Tuning of magnetic frustration in S = 1/2 Kagome lattices{[Cu3(CO3)2(bpe)3](ClO4)2}n and {[Cu3(CO3)2(bpy)3](ClO4)2}n through

rigid and flexible ligands

M. O. Ajeesha, A. Yogia, M. Padmanabhanb, R. Natha,∗

aSchool of Physics, Indian Institute of Science Education and Research, Thiruvananthapuram-695016, IndiabSchool of Chemistry, Indian Institute of Science Education and Research, Thiruvananthapuram-695016, India

Abstract

Single crystalline and polycrystalline samples of S = 1/2 Kagome lattices {[Cu3(CO3)2(bpe)3](ClO4)2}nand {[Cu3(CO3)2(bpy)3](ClO4)2}n, respectively were synthesized. Their structural and magnetic propertieswere characterized by means of x-ray diffraction and magnetization measurements. Both compounds crys-talize in a hexagonal structure (space group P − 6) consisting of CuO4 Kagome layers in the ab-plane butlinked along c direction through either rigid bpy or flexible bpe ligands to form 3D frame works. Magneticmeasurements reveal that both the compounds undergo ferromagnetic ordering (TC) at low temperaturesand the TC and the extent of frustration could be tuned by changing the nature of the pillar ligands.{[Cu3(CO3)2(bpe)3](ClO4)2}n which is made up of flexible bpe ligands has a TC of 5.7 K and a Curie-Weiss

temperature (θCW) of -39.7 K giving rise to a frustration parameter of |θCW|TC' 6.96. But the replacement of

bpe by a more rigid and electronically delocalized bpy ligand leads to an enhanced TC ' 9.3 K and a reduced

frustration parameter of |θCW|TC' 3.54.

Keywords: A. Magnetically ordered materials, D. Exchange and superexchange

1. Introduction

Frustrated magnetism is one of the most fasci-nating topics in condensed matter physics whichattracts enormous attention from both experimen-tal and theoretical researchers [1, 2]. The S = 1/2Kagome lattices consisting of vertex-sharing trian-gular plaquettes of antiferromagnetically (AF) in-teracting S = 1/2 ions in two-dimension (2D) areknown to be highly frustrated in nature. In realmaterials, the combination of geometric frustrationand strong quantum effects results in the persis-tence of spin fluctuations down to low tempera-tures. This leads to various unusual ground stateproperties including quantum spin liquid (QSL) [3].The exact ground state of S = 1/2 AF Kagomelattice is still controversial since theory predictsdifferent possibilities of the excitation spectra. Itcould be either gapped or gapless QSL ground state

∗Corresponding author. Tel. : +91 0471 2599427Email address: rnath@iisertvm.ac.in (R. Nath)

[2, 4, 5, 6, 7, 8]. With these variety of magneticground states, the Kagome system becomes an in-teresting candidate with possibilities of novel low-energy and low-temperature magnetic properties.

Cu3V2O7(OH)2.2H2O is the first material real-ization of S = 1/2 AF Kagome lattice in whichthe interaction was found to be anisotropic and itunder goes a weak magnetic ordering at low tem-perature [9, 10]. Later, ZnCu3(OH)6Cl2 was real-ized to be a perfect S = 1/2 Kagome lattice withisotropic AF Heisenberg interaction [11]. Neutronscattering and µSR experiments suggest that thematerial does not undergo magnetic ordering downto 50 mK [12, 13]. Heat capacity follows a powerlaw behaviour over a wide intermediate T -range [12]and NMR shift which is a measure of intrinsic sus-ceptibility follows a power law. All these exper-imental features point to a possible gapless QSLground state in ZnCu3(OH)6Cl2. A gapless QSLground state is also reported in vanadium oxyfluo-ride [NH4]2[C7H14N][V7O6F18] [14]. Subsequently,a series of Kagome lattice compounds have been

Preprint submitted to Elsevier August 28, 2021

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synthesized where BaCu3V2O8(OH)2 was found toorder at 9 K [15], SrCr9pGa12−9pO19 shows a spin-glass transition at Tg ' 4 K, but retains fluctua-tions down to low temperature [16], and also someof the compounds show different unusual groundstate properties [17, 18, 19].

