High-frequency magnetotransport in a viscous electron fluid under a Stern-Gerlach force

We apply a hydrodynamic theory to study transverse magnetosonic resonances in a viscous two-dimensional electron fluid under an in-plane Stern-Gerlach force (SGF), a perpendicular magnetic field with cyclotron frequency ${\ensuremath{\omega}}_{c}$, and an alternating electric field with frequency $\ensuremath{\omega}$. The SGF leads to a splitting in the dispersion curve of the transverse magnetosound wave and hinders the long-wavelength plasmonic excitation. The effective diagonal viscosity coefficient can be enhanced by about one order of magnitude due to the SGF. The variation of absorption power $Y$ with ${\ensuremath{\omega}}_{c}$ exhibits a viscoelastic (VE) resonance at ${\ensuremath{\omega}}_{c}=\ensuremath{\omega}/2$ and transverse magnetosound resonances. The SGF can raise the heights of all resonant peaks and leave the peak positions almost completely unchanged. The most substantial magnetosonic resonant peak, much weaker than the VE peak in the absence of SGF, can be tuned by the SGF to be well above the VE peak. Our results indicate that the SGF can be used to tune the VE resonance and transverse magnetosound resonances, which is relevant to the manipulation of photoresistance and photovoltaic effects in viscous electron fluids.