EXAFS investigation of the local structure in URu 2 -x Fe x Si 2 : Evidence for distortions below 100 K

X-ray absorption measurements at the U ${L}_{\\mathrm{III}}$, Ru $K$, and Fe $K$ edges are reported for the hidden order (HO) material ${\\mathrm{URu}}_{2\\ensuremath{-}x}{\\mathrm{Fe}}_{x}{\\mathrm{Si}}_{2}$ ($x=0$, 0.05, 0.08, 0.10, 0.12, 0.15, and 0.20) as a function of $x$ and temperature $T$. When Fe is substituted for Ru, the local structure about Fe shrinks slightly and the first neighbor Fe-Si bond length decreases by $\\ensuremath{\\approx}0.05\\phantom{\\rule{0.16em}{0ex}}\\AA{}$. More importantly excess disorder is observed below 80--100 K (the coherence temperature ${T}^{*}$) in plots of the Debye-Waller factor ${\\ensuremath{\\sigma}}^{2}$ ($\\ensuremath{\\sigma}$ is the width of the pair distribution function); at low $T$ the data deviate from the usual Einstein or correlated-Debye model plots. This excess disorder is most prominent for the Ru-Si bond, and ${\\ensuremath{\\sigma}}^{2}$ actually increases below 80 K. These results suggest a local orthorhombic distortion with ${B}_{1g}$-like symmetry that develops below 80--100 K. A model that describes these local distortions is presented, and discussed in terms of other measurements that indicate a breaking of fourfold symmetry at low $T$. In addition, the square root of the difference between ${\\ensuremath{\\sigma}}^{2}(T)$ for the Ru-Si pair and a Debye fit to these data serves as an order parameter for this orthorhombic distortion, in the temperature range below 100 K. This quantity is a length related to $a\\text{\\ensuremath{-}}b$, the difference between the $a$ and $b$ lattice constants in the orthorhombic phase, and provides a connection between this distortion and ${T}^{*}$. X-ray absorption near edge structure (XANES) measurements also show that there are no changes in the edge positions down to 0.1 eV for any edge as a function of $x$, for $T$ in the HO regime.