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Cluster-glass behavior in Al70Pd20Mn10
Journal of Magnetism and Magnetic Materials 241 (2002) 11–16
Cluster-glass behavior in Al70Pd20Mn10 Shigeki Nimoria,*, An Pang Tsaib a b
National Institute for Materials Sciences, 3-13 Sakura, Tsukuba 305-0003, Japan National Institute for Materials Sciences, 1-2-1 Sengen, Tsukuba 305-0047, Japan Received 4 December 2000; received in revised form 22 October 2001
Abstract We carried out precise magnetization measurements in an Al70 Pd20 Mn10 quasicrystalline system using a high-quality single crystal. A strange phenomena was observed at room temperature, which was a difference between zero field cooled and field cooled magnetization below 290 K. The thermoremanent magnetization also disappeared at 290 K. These experimental results suggest the forming of ferrimagnetic Mn ions clusters in Al70 Pd20 Mn10 below 290 K. In addition, high field magnetization in the temperature range between 4.2 and 30 K up to 12 T was also measured to investigate the anisotropic molecular field between clusters. r 2002 Elsevier Science B.V. All rights reserved. PACS: 61.44.Br; 75.30.Cr; 75.50.LK Keywords: Quasicrystal; Magnetization; Magnetic cluster; Spin glass; Ferromagnetism
1. Introduction Among quasicrystals [1], Al–Pd–Mn is known as the most stable system. Its physical properties have been extensively studied thus far. In the earlier stage of research on the Al–Pd–Mn system, metastable or poly-grained samples were used in experiments, and therefore serious sample dependence was observed. Due to the recent conspicuous progress in the field of crystal growth of quasicrystals, a large single crystal can be grown by the Bridgman method [2–4]. In the present, a single crystal is essential to investigate the physical properties of Al–Pd–Mn system.
*Corresponding author. Tel.: +81-298-59-5043; fax: +81298-59-5023. E-mail address: [email protected] (S. Nimori).
It has been believed that the magnetic properties have been completely studied by Chernikov [5] and Lasjaunias [6], who did considerable research using a single-grain Al–Pd–Mn alloy. They reported the magnetic properties of the Al–Pd–Mn system as follows: small magnetization compared to Mn concentration, negative Curie constant and spin-glass behavior below 10 K. The spin-glass phase, which originates in the Ruderman–Kittel– Kasuya–Yoshida (RKKY) interaction of Mn ions, was postulated because of AC susceptibility and specific heat measurements [6]. In addition, they inferred spin glass is not associated with quasiperiodicity. On the other hand, recently precise macroscopic measurement of the Zn–Mg–RE (RE=rare earth) quasicrystal has revealed magnetic ordering with icosahedral symmetry [7]. Therefore, we think the origin of the magnetic properties of Al–Pd–Mn is
0304-8853/02/$ - see front matter r 2002 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 8 8 5 3 ( 0 2 ) 0 0 0 0 7 - 0
12
S. Nimori, A.P. Tsai / Journal of Magnetism and Magnetic Materials 241 (2002) 11–16
still an issue, and that we should review the magnetic properties of the most familiar quasicrystalline Al–Pd–Mn system. In this paper, we perform precise magnetization measurements using a single crystal of Al–Pd–Mn alloy, and observe an anomalous magnetic behavior around room temperature. In Section 2, we describe the preparation of the single crystal and the magnetization measurements. Section 3 reviews the magnetization measurements and the anomalous increase of the field cooled magnetization is presented. In Section 4, we discuss the origin of the anomalous magnetic ordering at room temperature.
