Anisotropic magnetic, electrical, and thermal transport properties of the Y-Al-Ni-Co decagonal approximant

We have investigated anisotropic physical properties (magnetic susceptibility, electrical resistivity, thermoelectric power, Hall coefficient, and thermal conductivity) of Y-Al-Ni-Co decagonal approximant with composition ${\text{Al}}_{76}{\text{Co}}_{22}{\text{Ni}}_2$. The crystalline-direction-dependent measurements were performed along three orthogonal directions $a^{\ast }$, $b$, and $c$ of the Y-Al-Ni-Co unit cell, where $\left(a,c\right)$ monoclinic atomic planes are stacked along the perpendicular $b$ direction. Anisotropic magnetic susceptibility of conduction electrons is paramagnetic for the field lying within the $\left(a,c\right)$ atomic planes and diamagnetic for the field along the $b$ direction. Anisotropic electrical resistivity is low in all crystalline directions, appearing in the order ${\rho }_{a^{\ast }}>{\rho }_c⪢{\rho }_b$. Thermopower shows electron-phonon enhancement effect. Anisotropic bare thermopower (in the absence of electron-phonon interactions) was extracted, appearing in the same order as the resistivity, $\left|S_{a^{\ast }}^{\text{bare}}/T\right|>\left|S_c^{\text{bare}}/T\right|>\left|S_b^{\text{bare}}/T\right|$. Anisotropic thermal conductivity appears in the order ${\kappa }^b>{\kappa }^c>{\kappa }^{a^{\ast }}$, so that $b$ is the most conducting direction for both electricity and heat. Hall coefficient $R_H$ exhibits pronounced anisotropy, where the magnetic field in a given crystalline direction yields the same $R_H$ for the current along the other two crystalline directions in the perpendicular plane. These anisotropies are analyzed in terms of the anisotropic structure of the Y-Al-Ni-Co phase and the ab initio calculated anisotropic Fermi surface. The results are compared with the literature-reported anisotropy of the physical properties of the $d$-Al-Ni-Co decagonal quasicrystal.

Figure 1

(Color online) (i) Magnetization $M$ of Y-Al-Ni-Co as a function of the magnetic field $H$ at $T=5\text{K}$ with the field oriented along three orthogonal crystalline directions $a^{\ast }$, $b$, and $c$. (ii) Temperature-dependent magnetic susceptibility $\chi =M/H$ in the field $H=10\text{kOe}$ applied along the three crystalline directions.

Figure 2

(Color online) $M\left(H\right)$ curves from Fig. 1 on an expanded vertical scale [panel (i): $a^{\ast }$ direction, panel (ii): $b$ direction, and panel (iii): $c$ direction]. Solid curves are fits with Eq. (1), dashed lines represent the term of the magnetization linear in the magnetic field $kH$ (the Larmor core contribution and the contribution due to the conduction electrons), and dotted curves are the FM contribution. Fit parameters are given in Table . The $M\left(H\right)$ hysteresis of the FM contribution on an expanded horizontal scale around $H=0$ is shown as an inset in panel (i).

Figure 3

(Color online) $\chi \left(T\right)$ curves from Fig. 1 on an expanded vertical scale [panel (i): $a^{\ast }$ direction, panel (ii): $b$ direction, and panel (iii): $c$ direction]. Solid lines are fits with Eq. (2) and fit parameters are given in Table .

Figure 4

(Color online) Temperature-dependent electrical resistivity of Y-Al-Ni-Co along three orthogonal crystalline directions $a^{\ast }$, $b$, and $c$ (note that the vertical scale is logarithmic). The inset shows the resistivity ratios ${\rho }_i/{\rho }_j$ $\left(i,j=a^{\ast },b,c\right)$.

Figure 5

Theoretical electronic DOS of the Y-Al-Ni-Co phase, calculated ab initio for the structural model of Zhang et al. (Ref. 17). Ni atoms have been replaced by Co, so that the calculation was performed for the composition ${\text{Al}}_{75}{\text{Co}}_{25}$ instead of the Zhang composition ${\text{Al}}_{75}{\text{Co}}_{22}{\text{Ni}}_3$.

