Superconductivity in the Rh-based Heusler family $M{\text{Rh}}_2\text{Sn}$

Superconductivity and structural characterization is reported for the Heusler structure compounds ${\text{ScRh}}_2\text{Sn}$, ${\text{LuRh}}_2\text{Sn}$, and ${\text{YRh}}_2\text{Sn}$. The superconducting $T_{\text{c}}$’s are 2.0 K, 2.9 K, and 4.1 K, respectively. The electronic contributions to the specific heat and the Debye temperatures are reported, and suggest that the observed trend in $T_{\text{c}}$ is governed primarily by an increase in electron-phonon coupling on going from ${\text{ScRh}}_2\text{Sn}$ to ${\text{YRh}}_2\text{Sn}$. The electron-phonon coupling constant ${\lambda }_{\text{ep}}$ and the normalized specific-heat jump $\Delta C/\gamma T_{\text{c}}$ suggest that the $M{\text{Rh}}_2\text{Sn}$ system evolves from weak coupling to moderate coupling superconductivity.

Figure 1

(Color online) Observed (blue circles) and calculated (solid red line) powder x-ray diffraction pattern for ${\text{YRh}}_2\text{Sn}$ at room temperature. The difference plot is shown at the bottom and vertical bars represent the Bragg peak positions for the cubic $L{2}_1$ Heusler structure. The inset shows the full Heusler-type crystal structure. Refined structural parameters for ${\text{YRh}}_2\text{Sn}$ at 298 K: space group $Fm\overline{3}m$ (No. 225), $a=6.7139\left(2\right)\text{Å}$, calculated density $9.1\text{gm}{\text{cm}}^{-3}$. Figures of merit: goodness of fit $\left({\chi }^2\right)=1.83$, weighted profile residual $\left(R_{\text{wp}}\right)=20\mathrm{\%}$, profile residual $\left(R_{\text{p}}\right)=13\mathrm{\%}$, and residual on structure factors $\left[R\left(F^2\right)\right]=10\mathrm{\%}$.

Figure 2

(Color online) Temperature-dependent ac-susceptibility measurement for $M{\text{Rh}}_2\text{Sn}$, where $M=\text{Sc}$, Lu, and Y. Open (filled) symbols is the real (imaginary) part of the ac susceptibility. The inset shows zero-field cooling dc susceptibility versus temperature for ${\text{YRh}}_2\text{Sn}$. The demagnetization factor was used as described in the text.

Figure 3

(Color online) Field-dependent magnetization data $M\left(H\right)$ at constant temperature 2 K for ${\text{YRh}}_2\text{Sn}$. The red line corresponds to linear relation $\left(\sim {\mu }_{0}H\right)$ below 5.5 mT. The upper right inset shows deviation from a fitted linear dependence on ${\mu }_{0}H$. The lower left inset is the temperature dependence of the lower critical field $\left({\mu }_0{H}_{\text{c}1}\right)$ for ${\text{YRh}}_2\text{Sn}$.

Figure 4

(Color online) Electrical resistivity near superconducting transitions of $M{\text{Rh}}_2\text{Sn}$, $M=\text{Sc}$, Lu, and Y, under zero field. The inset shows the resistivity measurement measured from 0.4 K to room temperature.

Figure 5

(Color online) The upper critical field $\left({\mu }_0{H}_{\text{C}2}\right)$ from resistivity as a function of temperature. The dashed curve is predicted by the WHH expression. The inset shows the ${\text{YRh}}_2\text{Sn}$ low temperature resistivity $\left[\rho \left(T\right)\right]$ for applied magnetic fields. Superconductivity vanishes for ${\mu }_0{H}_{\text{C}}>1.35\text{T}$.

Figure 6

(Color online) Zero-field specific heat divided by temperature $\left(C_{\text{P}}/T\right)$ versus temperature for $M{\text{Rh}}_2\text{Sn}$, where $M=\text{Sc}$, Lu, and Y. The inset shows raw experimental data for ${\text{YRh}}_2\text{Sn}$ and blue solid line represents theoretical curve calculated based on BCS model with the $s$-wave gap as described in the text.

Figure 7

Electronic structure (left) and corresponding DOS (right) of ${\text{YRh}}_2\text{Sn}$. Inset shows a detail of the DOS near Fermi energy, $E_F$.