2. Experimental The mixture of Al, Pd and Mn metals that weighed 7:2:1 at mole ratio were melted in an argon atmosphere using an arc furnace. By using the resultant alloy, single quasicrystal was grown by the Bridgman method. The stoichiometry of the sample was checked by inductively coupled plasma atomic emission spectrometry (ICP-AES). For the magnetization measurement, the sample was shaped into a 1 1 3 mm form which weighed in the range from 50 to 70 mg. Temperature dependence of the magnetic susceptibility and magnetization curves up to 5 T were measured by a SQUID magnetometer (Quantum design). In these measurements, we used a plastic straw and resin tape to fix the sample at an appropriate position in the SQUID magnetometer. Since straws and Teflon have considerable diamagnetism, we have to take into account such a background for each measurement. In order to eliminate the background, we carried out magnetization measurements for the sample holder without samples in the same sequence each time. The demagnetization due to macromolecule of the straw or tape dose not exceed 107 emu within our experimental conditions, while the magnetic response by the sample were always more than 106 emu: High field magnetization curves up to 12 T were measured by use of the vibrating sample method.
3. Results Fig. 1 shows the temperature dependence of the inverse magnetic susceptibility, where the susceptibility was measured applying a field of 101 T after zero field cooling with increasing temperature. In the temperature region between 40 and 150 K, we can fit the Curie–Weiss law. By the least squares fit to the function of w ¼ w0 þ C=ðT YÞ; the values of w0jj ¼ 1:4870:97 106 emu=mol; w0> ¼ 1:4870:97 106 emu=mol for the temperature-independent susceptibility, Cjj ¼ 1:177 0:02 102 emu K=mol and C> ¼ 1:1270:02 102 emu K=mol for the Curie constant, and Yjj ¼ 2071 K and Y> ¼ 1972 K for the Curie temperature are obtained, respectively. From the Curie constant, the effective magnetic moment is estimated as 3:4 mB ; as an average [8]. Applying fields of 102 T; field cooled (FC) and zero field cooled (ZFC) magnetization deviate at 290 K as shown in Fig. 2(a), which was not observed when applying 101 T as shown in Fig. 2(b). The rise of FC magnetization below 290 K indicates a ferro-magnetic ordering that seems to originate in the finite range random spin freezing. To check this, we measured the thermoremanent magnetization (TRM) in the temperature range from 1.5 to 300 K. Fig. 3 shows the
Fig. 1. Temperature dependence of the inverse magnetic susceptibility applying 101 T parallel and perpendicular to the two-fold axis in Al70 Pd20 Mn10 : Solid lines indicate the fittings by the Curie–Weiss function.
S. Nimori, A.P. Tsai / Journal of Magnetism and Magnetic Materials 241 (2002) 11–16
13
Fig. 3. Temperature dependence of the thermoremanent magnetization of Al70 Pd20 Mn10 measured with increasing temperature after field cooled condition at 102 T: Note that temperature reversibility was checked below 290 K.
4. Discussion
Fig. 2. Temperature dependence of the magnetizations under zero field cooled and field cooled conditions at a field of 102 T(a) and 101 T(b) in Al70 Pd20 Mn10 : The field was applied perpendicular to the two-fold axis.
temperature dependence of TRM, where the magnetizations have been measured with increasing temperature after a field cooling process at 102 T: Apparently, the TRM vanishes at 290 K and reversibility to temperature was observed at several temperatures on the way to 290 K. This behavior suggests an occurrence of a random spin ordered state at 290 K.
Discussing magnetic properties of the Al–Pd– Mn system, first of all, we assume that the Pd and Mn atoms mainly govern the magnetic property of the Al–Pd–Mn system. For the Pd–Mn dilute system, many studies have been carried out so far [9,10]. In the Pd–Mn system, the higher concentration of Mn 10% causes a spin-glass behavior due to the competition between the ferro- and antiferro-magnetic interaction of Mn ions. The antiferromagnetic interaction influences within a ( and the ferromagnetic interaction distance of 5 A, ( The competidevelops for distances beyond 5 A. tion between the antiferro- and ferromagnetic interaction and quasiperiodicity yield ferrimagnetic clusters. The divergence of ZFC and FC magnetization at 290 K suggests a forming of the clusters. The small magnetization compared to Mn concentration [5,6] can be explained by the ferrimagnetic clusters. The formation of the magnetic clusters were also observed in other icosahedral quasicrystal Al37 Mn30 Si33 around 120 K [11]. In addition,
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S. Nimori, A.P. Tsai / Journal of Magnetism and Magnetic Materials 241 (2002) 11–16
with decreasing temperature, it is noticeable that the M–T curve of ZFC magnetization has a slight inflection point around 190 K, as shown in Fig. 4(a). It indicates a freezing of the clusters at 190 K. Indeed, a small peak in AC susceptibility was observed at 190 K (see Fig. 4(b)). Here we have to mention the Curie–Weiss behavior at the field of 101 T: The interaction between clusters is ferromagnetic because their ( Since the distance is regarded as above 5 A. cluster-glass behavior was observed in the comparatively weak field, the ferromagnetic interaction coefficient between the clusters is not so large.
