Thermal expansion measurements on Fe substituted URu$_{\mathrm{2}}$Si$_{\mathrm{2}}$*

The search for the order parameter of the hidden order (HO) phase in URu$_{\mathrm{2}}$Si$_{\mathrm{2}}$ has attracted an enormous amount of attention for the past three decades. The small antiferromagnetic moment of only \textasciitilde 0.03 $\mu_{\mathrm{B}}$/U found in the HO phase is too small to account for the entropy of \textasciitilde 0.2Rln(2) derived from the second order mean field BCS-like specific heat anomaly associated with the HO transition that occurs below To $=$ 17.5 K. A first order transition from the HO phase to a large moment antiferromagnetic (LMAFM) phase occurs under pressure. We have recently demonstrated that tuning URu$_{\mathrm{2}}$Si$_{\mathrm{2\thinspace }}$by substitution of Fe for Ru reproduces the temperature vs applied pressure phase diagram.and offers an opportunity to study the HO and LMAFM phases at atmospheric pressure. Motivated by this observation, we performed thermal expansion measurements on URu$_{\mathrm{2-x}}$Fe$_{\mathrm{x}}$Si$_{\mathrm{2}}$ single crystals for various values of x in both the HO and LMAFM regions of the phase diagram. Interesting preliminary results have emerged from these studies that shed light on the LMAFM phase and its relationship with the elusive HO phase.