UDK 548.4:537.633.2 ISSN 1580-2949 Original scientific article/Izvirni znanstveni članek MTAEC9, 44(1)9(2010) HALL EFFECT IN THE CRYSTALLINE ORTHOROMBIC 0-AI13C04 APPROXIMANT TO THE DECAGONAL QUASICRYSTALS HALLOV EFEKT V KRISTALINIČNEM ORTOROMBIČNEM PRIBLIŽKU 0-AI13C04 DEKAGONALNIM KVAZIKRISTALOM Jovica Ivkov1, Denis Stanič1,2, Petar Popcevic1, Ana Smontara1, Janez Dolinšek3, Peter Gille4 1Institute of Physics, Laboratory for the Study of Transport Problems, Bijenička 46, POB 304, HR-10000 Zagreb, Croatia 2Department of Physics, University of Osijek, Gajev trg 6, 31000 Osijek, Croatia 3J. Stefan Institute, University of Ljubljana, Jamova 39, SI-1000 Ljubljana, Slovenia 4Ludwig-Maximilians-Universität München, Theresienstrasse 41, D-80333 München, Germany ivkov@ifs.hr, dstanic@fizika.unios.hr Prejem rokopisa - received: 2009-07-24; sprejem za objavo - accepted for publication: 2009-11-27 We have investigated the anisotropic Hall effect of the o-Al13Co4 orthorhombic approximant to the decagonal phase. The crystalline-direction-dependent measurements were performed along the a, b and c directions of the orthorhombic unit cell. The Hall effect has been measured for all the combinations of the electrical current and magnetic field directions. The Hall coefficients RH change with the crystallographic direction from negative electron-like or zero to positive hole-like for different combinations of the current and field directions. The results for the anisotropy of RH is well correlated with the anisotropy of RH in the d-Al-Ni-Co and d-Al-Cu-Co quasicrystals. The Hall coefficients of the o-Al13Co4 phase were compared to the literature data on single crystals of the Al76Co22Ni2 and the Al80Cr15Fe5 approximants to the decagonal quasicrystals, allowing a study of the evolution of the Hall coefficient with an increasing structural complexity and unit-cell size. Keywords: complex intermetallics, quasicrystalline approximants, Hall effect Raziskali smo anizotropni Hallov efekt v ortorombičnemu približku o-Al13CO4 dekagonalni fazi. Meritve, odvisne od kristalne orientacije, so bile izvršene v smereh a, b in c ortorombične osnovne celice. Hallov efekt je bil izmerjen za vse kombinacije električnega toka in smeri magnetnega polja. Hallov koeficient RH se spremeni s kristalografsko orientacijo od negativnega podobnega elektronom, do pozitivnega, podobnega vrzelim, po različnih kombinacijah toka in smeri polja. Rezultati o anizotropiji za RH se dobro korelirajo z anizotropijo RH v kvazikristalih d-Al-Ni-Co in v d-Al-Cu-Co. Hallov koeficient faze o-Al13CO4 je bil primerjan s podatki iz literature o monokristalnih približkih Al76Co22Ni2 in Al80Cr15Fe5 dekagonalnim kvazikristalom, kar omogoča študij evolucije Hallovega koeficienta z naraščasjočo strukturno kompleksnostjo in velikostjo osnovne celice. Ključne besede: kompleksni intermetaliki, kvazikristalni približki, Hallov efekt d-QCs that are characterized by a large unit cell, which 1 INTRODUCTION periodically repeats in space, while the structure of the unit cell closely resembles d-QCs. Atomic layers that Decagonal quasicrystals (d-QCs) can be structurally correspond to the quasiperiodic layers are again stacked viewliasaaperiodic!tackofiua!iper:o?:catomic.planes' periodically and the periodicity lengths along the stacking direction are almost identical to those along the so that d-QCs are two-dimensional quasicrystals, whereas they are periodic crystals in a direction perpendicular to the quasiperiodic planes. A consequence of periodic direction of the d-QCs. Approximant phases this anisotropic structure are the anisotropic physical thus offer a valid comParison with the d-QCs. Here^we properties,1-9 when measured along the different report measurements of the anisotropic Hall coefficient crystalline directions. The anisotropy of the Hall coeffi- of the orthorhombic o-Al13Co4 complex metallic alloy, cient Rh of d-QCs is especially intriguing, being positive which belongs to the derivative of the Al13TM4 com- hole-like (Rh > 0) for the magnetic field lying in the pound' with four atomic layers within one periodic unit quasiperiodic plane, whereas it changes sign to negative of ^0 8 nm along the stacking direction and a unit cell (Rh < 0) for the field along the periodic direction, thus comprising I02 atoms. These measurements complement becoming electron-like. This RH anisotropy was reported our previous work on the anisotropic Hall coefficient of for the d-AlNiCo, d-AlCuCo and d-AlSiCuCo, and is the Al76Co22Ni2 and Al80Cr15Fe5 approximants to the considered to be a universal feature of d-QCs.5 6 The lack decagonal quasicrystals. Al76Co22Ni2 has two atomic of translational periodicity within the quasiperiodic layers within one periodic unit of ~0.4 nm and 32 atoms layers prevents any quantitative theoretical analysis of in a relatively small unit cell,10-12 and the Al80Cr15Fe5has this phenomenon. The problem can, however, be over- six atomic layers within one periodic unit of ~1.25 nm come by considering periodic approximant phases to the and 306 atoms in a giant unit cell.13-14 The o-Al13Co4 phase with four atomic layers and 102 atoms in the unit cell is thus intermediate to the other two approximant phases in terms of the number of layers in one periodic unit and the size of the unit cell. A comparison of the three phases can give us an insight into the way the anisotropic Hall coefficient of the approximant to the decagonal quasicrystals evolve with the increasing structural complexity and the unit cell size. 2 EXPERIMENTAL