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

Abstract

Significant deviations from Vegard's law in $\mathrm{Ce}{\mathrm{In}}_{3-x}{\mathrm{Sn}}_x$ suggest a continuous valence transition from trivalence for $x<\mathrm{}2.3\mathrm{}$ to a small amount of mixed-valence character for $x>\mathrm{}2.3\mathrm{}$. Results for the magnetic susceptibility $\chi \mathrm{}(x;T)\mathrm{}$ in the range 2-340 K (with the background $d$-orbital contribution estimated from the susceptibility of $\mathrm{La}{\mathrm{In}}_{3-x}{\mathrm{Sn}}_x$ and subtracted off) exhibit several significant features: (i) For $0.8<x<\mathrm{}3.0\mathrm{}$ the effective moment ${\mu }^2=\frac{T\chi }{C}$ is, to within a few percent, a function of a single scaled variable ${\mu }^2\mathrm{}(T,x)={\mu }^2\left(\frac{T}{T_{\mathrm{sf}}\mathrm{}\left(x\right)\mathrm{}}\right)$. 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) $T_{\mathrm{sf}}\mathrm{}\left(x\right)\mathrm{}$ oscillates with $x$ proportionally to the conduction-electron density of states $N({\epsilon }_F;x)$ (deduced from the electronic properties of $\mathrm{La}{\mathrm{In}}_{3-x}{\mathrm{Sn}}_x$); 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 $T=0\mathrm{}$ 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 $\mathcal{I}\overrightarrow{\sigma }·{\overrightarrow{\mathrm{S}}}_f$ 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.