Chemical Physics Letters 466 (2008) 155–158

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Chemical Physics Letters

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Magnetic properties of ErSc2N@C80, Er2ScN@C80 and Er3N@C80 fullerenes

Archana Tiwari a,*, Geraldine Dantelle a, Kyriakos Porfyrakis a, Andrew A.R. Watt a, Arzhang Ardavan b,G. Andrew D. Briggs a

a Department of Materials, Oxford University, Oxford OX1 3PH, United Kingdomb Clarendon Laboratory, Department of Physics, Oxford University, Oxford OX1 3PU, United Kingdom

a r t i c l e i n f o

Article history:Received 23 July 2008In final form 6 October 2008Available online 1 November 2008

0009-2614/$ - see front matter � 2008 Elsevier B.V. Adoi:10.1016/j.cplett.2008.10.062

* Corresponding author.E-mail address: archana.tiwari@materials.ox.ac.uk

a b s t r a c t

The magnetic properties of ErSc2N@C80, Er2ScN@C80 and Er3N@ C80 metallofullerenes are characterized inthe temperature range 2 to 300 K up to a magnetic field of 7 T. The magnetic susceptibility of these ful-lerenes follows the Curie–Weiss law. The fitting parameters to the Curie–Weiss law provide an effectivemagnetic moment leff of Er3þ ion in each of the fullerenes. The magnetic moment decreases with theincrease in number of Er3þ ions inside the cage. This is related to crystal-field effects, intramolecularinteractions and the local quenching of the angular momentum of the ion within the fullerene cage.

� 2008 Elsevier B.V. All rights reserved.

1. Introduction

The magnetic properties of rare-earth ions arise from their par-tially filled 4f orbitals, both in solids [1,2] and in chelatedcomplexes [3,4], and have led to numerous technological develop-ments in the field of biomedicines, nanomagnets, etc. [5,6]. Endo-hedral fullerenes containing one or more rare-earth ions arepromising for various types of applications, including magneticresonance imaging [7,8]. In fullerenes doped with only one rare-earth ion, M@C82 [9,10], the magnetic moment of the M3þ ion issignificantly smaller than that of the free M3þ ion, mainly becauseof strong antiferromagnetic coupling between M3þ and the C3�

82

cage and the crystal-field effects due to the cage on the angularmomentum states of M3þ [9].

The endohedral fullerenes containing more than one paramag-netic centre inside the carbon cage present challenges to measuretheir magnetic properties [11–14]. The presence of several para-magnetic centres encapsulated inside a carbon cage may allow sev-eral intramolecular interactions and can complicate theunderstanding of the system. In the Er2@C82 and Er2C2@C82 fuller-enes, the rare-earth ions appear to have a magnetic momentslightly smaller than the one of the free Er3þ ion, yet the twoEr3þ in the same carbon cage do not interact significantly with eachother [11]. The decrease of the magnetic moment with respect tothe free Er3þ ion is attributed to the cage crystal-field effect. Themagnetic moment of some Tri-metallic Nitride Template (TNT) ful-lerenes M3N@C80, where the incarcerated clusters are stabilized bythe donation of six electrons to the C80 cage, was also investigated[15,16]. The magnetic moment of the encaged cluster is twice thetheoretical magnetic moment of M3þ because of the strong ligand

ll rights reserved.

(A. Tiwari).

field within the M3N cluster [13,14]. However, Smirnova et al. esti-mated the magnetic moment of Er3N@C80 as 10.5 lB [12], i.e.slightly higher than that of the free Er3þ ion (9.6 lB) [17].

In this Letter, we examine the magnetic properties of theEr3�xScxN@C80 fullerenes, with x = 0, 1 or 2. We report the mag-

netic susceptibility and the magnetization of ErSc2N@C80 anddetermine the magnetic moment of Er3þ in this molecule. We alsostudy the evolution of the magnetic moment of Er3þ as a functionof the number of Er3þ ions inside the C80 cage.

2. Experimental

Erbium TNTs were supplied by Luna Innovations and were fur-ther purified by high performance liquid chromatography (HPLC).The initial sample purity was estimated to be around 70% (basedon peak areas from the chromatogram). Impurities including otherhigher fullerenes were removed by using recycling HPLC. About3 ml of the initial sample dissolved in toluene were injected in a5PYE column (10� 250 mm, flow rate 6 ml/min, pure toluene elu-ent). Sample impurities were removed progressively after each cy-cle. After five cycles the sample was isolated with an estimatedpurity of at least 95%.

ErSc2N@C80, Er2ScN@ C80 and Er3N@C80 samples used for themagnetic characterization were high purity dried powders. Theirmass was accurately calculated by measuring the area of theirHPLC peak. The HPLC peak corresponds to the absorption of themolecule at 312 nm. The HPLC peak area has previously been cal-ibrated with known masses of Er3N@C80, using Beer–Lambert’slaw. Because the masses used for this calibration were of the orderof a few milligrams, it was possible to determine their values usinga microbalance. The mass of ErSc2N@C80, Er2ScN@ C80 andEr3N@C80 was 45.4, 54.3 and 41.4 lg, respectively. The powdersamples were kept inside gelatin capsules and were sealed with

156 A. Tiwari et al. / Chemical Physics Letters 466 (2008) 155–158

a non-magnetic tape. The magnetization data for the ErSc2N@C80,Er2 ScN@C80 and Er3N@C80 powder were obtained using a Quan-tum Design SQUID magnetometer. Magnetization M (H, T) wasdetermined in magnetic fields up to 7 T and at temperatures rang-ing from 2 K to room temperature. A control experiment on thegelatin capsule sealed with the same non-magnetic tape was per-formed, confirming that its magnetic response was negligible incomparison with that of the metallofullerene samples.

