Spin-wave dynamics in the helimagnet FeGe studied by small-angle neutron scattering

We have studied the spin-wave stiffness of the Dzyaloshinskii-Moriya helimagnet FeGe in a temperature range from 225 K up to $T_C\approx 278.7\mathrm{K}$ by small-angle neutron scattering. The method we have used is based on [Grigoriev et al., Phys. Rev. B 92, 220415(R) (2015)] and was extended here for the application in polycrystalline samples. We confirm the validity of the anisotropic spin-wave dispersion for FeGe caused by the Dzyaloshinskii-Moriya interaction. We have shown that the spin-wave stiffness $A$ for the FeGe helimagnet decreases with a temperature as $A\left(T\right)=194[1-0.7{(T/T_C)}^{4.2}]{\mathrm{meV}\AA }^2$. The finite value of the spin-wave stiffness $A=58{\mathrm{meV}\AA }^2$ at $T_C$ classifies the order-disorder phase transition in FeGe as being the first-order one.

Figure 1

(a) Typical SANS scattering pattern from a monodomain helix structure below $H_{c2},T=250\mathrm{K}$ and a magnetic-field $H=0.075\mathrm{T}$. (b) Integral intensity of the marked Bragg peak against the magnetic field at different temperatures between 5 and 274 K. The solid lines are guides for the eyes. The inset shows an illustration of the determination of $H_{c2}$ at 60 K. The BJ model is used to provide the fitting function (see the text for more details).

Figure 2

The temperature dependence of the value of the helix wave-vector $k_s$ and both critical fields $H_{c1,2}$. The dashed lines are guides for the eyes.

Figure 3

The averaged intensity profile at $T=250\mathrm{K}$ and $H=0.3\mathrm{T}$. The sigmoid function fits the steplike part of the scattering. The cutoff angle is shown. The inset: SANS map above the critical field $T=250\mathrm{K}$ and $H=0.3\mathrm{T}$.

Figure 4

The azimuthally averaged intensities at $T=250\mathrm{K}$ for different magnetic fields between $H=0.25$ and $H=0.4\mathrm{T}$. The fitting functions are chosen analogously to Fig. 3. The curves are shifted by a constant with respect to each other for clarity.

Figure 5

(a) The temperature evolution of the intensity profiles from $T=196$ to $T=270\mathrm{K}$ at $H=0.35\mathrm{T}$. The curves are shifted by a constant with respect to each other for clarity. (b) The relative change in width of the steplike part $\delta$ for $H=0.35$. (c) The relative change in width of the steplike part $\delta$ for $T=246–277\mathrm{K}$ between $H=0.15$ and 0.45 T. The instrumental resolution is marked by the patterned area.

Figure 6

The field dependence of the square of the cutoff angle ${\theta }_C^2$ at $T=246$, 265, and 274 K. The intersections between the linear fits and the $H$ axis determine $H_{\mathrm{off}}$.

Figure 7

Temperature dependence of the spin-wave stiffness measured by the cutoff angle with the corresponding fit.