We have investigated anisotropic Hall coefficient of Y-Al-Ni-Co decagonal approximant of the Al76Co22Ni2 composition. The crystalline-direction-dependent studies were performed along three orthogonal directions a*, b and c of the Y-Al-Ni-Co unit cell, where (a,c) monoclinic atomic planes are stacked along the perpendicular b direction. Hall coefficient RH exhibits pronounced anisotropy, while at the same time 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 observed anisotropy is studied in terms of the anisotropic structure of the Y-Al-Ni-Co phase and Fermi surface. The results are compared to the anisotropy of the Hall coefficient of the d-Al-Ni-Co decagonal quasicrystal reported in literature.</p

Denis Stanić

Janez Dolinšek

Jovica Ivkov

Peter Gille

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 * Presented at the EU Workshop "Frontiers in Complex Metallic Alloys", Zagreb, October 2008. Dedicated to Professor Boran Leontić on the occasion of his 80th birthday. ** Authors to whom correspondence should be addressed. (E-mail: dstanic@ifs.hr) CROATICA CHEMICA ACTA CCACAA, ISSN 0011-1643, e-ISSN 1334-417X Croat. Chem. Acta 83 (1) (2010) 7–10.  CCA-3381  Original Scientific Paper Hall Coefficient of the Y-Al-Ni-Co Decagonal Approximant* Denis Stanić,a,** Jovica Ivkov,a Janez Dolinšek,b and Peter Gillec aLaboratory for the Physics of Transport Phenomena, Institute of Physics, Bijenička c. 46, P. O. Box 304,  HR-10001 Zagreb, Croatia bJožef  Stefan Institute, University of Ljubljana, Jamova 39, SI-1000 Ljubljana, Slovenia cLudwig-Maximilians-Universität München, Department of Earth and Environmental Sciences, Crystallography Section, Theresienstrasse 41, D-80333 München, Germany RECEIVED AUGUST 6, 2008; ACCEPTED FEBRUARY 16, 2009  Abstract. We have investigated anisotropic Hall coefficient of Y-Al-Ni-Co decagonal approximant of the Al76Co22Ni2 composition. The crystalline-direction-dependent studies were performed along three ortho-gonal directions a*, b and c of the Y-Al-Ni-Co unit cell, where (a,c) monoclinic atomic planes are stacked along the perpendicular b direction. Hall coefficient RH exhibits pronounced anisotropy, while at the same time 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 observed anisotropy is studied in terms of the anisotropic structure of the Y-Al-Ni-Co phase and Fermi surface. The results are compared to the aniso-tropy of the Hall coefficient of the d-Al-Ni-Co decagonal quasicrystal reported in literature. Keywords: complex metallic alloys, decagonal approximants, Y-Al-Ni-Co, Hall effect  INTRODUCTION Decagonal quasicrystals (d-QCs) can be structurally displayed as a periodic stack of quasiperiodic atomic planes, so that d-QCs are two-dimensional quasicrystals, whereas they are periodic crystals in a direction perpen-dicular to the quasiperiodic planes. This makes d-QCs especially suitable for studying the influence of quasipe-riodicity on the transport properties of the material, as a given property may be investigated on the same sample along the quasiperiodic (Q) and periodic (P) directions. A striking example of the anisotropic nature of d-QCs is their electrical resistivity, which shows positive tempe-rature coefficient with metallic values along the P direc-tion Pr.t.  40 µ cm in d-Al-Cu-Co and d-Al-Ni-Co,1 whereas the resistivity in the quasiperiodic plane is considerably larger Qr.t. ≈ 330 µ cm and exhibits a negative temperature coefficient. The degree of aniso-tropy is related to the structural details of a particular decagonal phase, depending on the number of quasipe-riodic layers in one periodic unit.2−4 The most anisotro-pic case belongs to the phases with just two layers, realized in d-Al-Ni-Co and d-Al-Cu-Co, where the peri-odicity length along the periodic axis is about 0.4 nm and the resistivity ratio at room temperature amounts typically to Q/P ≈ 6−10.1,5−8 Other d-phases contain more quasiperiodic layers