Recently, {[Cu3(CO3)2(bpe)3](ClO4)2}n (abbre-viated as Cu-bpe), with a planar S = 1/2 Kagomelayer pillared by a flexible organic ligand bpe [bpe= 1,2-di(4-pyridyl)ethane] was reported along withits structural and magnetic characterizations [20].It has a hexagonal structure with P − 6 spacegroup and lattice constants a = 9.3139(6) A,b = 9.3139(6) A, and c = 13.3133(9) A. As seenfrom the crystal structure [Fig. 1(a)], the Cu2+ ionsare chelated to CO3

2− anions to form a perfectly2D Kagome layer in the ab-plane. The adjacentKagome layers are further interconnected via bpepillar ligands along the c-axis forming a three di-mensional (3D) structure [Fig. 1(b)] [20]. In thelayer the Cu - O bond lengths vary from 1.949(4) Ato 2.763(5) A while both of the out of the plane Cu -N bond lengths are 1.987(3) A suggesting that theCuO4N2 octahdra takes a highly distorted struc-ture. Magnetic susceptibility χ(T ) shows a ferro-magnetic transition (TC) at low temperature. Themagnetization (M) vs. applied field (H) at T=2 Kis reported to show a small hysteresis loop with acoercive field of 8.5 Oe. Heat capacity data do notshow any well defined peak at the TC [20]. On theother hand, 1H NMR spin-lattice relaxation rate(1/T1) and spectral measurements by Kikuchi etal.,[21] clearly suggest the ferromagnetic orderingat the TC.

In this paper we report synthesis, structural,and magnetic characterization of a new Kagomesystem {[Cu3(CO3)2(bpy)3](ClO4)2}n [abbreviatedas Cu-bpy] which contains a very rigid and elec-tronically delocalized ligand bpy [bpy = 1,2-di(4-pyridyl)ethylene] interconnecting the adjacent lay-ers. To understand the role of pillar ligands onthe magnetic properties of the Kagome systemswe have also reinvestigated the recently reportedCu-bpe Kagome system with flexible bpe pillar lig-and having no electronic delocalization between theends.

2. Experimental Details

The Kagome compound Cu-bpe was synthe-sized following the procedure reported in Ref. [20].Hexagonal plate-like violet crystals formed (90%

a

b

Cu

O

C

a

b

c

(a)

(b)

Figure 1: (a) A section of the 2D Kagome layer in Cu-bpe formed by Cu2+ and CO3

2− in the ab-plane. (b) 3Dframework of Cu-bpe showing the Kagome layers pillared bythe bpe ligand along the c-axis.

yield) were filtered and washed with distilled wa-ter and then air-dried. A good quality single crys-tal with dimension [0.4 × 0.4 × 0.05] mm3 wasused for x-ray diffraction (XRD) (Bruker APEX-II machine with Mo Kα1 radiation of wavelengthλ = 0.71073 A) study. The phase purity of thesample was checked by powder XRD (PANalyticalmachine with Cu Kα radiation of λ = 1.54060 Aat room temperature) and matching with the sim-ulated pattern.

Since the above procedure failed to produce theexpected Kagome compound with the bpy ligand,we made use of a modified method for the syn-thesis of new compound Cu-bpy. To a solutionof Cu(ClO4)2.6H2O (1.853 g, 5 mM, in 100 mLdistilled water and 50 mL aqueous 20% ammo-nia), a bpy solution (0.912 g, 5 mM, in 50 mLaqueous 20% ammonia and 20 mL methanol) wasadded and stirred for 1 hour. After 3 days, blue-violet polycrystalline powder of Cu-bpy was formedin high yield (92%) by fixing atmospheric CO2 asCO3

2− anion. The solid compound was filtered,washed with water and methanol and then air-dried. Our repeated attempts to get single crystalform of Cu-bpy by varying experimental conditions

2

turned out to be unsuccessful. However, the poly-crystalline sample obtained was phase-pure form ofthe Kagome structure as confirmed by powder XRDstudies along with FTIR and CHN analysis.

