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Anisotropic Diamagnetic Susceptibility of AlNiCo Quasi-crystal

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1999 Jpn. J. Appl. Phys. 38 52

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Jpn. J. Appl. Phys. Vol. 38 (1999) pp. 52–55Part 1, No. 1A, January 1999c©1999 Publication Board, Japanese Journal of Applied Physics

Anisotropic Diamagnetic Susceptibility of AlNiCo Quasi-crystalYoshihiro YAMADA , Yoshihiko YOKOYAMA 1, Ken-ichi MATONO, Kenzo FUKAURA 1

and Hisakichi SUNADA 1

Department of Electrical Engineering, Faculty of Engineering, Himeji Institute of Technology, Shosha, Himeji, Hyogo 671-2201, Japan1Department of Materials Science & Engineering, Faculty of Engineering, Himeji Institute of Technology, Shosha, Himeji, Hyogo 671-2201, Japan

(Received April 8, 1998; accepted for publication October 9, 1998)

We have carried out magnetization measurements of a single decagonal Al72Ni12Co16 quasi-crystal for the cases of themagnetic field parallel and perpendicular to the periodic axis with a torsion-type magnetic balance in various magnetic fieldsup to 10 kOe from 4.2 K to room temperature. Anisotropic diamagnetic susceptibility was observed, which is closely correlatedto the electron motions in the quasi-crystal.

KEYWORDS: Al72Ni12Co16, quasi-crystal, decagonal phase, diamagnetism, anisotropic susceptibility

1. Introduction

Since the discovery of quasi-crystals, the study of theirintrinsic properties has been attracting much attention, be-cause of their unique atomic structure which exhibits quasi-periodicity and self similarity. The discovery of stable quasi-crystals has enabled the study of structural analysise.g. thedetermination of atomic arrangements for various types oficosahedral and decagonal phases. Besides, some intrinsicproperties of quasi-crystals have been revealed in the sta-ble quasi-crystals. The properties of stable icosahedral al-loys include high electrical resistivity,1) high hardness,2) highYoung’s modulus3) and pseudo-gap at the Fermi level in thedensity-of-states curve.4) On the other hand, the magneticbehaviour of quasi-crystals containing magnetic element(s)has been characterized as being similar to that of the spin-glass5–7) or inhomogeneous ferromagnetism.8) However, oneshould not draw hasty conclusion that those are the intrinsicmagnetic properties, because magnetic interactions often ap-pear in rapidly solidified samples due to excessive structuraland chemical disorder, especially in the case that magneticelement(s) such as iron and cobalt are contained.

Recently, Markertet al.9) reported on the electric and mag-netic properties of a single-domain decagonal Al70Ni15Co15

quasi-crystal. In their report the magnetic behaviour wascharacterized by a small ferromagnetic component,M0(H ),which is saturated in magnetic fields,H , higher thanabout 1 kOe and apositivedifferential susceptibility,χ0 =1M/1H , obtainable from high-field data. The observedmagnetization,M = χ0H + M0(H), is slightly anisotropic,and almost temperature independent below room temperatureexcept for a Curie-like increase ofχ0 below 30 K. Hereχ0

and M0(H ) in H > 1 kOe are 7–8× 10−7 emu/(g·Oe) and1.7–2× 10−3 emu/g, respectively.

On the other hand, Ohamaet al.10) carried out the magne-tization measurements of a single Al70Ni15Co15 quasi-crystalsample and NMR measurements of it and its powdered sam-ple. The results of the magnetization measurements arequalitatively different from the results obtained by Markertet al.9) as follows. The magnetization of the single quasi-crystal at 100 K initially increases with increasingH up toabout 5 kOe after which itdecreaseslinearly up to 40 kOe.Furthermore, the negative slopes are obviously different be-tween to thec-axis (the periodic axis) and in thec-plane(perpendicular to the periodic axis) of the direction of mag-netic fields. Namely the values ofχ0 in the equation of

More recently, Yokoyamaet al.11) have prepared a sin-gle decagonal Al72Ni12Co16 quasi-crystal by the Czochral-ski method. In this paper, we report the results of magneti-zation measurements of the single quasi-crystal sample anddiscuss intrinsic magnetic properties of decagonal AlNiCoquasi-crystal and the observed anisotropic diamagnetic sus-ceptibility.

