Ferromagnetic Resonance with Magnetic Phase Selectivity by Means of Resonant Elastic X-Ray Scattering on a Chiral Magnet

Cubic chiral magnets, such as ${\mathrm{Cu}}_2{\mathrm{OSeO}}_3$, exhibit a variety of noncollinear spin textures, including a trigonal lattice of spin whirls, the so-called skyrmions. Using magnetic resonant elastic x-ray scattering (REXS) on a crystalline Bragg peak and its magnetic satellites while exciting the sample with magnetic fields at gigahertz frequencies, we probe the ferromagnetic resonance (FMR) modes of these spin textures by means of the scattered intensity. Most notably, the three eigenmodes of the skyrmion lattice are detected with large sensitivity. As this novel technique, which we label REXS FMR, is carried out at distinct positions in reciprocal space, it allows us to distinguish contributions originating from different magnetic states, providing information on the precise character, weight, and mode mixing as a prerequisite of tailored excitations for applications.

Figure 1

Setup and typical REXS data. (a) Schematic view of the experimental setup. (b) Schematic zero-field cooled magnetic phase diagram of ${\mathrm{Cu}}_2{\mathrm{OSeO}}_3$. (c) Reciprocal space map around the (001) Bragg peak in the helical state. (d) Reciprocal space map in the conical state. The magnetic field is applied along the [110] axis, i.e., within the sample plane. (e),(f) Reciprocal space map in the skyrmion lattice state. The magnetic field is applied along the [001] axis, i.e., perpendicular to the sample plane. Under field cooling, the skyrmion lattice may be metastable frozen-in to lower temperatures.

Figure 2

REXS FMR on the structural (001) peak. (a) Intensity of the Bragg peak as a function of magnetic field applied parallel to the incoming x-ray beam, tracking the magnetization of the sample. Data are recorded at each field step with microwave excitation on (red curve) and off (gray curve). (b) Relative change of the intensity under excitation. (c) Reflected microwave power, $S_{11}$, as a function of field. The signature around zero field is attributed to the helimagnetic states. (d) Resonant modes for the magnetic field along the [001] axis at low temperature. Frequencies are normalized to their value at $H_{c2}$. Resonance fields inferred from REXS FMR (solid symbols) are compared to resonance frequencies inferred from microwave spectroscopy (open symbols).

Figure 3

REXS FMR on the magnetic satellites. (a) Intensity of a helical satellite as a function of magnetic field for different excitation frequencies. Data are recorded at each field step with microwave excitation on (red curves) and off (gray curves). The large value at 3.5 GHz is attributed to changes of the spin texture; see the text for details. (b) Relative reduction of the helical satellite intensity at zero field as a function of frequency. The sketch illustrates the position of the detector diode. Statistical error bars are typically much smaller than the symbol size. (c) Intensity at the reciprocal space position of a skyrmion lattice satellite. Around zero field, the tail of the broad helical satellite is observed at the skyrmion satellite position. (d) Relative reduction of the skyrmion satellite intensity at a field of 35 mT as a function of frequency.