In-plane anisotropy of single- q and multiple- q ordered phases in the antiferromagnetic metal CeRh2Si2

We performed magnetization, resistivity, and neutron diffraction measurements under uniaxial stress applied along the $[1\overline{1}0]$ direction on the tetragonal magnet ${\mathrm{CeRh}}_{2}{\mathrm{Si}}_{2}$ with commensurate magnetic orders. ${\mathrm{CeRh}}_{2}{\mathrm{Si}}_{2}$ has two successive antiferromagnetic (AFM) orders in zero magnetic field. The high temperature phase (AFM1 phase) has the magnetic modulation wave vector of $q=(\frac{1}{2},\frac{1}{2},0)$, and the low temperature phase (AFM2 phase) is characterized by the four $q$-vectors of $q=(\frac{1}{2},\frac{1}{2},0),(\frac{1}{2},\ensuremath{-}\frac{1}{2},0),(\frac{1}{2},\frac{1}{2},\frac{1}{2})$, and $(\frac{1}{2},\ensuremath{-}\frac{1}{2},\frac{1}{2})$. By measuring the uniaxial stress dependence of the magnetization, resistivity and the intensities of magnetic Bragg reflections, we confirmed that the AFM1 phase has the single-$q$ magnetic order with twofold rotational symmetry and the AFM2 phase has the multi-$q$ magnetic order with fourfold rotational symmetry. To understand the origin of multi-$q$ order of ${\mathrm{CeRh}}_{2}{\mathrm{Si}}_{2}$, we also performed inelastic neutron scattering measurement on the single crystal samples. We found a magnetic excitation at the transfer energy $\ensuremath{\hbar}\ensuremath{\omega}\ensuremath{\sim}\phantom{\rule{0.16em}{0ex}}8\phantom{\rule{0.16em}{0ex}}\mathrm{meV}$. By applying the linear spin-wave theory, we found that the nearest- and next-nearest neighbor exchange interactions on the $ab$ plane, ${J}_{1}$ and ${J}_{2}$, are dominant in the AFM2 phase. However, the ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ model cannot lift the degeneracy between the single-$q$ (AFM1) and multi-$q$ (AFM2) phases. We suggest that it can be lifted by taking into account the biquadratic interaction derived from the perturbative expansion for the Kondo lattice Hamiltonian [S. Hayami et al., Phys. Rev. B 95, 224424 (2017)].