Wavelength-resolved small-angle neutron spectroscopy of spin waves in MnSi under pressure

We report wavelength-resolved spin-wave small-angle neutron scattering (SWSANS) on the time-of-flight SANS instrument BL01 at the China Spallation Neutron Source and extend the method to pressure-cell measurements of MnSi. MnSi is used as a benchmark B20 helimagnet because its helimagnetic order and spin-wave stiffness are well characterized at ambient pressure. In a fixed magnetic field, the time-of-flight measurement provides a spectrum of neutron wavelengths. For each detector branch $s=\pm1$, the intensity profile is recentered relative to the wavelength-dependent Bragg angle $\theta_B (\lambda) = k_s \lambda / 2\pi$, and the cutoff angle $\theta_C (\lambda)$ is extracted in the local branch coordinate. The cutoff-derived spin-wave stiffness $A$ is obtained from a linear fit of $\theta_C^2$ as a function of $\lambda^2$. Ambient-pressure measurements reproduce the known stiffness scale of MnSi. Structural SANS at ambient pressure and at nominal 5 and 11 kbar verifies the magnetic state and provides an internal pressure-state check for the pressure-cell measurements. At nominal 11 kbar, within the present cutoff model, the cutoff-derived stiffness is substantially reduced, whereas the structural field scale $H_{C2}$ remains high. This contrast shows that $A$ cannot be inferred from static structural parameters alone under pressure. To our knowledge, these measurements constitute the first SWSANS implementation on a pulsed neutron source and the first SWSANS determination of spin-wave stiffness under pressure. The experiment also shows that reliable high-pressure SWSANS on a pulsed source requires high source brilliance, stable wavelength-dependent normalization, and sufficient statistics in each wavelength window.