Basal-plane anisotropy of field-induced multipolar order in tetragonal CeRh$_2$As$_2$

Unconventional superconductivity in Ce-based Kondo-lattice materials emerges almost exclusively in the vicinity of weak dipolar magnetic orders, while higher multipolar orders are only known to occur in a few Pr-based unconventional superconductors and possibly URu$_2$Si$_2$. The multiphase superconductor CeRh$_2$As$_2$ appears to be a notable exception from this trend. Showing clear signatures of magnetism, this tetragonal system is suspected to host a concomitant quadrupolar order, which could be causing the strong enhancement of the ordering temperature when a magnetic field is applied perpendicular to the fourfold ($c$) axis of the lattice. In this work, we show that the field-temperature phase diagram of CeRh$_2$As$_2$ has a remarkable basal-plane anisotropy. This finding supports the scenario of coupled magnetic and multipolar ordering, which may have implications for the pairing mechanism of the superconductivity, and guides the development of the next iteration of theoretical models.