Fig. 4. (a) Enlarged illustration of zero field cooled and field cooled magnetizations at 102 T: (b) Temperature dependence of ac magnetic susceptibility measured by 10 kHz under zero field cooled conditions.
In the small field, therefore, DC susceptibility behaves as paramagnetic and is well explained by the Curie–Weiss function in the high temperature region, which is a kind of superparamagnetism by ferrimagnetic clusters. In addition, we should take into account a contribution from Pd atoms. Pd causes a long range indirect ferromagnetic ordering due to the dband, which is proven by the ferromagnetic ordering in the low Mn concentration region in the Pd–Mn system. The growth of the Curie constant by substitution of Pd by Mn can not be explained only by the change of the effective magnetic moment [6]. We note that the molecular field of Mn or the influence of Pd contributes to the magnetic behavior. If Nð¼ 3kB C=m2eff Þ; which denotes the number of magnetic entities, increases with increasing Mn concentration proportionally, the observed Curie constants are too small by 101 or 102 : Especially, the large decrease from Mn9.6% to 7.5% in the Fig. 9 in Ref. [6] has a connection with the reverse of the correlation between Mn ions mentioned above. The deviation from linear behavior of the inverse susceptibility in Fig. 1 around above 170 K is caused by the temperature independent susceptibility w0 ; which originates in the paramagnetism of the band structure [12]. We also noticed a possibility to observe more obvious ferromagnetic behavior around room temperature. The Mn concentration of 10 at% corresponds to the critical point for the interaction between Mn ions. Therefore, the ferroand antiferro-interaction compete and would coexist in the system. Ferromagnetization was actually observed at room temperature for the decagonal Al–Pd–Mn–B alloy [13]. This ferromagnetic behavior originates from the quasicrystability or a spatial nonuniformity in the system. In addition, we would like to mention the result obtained by Lasjaunias [6]. He claimed that the universality of the magnetic part of the specific heat Cm among the Al–Mn series means the spinglass behavior of the Al–Pd–Mn at 0.5 K is not dependent rather on the crystal structure but the concentration of the Mn atoms in the system, and the quasiperiodicity may not necessarily explain the magnetic behaviors in the low temperature region [12]. In order to clarify this ambiguity, a
S. Nimori, A.P. Tsai / Journal of Magnetism and Magnetic Materials 241 (2002) 11–16
neutron diffuse scattering measurement or the decreasing of the polarizability of the incident polarized neutron beam by the spin ordered state will provide much information. Next, we discuss the spin-glass behavior below 1 K. In our single crystal, an enhancement of specific heat was observed at 0.5 K [14], which corresponds to a sharp cusp in ZFC magnetization and a peak in AC susceptibility observed by Chernikov and Lasjaunias [5,6]. In our scenario of the magnetism of AL–Pd–Mn system, the spin-glass behavior is the spin-freezing of the isolated Mn ions which do not form the ferrimagnetic cluster. It can be easily reasoned that some Mn ions remain isolated due to the icosahedral symmetry or inhomogeneity of the alloy, which is observed by the microscopic measurements [15]. Furthermore, we would like to discuss the origin of the spin glass behavior at low temperature. In the framework of the usual SK-model for spinglass, collinear Heisenberg-type interaction and a weak random anisotropic field coexist in the system. For the Heisenberg-type, which most kinds of spin-glasses systems belong to, the magnetic anisotropy is much smaller than the RKKY interaction by 101 or 102 : For an Al– Pd–Mn system, a significant difference of DC susceptibility between parallel and perpendicular to the two-fold axis was not observed. In addition, as shown in Fig. 5, the anisotropic magnetization behavior was not very significant in the high field region. These experimental results indicate the uniaxial anisotropy of the mean field theory is comparatively small and the cluster freezing occurred isotropically [16–18]. The difference of the ZFC magnetization between 101 and 102 T may infer a cross over from Heisenbergtype to Ising-type spin-glass according to a new approach for interpreting the spin- or cluster-glass ordering based on the chirality of the spin structure [19–21]. Since the quasiperiodic magnetic ordering is a non-collinear spin structure, we should recognize the importance of the chirality of the clusters. A detailed and macroscopic study using a sample with perfect quasiperiodicity would be necessary to draw a final conclusion about the Al–Pd–Mn system.