The o-Al13Co4 single crystal used in our study was grown using the Czochralski technique and its structure matched well with the orthorhombic unit cell.15 In order to perform crystalline-direction-dependent studies we cut three bar-shaped samples of dimensions 1x1x7 mm3 from the ingot, with their long axes along three orthogonal directions. The long axis of the first sample was along the [100] stacking direction (designated as a), which corresponds to the pseudo-tenfold axis of the o-Al13Co4 structure and is equivalent to the periodic (tenfold) direction in the related d-QCs. The (b, c) orthorhombic plane corresponds to the quasiperiodic plane in the d-QCs and the second sample was cut with its long axis along the [010] (b) direction and the third one along the [001] (c) direction. For each sample, the orientation of the other two crystalline directions was also known. The so-prepared samples enabled us to determine the anisotropic Hall coefficients of the o-Al13Co4 approximant to the decagonal quasicrystals along the three principal orthorhombic directions of the unit cell. The Hall-effect measurements were performed using a five-point method with a standard ac technique in magnetic fields up to 1 T.16 The current through the samples was in the range 10-50 mA. The measurements were performed in the temperature interval from 90 K to 390 K. 3 RESULTS The temperature-dependent Hall coefficient Rh = Ey/jxBz of the o-Al13Co4 is displayed in Figure 1. In order to determine the anisotropy of the Rh, three sets of experiments were performed with the current along the long axis of each sample (thus along a, b and c, respectively), whereas the magnetic field was directed along each of the other two orthogonal crystalline directions, making six experiments altogether. For all combinations of directions, the Rh values are typical of a metal, in agreement with the electrical resistivity (Figure 2a), of the order 10-10m3 C-1. RH exhibits pronounced anisotropy with the following regularity: the six Rh sets of data form three groups of two practically identical Rh curves, where the magnetic field in a given crystalline direction yields the same Rh for the current along the other two crystalline directions in the perpendicular plane. The room-temperature values of the Hall coefficient of these h Sr G is hole-like for the field along the in-plane b direction. For the field along the second in-plane direction c, Rch ~ G suggests that the electron-like and hole-like contributions are of comparable importance. This orientation-dependent mixed electron-like and hole-like behavior of the anisotropic Hall coefficient is analogous to the anisotropy of the thermopower measured on the same specimens, presented in Figure 2b, which also changes sign with crystalline orientation. In both cases there is no simple explanation of this dual behavior, which would require knowledge of the details of the Fermi surface pertinent to the o-Al13Co4 phase. experimental data. Comparing the Hall coefficient of the above approximants to the decagonal quasicrystals to the true d-QCs, we find that the two kinds of compounds are in complete analogy. A comparison with the currently best-studied d-Al-Ni-Co-type d-QCs with two atomic layers within one periodic unit shows the following similarities: the Hall coefficient is the lowest, negative and electronic-like for the magnetic field along the periodic direction, whereas RH changes sign to positive hole-like for the field along the in-plane directions.5 6 This duality is suggested to be a universal feature of d-QCs. 5 CONCLUSION The investigated approximants to the decagonal quasicrystals of increasing structural complexity exhibit an anisotropic Hall coefficient qualitatively similar to that of the decagonal quasicrystals. Both types of compounds have in common atomic planes that are stacked periodically. The stacked-layer structure appears to be at the origin of the anisotropy of the investigated Hall coefficient. 4 DISSCUSION We have measured the Hall coefficient of the ortho-rhombic o-Al13Co4 complex metallic alloy, with four atomic layers within one periodic unit. Our main objective was to determine the crystalline-direction-dependent anisotropy of the investigated Hall coefficients when measured within the (b,c) atomic planes, corresponding to the quasiperiodic planes in the related d-QCs, and along the stacking a direction perpendicular to the planes corresponding to the periodic direction in d-QCs. The Hall coefficient results point to a complicated Fermi surface that consists of electron-like and hole-like parts. Comparing the Hall coefficient of the three stacked-layer phases - the Al76Co22Ni2 two-layer phase, the o-Al13Co4 four-layer phase and the Al8GCr15Fe5 six-layer phase -some general conclusions can be drawn on the anisotropic Hall coefficient of the approximant to the decagonal quasicrystal with increasing structural complexity and unit-cell size. The anisotropic Hall coefficient shows the following regularity: the application of the field along the stacking direction always yields the lowest value of the Hall coefficient (for o-Al13Co4 and Al8GCr15Fe5, the corresponding Hall coefficient is negative, whereas for the Al76Co22Ni2, it is practically zero), whereas the application of the field in-plane results in higher RH values and a change of sign to positive for at least one of the in-plane directions. No systematic change of RH with increasing structural complexity can be claimed. 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