Nearly itinerant ferromagnetism in CaNi${}_2$ and CaNi${}_3$

Single crystals of CaNi${}_2$ and CaNi${}_3$ are successfully grown out of excess Ca. Both compounds manifest a metallic ground state with enhanced, temperature-dependent magnetic susceptibility. The relatively high Stoner factors of $Z=0.79$ and $0.87$ found for CaNi${}_2$ and CaNi${}_3$, respectively, reveal their close vicinity to ferromagnetic instabilities. The pronounced field dependence of the magnetic susceptibility of CaNi${}_3$ at low temperatures ($T<25$ K) suggests strong ferromagnetic fluctuations. A corresponding contribution to the specific heat with a temperature dependence of $T^3$ln$T$ is also observed.

Figure 1

Ca-Ni phase diagram after Notin et al. (Ref. 7). Starting compositions and temperature profile for CaNi${}_2$ and CaNi${}_3$ growths shown with blue lines (the dotted line represents rapid cooling).

Figure 2

(a) CaNi${}_2$ single crystal on a millimeter grid and (b) corresponding x-ray Laue back-reflection pattern. (c) CaNi${}_3$ single crystal on a millimeter grid and (d) corresponding x-ray Laue back-reflection pattern. Both diffraction patterns show the threefold rotation symmetry of {111} and {001} directions of their cubic and hexagonal unit cells, respectively.

Figure 3

X-ray-diffraction powder patterns of (a) CaNi${}_2$ and (b) CaNi${}_3$ together with fits based on the published cubic and hexagonal structures, respectively.

Figure 4

(a) Magnetic susceptibility $\chi =M/H$ per mol Ni of CaNi${}_2$. The moderate increase of $\chi \left(T\right)$ under cooling from 300 K to $T\approx 20$ K is followed by a significant increase at lower temperatures. The inset shows the inverse susceptibility. (b) Magnetization $M\left(H\right)$ as a function of field.

Figure 5

(a) Magnetic susceptibility $\chi =M/H$ of CaNi${}_3$ per mol Ni. The moderate increase of $\chi \left(T\right)$ under cooling from 300 K to $T\approx 20$ K is followed by a significant increase at lower temperatures. The inset shows the inverse susceptibility. Magnetization $M\left(H\right)$ as a function of field for $\mathit{H}\parallel \mathit{c}$ (b) and $\mathit{H}\perp \mathit{c}$ (c) at $T=2$ and 10 K.

Figure 6

Electrical resistivity of (a) CaNi${}_2$ and (b) CaNi${}_3$. CaNi${}_2$ shows metallic behavior with a linear $T$ dependence over a wide temperature range and a crossover to $T^2$ dependence at low $T$. An additional change of slope is observed for CaNi${}_3$ in the region around $T\approx 150$ K. (Absolute values are approximate due to the poorly defined geometry factor of the samples.) Insets: The magnetoresistance $\Delta \rho /{\rho }_0=({\rho }_H-{\rho }_0)/{\rho }_0$ plotted on a double-logarithmic scale at $T=2$ K is positive and approaches values of 22$\%$ and 46$\%$ at ${\mu }_{0}H=9$ T for CaNi${}_2$ and CaNi${}_3$, respectively.

Figure 7

Specific heat plotted as $C/T$ vs $T^2$ for (a) CaNi${}_2$ and (b) CaNi${}_3$. Additional contributions to the specific heat of an ordinary metal ($C/T=\gamma +\beta T^2$, indicated by the red lines) are observed below $T\approx 10$ K. Assuming a contribution of spin fluctuations of the form $C_{\mathrm{mag}}=A{T}^3\ln (T/T_{\mathit{SF}})$ leads to a $T$ dependence shown by the dashed blue line. Insets: specific heat as a function of temperature.