Anisotropic transport and magnetic properties and magnetic-field tuned states of CeZn${}_{11}$ single crystals

We present detailed temperature- and field-dependent data obtained from magnetization, resistivity, heat capacity, Hall resistivity and thermoelectric power measurements performed on single crystals of CeZn${}_{11}$. The compound orders antiferromagnetically at $\sim$2 K. The zero-field resistivity and thermoelectric power data show features characteristic of a Ce-based intermetallic with crystal-electric-field splitting and possible Kondo lattice effects. We constructed the $T-H$ phase diagram for the magnetic field applied along the easy [110] direction, which shows that the magnetic field required to suppress $T_N$ below 0.4 K is in the range of 45–47.5 kOe. A linear behavior of the $\rho \left(T\right)$ data, $\mathbf{H}\parallel$ [110], was observed only for $H=45$ kOe for 0.46 K $\le T\le$ 1.96 K followed by the Landau–Fermi-liquid regime for a limited range of fields 47.5 kOe $\le H\le$ 60 kOe. From the analysis of our data, it appears that CeZn${}_{11}$ is a local moment compound with little or no electronic correlations arising from the Ce 4$f$ shell. The thermoelectric and transport properties of CeZn${}_{11}$ are mostly governed by the crystal-electric-field effects. Given the very high quality of our single crystals, quantum oscillations are found for both CeZn${}_{11}$ and its nonmagnetic analog LaZn${}_{11}$.

Figure 1

Powder x-ray diffraction pattern of finely ground CeZn${}_{11}$ single crystals. The peaks that belong to CeZn${}_{11}$ are indexed to a tetragonal unit cell with $a=10.67\pm 0.02$ Å and $c=6.87\pm 0.01$ Å. The relatively few, low-intensity peaks that can be associated to Zn are not indexed, however, the markers of the peaks positions are given.

Figure 2

Powder x-ray diffraction pattern of finely ground LaZn${}_{11}$ single crystals. The peaks that belong to LaZn${}_{11}$ are indexed to a tetragonal unit cell with $a=10.69\pm 0.02$ Å and $c=6.89\pm 0.01$ Å. The relatively few, low-intensity peaks that can be associated to Zn are not indexed, however, the markers of the peaks positions are given.

Figure 3

(a) X-ray Laue backscattering pattern showing a fourfold rotation symmetry of the [001] direction, (b) x-ray Laue backscattering pattern showing a twofold rotation symmetry of the [110] direction, (c) a sketch of the sample with the main crystallographic directions, and (d) the picture of the sample with the mirrored triangular surface being the (101) plane. Solid lines show the extension of the sample to match the sketch in (c).

Figure 4

(a) Temperature-dependent magnetic susceptibility $M\left(T\right)/H$ of CeZn${}_{11}$, with the magnetic field applied along the [100], [110], [001], and [101] directions. The inset displays temperature-dependent, inverse magnetic susceptibilities for the field applied along the [100], [001], and of polycrystalline average ${\chi }_{\mathrm{poly}}=(2{\chi }_{100}+{\chi }_{001})/3$. (b) Temperature-dependent magnetic susceptibility $M\left(T\right)/H$ of LaZn${}_{11}$, with the magnetic field applied along the [100], [110], and [001] directions. The inset shows the enlarged low-temperature part of the $M\left(T\right)/H$. We would like to draw the reader's attention to the difference in the vertical scales of (a) and (b).

Figure 5

(a) Magnetization isotherms $M\left(H\right)$ of CeZn${}_{11}$ at 1.85 K for the magnetic field applied along the [100], [110], [001], and [101] directions. The inset: d$M$/d$H$ versus $H$ for $\mathbf{H}\parallel$ [110] with the arrow denoting a broad metamagneticlike feature seen in $M\left(H\right)$. (b) Magnetization isotherms $M\left(H\right)$ of LaZn${}_{11}$ at 1.85 K for the magnetic field applied along the [100], [110], and [001] directions.

Figure 6

Zero-field, temperature-dependent resistivity $\rho \left(T\right)$ data of CeZn${}_{11}$ and LaZn${}_{11}$. The inset in the upper left shows an enlarged, low-temperature part of the resistivity with the AFM transition $T_N$ marked with an arrow. The inset in the lower right shows the magnetic part of the resistivity ${\rho }_m=\rho$(CeZn${}_{11})-\rho$(LaZn${}_{11})$. The data shown in the insets are the same as shown in the main panel of the figure.