in a periodic unit and show smaller anisotropies. The basic question is whether the observed anisotropy is a consequence of complex local atomic order on the scale of near-neighbor atoms with no direct relationship to the quasiperiodicity. Approxi-mant phases are characterized by large unit cells, which periodically repeat themselves in space, but the structure of the unit cell resembles closely to d-QCs. Atomic layers are stacked periodically and the periodicity lengths along the stacking direction are almost identical to those along the periodic direction of d-QCs. More-over, atomic planes of approximants and d-QCs show locally similar quasiperiodic patterns, so that their struc-tures on the scale of near-neighbor atoms closely re-semble each other. Recently, the anisotropic transport properties (resistivity, Hall coefficient, ...) measured along three orthogonal crystalline directions, have been reported for the Al4(Cr,Fe) complex metallic alloy with composition Al80Cr15Fe5.9,10 The in-plane electrical resistivity of this compound exhibits nonmetallic beha-vior with negative temperature coefficient, while the resistivity along the stacking direction shows positive temperature coefficient. The anisotropy of the resistivity along the three orthorhombic directions is a consequence 8 D. Stanić et al., Hall Effect in Y-Al-Ni-Co Croat. Chem. Acta 83 (2010) 7. of local atomic order on the scale of nearest neighbor atoms, pertinent to the specific structure of the Al4(Cr,Fe) phase, with no direct relationship to the in-termediate-scale quasiperiodic patterns in the structure. Hall coefficient RH, shows a metallic behavior in all cases and exhibits pronounced anisotropy. As a part of the systematic investigation of the transport properties, we here report a study of the anisotropic Hall coefficient of a complex metallic alloy Al13-x(Co1–yNiy)4, known also as the Y-Al-Ni-Co phase, which is a monoclinic approximant of the decagonal phase with two atomic layers within one periodic unit along the stacking direc-tion and a relatively small unit cell, comprising 32 atoms. Due to the considerably smaller unit cell, the structure of Y-Al-Ni-Co is relatively simple as com-pared to the much higher complexity of the aforemen-tioned Al4(Cr,Fe) phase with 306 atoms/unit cell. The measurements of the anisotropy in Y-Al-Ni-Co thus allow a comparison of this simple decagonal approxi-mant to the Al4(Cr,Fe) phase,9,10 a decagonal approxi-mant with a considerably higher structural complexity as well as a comparison to the closely related d-Al-Ni-Co quasicrystal.11  EXPERIMENTAL The single crystal, used in our study, was grown from an incongruent Al-rich melt of initial composition Al81.9Co14.5Ni3.6 by the Czochralski method. The compo-sition of the crystal was Al76Co22Ni2 and its structure matched well to the monoclinic unit cell of the Zhang et al. model12 (who studied the composition Al75Co22Ni3). In order to perform crystalline-direction-dependent studies of Hall coefficient, we have cut from the ingot three bar-shaped samples of dimensions 2 × 2 × 6 mm3, with their long axes along three orthogonal directions. The long axis of the first sample was along [0 1 0] di-rection (designated in what follows as b), which corres-ponds to the periodic direction in the related d-Al-Ni-Co quasicrystal. The (a,c) monoclinic plane corresponds to the quasiperiodic plane in d-QCs and the second sample was cut with its long axis along [0 0 1] (c) direction, whereas the third one was cut along the direction per-pendicular to the (b,c) plane. This direction is designat-ed as a* (it lies in the monoclinic plane at an angle of 26° with respect to a and perpendicular to c). For each sample, the orientation of the other two crystalline di-rections was also known. The so-prepared samples enabled us to determine the anisotropic Hall coefficient along the three orthogonal directions of the investigated monoclinic Al76Co22Ni2, abbreviated henceforth as Y-Al-Ni-Co. The Hall effect measurements were per-formed by the five-point method using standard ac tech-nique in magnetic fields up to 10 kOe. The current through the samples was in the range of 10–50 mA. The measurements were performed in the temperature inter-val from 90 to 370 K.  