Ferromagnetism and re-entrant spin-glass transition in quasicrystal approximants Au–SM–Gd

(SM = Si, Ge)

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2013 J. Phys.: Condens. Matter 25 426004

(http://iopscience.iop.org/0953-8984/25/42/426004)

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J. Phys.: Condens. Matter 25 (2013) 426004 (6pp) doi:10.1088/0953-8984/25/42/426004

Ferromagnetism and re-entrant spin-glasstransition in quasicrystal approximantsAu–SM–Gd (SM = Si, Ge)T Hiroto1, G H Gebresenbut2, C Pay Gomez2, Y Muro3, M Isobe4,Y Ueda4, K Tokiwa5 and R Tamura1

1 Department of Materials Science and Technology, Tokyo University of Science, Niijuku,Tokyo 125-8585, Japan2 Department of Chemistry—Angstrom, Uppsala University, SE-751 21 Uppsala, Sweden3 Liberal Arts and Science, Toyama Prefectural University, Imizu, Toyama 939-0398, Japan4 Institute for Solid State Physics, The University of Tokyo, Kashiwa, Chiba 277-8581, Japan5 Department of Applied Electronics, Tokyo University of Science, Niijuku, Tokyo 125-8585, Japan

E-mail: tamura@rs.noda.tus.ac.jp

Received 14 June 2013, in final form 4 September 2013Published 27 September 2013Online at stacks.iop.org/JPhysCM/25/426004

AbstractMagnetic susceptibility and specific heat measurements on quasicrystalline approximantsAu–Si–Gd and Au–Ge–Gd reveal that a ferromagnetic (FM) transition occurs atTc = 22.5(5) K for Au–Si–Gd and at Tc = 13(1) K for Au–Ge–Gd, which are the firstexamples of ferromagnetism in crystalline approximants. In addition, a re-entrant spin-glass(RSG) transition is observed at TRSG = 3.3 K for Au–Ge–Gd in contrast to Au–Si–Gd. Thedifferent behaviors are understood based on the recent structural models reported byGebresenbut et al (2013 J. Phys.: Condens. Matter 25 135402). The RSG transition inAu–Ge–Gd is attributed to a random occupation of the center of the Gd12 icosahedron by Gdatoms; a central Gd spin hinders the long-range FM order.

(Some figures may appear in colour only in the online journal)

1. Introduction

Since the discovery of the first icosahedral quasicrystal (QC)by Shechtman et al [1], the influence of long-range aswell as short-range atomic order of icosahedral symmetryon the magnetic properties has been an exciting andfundamental issue in condensed matter physics and hasbeen investigated for almost 30 years [2–5]. As far asthe magnetism of the rare-earth (R) bearing QCs such asZn–Mg–R [2], Cd–Mg–R [3], Cd–R [6], etc, are concerned,no long-range magnetic order but only spin-glass-like freezinghas been observed to date and, hence, the spin-glassbehavior has been regarded as an intrinsic property ofmagnetic clusters with icosahedral symmetry [4]. However,it was recently shown that their crystalline counterparts,i.e., Cd6R approximants, exhibit antiferromagnetic andferrimagnetic transitions [7–11]. In this paper, we reportobservations of ferromagnetic (FM) transitions in the Au-based compounds Au–SM–Gd (SM = Si, Ge) [12], which

are 1/1 cubic approximants (Im3) composed of so-calledTsai-type icosahedral clusters [13, 14] (see figures 1 and 2).Figures 2(a) and (b) show the Gd positions in Au–SM–Gd(SM = Si, Gd), respectively, for comparison [12]. Thedifference in the Gd positions between the two compounds isnoticed at the center of the Gd12 icosahedron: in Au–Si–Gd,Gd occupies only the vertices of the icosahedron (24g)whereas in Au–Ge–Gd 10% of the cluster center (2a)is occupied by Gd atoms in addition to the 24g site.In Au–Ge–Gd, a re-entrant spin-glass transition is furtherobserved below Tc while it is not in Au–Si–Gd. The reasonfor the different behaviors will be discussed and understoodbased on the difference in their atomic structures as describedabove.

