Evolution of critical pressure with increasing Fe substitution in the heavy-fermion systemURu2−xFexSi2

Abstract

Measurements of electrical resistivity, $\ensuremath{\rho}(T)$, were performed under quasihydrostatic pressure up to $P\ensuremath{\sim}2.2$ GPa to determine the pressure dependence of the so-called hidden order (HO) and large-moment antiferromagnetic (LMAFM) phases for the ${\mathrm{URu}}_{2\ensuremath{-}x}{\mathrm{Fe}}_{x}{\mathrm{Si}}_{2}$ system with $x$ = 0.025, 0.05, 0.10, 0.15, and 0.20. As the Fe concentration ($x$) is increased, we observed that a smaller amount of external pressure, ${P}_{c}$, is required to induce the HO $\ensuremath{\rightarrow}$ LMAFM phase transition. A critical pressure of ${P}_{c}\ensuremath{\sim}1.2$ GPa at $x=0.025$ reduces to ${P}_{c}\ensuremath{\sim}0$ at $x=0.15$, suggesting the ${\mathrm{URu}}_{2\ensuremath{-}x}{\mathrm{Fe}}_{x}{\mathrm{Si}}_{2}$ system is fully expressed in the LMAFM phase for $x\phantom{\rule{4pt}{0ex}}\ensuremath{\ge}\phantom{\rule{4pt}{0ex}}{x}_{c}^{*}=0.15$, where ${x}_{c}^{*}$ denotes the ambient pressure critical concentration of Fe. Using a bulk modulus calculation to convert $x$ to chemical pressure, ${P}_{\mathrm{ch}}(x)$, we consistently found that the induced HO $\ensuremath{\rightarrow}$ LMAFM phase transition occurred at various combinations of ${x}_{c}$ and ${P}_{c}$ such that ${P}_{\mathrm{ch}}({x}_{c})+{P}_{c}\phantom{\rule{4pt}{0ex}}\ensuremath{\approx}1.5$ GPa, where ${x}_{c}$ denotes those critical concentrations of Fe that induce the HO $\ensuremath{\rightarrow}$ LMAFM phase transition for the ${\mathrm{URu}}_{2\ensuremath{-}x}{\mathrm{Fe}}_{x}{\mathrm{Si}}_{2}$ compounds under pressure. We performed exponential fits of $\ensuremath{\rho}(T)$ in the HO and LMAFM phases in order to determine the pressure dependence of the energy gap, $\mathrm{\ensuremath{\Delta}}$, that opens over part of the Fermi surface in the transition from the paramagnetic (PM) phase to the HO/LMAFM phase at the transition temperature, ${T}_{0}$. The change in the pressure variation of $\mathrm{\ensuremath{\Delta}}(P)$ at the HO $\ensuremath{\rightarrow}$ LMAFM phase transition is consistent with the values of ${P}_{c}$ determined from the ${T}_{0}(P)$ phase lines at the PM $\ensuremath{\rightarrow}$ HO/LMAFM transition.