RESULTS AND DISCUSSION Electrical resistivity  (T ), measured in all three crystal-line directions, is displayed in Figure 1. The resistivity along the direction perpendicular to the atomic mono-clinic plane b is considerably smaller than in-plane resistivities a* and c by a factor of around 3, while the two in-plane resistivities are much closer, a* /c ≈ 1.3 (Table 1). The obtained resistivity values reveal that Y-Al-Ni-Co is good electrical conductor along all three crystalline directions while in-plane resistivity of d-Al-Ni-Co quasicrystal is qualitatively different, showing nonmetallic temperature behaviour, and about 10 times larger value at room temperature than the resistivity along the periodic direction.5,13  The temperature-dependent Hall coefficient RH = Ey /jxBz is displayed in Figure 2. In order to determine the anisotropy of 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 expe-riments altogether. For all combinations of directions, Figure 1. Temperature-dependent electrical resistivity of Y-Al-Ni-Co along three orthogonal crystalline directions a*, b and c. T / K0 100 200 300 /  cm020406080Y-Al-Co-Nicba*Table 1. Anisotropic resistivity data (T ) of Y-Al-Ni-Co for various crystalline directions Crystalline direction  r.t. / µ cm  2 K / µ cm b 25 10 c 60 29 a* 81 34 D. Stanić et al., Hall Effect in Y-Al-Ni-Co 9 Croat. Chem. Acta 83 (2010) 7. the RH values are typical metallic values of the order of 10−10 m3 C−1, showing weak temperature dependence. This temperature dependence shows tendency to disap-pear at higher temperatures. RH's exhibit 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. Thus, identical Hall coefficients are obtained for combinations RHa* = Eb / jcBa* and RHa* = Ec / jbBa* (where additional superscript on the Hall coefficient denotes the direction of the magnetic field), being RHa*(r.t.) = 8.5 × 10−10 m3 C−1, RHb = Ea*/jcBb and RHb = Ec / ja*Bb with RHb(r.t.) ≈ 0 and RHc = Eb /ja*Bc and RHc = Ea* /jbBc with RHc(r.t.) ≈ 4.5 × 10−10 m3 C−1. The anisotropic RH values are also given in Table 2. The two rather high positive values RHa*and RHc for the field lying in the (a,c) atomic plane and the almost zero value of RHb for the field along the perpendicular b direction (periodic direction in d-QCs) reflect strong anisotropy of the Fermi sur-face14 that consists mostly of hole-like parts, whereas electron-like and hole-like parts are of comparable im-portance for the field perpendicular to the (a,c) plane. Comparing the RH anisotropy of Y-Al-Ni-Co to the d-QCs, we find qualitative similarity. For d-QCs, univer-sality of the Hall-effect anisotropy was reported for the d-Al-Ni-Co, d-Al-Cu-Co and d-Al-Si-Cu-Co,6,8 where RH > 0 for the field lying in the quasiperiodic plane (cor-responding to the in-plane coefficients RHa*, RHc > 0 of Y-Al-Ni-Co), whereas RH changes sign to negative for the field along the periodic direction (corresponding to RHb ≈ 0 of Y-Al-Ni-Co). The above d-QCs also exhibit similar weak temperature dependence of RH as Y-Al-Ni-Co, so that there is a good analogy between d-QCs and their approximant Y-Al-Ni-Co.  CONCLUSION We have studied Hall coefficient of the Y-Al-Ni-Co decagonal approximant. Hall coefficient RH of Y-Al-Ni-Co exhibits pronounced anisotropy. 