Figure 7

(a) Heat capacity $C_p\left(T\right)$ of CeZn${}_{11}$ ($•$: total), $\oplus$: heat capacity of LaZn${}_{11}$ (electronic and lattice), and $\circ$: magnetic [$C_m=C_p$(CeZn${}_{11})-C_p$(LaZn${}_{11}$)]. Dashed curve: modeled Schottky anomaly assuming that the energies of the first and second excited states are ${\Delta }_1=12.2$ K and ${\Delta }_2=65$ K added to heat-capacity data of LaZn${}_{11}$. (b) d$\rho$/d$T$, d($\chi T$)/d$T$, and $C_p$ as a function of temperature. The $\rho \left(T\right)$ data set was smoothed with the adjacent-averaging method with two points of window before derivative was taken. (c) Magnetic entropy $S_m$ calculated by integrating $C_m/T$ ($•$) and $\Delta C_m/T$ (line). (d) $\Delta C_m=C_p\left({\text{CeZn}}_{11}\right)-C_p\left({\text{LaZn}}_{11}\right)-C_{\mathrm{Sch}}$, where $C_{\mathrm{Sch}}$ is the contribution of the modeled Schottky anomalies, as a function of temperature. Red line is the low-temperature fit of the data with the function $A{T}^3{e}^{-E_g/T}$, which is expected for the magnon specific heat of an antiferromagnet with the energy gap $E_g$ in the magnon dispersion relation (Refs. 24 and 25).

Figure 8

Zero-field, temperature-dependent thermoelectric power $S\left(T\right)$ of CeZn${}_{11}$ and LaZn${}_{11}$. The inset: expanded, low-temperature portion of the plot.

Figure 9

Low-temperature parts of $\rho \left(T\right)$ curves for CeZn${}_{11}$ taken at different applied fields for $\mathbf{H}\parallel$ [110]. Subsequent data sets are shifted upward from each other by 0.3 $\mu \Omega$ cm for clarity. For $H\le$ 42.5 kOe, the arrows denote the transition temperature $T_N$ inferred from d$\rho$/d$T$. The inset shows the resistivity curves for $H=0$ and 140 kOe without any offset.

Figure 10

(a) $\rho \left(H\right)$ ($\mathbf{H}\parallel$ [110]) isotherms for CeZn${}_{11}$. Subsequent data sets are shifted upward by 0.1 $\mu \Omega$ cm from each other. The arrows denote the fields of magnetic ordering that were determined by the intersection of two lines that go through the $\mathrm{d}\rho /\mathrm{d}H$ data shown in (b). Solid dots represent the position of the minimum in the d$\rho$/d$H$ data in (b). (b) d$\rho$/d$H$ at 0.5 K as a function of magnetic field, with the criterion for the field of magnetic ordering and the minimum (${\mathrm{d}\rho /\mathrm{d}H)}_{\min }$. The $\rho \left(H\right)$ data set was smoothed with the adjacent-averaging method with a 2 points of window before derivative was taken.

Figure 11

Kohler plot (showing only every third data point), $\Delta \rho /\rho (0,T)$, for the highest and lowest field and temperature, where $\Delta \rho =\rho (H,T)-\rho (0,T)$, for CeZn${}_{11}$ for the field applied along the [110] direction. The dashed and solid lines denote two manifolds that the data appear to follow.

Figure 12

(a) Heat-capacity data for CeZn${}_{11}$ taken with the applied magnetic field $\mathbf{H}\parallel$ [110], (b) and (c) expanded, low-temperature part of heat-capacity curves. The arrows indicate peaks associated with the magnetic ordering.

Figure 13

$C_p/T$ of CeZn${}_{11}$ as a function of magnetic field measured at constant temperatures of 0.5, 1, and 3 K (solid symbol data) with the magnetic field along the [110] direction. Open symbols represent the data taken from $C_p{\left(T\right)|}_{H=\mathrm{const}}$ shown in Fig. 12.

Figure 14

Hall resistivity ${\rho }_H\left(H\right)$ of CeZn${}_{11}$ measured at different constant temperatures. The inset shows the data after the linear background, represented by a dashed line on the main graph, is subtracted. The arrow indicates the field of the maximum which corresponds to a transition from an ordered to a nonordered state at the lowest temperature. (The data sets were smoothed with the adjacent-point-averaging method with a 5 points of window.)