15
Fig. 5. Magnetization curves up to 12 T at various temperatures in Al70 Pd20 Mn10 : Magnetic fields were applied parallel and perpendicular to the two-fold axis.
Acknowledgements We gratefully acknowledge the participation of Dr. Itoh in obtaining the magnetization data. We also wish to thank to Dr. T.J. Sato for useful conversation.
References [1] D. Shechtman, I.A. Blech, D. Gratias, J.W. Cahn, Phys. Rev. Lett. 53 (1984) 1951. [2] A.P. Tsai, Y. Yokoyama, A. Inoue, T. Masumoto, Jpn. J. Appl. Phys. 29 (1990) L1161. [3] A.P. Tsai, A. Inoue, Y. Yokoyama, T. Masumoto, Mater. Trans., JIM 31 (1990) 98. [4] Y. Yokoyama, A.P. Tsai, A. Inoue, T. Masumoto, Mater. Trans., JIM 32 (1991) 1089. [5] M.A. Chernikov, A. Bernasconi, C. Beeli, A. Schilling, H.R. Ott, Phys. Rev. B 48 (1993) 3058. [6] J.C. Lasjaunias, A. Sulpice, N. Keller, J.J. Pr!ejean, M. de Boissieu, Phys. Rev. B 52 (1995) 886. [7] T.J. Sato, H. Takakura, A.P. Tsai, K. Shibata, K. Ohoyama, K.H. Andersen, Phys. Rev. B 61 (2000) 476. [8] S. Nimori, A.P. Tsai, G. Kido, Physica B 237–238 (1997) 565. [9] G.J. Nieuwenhuys, B.H. Verbeek, J. Phys. F 7 (1997) 1497. [10] B.R. Coles, H. Jamieson, R.H. Taylor, A. Tari, J. Phys. F 5 (1975) 565. [11] Ratnamala Chatterjee, R.A. Dunlap, V. Srinivas, R.C. O’Handley, Phys. Rev. B 42 (1990) 2337. [12] Z.M. Stadnik, D. Purdie, M. Garnier, Y. Baer, A.P. Tsai, A. Inoue, K. Edogawa, S. Takeuchi, K.H.J. Buschow, Phys. Rev. B 55 (1997) 10938.
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S. Nimori, A.P. Tsai / Journal of Magnetism and Magnetic Materials 241 (2002) 11–16
[13] Y. Yokoyama, A. Inoue, T. Masumoto, Mater. Trans., JIM 33 (1992) 1012. [14] S. Nimori, in preparation. [15] W.W. Warren, H.-S. Chen, G.P. Espinosa, Phys. Rev. B 34 (1986) 4902. [16] M. Gabay, G. Toulouse, Phys. Rev. Lett. 47 (1981) 201. [17] D.M. Cragg, D. Sherrington, M. Gabay, Phys Rev. Lett. 49 (1982) 158.
[18] D.M. Cragg, D. Sherrington, Phys Rev. Lett. 49 (1982) 1190. [19] H. Kawamura, Phys. Rev. Lett. 68 (1992) 3785. [20] H. Kawamura, Int. J. Mod. Phys. 7 (1996) 4220. [21] G. Kotliar, H. Sompolinsky, Phys. Rev. Lett. 53 (1984) 1751.
