Magnon dispersion shift in the induced ferromagnetic phase of noncentrosymmetric MnSi

A small angle neutron inelastic scattering measurement has been performed to study the magnon dispersion relation in the field-induced ferromagnetic phase of the noncentrosymmetric binary compound MnSi. For the magnons propagating parallel or antiparallel to the external magnetic field, we experimentally confirmed that the dispersion relation is asymmetrically shifted along the magnetic field direction. This magnon dispersion shift is attributed to the relativistic Dzyaloshinskii-Moriya interaction, which is finite in noncentrosymmetric magnets, such as MnSi. The shift direction is found to be switchable by reversing the external magnetic field direction.

Figure 1

Schematic illustration of the experimental setup for the small angle neutron inelastic measurements. The external magnetic field was fixed antiparallel $\left(H>0\right)$ or parallel $\left(H<0\right)$ to the momentum transfer $\vec{Q}$, which was set along the crystallographic $\left[111\right]$ direction.

Figure 2

(a)–(d) Neutron diffraction patterns observed under $H=0,3,4$, and 5 kOe. Solid lines are the fitting results using gaussian functions. (e) Phase boundary for the helical/conical and induced ferromagnetic phases in MnSi for $H\parallel \left[111\right]$. Filled circles stand for the estimated transition temperatures. Filled square indicates the $T$ and $H$ point, where the present small angle inelastic neutron scattering measurements were performed.

Figure 3

Representative constant-$\vec{Q}$ scans measured at $T=27$ K. (a) and (b) $h=0.04$ (r.l.u.). (c) and (d) $h=0.05$ (r.l.u.). (e) and (f) $h=0.06$ (r.l.u.). The external field was set to $H=5$ kOe for (a), (c), and (e), whereas the field was switched to $H=-5$ kOe for (b), (d), and (f). (g) and (h) Constant-$\vec{Q}$ scans measured at $T=27$ K and $h=0.05$ (r.l.u.) with the sample rotated for 180 degrees. The direction of magnetic field [5 kOe for (g) and $-5$ kOe for (h)] with respect to the incident neutron direction was unchanged. For all the spectra, background was removed using the base temperature data sets; the data around the elastic position were discarded since huge elastic background results in unacceptable uncertainties. The solid lines are the best fits to the model described in the text.

Figure 4

Obtained magnon dispersion relations in the induced ferromagnetic phase of MnSi. Open circles represent the excitation energies for $H=-5$ kOe, whereas filled circles for $H=5$ kOe. Magnon excitation energies were estimated from the inelastic spectra using resolution convoluted fitting to the Lorentzian-type function described in the text. Solid lines stand for the shifted quadratic dispersions for $H=\pm 5$ kOe given by Eq. (1) with the parameters $D_{\mathrm{s}}=21\left(1\right)$ meVÅ${}^2,E_0=0.02\left(1\right)$ meV. Dotted lines are expected dispersion relations centered at $Q=-|q_0|$.