Interplay between valence fluctuations and lattice instabilities across the quantum phase transition in EuCu2(Ge1−xSix)2

Abstract

Increasing Si concentrations in the ${\mathrm{EuCu}}_{2}{({\mathrm{Ge}}_{1\ensuremath{-}x}{\mathrm{Si}}_{x})}_{2}$ series tunes the divalent Eu antiferromagnetic (AF) compound ${\mathrm{EuCu}}_{2}{\mathrm{Ge}}_{2}$ $({T}_{N}=14\phantom{\rule{0.16em}{0ex}}\mathrm{K})$ to a nonmagnetic intermediate valence (IV) system ${\mathrm{EuCu}}_{2}{\mathrm{Si}}_{2}$. There is a collapse of the magnetic state and heavy quasiparticles occur at $x\ensuremath{\sim}0.7$ corresponding to a quantum critical point (QCP). We have systematically investigated the Eu-valence and magnetic states as well as the coupling to the lattice through the QCP in ${\mathrm{EuCu}}_{2}{({\mathrm{Ge}}_{1\ensuremath{-}x}{\mathrm{Si}}_{x})}_{2}$. This involved the $^{151}\mathrm{Eu}$ M\ossbauer effect spectroscopy and angle-resolved x-ray diffraction measurements as a function of Si concentration $(0\ensuremath{\le}x\ensuremath{\le}1)$ at variable temperatures in the range 300--4.2 K. The $^{151}\mathrm{Eu}$ probe indicates that the divalent Eu AF state is stable up to $x\ensuremath{\sim}0.5$, followed by a collapse of AF ordering for $xg0.6$, which is associated with a simultaneous sharp change of the valence state towards a nonmagnetic IV state. The crossover from the AF ordered state to the nonmagnetic IV state is found at a QCP corresponding to $x\ensuremath{\sim}0.7$, at which the nonmagnetic IV state is inhomogeneous and exhibits an enhanced $\mathrm{E}{\mathrm{u}}^{\ensuremath{\nu}+}$ mean valence $(\ensuremath{\nu}\ensuremath{\sim}2.5)$. We believe that the emergence of such an unusual valence state is related to the observed heavy quasiparticles at low temperatures near the QCP. Magnetic order and a nonmagnetic inhomogeneous IV state coexist in a narrow region $0.6\ensuremath{\le}xl0.7$, which evolves to a homogeneous IV state above $x\ensuremath{\sim}0.8$. The $\mathrm{ThCr}{\mathrm{Si}}_{2}$-type tetragonal structure is maintained throughout the series, although there is a precipitous increase in the $c/a$ ratio at 10 K when the valence fluctuations become enhanced at the critical concentration $x=0.7$. X-ray diffraction temperature scans at the critical concentration indicate conspicuous changes to steep temperature dependences of decreasing (increasing) values of $a$ $(c)$ lattice parameters and decreasing unit-cell volume at $Tl100 \mathrm{K}$, as the IV ground state become preferentially populated at low temperatures. Thus there is a clear manifestation of strong coupling between the lattice and the valence fluctuation process. A corresponding detailed phase diagram is constructed and compared with that obtained from recent external pressure studies on the system.