2. Experimental Procedures

As mentioned above, the sample used in the present exper-iments was prepared by Yokoyamaet al.11) The following isa report on preparation and characterization.

An Al–Ni–Co ternary master alloy was prepared by ar-gon arc melting. The starting elements, Al, Ni and Cowere degassed in a high vacuum state by a zone meltingmethod, before arc melting. The purities after the zone melt-ing, measured by the ICP method were 99.999, 99.996 and99.999 wt%, for Al, Ni and Co, respectively. The Czochral-ski method was used to produce a decagonal Al–Ni–Co sin-gle ingot with tenfold growth direction. The obtained ingotshowed the distinct tenfold face plane and no grain bound-ary with the composition close to Al72Ni12Co16. The singlequasi-crystallinity was examined by the back scattering X-raydiffraction pattern which was taken from 10 different pointson the tenfold plane. No anomalous diffuse scattering spotswere observed in the Laue pattern, indicating that the evensubgrain boundaries were not induced into the single ingot.

The magnetizations were measured with a torsion-typemagnetic balance in the magnetic-field directions, to thec-axis and in thec-plane in various magnetic fields up to 10 kOe

M = χ0H + M0(H) arenegative, −2.0× 10−7 emu/(g·Oe)to thec-axis and−3.8× 10−7 emu/(g·Oe) in thec-plane andM0(H ) in H > 5 kOe is about 4× 10−3 emu/g in both cases.The susceptibilities are almost temperature independent be-tween 4.2 K and 300 K. The59Co NMR shift of the reori-ented powder sample was also anisotropic: the shift in thefields with respect to thec-axis is smaller than that in thec-plane and almost temperature independent between 4.2 Kand 100 K, corresponding to the results of the magnetizationmeasurements. Thus they concluded that the AlNiCo quasi-crystal is a diamagnet with anisotropic susceptibility and thepositive increase of magnetization in low fields may originatefrom ferromagnetic impurities.

The difference between the results obtained by the twogroups may arise from the difference in quality of the sam-ples used in the experiments.

from 4.2 K to room temperature.

3. Results and Discussion

Figure 1 shows the magnetization curves at 4.2 K in twocases of the magnetic field direction, to thec-axis and in thec-plane.

In both cases, the magnetization,M, first increases withincreasing magnetic field and then decreases almost linearlyagainstH . The slopes of the decrease in higher fields areobviously different between the two cases. The amount ofthe first increase, however, is almost the same in both casesand the extrapolated value of magnetization toH = 0 fromhigh field plots is almost the same in the two magnetic-fielddirections. Such a field dependence of magnetization hardlychanges between 4.2 K and room temperature, which is thetemperature range of the present measurements. Thus thepresent magnetization data can be expressed by an equationM = χ0H + M0(H), whereχ0 is negative and different be-tween to thec-axis and in thec-plane, whileM0(H ), whichis common to both directions, first increases with increasingH and then is saturated in high fields. The field dependenceof M0(H ) is characteristic of ferromagnetism. Hereχ0 andM0(H ) values are almost temperature independent.

The above-mentioned results are qualitatively in goodagreement with the results of magnetization measurementsby Ohamaet al. described in §1. The values ofχ0 (shownin Fig. 2) are nearly equal to those observed by Ohamaet al.,while the values ofM0(H ) are smaller than those obtained bythem. Comparing the values at high fields, which are obtainedby the extrapolation of the high-field plots of the magnetiza-tion curve toH = 0, the present value of about 1×10−3 emu/gis about 1/4 of the result obtained by Ohamaet al. (see §1).

Jpn. J. Appl. Phys. Vol. 38 (1999) Pt. 1, No. 1A Y. YAMADA et al. 53

netism. Another is a very small ferromagnetic part (M0(H )),where the magnetization is almost saturated inH > 3 kOeand the Curie temperature is higher than room temperature,because the magnetization curve hardly changes up to roomtemperature. The present amount of the ferromagnetic part isdifferent from that reported by Ohamaet al.