Cluster-glass behavior in Al70Pd20Mn10 Shigeki Nimoria,*, An Pang Tsaib a b
National Institute for Materials Sciences, 3-13 Sakura, Tsukuba 305-0003, Japan National Institute for Materials Sciences, 1-2-1 Sengen, Tsukuba 305-0047, Japan Received 4 December 2000; received in revised form 22 October 2001
Abstract We carried out precise magnetization measurements in an Al70 Pd20 Mn10 quasicrystalline system using a high-quality single crystal. A strange phenomena was observed at room temperature, which was a difference between zero field cooled and field cooled magnetization below 290 K. The thermoremanent magnetization also disappeared at 290 K. These experimental results suggest the forming of ferrimagnetic Mn ions clusters in Al70 Pd20 Mn10 below 290 K. In addition, high field magnetization in the temperature range between 4.2 and 30 K up to 12 T was also measured to investigate the anisotropic molecular field between clusters. r 2002 Elsevier Science B.V. All rights reserved. PACS: 61.44.Br; 75.30.Cr; 75.50.LK Keywords: Quasicrystal; Magnetization; Magnetic cluster; Spin glass; Ferromagnetism
1. Introduction Among quasicrystals [1], Al–Pd–Mn is known as the most stable system. Its physical properties have been extensively studied thus far. In the earlier stage of research on the Al–Pd–Mn system, metastable or poly-grained samples were used in experiments, and therefore serious sample dependence was observed. Due to the recent conspicuous progress in the field of crystal growth of quasicrystals, a large single crystal can be grown by the Bridgman method [2–4]. In the present, a single crystal is essential to investigate the physical properties of Al–Pd–Mn system.
*Corresponding author. Tel.: +81-298-59-5043; fax: +81298-59-5023. E-mail address: [email protected] (S. Nimori).
It has been believed that the magnetic properties have been completely studied by Chernikov [5] and Lasjaunias [6], who did considerable research using a single-grain Al–Pd–Mn alloy. They reported the magnetic properties of the Al–Pd–Mn system as follows: small magnetization compared to Mn concentration, negative Curie constant and spin-glass behavior below 10 K. The spin-glass phase, which originates in the Ruderman–Kittel– Kasuya–Yoshida (RKKY) interaction of Mn ions, was postulated because of AC susceptibility and specific heat measurements [6]. In addition, they inferred spin glass is not associated with quasiperiodicity. On the other hand, recently precise macroscopic measurement of the Zn–Mg–RE (RE=rare earth) quasicrystal has revealed magnetic ordering with icosahedral symmetry [7]. Therefore, we think the origin of the magnetic properties of Al–Pd–Mn is
0304-8853/02/$ - see front matter r 2002 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 8 8 5 3 ( 0 2 ) 0 0 0 0 7 - 0
12
S. Nimori, A.P. Tsai / Journal of Magnetism and Magnetic Materials 241 (2002) 11–16
still an issue, and that we should review the magnetic properties of the most familiar quasicrystalline Al–Pd–Mn system. In this paper, we perform precise magnetization measurements using a single crystal of Al–Pd–Mn alloy, and observe an anomalous magnetic behavior around room temperature. In Section 2, we describe the preparation of the single crystal and the magnetization measurements. Section 3 reviews the magnetization measurements and the anomalous increase of the field cooled magnetization is presented. In Section 4, we discuss the origin of the anomalous magnetic ordering at room temperature.
2. Experimental The mixture of Al, Pd and Mn metals that weighed 7:2:1 at mole ratio were melted in an argon atmosphere using an arc furnace. By using the resultant alloy, single quasicrystal was grown by the Bridgman method. The stoichiometry of the sample was checked by inductively coupled plasma atomic emission spectrometry (ICP-AES). For the magnetization measurement, the sample was shaped into a 1 1 3 mm form which weighed in the range from 50 to 70 mg. Temperature dependence of the magnetic susceptibility and magnetization curves up to 5 T were measured by a SQUID magnetometer (Quantum design). In these measurements, we used a plastic straw and resin tape to fix the sample at an appropriate position in the SQUID magnetometer. Since straws and Teflon have considerable diamagnetism, we have to take into account such a background for each measurement. In order to eliminate the background, we carried out magnetization measurements for the sample holder without samples in the same sequence each time. The demagnetization due to macromolecule of the straw or tape dose not exceed 107 emu within our experimental conditions, while the magnetic response by the sample were always more than 106 emu: High field magnetization curves up to 12 T were measured by use of the vibrating sample method.
