Strong valence fluctuation effects in Sm$T{r}_2$Al${}_{20}$ ($Tr=\text{Ti}$, V, Cr)

We present a single-crystal study of low-temperature magnetism and transport in Sm$T{r}_2$Al${}_{20}$ ($Tr=\text{Ti}$, V, and Cr). Strong valence fluctuation is manifested as Kondo effects, including a large Sommerfeld coefficient $\gamma$, a weak temperature dependence of magnetic susceptibility, and a $-\ln T$ dependent resistivity. All the systems order antiferromagnetically at $T_{\mathrm{N}}=6.4$ K (Ti), 2.9 K (V), and 1.8 K (Cr). A systematic change in the susceptibility, specific heat, and resistivity indicates that stronger $c$-$f$ hybridization in SmV${}_2$Al${}_{20}$ and SmCr${}_2$Al${}_{20}$ than in SmTi${}_2$Al${}_{20}$ suppresses $T_{\mathrm{N}}$ and induces the valence fluctuations and, moreover, field-insensitive heavy fermion states.

Figure 1

(a) Temperature dependence of the $4f$ contribution to the specific heat $C_{4f}$ for SmTi${}_2$Al${}_{20}$ (circle), SmV${}_2$Al${}_{20}$ (square), and SmCr${}_2$Al${}_{20}$ (diamond) under ${\mu }_{0}H=0$ T (solid symbols) and 9 T (open symbols). Arrows indicate the transition temperatures defined as the peak temperature of $C_P\left(T\right)$. (b) Temperature dependence of the $4f$ electron contribution $S_{4f}$ to the entropy. The horizontal dashed lines indicate $S_{4f}=R\ln 2$ and $R\ln 4$, respectively. Inset: $T$ dependence of $C_{4f}/T$. To estimate the Sommerfeld coefficient $\gamma$ at $T=0$ and $S_{4f}$ at 0.4 K, a linear extrapolation (dashed straight line) of $C_{4f}/T$ to $T=0$ is used. The solid line indicates the fitting to the form $C/T=\gamma +A/T^3$ for SmTi${}_2$Al${}_{20}$.

Figure 2

Temperature dependence of the magnetic susceptibility of the $4f$ electron contribution ${\chi }_{4f}$ for SmTi${}_2$Al${}_{20}$ (circle), SmV${}_2$Al${}_{20}$ (square), and SmCr${}_2$Al${}_{20}$ (diamond) and under ${\mu }_{0}H=0.5\text{T}\parallel \left[110\right]$. No anisotropy is found under the field below 0.5 T. The solid and dotted lines show ${\chi }^{3+}\left(T\right)$ and ${\chi }^{2+}\left(T\right)$ calculated for $4f^5$ $J=5/2$ and $4f^6$ $J=0$ single-ion ground states, respectively. Left-hand inset: $\chi \left(T\right)$ of La$T{r}_2$Al${}_{20}$. Right-hand inset: Low-temperature part of $\chi$ for SmTi${}_2$Al${}_{20}$ and SmV${}_2$Al${}_{20}$. The arrows indicate the transition temperatures defined as the cusp temperatures in $\chi \left(T\right)$.

Figure 3

Temperature dependence of the electrical resistivity $\rho$ of Sm$T{r}_2$Al${}_{20}$ ($Tr=$Ti, V, Cr). The arrows indicate the transition temperatures defined at the peak temperature of the specific heat. The dashed lines indicate the fitted curve using Hamann's expression[30] (see text). The solid lines indicate the inelastic component of the resistivity $\rho \left(T\right)-{\rho }_0$ of La$T{r}_2$Al${}_{20}$ with a residual resistivity ${\rho }_0=0.5$ $(\mu \Omega$ cm) (Ti), 11.6 $(\mu \Omega$ cm) (V), and 51 $(\mu \Omega$ cm) (Cr).

Figure 4

$T$-$H$ phase diagram of Sm$T{r}_2$Al${}_{20}$ ($Tr=\text{Ti}$, V, Cr) constructed by measurements made under fields along [100] (diamond), [110] (square), and [111] (circle). The open symbols are determined from the cusp of $\chi \left(T\right)$ and the solid symbols are determined from the peak of $C_P\left(T\right)$. The solid lines are guides to the eye.