemical substitution extracted from SANS data. The corresponding chemical formulas of the studied compounds are shown in (a)–(e). The labels $T_{\text{C}}^{\left(2\right)}$ in (b) and (d) refer to the transition temperature of the secondary phase as explained in the text. The white circles denote the phase boundaries of the SkL state inferred from the $I\left(H\right)$ curves as discussed in the text.

Figure 5

The correlation between the experimentally extracted microscopic parameters. (a) The temperature range of the SkL phase in the substituted compounds $T_{\text{A}}$ is the lowest temperature at which the SkL can be nucleated in the applied magnetic field (absolute in K and normalized to $T_{\text{C}}$). (b) The SkL stability versus $T_{\text{C}}$ for all the studied compounds. (c) The helical propagation vector of each compound. (d) The SkL temperature stability versus the normalized propagation vector $k_{\text{s}}\left(0\right)$ is the propagation vector of pure ${\mathrm{Cu}}_2{\mathrm{OSeO}}_3$. (e) The extracted values of the DMI constant for samples with different substitution level. The solid lines are a guide to the eye. (f) The SkL stability versus the normalized DMI, $D\left(0\right)$, stands for the DMI strength in pure ${\mathrm{Cu}}_2{\mathrm{OSeO}}_3$. The solid line is a linear fit, the dashed line is a linear extrapolation.