3. Results Fig. 1 shows the temperature dependence of the inverse magnetic susceptibility, where the susceptibility was measured applying a field of 101 T after zero field cooling with increasing temperature. In the temperature region between 40 and 150 K, we can fit the Curie–Weiss law. By the least squares fit to the function of w ¼ w0 þ C=ðT YÞ; the values of w0jj ¼ 1:4870:97 106 emu=mol; w0> ¼ 1:4870:97 106 emu=mol for the temperature-independent susceptibility, Cjj ¼ 1:177 0:02 102 emu K=mol and C> ¼ 1:1270:02 102 emu K=mol for the Curie constant, and Yjj ¼ 2071 K and Y> ¼ 1972 K for the Curie temperature are obtained, respectively. From the Curie constant, the effective magnetic moment is estimated as 3:4 mB ; as an average [8]. Applying fields of 102 T; field cooled (FC) and zero field cooled (ZFC) magnetization deviate at 290 K as shown in Fig. 2(a), which was not observed when applying 101 T as shown in Fig. 2(b). The rise of FC magnetization below 290 K indicates a ferro-magnetic ordering that seems to originate in the finite range random spin freezing. To check this, we measured the thermoremanent magnetization (TRM) in the temperature range from 1.5 to 300 K. Fig. 3 shows the
Fig. 1. Temperature dependence of the inverse magnetic susceptibility applying 101 T parallel and perpendicular to the two-fold axis in Al70 Pd20 Mn10 : Solid lines indicate the fittings by the Curie–Weiss function.
S. Nimori, A.P. Tsai / Journal of Magnetism and Magnetic Materials 241 (2002) 11–16
13
Fig. 3. Temperature dependence of the thermoremanent magnetization of Al70 Pd20 Mn10 measured with increasing temperature after field cooled condition at 102 T: Note that temperature reversibility was checked below 290 K.
4. Discussion
Fig. 2. Temperature dependence of the magnetizations under zero field cooled and field cooled conditions at a field of 102 T(a) and 101 T(b) in Al70 Pd20 Mn10 : The field was applied perpendicular to the two-fold axis.
temperature dependence of TRM, where the magnetizations have been measured with increasing temperature after a field cooling process at 102 T: Apparently, the TRM vanishes at 290 K and reversibility to temperature was observed at several temperatures on the way to 290 K. This behavior suggests an occurrence of a random spin ordered state at 290 K.
Discussing magnetic properties of the Al–Pd– Mn system, first of all, we assume that the Pd and Mn atoms mainly govern the magnetic property of the Al–Pd–Mn system. For the Pd–Mn dilute system, many studies have been carried out so far [9,10]. In the Pd–Mn system, the higher concentration of Mn 10% causes a spin-glass behavior due to the competition between the ferro- and antiferro-magnetic interaction of Mn ions. The antiferromagnetic interaction influences within a ( and the ferromagnetic interaction distance of 5 A, ( The competidevelops for distances beyond 5 A. tion between the antiferro- and ferromagnetic interaction and quasiperiodicity yield ferrimagnetic clusters. The divergence of ZFC and FC magnetization at 290 K suggests a forming of the clusters. The small magnetization compared to Mn concentration [5,6] can be explained by the ferrimagnetic clusters. The formation of the magnetic clusters were also observed in other icosahedral quasicrystal Al37 Mn30 Si33 around 120 K [11]. In addition,
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S. Nimori, A.P. Tsai / Journal of Magnetism and Magnetic Materials 241 (2002) 11–16
with decreasing temperature, it is noticeable that the M–T curve of ZFC magnetization has a slight inflection point around 190 K, as shown in Fig. 4(a). It indicates a freezing of the clusters at 190 K. Indeed, a small peak in AC susceptibility was observed at 190 K (see Fig. 4(b)). Here we have to mention the Curie–Weiss behavior at the field of 101 T: The interaction between clusters is ferromagnetic because their ( Since the distance is regarded as above 5 A. cluster-glass behavior was observed in the comparatively weak field, the ferromagnetic interaction coefficient between the clusters is not so large.