DC magnetic susceptibility χ (= M/H, where Mis magnetization and H is applied magnetic field)was measured as a function of T (2 K ≤ T ≤ 300K) and at different applied fields. A magnetizationisotherm (M vs. H) was measured at T = 4 Kby varying the magnetic field up to 7 T. Both χand magnetization isotherm were measured using a7 T SQUID - VSM (Quantum Design). AC mag-netic susceptibility (χac = χ′ + iχ′′, where χ′ isthe real part and χ′′ is the imaginary part of thesusceptibility) measurements were performed usinga separate AC susceptibility setup (Cryobind ACsusceptometer) as a function of T and at differentfrequencies.

3. Results

3.1. X-ray diffraction

Single crystal XRD was performed on a goodquality single crystal of Cu-bpe. It is foundto be crystallizing in the hexagonal structurewith space group P − 6 and lattice constantsa = 9.4102(6) A, b = 9.4102(6) A, c = 13.3253(8) A,and Vcell = 1021.89(11) A3 which are consistentwith the previous report [20]. Powder XRD dataof Cu-bpe is shown in Fig. 2(a) where all the peaksare indexed based on the above structural data. Asshown in Fig. 2(b), very similar peaks appear in thepowder XRD pattern of Cu-bpy suggesting that Cu-bpy is isostructural to Cu-bpe. Rietveld refinementwas performed using the FullProf software with thestructural parameters reported in Ref. [20] as thestarting parameters [22]. Since bpy is restricted inthe trans-configuration because of the -HC=CH-double bond between the pyridyl moieties, C andH atoms corresponding to the orientational disor-der (C9 and H9) seen in Cu-bpe were removed andthe occupancy of C8 and H8 atoms were correctedto one. The room-temperature powder XRD pat-tern along with the Rietveld refinement fit is shownin Fig. 2(b). The Rietveld refinements confirmedthe phase purity of Cu-bpy and also the hexagonalstructure (space group: P −6), same as that of Cu-bpe. The best fit was obtained with χ2 ' 1.86 andthe lattice parameters obtained from refinement area = 9.3024(5) A, b = 9.3024(5) A, c = 13.3724(7) A,and Vcell = 1157.17 A3.

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Figure 2: (a) Powder XRD pattern of Cu-bpe recordedat room temperature. (hkl) values of the correspondingpeaks are indicated. (b) Powder XRD pattern (open circles)recorded at room temperature for Cu-bpy. The solid linethrough the experimental points are the Rietveld refinementprofile calculated using structural parameters of Cu-bpe. Theshort vertical bars mark the fitted Bragg peak positions. Thelowermost curve represents the difference between the exper-imental and calculated intensities.

3.2. DC Magnetization

The DC magnetic susceptibility (χ) data of Cu-bpe and Cu-bpy as a function of T at an appliedmagnetic field of 1 T are shown in Fig. 3(a) and3(b), respectively. At high T s, χ(T ) increases ina Curie-Weiss manner with decreasing T and thenshows a rapid increase at low temperature. Thisrapid increase which occurs below about 20 K forboth the compounds is an indication of ferromag-netic (FM) correlation.

In order to extract the magnetic parameters, theχ(T ) data at high T region are fitted by the expres-sion

χ = χ0 +C

T + θCW, (1)

where χ0 is the temperature independent contri-bution consisting of core diamagnetism of the coreshells and Van-Vleck paramagnetism of the openshells of Cu2+ ions. The second term is the Curie-Weiss (CW) law with C (= NAµ

2eff/3kB , where NA

is Avogadro’s number, µeff is the effective magneticmoment, and kB is Boltzmann’s constant) beingthe Curie constant and θCW the Curie-Weiss tem-perature. The extracted parameters for both the

3

Figure 3: DC Magnetic susceptibility χ (left y-axis) and χ−1

(right y-axis) of (a) Cu-bpe and (b) Cu-bpy vs. temperatureT at an applied magnetic field H = 1 T. The solid red linesare the CW fits to the data for the temperature range 189 -300 K and 154 - 185 K for Cu-bpe and Cu-bpy, respectively.Insets: ZFC and FC susceptibilities of Cu-bpe and Cu-bpyvs. T at low fields.

compounds are mentioned in Table-1. The cal-culated values of µeff from C for both the com-pounds are in good agreement with the theoreti-cal value [µeff = g

√S(S + 1)µB ] of 1.73 µB ex-

pected for S = 1/2 systems assuming g-factorg = 2. The core diamagnetic susceptibility (χcore)was calculated by adding the contributions from in-dividual ions to be −5.2534 × 10−4 cm3/mol and−4.9126 × 10−4 cm3/mol for Cu-bpe and Cu-bpy,respectively [23]. The Van-Vleck paramagneticsusceptibility (χVV) was estimated by subtractingχcore from χ0 to be ∼ 4.974 × 10−4 cm3/mol and∼ 3.012 × 10−4 cm3/mol for Cu-bpe and Cu-bpy,respectively.