2. Experimental details

Au–SM–Gd (SM = Si, Ge) 1/1 approximants were preparedby melting high-purity elements (>99.99%). The raw

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J. Phys.: Condens. Matter 25 (2013) 426004 T Hiroto et al

Figure 1. The Tsai-type icosahedral cluster composed of a series of concentric polyhedral shells; from the center, a dodecahedron (firstshell), a rare-earth (Gd) icosahedron (second, light blue shell), an icosidodecahedron (third shell) and a defect rhombic triacontahedron(fourth shell). Parentheses indicate the Wyckoff letter and occupancy, respectively. The second icosahedral shell is fully occupied by 12 Gd(24g) atoms. In the inner part of the cluster, there are four atoms, i.e., an orientationally disordered tetrahedron made by 4 Si(occupancy0.249)/Au(0.0843) or 4 Ge. For the Au–Ge–Gd, 10% of the cluster center (2a) is occupied by a single Gd atom, instead of an orientationallydisordered tetrahedron. The detailed crystal structures of Au–SM–Gd (SM = Si, Gd) are reported by Gebresenbut et al [12].

materials were placed into an alumina crucible and sealedinside a stainless steel tube under Ar atmosphere. Thenthey were heated and melted in an electronic furnace. Thedetails of sample preparation were reported elsewhere [12].The phase purity of the samples was confirmed bypowder x-ray diffraction (XRD) and scanning electronmicroscope (SEM). Structural refinements were performedon single grains picked out from polycrystalline samplesand the refined compositions were Au69.9Si15.9Gd14.2 andAu67.2Ge18.5Gd14.3 [12]. The dc magnetic susceptibility wasmeasured in a temperature range between 1.8 and 300 Kby a superconducting quantum interference device (SQUID)magnetometer (Quantum Design, MPMS) with external dcfields up to 5 T, and the magnetic relaxation was measured onzero-field-cooled samples as a function of time immediatelyafter application of 1 mT. The ac susceptibility was measuredin a temperature range between 2 and 6 K by using PPMS(Quantum Design) with frequencies of ω/2π = 111–1111 Hzand external ac field of 1 mT. Specific heat was measured bya relaxation method from 1.8 to 50 K in magnetic fields upto 9 T.

3. Results and discussion

Figure 3 shows magnetic susceptibilities of Au–Si–Gd andAu–Ge–Gd measured at 0.1 T in a temperature range between1.8 and 300 K. Both the magnetic susceptibilities obey theCurie–Weiss law in the high-temperature range above 50 K.The effective magnetic moment µeff and a paramagneticCurie temperature 2p were determined by least-square fits

to the modified Curie–Weiss law χ(T) =NAµ

2effµ

2B

3kB(T−2p)+

χ0, where kB,NA and µB are the Boltzmann constant,Avogadro’s number and the Bohr magneton, respectively,and χ0 is a temperature independent term which includesother contributions such as the diamagnetic, Pauli spin andLandau susceptibilities. The parameters obtained from thefits are listed in table 1. The obtained effective magneticmoments are close to the theoretical value of a Gd3+ free

Table 1. The effective magnetic moment and paramagnetic Curietemperature 2p obtained from least-squares fits of the magneticsusceptibility data to the modified Curie–Weiss law, and theferromagnetic transition temperature Tc determined from thespecific heats of Au–SM–Gd (SM = Si, Ge).

µeff (µB) 2p (K) Tc (K)

Au–Si–Gd 7.91(2) 22.7(1) 22.5(5)Au–Ge–Gd 8.00(2) 12.2(2) 13(1)

ion (g√

J(J + 1) = 7.94 µB) in both systems showing awell-localized character of the Gd3+ spins, where g is theLande g factor (g = 2) and J is the total angular momentum(J = 7/2). The positive 2p values indicate that the majorinteraction between localized Gd3+ spins is ferromagnetic,which is in contrast with the negative 2p values observedin other approximants [7–9, 15] and quasicrystals withoutexception [2–4].

Now we focus on the low-temperature behavior below50 K measured at 1 mT with zero-field-cooled (ZFC) andfield-cooled (FC) modes. As seen from figures 4(a) and (b),both the ZFC and FC curves increase sharply at Tc = 22.5 K inAu–Si–Gd and Tc = 13 K in Au–Ge–Gd. These temperaturescorrespond well to those of the anomalies observed in thespecific heats (figures 5(a) and (b)). In addition, a decreasein χ accompanying a difference between the ZFC and FCcurves is noticed below 13 K only in Au–Ge–Gd, the reasonfor which will be addressed later. Figures 6(a) and (b)show the magnetic field dependence of the magnetizationmeasured for the Au–SM–Gd (SM = Si, Ge) approximants,respectively. FM hysteresis loops are observed below Tc, i.e.,at 2–20 K in Au–Si–Gd and at 2–10 K in Au–Ge–Gd. At thelowest temperature of 2 K, magnetic saturation behavior isobserved in both systems. The saturation magnetizations areestimated to be 6.70 µB/Gd for Au–Si–Gd and 6.87 µB/Gdfor Au–Ge–Gd. These values are close to the saturationmagnetization of a Gd3+ free ion based on Hund’s rule, i.e.,gJ = 7.00 µB/Gd, which clearly indicates the occurrence of a

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Figure 2. The Gd positions in (a) Au–Si–Gd and (b) Au–Ge–Gdfrom [12]. In (b), an additional Gd atom (with 10% occupancy) atthe cluster center (2a) of Gd12 icosahedron (24g) is shown in green.Typical Gd–Gd distances are also shown in the figures where thesame distances are omitted for clarity. Note that the shortest Gd–Gddistance (5.2319 A) in (b) occurs between the central Gd (2a) andits surrounding 12 Gd (24g) whereas such a central Gd (2a) atom ismissing in (a). The distance between the central Gd and the secondnearest Gd (9.1707 A) is also shown by a dashed line.

