Possible devil's staircase in the Kondo lattice CeSbSe

The temperature- ($T$) magnetic-field ($H$) phase diagram for the tetragonal layered compound CeSbSe is determined from magnetization, specific heat, and electrical resistivity measurements. This system exhibits complex magnetic ordering at $T_{\mathrm{M}}=3\mathrm{K}$ and the application of a magnetic field results in a cascade of magnetically ordered states for $H\lesssim 1.8\mathrm{T}$ which are characterized by fractional integer size steps: i.e., a possible devil's staircase is observed. Electrical transport measurements show a weak temperature dependence and large residual resistivity which suggest a small charge-carrier density and strong scattering from the $f$ moments. These features reveal Kondo lattice behavior where the $f$ moments are screened incompletely, resulting in a fine balanced magnetic interaction between different Ce neighbors that is mediated by the Ruderman-Kittel-Kasuya-Yosida interaction. This produces the nearly degenerate magnetically ordered states that are accessed under an applied magnetic field.

Figure 1

(Left) Crystal structure of CeSbSe, which forms in the tetragonal space-group $P4/nmm$ (No. 129) with unit-cell parameters $a=4.2164\left(1\right)$ and $c=9.105\left(1\right)\AA$. The details are summarized in Tables 1 and 2. (Right) The $\left(hk0\right)$ plane reconstructed from the single-crystal x-ray-diffraction measurement.

Figure 2

(a) Magnetic susceptibility $\chi =M/H$ vs temperature $T$ collected in a magnetic field of $H=0.5\mathrm{T}$ applied parallel $\parallel$ and perpendicular $\perp$ to the $c$ axis of CeSbSe. (b) ${\chi }^{-1}$ vs $T$ for $H\parallel$ and $\perp$ to the $c$ axis. The straight dotted lines are fits to the data using the Curie-Weiss expression as described in the text. (c) $\chi \left(T\right)$ in several magnetic fields of $H\le 2\mathrm{T}$.

Figure 3

Magnetization $M$ vs magnetic-field $H$ for $H$ applied parallel $\parallel$ and perpendicular $\perp$ to the $c$ axis of CeSbSe.

Figure 4

(a) Magnetization $M$ vs magnetic-field $H$ for $H$ applied parallel $\parallel$ to the $c$ axis. Several hysteretic phase transitions occur, which broaden and decrease in $H$ with increasing $T$. (b) Zoom of $M\left(H\right)$ in the region of the first hysteretic phase transition. Up-sweep and down-sweep directions are indicated by arrows. (c) $T-H$ phase diagram for $H\parallel c$ constructed from the $M\left(H\right)$ data in panel (a). (d) The magnetization $M$ where the low-field linear slope region has been subtracted from the data and afterwards normalized to the value of $\mathrm{\Delta }M$ at 2.5 T. The data are plotted this way to emphasize the relative sizes of the steps, which all assume integer fractional values.

Figure 5

(a) Heat capacity divided by temperature $C/T$ vs $T$ for CeSbSe. (b) $C/T$ vs $T^2$. The dotted line is a fit to the data using the expression for a Fermi-liquid $C/T=\gamma +\beta T^2$, where $\gamma$ is the electronic coefficient of the heat capacity and $\beta T^2$ is the low-temperature limit of the lattice term. (c) The $4f$ contribution to the entropy $S_{4f}$ vs $T$, calculated as described in the text. (d) Electrical resistivity $\rho$ vs $T$ for $T\le 20\mathrm{K}$. (e) $\rho \left(T\right)$ over the temperature range of $500\mathrm{mK}\le T\le 300\mathrm{K}$.

Figure 6

(a) Electrical resistance $R$ vs magnetic-field $H$ with $H$ and the electrical current applied along the $c$ axis for hydrostatic pressures of $P\le 19\mathrm{kbars}$ in CeSbSe. (b) $R\left(T\right)$ near the magnetic phase transition at different $P$'s.