We also measured the low temperature Zero FieldCooled(ZFC) and Field Cooled(FC) susceptibilitiesat a small applied field [see insets of Fig. 3(a) and3(b)]. No significant splitting between ZFC andFC susceptibilities was observed for both the com-pounds. This confirms the absence of any glassycomponent and spin reorientation effect in the or-dered state. To further confirm the FM correlationand also to check whether there is any field inducedeffect at low temperature, we measured M vs. H at

Table 1: Magnetic parameters obtained by fitting Eq. 1 toχ(T ) data in the T -range (189 - 300 K) and (154 - 185 K) forCu-bpe and Cu-bpy, respectively. µeff was calculated usingthe experimental C value.

χ0 C θCW µeff

(cm3/mol.Cu) (cm3.K/mol.Cu) (K) (µB)

Cu-bpe -0.279(5)×10−4 0.378(4) -39.7(9) 1.738(2)

Cu-bpy -1.904(4)×10−4 0.397(6) -33.0(2) 1.781(3)

Figure 4: M vs. H for (a) Cu-bpe and (b) Cu-bpy at T =4 K.

T = 4 K for both the compounds (Fig. 4). A typ-ical hysteresis loop was observed with a coercivefield Hc ' 600 Oe and 60 Oe for Cu-bpe and Cu-bpy, respectively suggesting a weak ferromagnetismin both the compounds below TC. Moreover, thevalue of Hc reported in Ref. [20] for Cu-bpe is twoorders of magnitude less than our observed value.The magnetization was found to reach a saturationvalue of 0.9 µB/Cu at about 1.6 T for both thecompounds which is close to the expected spin onlyvalue of (= gSµB) 1 µB , assuming g = 2. No sig-nature of any field induced transition was obtainedin the M vs. H curve.

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Figure 5: Real part of AC magnetic susceptibility (χ′ac) of(a) Cu-bpe and (b) Cu-bpy as a function of T at an appliedAC field of Hac = 0.177 Oe for different frequencies.

3.3. AC Susceptibility

Since AC susceptibility (χac) is very sensitive tomagnetic ordering, one can gain information aboutthe nature of the magnetic ordering by measuringthe frequency dependent χac. Figure 5(a) and 5(b)present the real part of AC susceptibility (χ′ac) ofCu-bpe and Cu-bpy, respectively as a function of Tmeasured at an applied AC field of Hac = 0.177 Oefor three different frequencies 15 Hz, 420 Hz, and1000 Hz. The χ′ac for Cu-bpe shows a broad maxi-mum at TC ' 5.7 K while for Cu-bpy the maximumis more pronounced at TC ' 9.3 K, reflecting theirTCs. The broad maxima for both the compoundsremain frequency independent, indicating the ab-sence of spin-glass behaviour below TC [24]. This isalso a characteristic feature of bulk ferromagnet.

4. Discussion and Conclusion

In the crystal structure, the angle ∠Cu-O-Cuis 1700 in the Kagome plane. According toGoodenough-Kanamori rule, the superexchange in-teraction through a non-magnetic ion will favourferromagnetism if the angle between them is closeto 900 and antiferromagnetism if the angle is closeto 1800 [25, 26]. This suggests that the intra-layer exchange interaction (J1) in both the com-pounds should be antiferromagnetic. According tothe mean field theory θCW is the sum of all theexchange couplings [27]. But the negative value of

θCW indicates that the dominant interaction is FM.Since J1 is expected to be AFM, this dominant FMinteraction is most likely originating from the inter-layer superexchange (J2) through bpe and bpy lig-ands between Cu2+ ions in the adjacent layers. Inthe present case, estimation of individual exchangecouplings from the values of θCW and TC is not triv-ial since it may involve another exchange couplingJ3 along the hexagon. An estimation of individualexchange couplings through electronic band struc-ture calculations would be useful to understand theexchange mechanism in such compounds [28]. FMinter-layer interactions are also reported in Kagomesystems Cu(1,3-bdc) and KFe3(OH)6(SO4)2 withsimilar geometries [29, 30]. There are also othercopper based metal-organic complexes having sim-ilar ligands which are reported to show dominantFM interactions [31].

