Superconductivity in the complex metallic alloy $\beta \text{−}{\mathrm{Al}}_3{\mathrm{Mg}}_2$

Transport and thermodynamic properties were studied for the complex metallic compound $\beta \text{−}{\mathrm{Al}}_3{\mathrm{Mg}}_2$, composed of 925 atoms per unit cell. $\beta \text{−}{\mathrm{Al}}_3{\mathrm{Mg}}_2$ exhibits bulk superconductivity below $T_c=0.87\mathrm{K}$. An exponential temperature dependence of the specific heat well below $T_c$ indicates BCS-like behavior with a nodeless gap of width ${\Delta }_{\mathit{BCS}}\left(0\right)\approx 1.5\mathrm{K}$. The coherence length is derived as ${\xi }_0=4.85\times {10}^{-8}\mathrm{m}$ and the Ginzburg Landau parameter ${\kappa }_{\mathrm{GL}}\approx 13$, characterizing $\beta \text{−}{\mathrm{Al}}_3{\mathrm{Mg}}_2$ as a type II superconductor. Superconductivity in $\beta \text{−}{\mathrm{Al}}_3{\mathrm{Mg}}_2$ occurs in the absence of inversion symmetry of the crystal. Surprisingly, in spite of the rather complex crystal structure of $\beta \text{−}{\mathrm{Al}}_3{\mathrm{Mg}}_2$, physical properties turn out to be quite simple.

Figure 1

(Color online) (a) Temperature dependent electrical resistivity $\rho$ of $\beta \text{−}{\mathrm{Al}}_3{\mathrm{Mg}}_2$. The solid line is a least squares fit according to Eq. (1). The inset shows the onset of a superconducting transition at $T_c^{\mathit{mid}}=0.9\mathrm{K}$. The application of magnetic fields suppresses superconductivity. (b) Temperature dependent upper critical field $H_{c2}$. The dashed line corresponds to $H_{c2}\left(T\right)$ derived in terms of the model of Werthamer et al. (Ref. 12) for $\alpha ={\lambda }_{\mathit{so}}=0$, revealing ${\mu }_0{H}_{c2}^{\prime }\approx -0.23\mathrm{T}∕\mathrm{K}$.

Figure 2

(Color online) Temperature dependent specific heat $C_p$ of $\beta \text{−}{\mathrm{Al}}_3{\mathrm{Mg}}_2$ plotted as $C_p∕T$ vs $T$. The inset shows low temperature heat capacity data, evidencing bulk superconductivity. The solid line adjusts the numerical data of Mühlschlegel (Ref. 17) to the present experiment.

Figure 3

(Color online) Temperature dependent specific heat $C_p$ of $\beta \text{−}{\mathrm{Al}}_3{\mathrm{Mg}}_2$, plotted as $(C_p-\gamma T)∕T^3$ vs $\ln T$. The dashed line is a least squares fit of the experimental data using the model described in the text with two Einstein modes ${\omega }_{\mathit{EL}1}=55\mathrm{K}$ with width of $14\mathrm{K}$ and ${\omega }_{\mathit{EL}2}=150\mathrm{K}$ with width of $116\mathrm{K}$. The Debye temperature ${\theta }_D=354\mathrm{K}$. The solid line sketches the phonon spectral function $F\left(\omega \right)$ plotted as $(5∕4)R{\pi }^4{\omega }^{-2}F\left(\omega \right)$ vs $\omega ∕4.93$, where $\omega$ is given in kelvin.

Figure 4

(Color online) Optical reflectivity and complex dielectric function of $\beta \text{−}{\mathrm{Al}}_3{\mathrm{Mg}}_2$.

Figure 5

(Color online) Temperature dependence of the Knight shift $\left({}^{27}\mathrm{Al}\right)$ of $\beta \text{−}{\mathrm{Al}}_3{\mathrm{Mg}}_2$ at $H=9.4\mathrm{T}$. The inset shows the ${}^{27}\mathrm{Al}$ spectrum at $10\mathrm{K}$.

Figure 6

Temperature dependence of the nuclear spin-lattice relaxation rate of $\beta \text{−}{\mathrm{Al}}_3{\mathrm{Mg}}_2$. The main panel displays $1∕T_{1}T$ vs $T$ and the inset shows a $1∕T_1$ vs $T$ plot. The broken line refers to a $T_{1}T=\mathrm{const}$ relation.