Figure 2 shows the temperature dependence of the suscep-tibilities, χ0, to thec-axis and in thec-plane obtained as theslope of the straight line fitted to the magnetization plots inH > 3 kOe. Bothχ0 values are almost temperature inde-pendent. In detail, however, a slight increase with increasingtemperature can be seen, and with decreasing temperature avery slight increase, comparable to experimental errors, canbarely be seen also atT < 30 K in both cases. These detailedsituations are also seen in the results obtained by Ohamaetal.

The slight increase ofχ0 at high temperatures can be con-sidered to be a contribution from the ferromagnetic part, anincrease of the gradient ofM0(H ) in high fields with increas-ing temperature. (Though, strictly speaking, with increasingtemperature the magnetization curve should show a negativecurvature even in higher fields, however, we could not observeit owing to the very small magnetizations.) This is because,associated with the increase ofχ0 (the slope of a straightline), the extrapolated value of the straight line toH = 0,which roughly corresponds to the ferromagnetic spontaneousmagnetization, also shows a small change, a decrease with in-creasing temperature (about−20% at room temperature). Insome nonmagnetic quasi-crystals an upward turn of suscepti-bility at high temperatures is observed, which is explained asthe temperature dependence of Pauli paramagnetism with apseudogap at the Fermi level in the density-of-state curve.12)

Though, also in the present case the observed increase of sus-ceptibilities at high temperatures may include the tempera-ture dependence of Pauli paramagnetism, we cannot separateit from the measured susceptibilities, so we cannot refer to it.

On the other hand, the increase in susceptibility forT <

A reasonable explanation for the above results includingthose by Ohamaet al. is as follows: The sample consists,magnetically, of two parts. One is a diamagnetic part (χ0H )with anisotropic susceptibility. There is, of course, a possibil-ity that it includes a small contribution from Pauli paramag-

Fig. 1. Magnetisation curves in the magnetic fields to thec-axis (closedcircles) and in thec-plane (open circles) at 4.2 K.

Fig. 2. Temperature dependence of the susceptibilities (negative coeffi-cients of the field-proportional terms in the magnetization curves) to thec-axis (closed circles) and in thec-plane (open circles).

30 K will be, magnetically, the third part in the present sam-ple. If it is true this may suggest the existence of a Curie-typeparamagnetism term which is apparently seen in the data ofMarkertel al.9)

The origins of very small amounts of ferromagnetism andCurie-type paramagnetism (if it exists) may possibly be Niand/or Co clusters at phason boundaries, which are formedeven in ideal quasi-crystals. However, we think that the ferro-magnetism at least, may probably originate from a very smallamount of a second phase(s) formed mainly by Ni and/or Co,because it may be unnatural for stable ferromagnetism to beformed in a diamagnetic matrix.

Accordingly, we conclude here that the decagonal AlNiCoquasi-crystal is essentially a diamagnet with anisotropic sus-ceptibility. From the above mentioned discussion, as thevalues of the diamagnetic susceptibilities we should con-sider the largest negative values in Fig. 2,−2.0 and−3.7×10−7 emu/(g·Oe) in thec-plane (quasiperiodic plane) and tothec-axis (periodic axis), respectively. To check the quanti-tative adequacy of the observed susceptibilities, we estimatedthe ionic diamagnetic susceptibility of Al72Ni12Co16 using thetheoretical table values of the constituents. If we use−2,−12 and−12×10−6 emu/(mol·Oe) for aluminium, cobalt andnickel, assuming Al3+, Co2+ and Ni2+ ions,13) respectively,we obtain−1.3× 10−7 emu/(g·Oe) as the ionic diamagneticsusceptibility of Al72Ni12Co16. This value is smaller than ei-ther of the observed ones to thec-axis and in thec-plane,but close to that in thec-plane. This result suggests that theobserved susceptibility in thec-plane mainly originates fromthe ionic one and the contribution from Pauli paramagnetismis negligibly small in this material.