As discussed before, the distorted CuO4N2 oc-tahedra gives rise to an anisotropic CuO4 arrange-ment in the plane. In such a geometry, the dx2−y2

orbital of Cu2+ ion and 2p orbital of O2− ion, whichare responsible for super-exchange are aligned or-thogonal to each other [32]. Due to this kind oforbital arrangements, the super-exchange betweenCu2+ ions are very weak in the plane and the inter-action between the planes via ligands dominates.

With the estimated values of θCW and TC, thefrustration in the spin system can be quantified.The frustration parameter f , which is an empiricalmeasure of frustration [33] is given by,

f =|θCW|TC

. (2)

Typically spin systems with f > 5-10 are consid-ered to be moderately frustrated. The frustrationparameter f for Cu-bpe and Cu-bpy was found tobe 6.96 and 3.54, respectively suggesting that Cu-bpe is more frustrated than Cu-bpy. This can beexplained by the structural differences seen in bpeand bpy ligands which is evident from Fig. 6. Thedifference between the bpe and bpy ligands is that,the spacer between the pyridyl rings is having asingle bond ( -CH2-CH2- ) in bpe compared to adouble bond ( -HC=CH- ) in bpy. The presence ofdouble bond in Cu-bpy is responsible for facilitatingstrong exchange interaction between the Kagomelayers compared to Cu-bpe. Therefore, replacementof the flexible bpe by a more rigid and electroni-cally delocalized bpy ligand leads to an increase ofTC from 5.7 K to 9.3 K and decrease of f from 6.96to 3.54.

5

( (

N

N

C

C

C C

C C

C

C C

C C

C C

C C

C C

C C

C CC

C

CH

H

H

H

H

H

HH

H

H H

H

HH

HH

H

H

HH

HH

spacer

pyridyl ring

Figure 6: Structure of (a) bpe and (b) bpy ligands. Theportion enclosed by the circle in (a) is pyridyl ring and in(b) is the spacer.

Ground state properties of such complexes canfurther be tuned by modifying the nature of the pil-lar ligand and increasing the inter-planar distance.Owing to the perfectly planar Kagome structureand the tunability of inter-layer exchange couplingthrough appropriate linker molecules, this kind ofKagome systems would serve as promising candi-dates for exploring exotic ground state properties.

Acknowledgments

We would like to thank Dr. B. R. Sekhar (IOPBhubaneswar) for SQUID-VSM and Dr. P. S. AnilKumar (IISc Bangalore) for AC susceptibility mea-surements. DST India is acknowledged for financialsupport.

References

[1] G. Misguich and C. Lhuillier,Frustrated Spin Systems, edited by H. T. Diep(World Scientific, Singapore, 2005).

[2] C. Lacroix, P. Mendels, and F. Mila,Introduction to Frustrated Magnetism (Springer,Berlin, 2010).

[3] L. Balents, Nature 464 (2010) 199.[4] S. Yan, D. A. Huse, and S. R. White, Science 332 (2011)

1173.[5] S. Depenbrock, I. P. McCulloch, and U. Schollwck,

Phys. Rev. Lett. 109 (2012) 067201.[6] Y. Ran, M. Hermele, P. A. Lee, and X.-G. Wen, Phys.

Rev. Lett. 98 (2007) 117205.[7] M. Hermele, Y. Ran, P. A. Lee, and X.-G. Wen, Phys.

Rev. B. 77 (2008) 224413.[8] Y. Iqbal, F. Becca, and D. Poilblanc, Phys. Rev. B 84

(2011) 020407(R).[9] Z. Hiroi, M. Hanawa, N. Kobayashi, M. Nohara, H.

Takagi, Y. Kato, and M. Takigawa, J. Phys. Soc. Jpn.70 (2001) 3377.

[10] M. Yoshida, M. Takigawa, H. Yoshida, Y. Okamoto,and Z. Hiroi, Phys. Rev. Lett. 103 (2009) 077207.

