Anomalous helimagnetic domain shrinkage due to the weakening of the Dzyaloshinskii-Moriya interaction in CrAs

CrAs is a well-known helimagnet with the double-helix structure originating from the competition between the Dzyaloshinskii-Moriya interaction (DMI) and antiferromagnetic exchange interaction $J$. By resonant soft-x-ray scattering, we observe the magnetic peak (0 0 $q_m$) that emerges at the helical transition with $T_S\approx 267.5\mathrm{K}$. Intriguingly, the helimagnetic domains significantly shrink on cooling below $\sim 255\mathrm{K}$, opposite to the conventional thermal effect. The weakening of DMI on cooling is found to play a critical role here. It causes the helical wave vector to vary, ordered spins to rotate, and extra helimagnetic domain boundaries to form at local defects, thus leading to the anomalous shrinkage of helimagnetic domains. Our results indicate that the size of magnetic helical domains can be controlled by tuning DMI in certain helimagnets.

Figure 1

(a) Resistivity of CrAs single crystal. The helical transition appears at $T_S=263\mathrm{K}$. The inset panel shows the CrAs crystal with a needlelike shape. (b) X-ray absorption spectroscopy (XAS) in total electron yield (TEY) mode of CrAs at the Cr $L$-edge (red solid line), in comparison with two reference compounds ${\mathrm{Cr}}_2{\mathrm{O}}_3$ (blue dashed line) and ${\mathrm{CrO}}_2$ (olive dashed line) from the literature [22]. The bulk sensitive total fluorescence yield (TFY) spectra of CrAs (black dots) was simultaneously collected.

Figure 2

(a) Illustration of the helical spin order in CrAs and the RSXS scattering geometry. The gray and green dashed lines denote the double spin helix chains running along the $c$ axis. The red dashed lines denote the nearest-neighboring spins in a unit cell. (b) $L$ scans of the (0 0 $q_m$) magnetic peak with the resonant energy $E=578.7$ eV (black dots) and nonresonant energy $E=570$ eV (red circles) at $T=20\mathrm{K}$. The incident photons are $\pi$-polarized.

Figure 3

Resonant profiles around (0 0 $q_m$) with (a) $\sigma$- or (b) $\pi$-polarized incident photons at $T=20\mathrm{K}$. The resonance profiles are plotted as a function of photon energy covering the Cr $L$-edge and reciprocal lattice (0 0 $L$). All data were measured by a photodiode detector, and the fluorescence background has been subtracted. The color bar indicates scattering intensity in arbitrary units. (c) Integrated intensity along the $L$ direction of the resonances in (a,b) as a function of the incident photon energy. The black and red lines represent the $\sigma$- and $\pi$-polarized incident photons, respectively. The dashed blue line is the XAS curve.

Figure 4

Temperature dependence of the magnetic peak in CrAs single crystals probed by (a) RSXS and (b) ND in the warming process. The temperature range is from 20 to 270 K. The neutron diffraction peaks are much broader than the ones from RSXS. Comparison of the (c) intensity, (d) propagation wave vector, and (e) FWHM of a magnetic peak measured by RSXS (red dots) and neutron diffraction (black dots) as a function of temperature. The solid lines are guides to the eye.

Figure 5

Temperature-dependent evolution of the (0 0 $q_m$) resonant peak along (a) $L$ and (b) $H$ directions in the temperature range from 267.5 to 20 K. The incident photon energy is 578.7 eV with $\pi$ polarization. The sample was warmed up from 20 to 267.5 K. The solid lines in (a) and (b) are Lorentz and Gauss function fittings, respectively. The adjusted $R$-square ${\overline{R}}^2$ of these fittings (${\overline{R}}^2>0.994$) are shown in the panels. (c) Integrated intensity of the resonant peak and (d) the average helimagnetic domain size $\xi$ vs temperature for the $L$ (red dots) and $H$ (black dots) scans. The solid lines are guides to the eye.

Figure 6

Temperature dependence of (a) resonant peak intensity and (b) correlation length ${\xi }_c$ in the cooling (step 1, blue circles) and warming (step 2, red dots) sequences. The inset of (a) shows the hysteresis between cooling and warm-up curves around $T_S$. The solid lines are guides to the eye.

Figure 7

Cartoon illustration of the angle (${\beta }_{12}$) between ${\vec{S}}_1$ and ${\vec{S}}_2$ and helimagnetic domains in the ac plane at (a) 255 K and (b) 20 K. The values of ${\beta }_{12}$ are from Ref. [13]. As the DMI term in the magnetic Hamiltonian has the form ${\vec{D}}_{12}·({\vec{S}}_1\times {\vec{S}}_2$), thus ${\vec{D}}_{12}$ favors noncollinear spin alignment. The tendency to antiferromagnetic spin alignment between ${\vec{S}}_1$ and ${\vec{S}}_2$ from 255 to 20 K indicates that the DMI gets weaker on cooling.