Nonlinear Ultrafast Spin Scattering in the Skyrmion Phase of ${\mathrm{Cu}}_2{\mathrm{OSeO}}_3$

Ultrafast x-ray scattering studies of the topological Skyrmion phase in ${\mathrm{Cu}}_2{\mathrm{OSeO}}_3$ show the dynamics to be strongly dependent on the excitation energy and fluence. At high photon energies, where the electron-spin scattering cross section is relatively high, the excitation of the topological Skyrmion phase shows a nonlinear dependence on the excitation fluence, in contrast to the excitation of the conical phase which is linearly dependent on the excitation fluence. The excitation of the Skyrmion order parameter is nonlinear in the magnetic excitation resulting from scattering during electron-hole recombination, indicating different dominant scattering processes in the conical and Skyrmion phases.

Figure 1

Experimental scattering geometry. The magnetic field is applied perpendicular to the scattering plane. The Skyrmion peaks appear as satellites to the (001) lattice peak.

Figure 2

(a) Comparison of dynamics for above-gap (3.0 eV, circles) and below-gap (1.5 eV, squares) excitation. The excitation density at both energies was $2.4\mathrm{mJ}/{\mathrm{cm}}^2$. A 3.0 eV excitation results in faster dynamics in both conical (open symbols) and Skyrmion (solid symbols) phases. The time traces have been normalized to $-1$. (b) Ultrafast dynamics in Skyrmion and conical phases with above-gap pump energy. Solid lines show three-time-scale fits to the function represented in Eq. (1), with ${\tau }_i$ of 1.5, 60, and 300 ps.

Figure 3

Fluence dependence of the dynamics for the Skyrmion (a) and conical (b) phases with 3 eV excitation.

Figure 4

Fluence dependence of the differential scattering signal with 3 eV excitation on the 1 ns (a) and 60 ps (b) time scales. Fit parameter ${\alpha }_i$ is shown for the 1.5 ps (c) time-scale component. Diamonds in (b) indicate the resolution-limited decay component measured with 60 ps resolution at the ALS. Other symbols are the total loss of intensity at 60 ps, corresponding to the sum of decay components ${\alpha }_i$ with 1.5 and 60 ps, measured with 100 fs resolution from the LCLS. Lines in (b) are fits to saturation functions as described in the text. The line in (c) represents an $F^2$ fluence dependence, which we postulate is the result of multiphoton absorption.