[11] M. P. Shores, E. A. Nytko, B. M. Bartlett, and D. G.Nocera, J. Am. Chem. Soc. 127 (2005) 13462.

[12] J. S. Helton, K. Matan, M. P. Shores, E. A. Nytko, B.M. Bartlett, Y. Yoshida, Y. Takano, A. Suslov, Y. Qiu,J. H. Chung, D. G. Nocera, and Y. S. Lee, Phys. Rev.Lett. 98 (2007) 107204.

[13] P. Mendels, F. Bert, M. A. de Vries, A. Olariu, A. Har-rison, F. Duc, J. C. Trombe, J. S. Lord, A. Amato, andC. Baines, Phys. Rev. Lett. 98 (2007) 077204.

[14] L. Clark, J. C. Orain, F. Bert, M. A. De Vries, F. H.Aidoudi, R. E. Morris, P. Lightfoot, J. S. Lord, M. T.F. Telling, P. Bonville, J. P. Attfield, P. Mendels, andA. Harrison, Phys. Rev. Lett. 110 (2013) 207208.

[15] Y. Okamoto, H. Yoshida, and Z. Hiroi, J. Phys. Soc.Jpn. 78 (2009) 033701, M. Yoshida, Y. Okamoto, M.Takigawa, and Z. Hiroi, J. Phys. Soc. Jpn. 82 (2013)013702.

[16] A. P. Ramirez, B. Hessen, and M. Winklemann, Phys.Rev. Lett. 84 (2000) 2957.

[17] N. Oba, C. Michioka, M. Kato, K. Yoshimura, and K.Mibu, J. Phys. Chem. Solids 66 (2005) 1438.

[18] N. Rogado, G. Lawes, D. A. Huse, A. P. Ramirez, andR. J. Cava, Solid State Commun. 124 (2002) 229.

[19] C. N. R. Rao, E. V. Sampathkumaran, R. Nagara-jan, G. Paul, J. N. Behera, and A. Choudhury, Chem.Mater. 16 (2004) 1441.

[20] P. Kanoo, C. Madhu, G. Mostafa, T. K. Maji, A. Sun-daresan, S. K. Pati, and C. N. R. Rao, Dalton Trans.26 (2009) 5037.

[21] H. Kikuchi, Y. Fujii, H. Nakata, T. Taniguchi, W.Zhang, S. Okubo, and H. Ohta, J. Phys. Soc. (Conf.Proc.) 1 (2014) 012019.

[22] J. Rodrıguez-Carvajal, Physica B 192 (1993) 55.[23] P. W. Selwood, Magnetochemistry (Interscience, New

York, 1956).[24] J. A. Mydosh, Magn. Magn. Matter. 157/158 (1996)

606.[25] J. B. Goodenough, Magnetism and the Chemical Bond,

(Interscience Publisher, New York, 1963).[26] J. Kanamori, J. Phys. Chem. Solid 10 (1959) 87.[27] R. G. Misenheimer and J. D Swalen, Phys. Rev. 123

(1961) 831.[28] R. Nath, M. Padmanabhan, S. Baby, A. Thirumurugan,

and A. A. Tsirlin, arXiv:1407.7813.[29] M. Takano, T. Shinjo, and T. Takada, J. Phys. Soc.

Jpn. 30 (1970) 1049.[30] E. A. Nytko, J. S. Helton, P. Muller, and D. G. Nocera,

J. Am. Chem. Soc. 130 (2008) 2922.[31] S. Mukhopadhyay, P. B. Chatterjee, D. Mandal. G.

Mostafa, A. Caneschi, J. V. Slageren, T. J. R. Weakley,and M. Chaudhury, Inorg. Chem. 43 (2004) 3413.

[32] P. Jeffrey, J. C. Thibeault, and R. Hoffmann, J. Am.Chem. Soc 97 (1975) 4884, F. Tuna, L. Patron, Y.Journaux, M. Andruh, W. Plass, and J.-C. Trombe, J.Chem. Soc., Dalton Trans. 4 (1999) 539, H. W. Lee, N.Sengottuvelan, H.-J. Seo, J. S. Choi, S. K. Kang, andY.-I. Kim, Bull. Korean Chem. Soc. 29 (2008) 1711.

[33] A. P. Ramirez, Annu. Rev. Mater. Sci. 24 (1994) 453.

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