Figure 6

(Color online) Fermi surface of Y-Al-Ni-Co in the first Brillouin zone, calculated ab initio for the structural model of Zhang et al. (Ref. 17) (considering the composition ${\text{Al}}_{75}{\text{Co}}_{25}$ instead of the Zhang composition ${\text{Al}}_{75}{\text{Co}}_{22}{\text{Ni}}_3$). Orientation of the reciprocal space axes $a^{\ast }$, $b^{\ast }$, and $c^{\ast }$ is also shown. While $a^{\ast }$ and $c^{\ast }$ are perpendicular to $b^{\ast }$, the angle between $a^{\ast }$ and $c^{\ast }$ amounts $63.83°$.

Figure 7

(Color online) Temperature-dependent thermoelectric power (the Seebeck coefficient $S$) of Y-Al-Ni-Co along three orthogonal crystalline directions $a^{\ast }$, $b$, and $c$. Solid curves are fits with Eqs. (6, 8) and the fit parameters are given in Table . Bare thermopowers (in the absence of electron-phonon interactions) are shown by dashed lines.

Figure 8

(Color online) Anisotropic temperature-dependent Hall coefficient $R_H=E_y/j_x{B}_z$ of Y-Al-Ni-Co for different combinations of directions of the current $j_x$ and magnetic field $B_z$ (given in the legend). The superscript $a^{\ast }$, $b$, or $c$ on $R_H$ denotes the direction of the magnetic field.

Figure 9

(Color online) (i) Thermal conductivity $\kappa$ of Y-Al-Ni-Co along the three crystalline directions $a^{\ast }$, $b$, and $c$. Electronic contributions ${\kappa }_{\text{el}}$, estimated from the Wiedemann-Franz law, are shown by solid curves. Note the logarithmic temperature scale. (ii) Phononic thermal conductivity ${\kappa }_{\text{ph}}=\kappa -{\kappa }_{\text{el}}$ along the three crystalline directions.

Figure 10

(Color online) (i) Visualization of the Al-only atomic chains along $b$ direction of the ${\text{Al}}_{13}{\text{TM}}_4$ structural model by Zhang et al. (Ref. 17). A “supercell,” composed of three unit cells along $b$, is shown. There are two types of Al-only chains: $\text{Al}\left(3\right)\text{-Al}\left(3\right)\text{-Al}\left(3\right)\text{−}\cdots$ with the interatomic distance $d_{\text{Al-Al}}=2.59\text{Å}$ (connected black small atoms, online blue colored) and $\text{Al}\left(5\right)\text{-Al}\left(5\right)\text{-Al}\left(5\right)\text{−}\cdots$ with $d_{\text{Al-Al}}=2.67\text{Å}$ (connected gray small atoms, online green colored). In searching for the Al-only atomic chains within the $\left(a,c\right)$ monoclinic plane, we find no connected chains along either $a^{\ast }$ or $c$ direction for the Al-Al distances $d_{\text{Al-Al}}<2.8\text{Å}$ [panel (ii), all interatomic distances smaller than $2.8\text{Å}$ are drawn by solid lines]. By increasing allowed Al-Al distances to $d_{\text{Al-Al}}<3.0\text{Å}$, connected Al-only chains appear along the $c$ direction [panel (iii)] but not along the $a^{\ast }$ (or $a$) direction. By increasing Al-Al distances further to $d_{\text{Al-Al}}<3.1\text{Å}$ [panel (iv)], there are still no connected chains along $a^{\ast }$ (or $a$). Representative triangular and square configurations of Al atoms are highlighted with thicker lines (online green colored) in panels (ii) and (iii). These configurations can be viewed as planar closed current loops in the $\left(a,c\right)$ plane for the magnetic field along direction, contributing to the Landau orbital diamagnetism of conduction electrons.