Search for ${\mathrm{Sc}}_{3}X\mathrm{B}$ $(X=\mathrm{In},\mathrm{Tl},\mathrm{Ga},\mathrm{Al})$ perovskites superconductors and proximity of weak ferromagnetism

A possibility for an additional family of intermetallic perovskite superconductors ${\mathrm{Sc}}_{3}X\mathrm{B}$, with $X=\mathrm{Tl}$, In, Ga, and Al, is presented as a result of Korringa-Kohn-Rostoker (KKR) electronic structure and pseudopotential phonon calculations. The large values of computed McMillan-Hopfield parameters on scandium suggest the appearance of superconductivity in ${\mathrm{Sc}}_{3}X\mathrm{B}$ compounds. On the other hand, the possibility of weak itinerant ferromagnetic behavior of ${\mathrm{Sc}}_{3}X$ systems is indicated by the small magnetic moment on Sc atoms in the two cases of $X=\mathrm{Tl}$ and In. In addition, the electronic structure and resulting superconducting parameters for the realistic case of boron-deficient systems ${\mathrm{Sc}}_{3}X{\mathrm{B}}_x$ are computed, using KKR method with the coherent potential approximation, by replacing boron atom with a vacancy. The comparison of the calculated McMillan-Hopfield parameters of the ${\mathrm{Sc}}_{3}X\mathrm{B}$ series with corresponding values in related $\mathrm{Mg}\mathrm{C}{\mathrm{Ni}}_3$ and $\mathrm{Y}{\mathrm{Rh}}_3\mathrm{B}$ superconductors is also shown, finding favorable trends for superconductivity.

Figure 1

(Color online) Crystal structure of the ${\mathrm{Sc}}_{3}X\mathrm{B}$ perovskite. The atomic positions are: $X$: 1a (0,0,0), B: 1b $(1∕2,1∕2,1∕2)$, and Sc: 3c $(0,1∕2,1∕2)$, $(1∕2,0,1∕2)$, $(1∕2,1∕2,0)$. If the central B atom is removed, perovskite structure changes into ${\mathrm{Cu}}_3\mathrm{Au}$-type one.

Figure 2

(Color online) KKR total DOS of isoelectronic ${\mathrm{Sc}}_{3}X\mathrm{B}$ perovskites, calculated at equilibrium lattice constants $a_0$. Site-decomposed densities for $X$, B, Sc, are plotted in brown (dotted line), red (dash-dotted line), and blue (dashed line), respectively. The Fermi level is shifted to zero and marked by a vertical line.

Figure 3

Electronic dispersion curves $E\left(\mathbf{k}\right)$ along high-symmetry directions in ${\mathrm{Sc}}_3\mathrm{In}\mathrm{B}$ perovskite, calculated at equilibrium lattice constant $a_0$. The Fermi level is shifted to zero and marked by a horizontal line.

Figure 4

Phonon DOS $F\left(\omega \right)$ in ${\mathrm{Sc}}_{3}X\mathrm{B}$ perovskites, calculated at equilibrium lattice constants $a_0$.

Figure 5

(Color online) Influence of the ${\mu }^{\star }$ parameter on critical temperature $T_c$. Vertical line marks ${\mu }^{\star }=0.13$.

Figure 6

(Color online) KKR DOS of $\mathrm{Y}{\mathrm{Rh}}_3\mathrm{B}$ calculated at experimental lattice parameter. Site-decomposed densities for Y, B, and Rh are plotted in brown (dotted line), red (dash-dotted line), and blue (dashed line), respectively. The Fermi level is shifted to zero and marked by a vertical line.

Figure 7

(Color online) Effect of B-sublattice deficiency in ${\mathrm{Sc}}_{3}X{\mathrm{B}}_x$ on site-decomposed DOS at the Fermi level (upper panels) and corresponding McMillan-Hopfield parameters (lower panels) computed from KKR-CPA method (see text). In both panels, the corresponding values for B (in red), Sc (in blue), and $X$ (in green) are marked by circles, squares, and triangles, respectively. Lines connecting calculated points are added as a guide to the eye.

Figure 8

(Color online) Effect of B-sublattice deficiency in ${\mathrm{Sc}}_{3}X{\mathrm{B}}_x$ on EPC constant $\lambda$ (upper panels) and corresponding critical temperature (lower panels). Lines connecting calculated points are added as a guide to the eye.

Figure 9

KKR nonpolarized total DOS in ${\mathrm{Cu}}_3\mathrm{Au}$-type ${\mathrm{Sc}}_3\mathrm{Ga}$ and ${\mathrm{Sc}}_3\mathrm{Al}$, calculated at equilibrium lattice constants $a_0$. The Fermi level is shifted to zero and marked by a vertical line.

Figure 10

KKR polarized total DOS in ${\mathrm{Cu}}_3\mathrm{Au}$-type ${\mathrm{Sc}}_3\mathrm{Tl}$ and ${\mathrm{Sc}}_3\mathrm{In}$, calculated at equilibrium lattice constant $a_0$. The Fermi level is shifted to zero and marked by a vertical line.

Figure 11

Magnetic moment on the scandium atom in ${\mathrm{Sc}}_3\mathrm{Tl}$ and ${\mathrm{Sc}}_3\mathrm{In}$ as a function of the lattice constant. Lines are added as a guide for the eye.

Figure 12

Effect of vacancy on total density of states in ${\mathrm{Sc}}_3\mathrm{In}{\mathrm{B}}_x$ (upper panels) and $\mathrm{Mg}{\mathrm{C}}_x{\mathrm{Ni}}_3$ (lower panels) from KKR-CPA calculations. Note a remarkable evolution of electronic states in the vicinity of the Fermi level: from high DOS at $E_F$ in C-rich and B-rich samples (left side: i.e., near full $\mathrm{C}∕\mathrm{B}$ occupancy and superconductivity limit) through a deep DOS minimum (intermediate concentrations; i.e., near 50% C in $\mathrm{Mg}{\mathrm{C}}_x{\mathrm{Ni}}_3$ and $\sim 80\%$ B in ${\mathrm{Sc}}_3\mathrm{In}{\mathrm{B}}_x$) to again large DOS, which satisfy the Stoner criterion (right side: i.e., near empty $\mathrm{C}∕\mathrm{B}$ sublattice limit). The Fermi level is at zero, marked by a vertical line.

Figure 13

The nonpolarized electronic dispersion curves $E\left(k\right)$ along high-symmetry directions in cubic ${\mathrm{Sc}}_3\mathrm{In}$, calculated at equilibrium lattice constant $a_0$. The Fermi level is marked by a horizontal line.