Neutron scattering study of URu$_2$Si$_2$ magnetic properties: from hydrostatic pressure to uniaxial stress

Since the discovery of the unusual magnetic and superconducting properties of URu$_2$Si$_2$ in 1985 by Palstra~[1], this heavy fermion has been extensively studied. A ``Hidden Order'' evidences by bulk properties like specific heat, has been found below $T_0$=17.8K. Neutron scattering in this case is an efficient probe for the study of this compound as large magnetic excitations and an irremovable tiny antiferromagnetic moment are present in this sample. Even though the tiny antiferromagnetic moment aligned along the $c$-axis at $Q_0$ is only $\sim0.01 \mu_B$, the magnetic excitations seem to be associated to a large magnetic moment of $\sim$ 1 $\mu_B$ and show two minimums at $Q_0$=(1,0,0) but also at $Q_1$=(0.6,0,0). These magnetic responses have been intensively studied in normal conditions by Broholm~[2,3] and our group[4], but also versus magnetic field~[5], and more recently under hydrostatic pressure~[6]. The result of these experiments seem to indicate that the Hidden Order is linked to the excitation at $Q_0$ and not to the excitation at $Q_1$. We will present the revisited magnetic properties of URu$_2$Si$_2$ under uniaxial stress along the $a$-axis~[7,8]. Both elastic and inelastic contributions have been measured versus the constraints. In the HO state, as the constraint increases, the AF gap excitation at $Q_0$ decreases and the tiny moment increases: it seems also that there is a relation between both parameters. On the other hand, the excitation gap at $Q_1$ is slightly increasing. From our measurement we infer a critical pressure of $\sim$ 0.33~GPa, with a large increase of the antiferromagnetic moment. This behavior is very similar to results under hydrostatic pressure. Combining hydrostatic pressure, uniaxial stress along the $a$-axis and neutron Larmor diffraction measurements, that gives the lattice distribution of our URu$_2$Si$_2$ crystal, we conclude that the magnetic exchange integrals are dominated by the lattice parameter $a$ and not the ratio $c/a$ as usually believed. \\ \noindent[1]~T.~T.~M. Palstra, \textit{et al.}, Physical Review Letters {\bf 55}, 2727 (1985).\\ \noindent[2]~C. Broholm, \textit{et al.}, Physical Review Letters {\bf 58}, 1467 (1987).\\ \noindent[3]~C. Broholm, \textit{et al.}, Physical Review B {\bf 43}, 12809 (1991).\\ \noindent[4]~F. Bourdarot, \textit{et al.}, Journal of the Physical Society of Japan {\bf 79}, 064719 (2010).\\ \noindent[5]~F. Bourdarot, \textit{et al.}, Physical Review Letters {\bf90}, 067203 (2003).\\ \noindent[6]~A. Villaume, \textit{et al.}, Physical Review B {\bf 78}, 012504 (2008).\\ \noindent[7]~M. Yokoyama, \textit{et al.}, Physical Review B {\bf 72}, 214419 (2005).\\ \noindent[8]~F. Bourdarot, \textit{et al.}, Physical Review B {\bf 84}, 184430 (2011).