Intrinsic electrical, magnetic, and thermal properties of single-crystalline ${\mathrm{Al}}_{64}{\mathrm{Cu}}_{23}{\mathrm{Fe}}_{13}$ icosahedral quasicrystal: Experiment and modeling

In order to test for the true intrinsic properties of icosahedral $i\text{−}\mathrm{Al}\text{−}\mathrm{Cu}\text{−}\mathrm{Fe}$ quasicrystals, we performed investigations of magnetism, electrical resistivity, thermoelectric power, and thermal conductivity on a single-crystalline ${\mathrm{Al}}_{64}{\mathrm{Cu}}_{23}{\mathrm{Fe}}_{13}$ quasicrystal grown by the Czochralski technique. This sample shows superior quasicrystallinity, an almost phason-free structure, and excellent thermal stability. Magnetic measurements revealed that the sample is best classified as a weak paramagnet. Electrical resistivity exhibits a negative temperature coefficient with ${\rho }_{4\mathrm{K}}=3950\mu \Omega \mathrm{cm}$ and $R={\rho }_{4\mathrm{K}}∕{\rho }_{300\mathrm{K}}=1.8$, whereas the thermopower exhibits a sign reversal at $T=278\mathrm{K}$. Simultaneous analysis of the resistivity and thermopower using spectral-conductivity model showed that the Fermi energy is located at the minimum of the pseudogap in the spectral conductivity $\sigma \left(\epsilon \right)$. Thermal conductivity is anomalously low for an alloy of metallic elements. Comparing the physical properties of the investigated single-crystalline ${\mathrm{Al}}_{64}{\mathrm{Cu}}_{23}{\mathrm{Fe}}_{13}$ quasicrystal to literature reports on polycrystalline $i\text{−}\mathrm{Al}\text{−}\mathrm{Cu}\text{−}\mathrm{Fe}$ material, we conclude that there are no systematic differences between the high-quality single-crystalline and polycrystalline $i\text{−}\mathrm{Al}\text{−}\mathrm{Cu}\text{−}\mathrm{Fe}$ quasicrystals, except for the hindering of long-range transport by grain boundaries in the polycrystalline material. The so far reported physical properties of $i\text{−}\mathrm{Al}\text{−}\mathrm{Cu}\text{−}\mathrm{Fe}$ appear to be intrinsic to this family of icosahedral quasicrystals, regardless of the form of the material.

Figure 1

(a) Magnetization $M$ as a function of the magnetic field at $T=5\mathrm{K}$. The fit (solid line) was made with Eq. (1). The paramagnetic (para), ferromagnetic (FM), and linear (lin) contributions are shown separately. (b) Temperature-dependent magnetic susceptibility $\chi =M∕H$ in a field $H=10\mathrm{kOe}$. The solid line is the fit with Eq. (2). The fit parameters are collected in Table .

Figure 2

(Color online) (a) Temperature-dependent electrical resistivity and (b) thermopower of the single-crystalline ${\mathrm{Al}}_{64}{\mathrm{Cu}}_{23}{\mathrm{Fe}}_{13}$. The fits (solid lines) of both quantities were made simultaneously by the Kubo-Greenwood formalism using the spectral resistivity function $\rho \left(\epsilon \right)$ displayed in (c). $\rho \left(\epsilon \right)$ (solid line) is a superposition of two Lorentzians, shown by the dashed and dash-dot lines. The dotted bell-shaped curve at the bottom of the graph shows the thermal observation window $-\partial f∕\partial \epsilon$ (the derivative of the Fermi-Dirac function) at $T=300\mathrm{K}$. In (d), the spectral conductivity $\sigma \left(\epsilon \right)=1∕\rho \left(\epsilon \right)$ is shown.

Figure 3

(Color online) (a) Temperature-dependent thermal conductivity $\kappa \left(T\right)$ of the single-crystalline ${\mathrm{Al}}_{64}{\mathrm{Cu}}_{23}{\mathrm{Fe}}_{13}$. The fit (solid line) was made by Eq. (8) and the three contributions to the total $\kappa \left(T\right)$ (electronic ${\kappa }_{el}$, Debye ${\kappa }_D$, and hopping ${\kappa }_H$) are shown separately. (b) Temperature-dependent effective Lorenz number calculated from Eq. (11).