Fig. 4. (a) Enlarged illustration of zero field cooled and field cooled magnetizations at 102 T: (b) Temperature dependence of ac magnetic susceptibility measured by 10 kHz under zero field cooled conditions.
In the small field, therefore, DC susceptibility behaves as paramagnetic and is well explained by the Curie–Weiss function in the high temperature region, which is a kind of superparamagnetism by ferrimagnetic clusters. In addition, we should take into account a contribution from Pd atoms. Pd causes a long range indirect ferromagnetic ordering due to the dband, which is proven by the ferromagnetic ordering in the low Mn concentration region in the Pd–Mn system. The growth of the Curie constant by substitution of Pd by Mn can not be explained only by the change of the effective magnetic moment [6]. We note that the molecular field of Mn or the influence of Pd contributes to the magnetic behavior. If Nð¼ 3kB C=m2eff Þ; which denotes the number of magnetic entities, increases with increasing Mn concentration proportionally, the observed Curie constants are too small by 101 or 102 : Especially, the large decrease from Mn9.6% to 7.5% in the Fig. 9 in Ref. [6] has a connection with the reverse of the correlation between Mn ions mentioned above. The deviation from linear behavior of the inverse susceptibility in Fig. 1 around above 170 K is caused by the temperature independent susceptibility w0 ; which originates in the paramagnetism of the band structure [12]. We also noticed a possibility to observe more obvious ferromagnetic behavior around room temperature. The Mn concentration of 10 at% corresponds to the critical point for the interaction between Mn ions. Therefore, the ferroand antiferro-interaction compete and would coexist in the system. Ferromagnetization was actually observed at room temperature for the decagonal Al–Pd–Mn–B alloy [13]. This ferromagnetic behavior originates from the quasicrystability or a spatial nonuniformity in the system. In addition, we would like to mention the result obtained by Lasjaunias [6]. He claimed that the universality of the magnetic part of the specific heat Cm among the Al–Mn series means the spinglass behavior of the Al–Pd–Mn at 0.5 K is not dependent rather on the crystal structure but the concentration of the Mn atoms in the system, and the quasiperiodicity may not necessarily explain the magnetic behaviors in the low temperature region [12]. In order to clarify this ambiguity, a
S. Nimori, A.P. Tsai / Journal of Magnetism and Magnetic Materials 241 (2002) 11–16
neutron diffuse scattering measurement or the decreasing of the polarizability of the incident polarized neutron beam by the spin ordered state will provide much information. Next, we discuss the spin-glass behavior below 1 K. In our single crystal, an enhancement of specific heat was observed at 0.5 K [14], which corresponds to a sharp cusp in ZFC magnetization and a peak in AC susceptibility observed by Chernikov and Lasjaunias [5,6]. In our scenario of the magnetism of AL–Pd–Mn system, the spin-glass behavior is the spin-freezing of the isolated Mn ions which do not form the ferrimagnetic cluster. It can be easily reasoned that some Mn ions remain isolated due to the icosahedral symmetry or inhomogeneity of the alloy, which is observed by the microscopic measurements [15]. Furthermore, we would like to discuss the origin of the spin glass behavior at low temperature. In the framework of the usual SK-model for spinglass, collinear Heisenberg-type interaction and a weak random anisotropic field coexist in the system. For the Heisenberg-type, which most kinds of spin-glasses systems belong to, the magnetic anisotropy is much smaller than the RKKY interaction by 101 or 102 : For an Al– Pd–Mn system, a significant difference of DC susceptibility between parallel and perpendicular to the two-fold axis was not observed. In addition, as shown in Fig. 5, the anisotropic magnetization behavior was not very significant in the high field region. These experimental results indicate the uniaxial anisotropy of the mean field theory is comparatively small and the cluster freezing occurred isotropically [16–18]. The difference of the ZFC magnetization between 101 and 102 T may infer a cross over from Heisenbergtype to Ising-type spin-glass according to a new approach for interpreting the spin- or cluster-glass ordering based on the chirality of the spin structure [19–21]. Since the quasiperiodic magnetic ordering is a non-collinear spin structure, we should recognize the importance of the chirality of the clusters. A detailed and macroscopic study using a sample with perfect quasiperiodicity would be necessary to draw a final conclusion about the Al–Pd–Mn system.