Figure 15

The semilog plot of the temperature-dependent thermoelectric power $S\left(T\right)$ of CeZn${}_{11}$ measured with different applied magnetic fields $\mathbf{H}\parallel$ [110]. The inset illustrates the evolution of the two local maxima as a function of applied field.

Figure 16

(a) Field-dependent thermoelectric power $S\left(H\right)$ of CeZn${}_{11}$ at 2.3 K. The inset: FFT spectrum of the oscillations obtained from TEP at 2.3 K.

Figure 17

(a) $\mathrm{d}\rho /\mathrm{d}T$ as a function of temperature. Arrows denote the AFM transition temperature and a broad shoulder in d$\rho$/d$T$. The $\rho \left(T\right)$ data set was smoothed with the adjacent-averaging method with a 2 points of window before derivative was taken. (b) $C_p/T$ as a function of temperature, arrows indicate a peak associated with the magnetic ordering and the maximum in $C_p/T$ that emerges at $H\ge 47.5$ kOe.

Figure 18

(a), (b) $H-T$ phase diagram of CeZn${}_{11}$ for $\mathbf{H}\parallel$ [110]. Long-range magnetic order (LMRO) region is marked on the phase diagram. Legends: $▴$: d$M$/d$H$; $▵$: d($\chi T$)/d$T$; $\blacksquare$ and $\square$: d$\rho$/d$T$ ($T_N$ and broad maximum, respectively); $•$ and $\oplus$: d$\rho$/d$H$ ($T_N$ and minimum, respectively); $☆$: $C_p$ ($T_N$); +: broad peak in $C_p$; $\times$: max in $C_p/T$; open stars: features seen in $C_p\left(H\right)$; $*$: maximum in $\Delta {\rho }_H$; $⊲$: $S_{\min }$; $\ominus$: $S_{\pm }$; $\circ$: $S_{\mp }$; and $◂:S\left(H\right)$. Dashed lines that run through the data points are guides to the eye. Dashed line at 0.4 K is the temperature limit of our measurements.

Figure 19

(a) $\rho \left(T\right)$ curves for CeZn${}_{11}$ taken at different applied fields for $\mathbf{H}\parallel$ [110] as a function of $T^3$ (main graph) and $T^2$ (inset). (b) Log-log plot of $\Delta \rho \left(T\right)=\rho -{\rho }_0$ for CeZn${}_{11}$, 45 kOe $\le H\le$ 60 kOe. Dashed and solid lines represent $T$ and $T^2$ dependencies, respectively. Arrows denote the temperatures where the data deviate from linear and quadratic dependencies.

Figure 20

Semilog plot of the magnetic part [$C_m=C_p$(CeZn${}_{11})-C_p$(LaZn${}_{11}$)] of the heat capacity $C_m/T$ as a function of $T$. The inset shows the data sets for 45 kOe $\le H\le$ 50 kOe.

Figure 21

(a) $C/T$ at 0.4 K, (b) resistivity at 0.46 K and ${\rho }_0$, obtained from ln($\rho -{\rho }_0)=$ ln($A{T}^n$) fit, as a function of applied magnetic field. (c) The exponent $n$ from ln($\rho -{\rho }_0)=$ ln($A{T}^n$). (d) The range of temperatures where log($\rho -{\rho }_0)=$ ln($A{T}^n$) fit was performed.

Figure 22

Magnetization isotherms of LaZn${}_{11}$ for $\mathbf{H}\parallel$ [110] and $\mathbf{H}\parallel$ [001] at $T=1.85$ K plotted versus $1/H$.

Figure 23

FFT spectra of the dHvA data of LaZn${}_{11}$ for $\mathbf{H}\parallel$ [110] and $\mathbf{H}\parallel$ [001]. Inset: temperature dependence of the FFT amplitudes $A$ of the observed oscillations for $\mathbf{H}\parallel$ [110].

Figure 24

Kohler plot (showing every third data points), $\Delta \rho /\rho (0,T)$, where $\Delta \rho =\rho (H,T)-\rho (0,T)$, for CeZn${}_{11}$ for the field applied along the [110] direction. The dashed and solid lines denote two manifolds that the data appear to follow.

Figure 25

Hall coefficient $R_H={\rho }_H/H$ versus temperature for CeZn${}_{11}$ at $H=10$, 50, 90, and 140 kOe. The inset: low-temperature part of the Hall coefficient data. (The data sets were smoothed with the adjacent-point-averaging method with a 5 points of window.)