Thermodynamic Measurement of Angular Anisotropy at the Hidden Order Transition of URu$_{\mathrm{2}}$Si$_{\mathrm{2}}$

The heavy fermion compound URu$_{\mathrm{2}}$Si$_{\mathrm{2}}$ continues to attract great interest due to the unidentified hidden order it develops below 17.5 K. The unique Ising character of the spin fluctuations and low-temperature quasiparticles is well established. We present detailed measurements of the angular anisotropy of the nonlinear magnetization that reveal a $\cos^{4}\theta $ Ising anisotropy both at and above the ordering transition. With Landau theory, we show this implies a strongly Ising character of the itinerant hidden order parameter.