15
Fig. 5. Magnetization curves up to 12 T at various temperatures in Al70 Pd20 Mn10 : Magnetic fields were applied parallel and perpendicular to the two-fold axis.
Acknowledgements We gratefully acknowledge the participation of Dr. Itoh in obtaining the magnetization data. We also wish to thank to Dr. T.J. Sato for useful conversation.
References [1] D. Shechtman, I.A. Blech, D. Gratias, J.W. Cahn, Phys. Rev. Lett. 53 (1984) 1951. [2] A.P. Tsai, Y. Yokoyama, A. Inoue, T. Masumoto, Jpn. J. Appl. Phys. 29 (1990) L1161. [3] A.P. Tsai, A. Inoue, Y. Yokoyama, T. Masumoto, Mater. Trans., JIM 31 (1990) 98. [4] Y. Yokoyama, A.P. Tsai, A. Inoue, T. Masumoto, Mater. Trans., JIM 32 (1991) 1089. [5] M.A. Chernikov, A. Bernasconi, C. Beeli, A. Schilling, H.R. Ott, Phys. Rev. B 48 (1993) 3058. [6] J.C. Lasjaunias, A. Sulpice, N. Keller, J.J. Pr!ejean, M. de Boissieu, Phys. Rev. B 52 (1995) 886. [7] T.J. Sato, H. Takakura, A.P. Tsai, K. Shibata, K. Ohoyama, K.H. Andersen, Phys. Rev. B 61 (2000) 476. [8] S. Nimori, A.P. Tsai, G. Kido, Physica B 237–238 (1997) 565. [9] G.J. Nieuwenhuys, B.H. Verbeek, J. Phys. F 7 (1997) 1497. [10] B.R. Coles, H. Jamieson, R.H. Taylor, A. Tari, J. Phys. F 5 (1975) 565. [11] Ratnamala Chatterjee, R.A. Dunlap, V. Srinivas, R.C. O’Handley, Phys. Rev. B 42 (1990) 2337. [12] Z.M. Stadnik, D. Purdie, M. Garnier, Y. Baer, A.P. Tsai, A. Inoue, K. Edogawa, S. Takeuchi, K.H.J. Buschow, Phys. Rev. B 55 (1997) 10938.
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S. Nimori, A.P. Tsai / Journal of Magnetism and Magnetic Materials 241 (2002) 11–16
[13] Y. Yokoyama, A. Inoue, T. Masumoto, Mater. Trans., JIM 33 (1992) 1012. [14] S. Nimori, in preparation. [15] W.W. Warren, H.-S. Chen, G.P. Espinosa, Phys. Rev. B 34 (1986) 4902. [16] M. Gabay, G. Toulouse, Phys. Rev. Lett. 47 (1981) 201. [17] D.M. Cragg, D. Sherrington, M. Gabay, Phys Rev. Lett. 49 (1982) 158.
[18] D.M. Cragg, D. Sherrington, Phys Rev. Lett. 49 (1982) 1190. [19] H. Kawamura, Phys. Rev. Lett. 68 (1992) 3785. [20] H. Kawamura, Int. J. Mod. Phys. 7 (1996) 4220. [21] G. Kotliar, H. Sompolinsky, Phys. Rev. Lett. 53 (1984) 1751.