Still open questions
Why the resistivity decreases with the increase of disorder?
Figure 1. Electrical resistivity of
as a function of temperature.
Figure 2. The Hall coefficient of
as a function of susceptibility times ρ2
(and normalized to ρ2RT).
D. Stanić et al., Z.Kristallogr. 224 (2009) 49.
J. Ivkov et al., Croat. Chem. Acta 83 (2010) 11.
In complex metallic alloys it is often the case that the electrical resistivity, i.e. the property which one usually considers as an easiest to interpret, decreases with the increase of topological (as induced by neutron radiation, for example) or chemical disorder. This is illustrated in Figure 1. with our results for T-Al73Mn27-x(Pd,Fe)x alloys. It is supposed that the reason for this is the same one that leads to the large resistivity of these alloys, and this is the Fermi surface-Brilloiun zone interaction.
In complex metallic alloys the larger the unit cell, the greater the number of Brillouin zone planes which interact with Fermi surface. FS-BZ interaction has a number of consequences as are the formation of pseudogaps, flat or dispersionless energy bands, high electron effective mass, low electron velocities and so on. From all this follows the large electrical resistivity of CMAs. At the same time the introduction of disorder weakens FS-BS interaction, reduces its effects and hence reduces the resistivity.
In support of this interpretation are our results for the Hall coefficient of T-Al73Mn27-x(Pd,Fe)x alloys presented in Figure 2.
T-Al73Mn27-x(Pd,Fe)x alloys are spin glasses, and the results presented correspond to paramagnetic phase above the spin freezing temperatures.
In the high resistive transition-metal based alloys it is expected that the anomalous Hall coefficient, RS, is proportional to the square of the resistivity, ρ2. The anomalous Hall coefficient (which corresponds to the slope of the pllots in the Figure 2.) of all these alloys indeed is very large, due to the high resistivity, and is of the order of 10-7 m3C1. However, while the resistivity of these alloys significantly depends on the composition, and changes almost for an order of magnitude, anomalous Hall coefficient does not. This indicates that, upon the alloying, a number of changes in the electronic structures are taking place simultaneously which cancel out the impact of the resistivity onto the anomalous Hall coefficient.
Finally it ought to note that the dependence of the electrical resistivity on disorder is even more pronounced in icosahedral quasicrystals, and the metal-insulator transition is observed to follow the increasing stuctural quality of i-AlPdRe samples.
What is behind the correlation of the anisotropies of the Hall effect in
regular crystals and d-QCs?
A consequence of the anisotropic and layered structure of both d-QCs and their
approximants is distinct anisotropy of electrical and thermal transport properties (electrical resistivity, thermoelectric power, Hall coefficient, thermal conductivity) when measured along different crystalline directions
The anisotropic Hall coefficient RH of d-QCs is positive hole-like (RH > 0) for the magnetic field lying in the quasiperiodic plane, whereas it changes sign to negative (RH < 0) for the field along the periodic direction, thus becoming electron-like. This RH anisotropy was reported for the d-Al-Ni-Co, d-Al-Cu-Co and d-Al-Si-Cu-Co and is considered to be a universal feature of d-QCs.
Figure 1. Anisotropic Hall ceofficient
of single crystals of monoclinic Al13(Fe,Ni)4
alloy with magnetic field paralel to the orthogonal a*, b and c axes.
The exact composition is
The angle between a and a* is 17.7o.
P.Popčević et al., Phys. Rev. B 81 (2010) 184203.
We have measured the anisotropic electrical properties in four Al13TM4 complex metallic compounds which are approximants to the decagonal quasicrystals. These are monoclinic Y-Al-Ni-Co (Al76Ni22Co2), orthorhombic Al13Co4 and monoclinic Al13Fe4 and Al13(Fe,Ni)4 (Al76.5Fe21.3Ni2.2) complex metallic alloys.
A correlation found for the anisotropy of RH and ρ in Al13TM4 alloys and d-QCs can be summarised with the following Table
*Except for RH for Bz II b in Al13Fe3 as for this case RH strongly depends on temperature and changesthe sign with it.
From this correlation it follows that the anisotropy in d-QCs originates from the specific stacked-layer structure and the chemical decoration of the atomic clusters and not from the quasiperiodicity within the stacked planes.
The anisotropic RH reflects the complicated structure of the anisotropic Fermi surface that contains electron-like and hole-like contributions. Depending on the combination of the crystallographic directions, electron-like (RH < 0) or hole-like (RH > 0) contributions dominate, or the two contributions compensate each other (RH ≈ 0)
Figure 2. The quasi-Brillouin zone (a) and (b), and Fermi surface of
the decagonal quasicrystals (c).
Y.P. Wang et al., Phys. Rev. B 48 (1993) 10544.
For d-QCs a simple interpretation
of the results is proposed. From the most important Fourier components in reciprocal space, which were obtained by electron or x-ray diffraction, the Jones zone (quasi Brillouin zone) was constructed, as shown in Figure 2.. Next, the Fermi surface which touch and interacts with this zone is obtained with the assumption that the average valence electron numbers are close to 2 (in accordance with the Hume-Rothery law which seems to hold for these alloys). As can be seen in the Figure 2. the Fermi surface is electron like for the electrons that move in the quasiperiodic plane (RH < 0), and is hole like for the electrons that move in the planes perpendicular to this plane (RH > 0). However, the lack of transitional periodicity within the quasiperiodic layers prevents any further quantitative theoretical analysis.
At he same time, the translational periodicity of decagonal approximants may enable the straightforward theoretical simulation of the physical properties. When the chemical order enables the calculation of the Fermi surface, and the weak temperature dependence of RH(T) justifies the approximation of a single and isotropic scattering time, theory reproduces the experimental results for RH either qualitatively as for o-AlH13Co4, or even quantitatively as for Y-Al-Ni-Co. The Fermi surfaces for o-AlH13Co4 and Y-Al-Ni-Co are presented in Figures 3. and 4., respectively. It is transparent that the Fermi surfaces are highly anisotropic, which is at the origin of the experimentaly observed anisotropy of the electrical properties along different crystallographic directions.
Fermi surface in the first Brillouin zone, calculated ab-initio for the two
simillar structural models for
o-Al13Co4. a*, b* and c* are
the orthogonal reciprocal space axes.
M.Komelj et al., Phys. Rev. B 79 (2009) 184201
Stacking directions for o-Al13Co4 and
Y-Al-Ni-Co are, in real space,
b and a axes respectively.
Fermi surface in the first Brillouin zone, calculated ab-initio for the two
structural models for Y-Al-Ni-Co. Reciprocal space axes
a* and c* are perpendicular to b*,
while the angle between them amounts 63,83o.
M.Komelj et al., Solid State Commun. 149 (2009) 515
However, the nice simplicity of the Figure 2. is lost. Of course, it must be noted that this simplicity is greatly due to the neglect of s-d hybridization which is characteristic for TM based alloys. The question still remains whether it is possible to facilitate the reading of the Fermi surfaces (depicted in Figures 3. and 4.) by unfolding them in the expanded zone scheme, and by neglecting the parts with the low dispersion which do not contribute much to the electrical transport.