Electro-nuclear transition into a spatially modulated magnetic state in YbRh$_2$Si$_2$

The nature of the antiferromagnetic order in the heavy fermion metal YbRh$_2$Si$_2$, its quantum criticality, and superconductivity, which appears at low mK temperatures, remain open questions. We report measurements of the heat capacity over the wide temperature range 180 $\mu$K - 80 mK, using current sensing noise thermometry. In zero magnetic field we observe a remarkably sharp heat capacity anomaly at 1.5 mK, which we identify as an electro-nuclear transition into a state with spatially modulated electronic magnetic order of maximum amplitude 0.1$\mu_B$. We also report results of measurements in magnetic fields in the range 0 to 70 mT, applied perpendicular to the c-axis, which show eventual suppression of this order. These results demonstrate a coexistence of a large moment antiferromagnet with putative superconductivity.