Scaling behavior near a valence instability: The magnetic susceptibility ofCeIn3−xSnx

Abstract

Significant deviations from Vegard's law in $\mathrm{Ce}{\mathrm{In}}_{3\ensuremath{-}x}{\mathrm{Sn}}_{x}$ suggest a continuous valence transition from trivalence for $xl2.3$ to a small amount of mixed-valence character for $xg2.3$. Results for the magnetic susceptibility $\ensuremath{\chi}(x;T)$ in the range 2-340 K (with the background $d$-orbital contribution estimated from the susceptibility of $\mathrm{La}{\mathrm{In}}_{3\ensuremath{-}x}{\mathrm{Sn}}_{x}$ and subtracted off) exhibit several significant features: (i) For $0.8lxl3.0$ the effective moment ${\ensuremath{\mu}}^{2}=\frac{T\ensuremath{\chi}}{C}$ is, to within a few percent, a function of a single scaled variable ${\ensuremath{\mu}}^{2}(T,x)={\ensuremath{\mu}}^{2}(\frac{T}{{T}_{\mathrm{sf}}(x)})$. This is interpreted as single-energy-scale characteristic-energy behavior, where $k{T}_{\mathrm{sf}}$ is a characteristic energy for spin fluctuations which varies from 50 to 200 K. (ii) ${T}_{\mathrm{sf}}(x)$ oscillates with $x$ proportionally to the conduction-electron density of states $N({\ensuremath{\epsilon}}_{F};x)$ (deduced from the electronic properties of $\mathrm{La}{\mathrm{In}}_{3\ensuremath{-}x}{\mathrm{Sn}}_{x}$); this provides strong evidence that the spin fluctuations arise form interactions of the $4f$ spins with conduction electrons. (iii) The indium-rich alloys order magnetically at low temperature in some version of antiferromagnetism. The phase diagram, in which there is a $T=0$ phase transition from the antiferromagnetic ground state to a nonmagnetic trivalent spin-fluctuation ground state, is presented. This transition may correlate with an increase in the coupling $\mathcal{I}\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\sigma}}\ifmmode\cdot\else\textperiodcentered\fi{}{\stackrel{\ensuremath{\rightarrow}}{\mathrm{S}}}_{f}$ of conduction electrons to the $4f$ spins, as recently proposed. The scaling behavior breaks down in the vicinity of the ordered phase as the magnetic interactions stabilize the low-temperature moment.