Ni-based superconductor: Heusler compound ${\text{ZrNi}}_2\text{Ga}$

This work reports on the Heusler superconductor ${\text{ZrNi}}_2\text{Ga}$. Compared to other nickel-based superconductors with Heusler structure, ${\text{ZrNi}}_2\text{Ga}$ exhibits a relatively high superconducting transition temperature of $T_c=2.9\text{K}$ and an upper critical field of ${\mu }_0{H}_{c2}=1.5\text{T}$. Electronic structure calculations show that this relatively high $T_c$ is caused by a Van Hove singularity, which leads to an enhanced density of states at the Fermi energy $N\left({ϵ}_F\right)$. The Van Hove singularity originates from a higher-order valence instability at the $L$ point in the electronic structure. The enhanced $N\left({ϵ}_F\right)$ was confirmed by specific-heat and susceptibility measurements. Although many Heusler compounds are ferromagnetic, our measurements of ${\text{ZrNi}}_2\text{Ga}$ indicate a paramagnetic state above $T_c$ and could not reveal any traces of magnetic order down to temperatures of at least 0.35 K. We investigated in detail the superconducting state with specific-heat, magnetization, and resistivity measurements. The resulting data show the typical behavior of a conventional weakly coupled BCS ($s$-wave) superconductor.

Figure 1

The cubic $\text{L}{2}_1$ Heusler structure of ${\text{ZrNi}}_2\text{Ga}$. Zr atoms are black, Ga atoms are white, and Ni atoms are gray. The Zr atoms are placed on Wyckoff position $4a$ (0,0,0), Ga on $4b$ $\left(\frac{1}{2},\frac{1}{2},\frac{1}{2}\right)$, and Ni on $8c$ $\left(\frac{1}{4},\frac{1}{4},\frac{1}{4}\right)$. The Ni atoms build up a simple-cubic sublattice. The centers of the cubes formed by Ni are alternately occupied by Zr and Ga atoms corresponding to a perfect $2^3$ CsCl superstructure.

Figure 2

(Color online) Electronic structure of ${\text{ZrNi}}_2\text{Ga}$. (a) displays the band structure and (b) the density of states. The inset in (b) shows the dispersion of the bands that cause the Van Hove singularity at the $L$ point on an enlarged scale.

Figure 3

The calculated vibrational spectrum of ${\text{ZrNi}}_2\text{Ga}$. (a) displays the phonon dispersion and (b) the corresponding density of states.

Figure 4

Powder x-ray diffraction of ${\text{ZrNi}}_2\text{Ga}$ at 300 K (black). The difference curve (gray) shows the difference between the observed data and the Rietveld refinement.

Figure 5

The resistance of ${\text{ZrNi}}_2\text{Ga}$ as a function of temperature. The inset shows an enlargement of the superconduction transition at $T_c^{\text{mid}}=2.87\text{K}$.

Figure 6

(Color online) Magnetization measurements in the superconducting state of ${\text{ZrNi}}_2\text{Ga}$. (a) shows the temperature-dependent magnetization under ZFC and FC conditions. (b) shows the field-dependent magnetization at a temperature of 2 K.

Figure 7

Electronic contribution to the specific heat of ${\text{ZrNi}}_2\text{Ga}$ divided by temperature $T$ at various magnetic fields. The continuous line represents the calculated behavior of a weak-coupling BCS superconductor at zero magnetic field.

Figure 8

Electronic contribution to the specific heat of ${\text{ZrNi}}_2\text{Ga}$ at zero field divided by ${\gamma }_n{T}_c/T$ vs $T_c/T$. The inset shows $C_e/T$ at $T=0.5$ vs the magnetic field.

Figure 9

Temperature dependence of the upper critical field $H_{c2}$ of ${\text{ZrNi}}_2\text{Ga}$. Shown is a summary of the resistance and specific-heat measurements. The continuous line represents a calculation of the WHH model with $\alpha =0$ and ${\lambda }_{\text{so}}=0$, which is identical to a finite $\alpha$ and ${\lambda }_{\text{so}}\to \infty$.

Figure 10

Susceptibility ${\chi }_{\text{dc}}=M/H$ of ${\text{ZrNi}}_2\text{Ga}$ in a magnetic field of ${\mu }_{0}H=2\text{T}>{\mu }_0{H}_{c2}$. The susceptibility of the normal state shows Pauli-type behavior without any indications of magnetic order. At low temperatures there is a small Curie-Weiss-type upturn, which may be attributed to sample inhomogeneities or impurities.

Figure 11

(Color online) Powder x-ray diffraction of the alloys ${\text{Zr}}_{1-x}{\text{Nb}}_x{\text{Ni}}_2\text{Ga}$ at 300 K. Shown is the region around the (220) reflection, which determines the cubic lattice parameter. The signals are splitted in $\text{Mo}K\alpha 1$ and $\text{Mo}K\alpha 2$ peaks.

Figure 12

(Color online) Superconducting transitions of the alloys ${\text{Zr}}_{1-x}{\text{Nb}}_x{\text{Ni}}_2\text{Ga}$ under ZFC conditions. The measurements were performed with magnetic field of ${\mu }_{0}H=2.5\text{mT}$.