Figure 3. Temperature dependences of the inverse magneticsusceptibility of Au–Si–Gd (red, open circle) and Au–Ge–Gd (lightgreen, open triangle) measured at 0.1 T, after first cooling to 1.8 Kin ZF. The solid lines are fits to the modified Curie–Weiss law. Insetshows low-temperature region of the magnetic susceptibilities.A ferromagnetic transition is observed in both systems.

Figure 4. Zero-field-cooled (ZFC, open blue circle) andfield-cooled (FC, open red circle) magnetic susceptibilitiesmeasured at 1 mT of (a) Au–Si–Gd and (b) Au–Ge–Gd.Ferromagnetic transitions were observed at 22.5 K for Au–Si–Gdand 13 K for Au–Ge–Gd.

FM transition in both systems. We note that these are the firstexamples of ferromagnetism in approximant crystals.

On the other hand, the coercivity and remanencemagnetization are very small in both compounds, indicatinga very soft magnetic nature. In Au–Si–Gd the magneticsaturation occurs at a much lower magnetic field at 2 K

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Figure 5. Specific heat divided by temperature (Cp/T) measured atzero field and at fields up to 9 T for (a) Au–Si–Gd and(b) Au–Ge–Gd approximants, respectively. A jump due to theferromagnetic transition is seen at 22.5 K for Au–Si–Gd and at 13 Kfor Au–Ge–Gd at zero field. The transition temperatures (Tc’s) aredetermined from the midpoint of the Cp/T jump. As expected, theanomalies due to the ferromagnetic transitions disappear byapplying magnetic fields.

compared to Au–Ge–Gd where the saturation proceeds ratherslowly, the reason for which will be discussed later. The originof the soft magnetic behavior in Au–SM–Gd (SM = Si, Ge)is partly attributed to the weak crystal field effect owing tothe spherical 4f orbital of Gd. Figures 5(a) and (b) showthe temperature dependence of the specific heat divided bytemperature, Cp/T , measured at zero field and in magneticfields up to 9 T for Au–Si–Gd and Au–Ge–Gd approximants,respectively. A clear Cp/T jump is observed at Tc = 22.5(5)Kin Au–Si–Gd and Tc = 13(1) K in Au–Ge–Gd, which isconsistent with the occurrence of a FM transition observedin the χ–T curves.

Furthermore, a remarkable feature is observed inAu–Ge–Gd as manifested by the deviation between the ZFCand FC curves and also by a broad peak at 3.3 K in Cp/T . Bothare characteristic features observed in spin-glass freezing.Also, the broad peak at 3.3 K is found to be suppressedwith increasing magnetic field, which is consistent with thoseobserved in other spin-glass systems such as CuMn [16].Here, the faint shoulder of Cp/T around 6 K in Au–Si–Gd isnot from the same origin as the peak of Au–Ge–Gd since thereis no corresponding anomaly in the dc magnetization curve ofAu–Si–Gd. Thus, in Au–Ge–Gd, the FM state becomes a spinglass at 3.3 K. Such a spin-glass state below a FM state has

Figure 6. Magnetization curves of (a) Au–Si–Gd and(b) Au–Ge–Gd approximants measured at various temperatures.Magnetic saturation occurs below Tc in both systems. Insets showthe low-field region of magnetization curves.

been reported in a class of disordered ferromagnets [16] andis known as a re-entrant spin glass (RSG).

In order to confirm the occurrence of spin-glass freezing,we measured frequency dependence of the ac susceptibility ofAu–Ge–Gd. As seen in figure 7(a), χ ′(ω) shows a decreasebelow 6 K in agreement with the ZFC dc susceptibilityin figure 4(b). A frequency dependence is clearly noticedin χ ′(ω); the decrease below 6 K becomes larger as thefrequency increases. On the other hand, χ ′′(ω) exhibits apeak at ∼2.2 K at low frequencies as seen in figure 7(b)and both peak intensity and peak temperature are foundto increase with increasing frequency. These frequencydependences of χ ′(ω) and χ ′′(ω) are in good agreementwith those observed in well-known RSG systems [17]. Inorder to further clarify the difference between Au–Ge–Gdand Au–Si–Gd, we measured the time dependence of thedc susceptibility for both compounds. Figures 8(a) and(b) show the normalized magnetization of Au–Si–Gd andAu–Ge–Gd, respectively, as a function of time measuredwith the dc field of 1 mT. In Au–Si–Gd, the magnetizationdepends weakly on time and no appreciable difference isobserved between the susceptibilities measured above andbelow Tc. On the other hand, a significant increase of themagnetization with time is noticed at 2 K in Au–Ge–Gd.Such a distinct time dependence, i.e., aging effect, isone of the main characteristics of spin glasses [16, 17].The frequency dependence of the ac susceptibility and the