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. Two rather high positive values RHa*and RHc for the field lying in the (a,c) atomic plane and the almost zero value of RHb for the field along the perpendicular b direction reflect strong anisotropy of the Fermi surface that consists mostly of hole-like parts, whereas electron-like and hole-like parts are of compa-rable importance for the field perpendicular to the (a,c) plane. There is a complete analogy between the RH anisotropy of Y-Al-Ni-Co and d-QCs, where, in the latter case RH > 0 for the field lying in the quasiperiodic plane (corresponding to the in-plane coefficients RHa*, RHc > 0 of Y-Al-Ni-Co), whereas RH changes sign to negative for the field along the periodic direction (cor-responding to RHb ≈ 0 of Y-Al-Ni-Co). Therefore, the results confirm the analogy between the anisotropic Hall coefficient of the quasiperiodic decagonal quasicrystal on one hand and the periodic decagonal approximants on the other hand. This suggests that the long-range quasiperiodicity of the structure is of marginal impor-tance for the anisotropy, which originates from the complex local atomic order on the scale of nearest-neighbor atoms. Acknowledgements. This work has been done within the ac-tivities of the 6th Framework EU Network of Excellence "Complex Metallic Alloys" (Contract No. NMP3-CT-2005-500140), and has been supported in part by the Ministry  of Science, Education and Sports of the Republic of Croatia through the Research Project No. 035-0352826-2848. We thank A. Smontara for useful discussion.  Figure 2. Anisotropic temperature-dependent Hall coefficientRH = Ey / jxBz of Y-Al-Ni-Co for different combinations ofdirections of the current jx and magnetic field Bz: (open trian-gles ( jb, Ba*) and full triangles ( jc, Ba*); open circles ( ja*, Bc) and full circles ( jb, Bc); open squares ( jc, Bb) and full squares( ja*, Bb)). The superscript a*, b or c on RH denotes the direc-tion of the magnetic field. T / K100 200 300 4001010 RH / m3  C-104812Y-Al76Co22Ni2RHRHRHa*cbTable 2. Anisotropic Hall coefficient RH = Ey / jxBz of Y-Al-Ni-Co for various directions of the current Current direction ( jx) Magnetic field direction (Bz) 10 r.t.H3 –110m CR    a* b 0.0 c 4.6 b   a* 8.5 c 4.3 c   a*   8.5 b –0.2  1010 RH/m3 C–1 a* c Hb 10 D. Stanić et al., Hall Effect in Y-Al-Ni-Co Croat. Chem. Acta 83 (2010) 7. REFERENCES 1. S. Martin, A. F. Hebard, A. R. Kortan, and F. A. Thiel, Phys. Rev. Lett. 67 (1991) 719−722. 2. M. Krajčí and J. Hafner, Phys. Rev. B 58 (1998) 5378−5383. 3. G. T. de Laissardière and T. Fujiwara, Phys. Rev. B 50 (1994) 9843−9850. 4. J. Dolinšek and A. Smontara, Anisotropic Physical Properties of Complex Metallic Alloys, in: Esther Belin-Ferre (Ed.), Complex Metallic Alloys: A Primer, London WC2H 9HE, England World Scientific Publishing (UK) Ltd., 2010, in press. 5. T. Shibuya, T. Hashimoto, and S. Takeuchi, J. Phys. Soc. Jpn. 59 (1990) 1917−1920. 6. Y. P. Wang and D. L. Zhang, Phys. Rev. B 49 (1994) 13204−13207. 7. S. Y. Lin, X. M. Wang, L. Lu, D. L. 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SAŽETAK  Hallov koeficijent dekagonalnog aproksimanta Y-Al-Ni-Co  Denis Stanić,a Jovica Ivkov,a Janez Dolinšekb i Peter Gillec aLaboratorij za fiziku transportnih svojstava, Institut za fiziku, Bijenička c. 46, P. P. 304, HR-10001 Zagreb, Hrvatska  bJožef Stefan Institute, University of Ljubljana, Jamova 39, SI-1000 Ljubljana, Slovenia  cLudwig-Maximilians-Universität München, Department of Earth and Environmental Sciences, Crystallography Section, Theresienstrasse 41, D-80333 München, Germany Prikazani su rezultati ispitavanja anizotropije Hallovog koeficijenta RH monokristala Al76Co22Ni2 slitine. Ta je sli-tina dekagonalni aproksimant Y-Al-Ni-Co sustava. Hallov koeficijent je mjeren za tri kristalografska smjera a*, b i c jedinične ćelije Y-Al-Ni-Co, kod koje su monoklinske atomske ravnine (a,c) naslagane duž b smjera okomitog na njih. RH pokazuje zamjetnu anizotropiju koja je posljedica anizotropne strukture kao i Fermijeve površine. Re-zultati su uspoređeni s anizotropijom Hallovog koeficijenta dekagonalnog kvazikristala d-Al-Ni-Co iz literature. 

Hall Coefficient of the Y-Al-Ni-Co Decagonal Approximant

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