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We performed magnetization, resistivity, and neutron diffraction measurementsunder uniaxial stress applied along [1-10] direction on the tetragonal magnetCeRh$_2$Si$_2$ with commensurate magnetic orders.  CeRh$_2$Si$_2$ has two successive antiferromagnetic (AF) orders in zeromagnetic field.  The high temperature phase (AF1 phase) has the magnetic modulation wavevector of $q = (\frac{1}{2}, \frac{1}{2}, 0)$, and the low temperature phase(AF2 phase) is characterized by the four $q$-vectors of $q = (\frac{1}{2},\frac{1}{2}, 0), (\frac{1}{2}, -\frac{1}{2}, 0), (\frac{1}{2}, \frac{1}{2},\frac{1}{2})$, and $(\frac{1}{2}, -\frac{1}{2}, \frac{1}{2})$.  By measuring the uniaxial stress dependence of the magnetization, resistivityand the intensities of magnetic Bragg reflections, we confirmed that the AF1phase has the single-$q$ magnetic order with two-fold rotational symmetry andthe AF2 phase has the multi-$q$ magnetic order with four-fold rotationalsymmetry.  In order to understand the origin of multi-$q$ order of CeRh$_2$Si$_2$, wealso performed inelastic neutron scattering measurement on the single crystalsamples.  We found a magnetic excitation at the transfer energy $\hbar \omega \sim$ 8meV.  By applying the linear spin-wave theory, we found that the nearest and thenext-nearest neighbor exchange interactions on the $ab$-plane, $J_1$ and $J_2$,are dominant in the AF2 phase.  However, the $J_1$-$J_2$ model cannot lift the degeneracy between thesingle-$q$ (AF1) and multi-$q$ (AF2) phases.  We suggest that it can be lifted by taking into account the biquadraticinteraction derived from the perturbative expansion for the Kondo latticeHamiltonian. [S. Hayami et al., Phys. Rev. B 95, 224424 (2017).

physical review. b./physical review. b

In-plane anisotropy of the single-$q$ and multiple-$q$ ordered phases in  the antiferromagnetic metal CeRh$_2$Si$_2$ unveiled by the bulk measurements  under uniaxial stress and neutron scattering