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Figure 7. Temperature dependences of the ac susceptibility,(a) χ ′(ω) and (b) χ ′′(ω), of Au–Ge–Gd measured with frequenciesω/2π = 111–1111 Hz. The amplitude of the magnetic field is 1 mT.

relaxation phenomenon of the dc susceptibility together withthe broad peak at 3.3 K in the specific heat consistently showthat Au–Ge–Gd becomes a spin glass below 3.3 K. We notethat the slower magnetic saturation at 2 K in Au–Ge–Gd (seefigure 6(b)) is attributed to the existence of frustration whichis responsible for the spin-glass behavior.

The difference in the two closely related compoundsmeans that the occurrence of RSG in Au–Ge–Gd is attributedto the existence of both disorder and frustration, which areabsent in Au–Si–Gd. As shown in figures 2(a) and (b), thedifference in the Gd positions between the two compoundsexists only at the center of the Gd12 icosahedron: inAu–Si–Gd, Gd occupies only the vertices of the icosahedron(24g) whereas in Au–Ge–Gd, 10% of the cluster center (2a) isoccupied by a Gd atom in addition to the 24g site. Such partialoccupancy in Au–Ge–Gd induces site disorder of Gd spinsgiving rise to disorder in the magnetic interaction, i.e., RKKYinteraction. Considering the fact that no RSG occurs inAu–Si–Gd, the spin-glass freezing behavior of Au–Ge–Gd isattributed to the random occupation of the 2a site (center ofeach Gd12 icosahedron) by Gd atoms.

The occurrence of RSG means that frustration is alsoinduced by the partial occupation of the 2a site by Gd atoms.Figures 2(a) and (b) show the nearest Gd–Gd distances in bothcompounds [12]. The Gd–Gd distances between the centralGd and the surrounding 12 Gd atoms are the shortest andalmost the same (5.2319 A), and appreciably smaller thanthose (5.4654–5.5047 A) between the nearest Gd atoms on

Figure 8. Time dependence of the normalized dc magnetizationM(t)/M(t = 0) curves of (a) Au–Si–Gd and (b) Au–Ge–Gdmeasured at 2, 10 and 30 K. The magnetization was measured onzero-field-cooled samples at each temperature immediately afterapplying the field of 1 mT.

the Gd icosahedron. Therefore, to the first approximationthe type of interaction between the central Gd spin and thesurrounding 12 Gd spins is expected to be the same, i.e., eitherFM or AFM, based on the RKKY interaction which is afunction of only the distance between spins. In both cases,however, no frustration would occur inside the Gd13 cluster.Hence, it is likely that the frustration is induced by magneticinteractions between the central Gd spin and the next-nearestGd spins which are located at the vertices of the nearesttriangle faces of the neighboring Gd12 icosahedra as denotedin figure 2(b). In this scheme, Gd12 clusters form a largeFM ‘cluster’ with neighboring Gd12 clusters while a Gd13cluster behaves as a kind of magnetic impurity. The simplestanalog of this new RSG material may be a ferromagnetic bcccrystal containing magnetic impurities (∼10%), i.e., with themagnetic icosahedra being magnetic ‘superatoms’.

4. Conclusion

Ferromagnetic transitions with Tc = 22.5(5) K and Tc =

13(1) K are observed in the quasicrystalline approximantsAu–SM–Gd (SM= Si, Ge), respectively, which are describedas bcc packings of Gd icosahedra. In addition, for theAu–Ge–Gd compound, a re-entrant spin-glass (RSG) transi-tion is observed at TRSG = 3.3 K in contrast to Au–Si–Gd. Thedifference in behavior of the two similar compounds is ex-plained by site disorder of the Gd atoms in Au–Ge–Gd, i.e., arandom occupation of the center of a Gd12 spin icosahedron.

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Acknowledgments

This work was supported by Grants-in-Aid for ScientificResearch (KAKENHI (24560808)). TH acknowledges Grant-in-Aid for JSPS Fellows (12J07852) from Japan Society forthe Promotion of Science. This work was carried out by thejoint research in the Institute for Solid State Physics, theUniversity of Tokyo. Illustrations of structure were producedusing the VESTA program package [18].

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