The origin of the additional diamagnetic susceptibility tothe c-axis direction may be located in the decagonal struc-ture of the present quasi-crystal. According to the structuralmodel of the atomic cluster of the present quasi-crystal by Hi-ragaet al.,14) aluminium and transition metal atoms are circu-larly arranged in the projection ofz = 0 andz = 1/2 layersperpendicular to the tenfold axis. Figure 3 shows the high-resolution transmission electron micrograph (HRTEM) of thepresent single decagonal ingot, which was taken by the inci-dent beam parallel to the tenfold axis [000001]. In fact, wecan see many ring contrasts in the micrograph. If the ring hasone or more electrons which can freely move in the ring, itmay be the origin of the additional diamagnetic susceptibility.This is the same idea as that which explains the well-knownanisotropic diamagnetic susceptibility of benzene shells. Toverify whether the idea can explain the value of the observedadditional susceptibility in order of magnitude or not, we usedthe following calculation.

Some kinds of ring contrasts with different sizes can beseen in the micrograph. The large ones of the radius, about1 nm are dominant. Therefore, we estimated the contributionfrom 1 nm rings. There are about thirty ring contrasts within13.3× 13.3 nm2 on the micrograph. The ring contrasts in themicrograph are made by the projection ofz= 0 andz= 1/2layers in one period to thec-axis, so about thirty rings exist inthe volume of 13.3× 13.3× 0.4 nm3 (the lattice constant,c,is about 0.4 nm). From the number of rings (30), the volume(13.3× 13.3× 0.4 nm3) and the specific gravity (4.34), weobtained 1.0× 1020 as the number of the rings per gram. Weused the equation,

χ = −N ne2

4mc2r 2, (1)

to calculate the diamagnetic susceptibility of the rings, whereN is the number of rings (1.0×1020), n, the movable electronnumber in a ring,r , the radius of the ring (1× 10−7 cm), e,electron charge,m, the electron mass andc, the light velocity.If n = 1, we obtain−0.7× 10−7 emu/(g·Oe) as the suscep-tibility. This value is of the same order of magnitude as theobserved additional susceptibility,−1.7 × 10−7 emu/(g·Oe)to thec-axis. This result implies that the idea is a reasonableone for explaining the anisotropic magnetic susceptibility ofthe present material.

Thus we propose a picture of the motion of electrons in adecagonal quasi-crystal that some electrons can freely movealong atoms arranged in a ring on the quasiperiodic plane.The ring is made up ofz = 0 andz = 1/2 layers, becausecircular arrangements of atoms cannot be seen in only onelayer, but in the projection of the two layers. Since the twolayers are equivalent to each other except for the 2π /10 ro-tation, these electrons should also move freely on a cylinder

Fig. 3. The high-resolution transmission electron micrograph of thepresent single decagonal ingot, which was taken by the incident beam par-allel to the tenfold axis [000001].

made by stacking the rings to thec-axis direction. Note thatthe proposed picture could also explain the anisotropy of theelectrical conductivity of this quasi-crystal; the conductivityalong thec-axis is much larger than that in thec-plane.9)

4. Summary and Concluding Remarks

We have carried out the magnetization measurements of thedecagonal Al72Ni12Co16 quasi-crystal in two cases of the ex-ternal magnetic field parallel and perpendicular to the periodicaxis. From the results, it has been found that the decago-nal AlNiCo quasi-crystal is essentially a diamagnet withanisotropic susceptibility,−2.0 and−3.7× 10−7 emu/(g·Oe)in thec-plane (quasiperiodic plane) and to thec-axis (periodicaxis), respectively. The estimated ionic diamagnetic suscepti-bility using the theoretical table values of the constituents wasclose to the observed one in thec-plane.

We proposed a picture of the motion of electrons in adecagonal quasi-crystal which can explain the additional dia-magnetic susceptibility to thec-axis. The picture can alsoqualitatively explain the observed anisotropy of the electricalconductivity of this quasi-crystal. However, the proposed pic-ture is, of course, rough and incomplete. Further theoreticalstudies of the electronic state, especially the electron motion,of the decagonal quasi-crystal are highly desired.

54 Jpn. J. Appl. Phys. Vol. 38 (1999) Pt. 1, No. 1A Y. YAMADA et al.

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