Competing anisotropies in the chiral cubic magnet ${\mathrm{Co}}_8{\mathrm{Zn}}_8{\mathrm{Mn}}_4$ unveiled by resonant x-ray magnetic scattering

The cubic $\beta$-Mn-type alloy ${\mathrm{Co}}_8{\mathrm{Zn}}_8{\mathrm{Mn}}_4$ is a chiral helimagnet that exhibits a peculiar temperature-dependent behavior in the spiral pitch, which decreases from 130 nm at room temperature to 70 nm below 20 K. Notably, this shortening is also accompanied by a structural transition of the metastable skyrmion texture, transforming from a hexagonal lattice to a square lattice of elongated skyrmions. The underlying mechanism of these transformations remains unknown, with interactions potentially involved including the temperature-dependent Dzyaloshinskii-Moriya interaction, magnetocrystalline anisotropy, and exchange anisotropy. Here, x-ray resonant magnetic small-angle scattering in vectorial magnetic fields was employed to investigate the temperature dependence of the anisotropic properties of the helical phase in ${\mathrm{Co}}_8{\mathrm{Zn}}_8{\mathrm{Mn}}_4$. Our results reveal quantitatively that the magnitude of the anisotropic exchange interaction increases by a factor of 4 on cooling from room temperature to 20 K, leading to a 5% variation in the helical pitch within the (001) plane at 20 K. While the anisotropic exchange interaction contributes to the shortening of the spiral pitch, its magnitude is insufficient to explain the variation in the spiral periodicity from room to low temperatures. Finally, we demonstrate that magnetocrystalline and exchange anisotropies compete, with each favoring different orientations of the helical vector in the ground state.

Figure 1

(a) SEM image of the (001) ${\mathrm{Co}}_8{\mathrm{Zn}}_8{\mathrm{Mn}}_4$ thin plate (purple color) attached to a ${\mathrm{Si}}_3{\mathrm{N}}_4$ membrane by Pt contacts (green). The circular aperture drilled in the gold layer on the back side of the membrane is shown as a dashed line. (b) Zero-field REXS pattern measured at $T=50$ K after the field training ${\mu }_{0}H=0.12$ T applied at $\theta ={45}^{\circ }$. (c) REXS patterns measured at 50 K summed up over all azimuthal magnetic field training angles $\theta =0...{180}^{\circ }$ with a $3^{\circ }$ step.

Figure 2

(a) Zero-field REXS pattern measured at $T=200$ K after the field training ${\mu }_{0}H=0.12$ T applied at $\theta =0^{\circ }$. (b) SXTM image of the aligned helical texture at $T=200$ K obtained using circularly polarized x rays, which are sensitive to the out-of-plane component of magnetization.

Figure 3

Polar plots of the helical wave vector magnitude $Q$ in ${\mathrm{nm}}^{-1}$ units as a function of azimuthal angle $\theta$ at (a) 20 K, (b) 50 K, (c) 100 K, (d) 150 K, (e) 200 K, (f) 250 K, (g) 275 K. The data are symmetrized along the horizontal axis. Solid lines correspond to the fit according to Eq. (1). The dashed line in panel (g) corresponds to the direction of the uniaxial anisotropy.

Figure 4

Temperature dependence of (a) spiral wave vector $Q_0$, (b) the exchange anisotropy constant $F$, and (c) the strain-induced uniaxial anisotropy constant $Z$ extracted from the fit of $Q\left(\theta \right)$ according to Eq. (1).

Figure 5

Comparison between the $F/J$ ratios vs reduced temperatures for FeGe [35], Zn-doped ${\mathrm{Cu}}_2{\mathrm{OSeO}}_3$ [41], pristine ${\mathrm{Cu}}_2{\mathrm{OSeO}}_3$ [38], and ${\mathrm{Co}}_8{\mathrm{Zn}}_8{\mathrm{Mn}}_4$ (this work).