Magnetoresistance and Hall effect of the complex metal alloy ${\text{Mg}}_2{\text{Al}}_3$

Unusual electronic transport properties have been found in the rhombohedral ${\beta }^{\prime }$-phase of the complex metallic alloy ${\text{Mg}}_2{\text{Al}}_3$. The magnetoresistance (MR) is 2 orders of magnitude larger than in the related cubic $\beta -{\text{Mg}}_2{\text{Al}}_3$-phase and Kohler’s rule is strongly violated in the ${\beta }^{\prime }$-phase at higher temperatures. Above about 100 K the Hall coefficient $R_H$ of the $\beta$- and ${\beta }^{\prime }$-phases are similar and free-electron-like, while in the ${\beta }^{\prime }$-phase, $R_H$ changes sign with decreasing temperature at low fields. We have inquired into the sources of these transport anomalies, but have not been able to clearly identify the grounds. Several conventional mechanisms for a large magnetoresistance are discussed, and found not to be applicable. The different properties in the $\beta$- and the ${\beta }^{\prime }$-phases are puzzling since the magnitudes of the electrical resistivities are similar and ${\omega }_c\tau$ (cyclotron $\text{frequency}\times \text{scattering}$ time) is equally small in both phases. The similar temperature range in which anomalies occur in the ${\beta }^{\prime }$-phase in the resistivity, the Hall effect, and the magnetoresistance indicates an electronic transition or a change of the electron structure in this phase below about 100 K.

Figure 1

$\rho$ vs $T$ for one sample in the ${\beta }^{\prime }$-phase, one sample with a mixture of $\beta$ and ${\beta }^{\prime }$-phases, and one sample in a pure $\beta$-phase. For the two top curves an as-grown sample was annealed for 72 h at the temperatures indicated.

Figure 2

Hall field $E_y$ vs $B$ at 295 K. $•$; the ${\beta }^{\prime }$-phase sample from Fig. 1. $\circ$; the $\beta$-phase sample from Fig. 1. Inset: Hall constant $R_H$ vs $T$ for the same samples at a few temperatures. The results for the ${\beta }^{\prime }$-phase below 100 K are shown in Fig. 3.

Figure 3

Hall field $E_y$ for the ${\beta }^{\prime }$-phase vs $B$ at low temperatures. Inset: Results at 4.2 K from $-12$ to $+12\text{T}$.

Figure 4

Transverse magnetoresistance $\Delta \rho \left(B\right)/\rho \left(0\right)$ vs B for ${\beta }^{\prime }$-and $\beta$-phase samples. Upper panel: Results for a ${\beta }^{\prime }$-phase sample in the temperature range 4.2–270 K. Inset: Kohler plot; ${\rho }_o=\rho \left(295\text{K}\right)$. Deviations from Kohler’s rule can be seen for $T\ge 25\text{K}$. Lower panel: Two $\beta$-phase samples at 50 K: $•$; as-grown, $\circ$; annealed for ten days at $200°\text{C}$.

Figure 5

Maximum magnetoresistance, ${\left|\Delta \rho /\rho \right|}^{\text{max}}$ vs $\rho \left(4\text{K}\right)$ for several metallic alloys including crystalline CuGe and complex metallic alloys, such as amorphous metals, decagonal and icosahedral quasicrystals and crystalline approximants (Ref. 15). This $\Delta \rho /\rho$ arises in disordered electron systems from weak localization and enhanced electron-electron interactions. The present alloys are depicted by solid circles. For the $\beta$-phase, ${\left|\Delta \rho /\rho \right|}^{\text{max}}$ is consistent with electronic disorder effects. For the ${\beta }^{\prime }$-phase, it is more than 2 orders of magnitude larger.

Figure 6

$\Delta \rho \left(B\right)/\rho \left(0\right)$ of a ${\beta }^{\prime }$ sample at 50 K as a function of $B$. Transverse and longitudinal magnetoresistances are shown. Inset: Magnetoresistance for the same sample at 8 T and 50 K as a function of angle between $\mathbf{j}$ and $\mathbf{B}$. At $\theta =0^o,\mathbf{B}\parallel \mathbf{j}$.

Figure 7

$\Delta \rho \left(B\right)/\rho$ (0) vs $B$ at 50 K for one sample, starting from the $\beta$-phase (as-grown) and after annealing for several days at the temperatures indicated and in the sequence of increasing temperatures. The two $\beta$-phase samples in Fig. 4 have here collapsed onto one curve at the bottom of the figure.