Unusual phase boundary of the magnetic-field-tuned valence transition in ${\mathrm{CeOs}}_4{\mathrm{Sb}}_{12}$

The phase diagram of the filled skutterudite ${\mathrm{CeOs}}_4{\mathrm{Sb}}_{12}$ has been mapped in fields ${\mu }_{0}H$ of up to 60 T and temperatures $T$ down to 0.5 K using resistivity, magnetostriction, and megahertz conductivity. The valence transition separating the semimetallic low-$H$, low-$T$ $\mathcal{L}$ phase from the metallic high-$H$, high-$T$ $\mathcal{H}$ phase exhibits a very unusual, wedge-shaped phase boundary, with a nonmonotonic gradient alternating between positive and negative. The expected “elliptical” behavior of the phase boundary of a valence transition with $H^2\propto T^2$ originates in the $H$ and $T$ dependence of the free energy of the $f$ multiplet. Here, quantum oscillation measurements suggest that additional energy scales associated with a quantum critical point are responsible for the deviation of the phase boundary of ${\mathrm{CeOs}}_4{\mathrm{Sb}}_{12}$ from this textbook behavior at high $H$ and low $T$. The distortion of the low-$H$, high-$T$ portion of the phase boundary may be associated with the proximity of ${\mathrm{CeOs}}_4{\mathrm{Sb}}_{12}$ to a topological semimetal phase induced by uniaxial stress.

Figure 1

$T\text{−}H$ phase diagram of ${\mathrm{CeOs}}_4{\mathrm{Sb}}_{12}$ derived from data in this work. Points are from resistivity (solid diamonds: $T_{\min }$, solid squares: $T_{\mathrm{infl}}$; different colors represent different samples), magnetostriction (solid circles), and MHz conductivity (solid triangles); SDW phase boundary is from Refs. [8, 9, 10, 11] (gray symbols). The dotted line is a guide to the eye of a plausible $\mathcal{L}\text{−}\mathcal{H}$ phase boundary completion. Top inset: example of the elliptical $H^2\propto T^2$ phase boundary expected for valence transitions. Bottom inset: field dependence of the effective mass.

Figure 2

(a) Resistivity $\rho$ [normalized to $\rho (300\mathrm{K}$)] of all four measured crystals (B1–B4) at $H=0$ for $0.6\le T\le 140\mathrm{K}$. Inset: resistivity hysteresis between warming (red) and cooling (blue) for sample B4 at low fields. Arrows mark the minimum. (b) Normalized $\rho \left(T\right)$ of sample B4 for several fields $\le 15\mathrm{T}$. An arrow at high temperatures indicates increasing field; note that the resistivity maximum at low temperatures decreases with increasing field. Inset: low-$T$ behavior of $\rho \left(T\right)$ between 2.5 and 6 T . Up arrows mark the emerging maximum for ${\mu }_{0}H\ge 3$ T; down arrows mark the SDW transition. (c) Normalized resistivity of sample B1 for $15\le {\mu }_{0}H\le 30\mathrm{T}$. Curves are offset for clarity. Black arrows mark the inflection point for ${\mu }_{0}H>15\mathrm{T}$. Inset: $\rho$ minimum; arrows track the suppression of $T_{\min }$ with increasing field.

Figure 3

$T\text{−}H$ phase diagram of ${\mathrm{CeOs}}_4{\mathrm{Sb}}_{12}$ with logarithmically scaled axes. Points are the same as in Fig. 1 with the addition of $T_{\max }$ (open diamonds). $T_{\max }$ does not mark a phase transition, but the precursor of the return to metallic behavior at low $T/\mathrm{high}H$.

Figure 4

(a) PDO frequency change $-\mathrm{\Delta }f$ in pulsed fields. Note the hysteresis between up and down sweeps. (b) Pulsed-field magnetostriction $\mathrm{\Delta }L/L$ (data are offset for clarity). Arrows mark the valence transition in (a) and (b). (c) Oscillatory part of $-\mathrm{\Delta }f$ for $0.57\le T\le 4.27\mathrm{K}$, and field dependence of the effective mass of the $F=1.6\mathrm{kT}$ quantum oscillations; $m_{\mathrm{e}}$ is the bare-electron mass.