3. Temperature-dependent magnetic susceptibility

To characterize the magnetic behavior of ErSc2N@ C80,Er2ScN@C80 and Er3 N@C80, the magnetization was measured inthe temperature range 2 to 300 K and in the zero-field cooledprocess.

The effective magnetic moment, leff , of the Er3þ ion in each ful-lerene can be obtained from the Curie–Weiss law using the para-magnetic susceptibility, v. According to the Curie–Weiss law:

v ¼ v0 þC

T � h; ð1Þ

where C ¼ N0l2eff=3AkB is the Curie constant, h is the Weiss-temper-

ature which reflects the strength of the interactions between themolecules, v0 is the diamagnetic contribution to the magnetic sus-ceptibility, N0 is the Avogadro’s number and A is the molecularweight per mole.

Fig. 1a shows the magnetization M for ErSc2N@C80, Er2ScN@C80

and Er3N@C80 as a function of temperature in an applied magneticfield of 0.5 T. Plotted in Fig. 1b is the inverse of magnetic suscepti-

a

Fig. 1. (a) Magnetization as a function of temperature in the range 2 to 300 K and (b)constant magnetic field strength of 0.5 T. The inverse data are linear in the temperature

Table 1The fitting parameters to the Curie–Weiss law in the temperature range of 4 to 50 K. The mathe Curie–Weiss (CW) law is also shown.

FullereneEr3�xScxN@C80

C C

ðemu K Oe�1g�1Þ (lBKT�1ion�1)

ErSc2N@C80 0:0098� 0:0003 21:61� 0:08Er2ScN@C80 0:0099� 0:0001 12:10� 0:04Er3N@C80 0:0113� 0:0001 9:97� 0:02

bility as a function of temperature. The data fit well to Eq. (1) in therange 4 to 50 K as shown as dotted lines in Fig. 1b. The inverse ofsusceptibility varies linearly within the temperature range 4 to50 K implying that the magnetic moment, derived from the slopeof the line, has negligible variation with the temperature in thisrange.

A least-square fitting of the susceptibility data of ErSc2N@C80 toEq. (1) gives a Curie constant C ¼ 0:0098� 0:0003 emu K Oe�1 g�1,Weiss temperature, h ¼ �0:4� 0:1 K, and the diamagnetic suscep-tibility, v0 ¼ 1:5� 10�4 emu Oe�1g�1. The derived Curie constantof ErSc2N@C80 corresponds to an effective magnetic moment of9.8 � 0.5 lB. This value of the effective magnetic moment, withinthe error limit, is similar to the value for a free Er3þ ion (9:6 lB).The Weiss temperature is found to be small and negative, indicat-ing the presence of weak antiferromagnetic interactions among thespins on neighbouring ErSc2N clusters. The constant term v0 in Eq.(1) was observed to be slightly higher than the diamagnetic contri-bution to the susceptibility from the capsule (10�5 emu Oe�1g�1).We believe that in ErSc2 N@C80, the delocalized p-electrons onthe C80 cage contribute towards the diamagnetic susceptibilityv0. However this contribution is negligible in comparison withthe paramagnetic effect from the magnetic entities.

In Er2ScN@C80 and Er3N@ C80 fullerenes, the observed suscepti-bility as a function of temperature again fits well to Eq. (1). The fit-ting parameters for the three fullerenes are given in Table 1. TheWeiss temperature h, in each case is small and negative indicatingthat these fullerenes exhibit fairly weak antiferromagnetic interac-tions in the powder. The diamagnetic susceptibility from all thethree fullerenes was found negligible in comparison to the

b

the inverse of magnetic susceptibility as a function of temperature measured at arange 4 to 50 K, implying that they follow the Curie–Weiss law.

gnetic moment of the Er3þ ion in ErSc2N@C80, Er2ScN@C80 and Er3N@C80 derived from

v0 h leff

ðemu Oe�1g�1Þ (K) ðlBÞ

1:5� 10�4 �0:4� 0:1 9:8� 0:53:0� 10�5 �1:0� 0:3 7:3� 0:16:2� 10�5 �0:7� 0:3 6:7� 0:2

a

b0.6

0.8

1.0

ion J=4.5

A. Tiwari et al. / Chemical Physics Letters 466 (2008) 155–158 157

paramagnetic susceptibility. The effective magnetic moment of theEr3þ ion in Er2ScN@C80 and Er3 N@C80 was found to be 7:3� 0:1and 6:7� 0:2 lB, respectively. Thus the moment of the Er3þ ionin Er3�xScxN@C80 fullerenes decreases from 9.8 to 6:7lB with an in-crease in number of incarcerated Er3þ ions from one to three insidethe cage.

c0.0

0.2

0.4

0.0

0.2

0.4

0.6

0.8

1.0

0 1 2 3 4 5

Nor

mal

ized

mag

netiz

at

J=1.5J=3.5J=5.5

g=2g=4g=6

g=2

Fig. 3. (a) Magnetization versus applied magnetic field normalized with temper-ature at 2 K for ErSc2N@C80 (black), Er2ScN@C80 (red) and Er3N@C80 (blue) sample.The simulated magnetization as a function of H/T at a 2 K with, (b) constant J-valueof 4.5 and varying the g-values between 2 and 6, and (c) constant g-value of 2 andvarying the J-values between 3/2 and 11/2, is also shown.

4. Isothermal magnetization

Fig. 2 shows the magnetization as a function of H/T in the tem-perature range 2 to 300 K. The inset of Fig. 2 is an expanded low-field region which shows that the curves overlay in the 2 K to300 K range. These effects were also evident in Er2ScN@C80 andEr3N@C80 fullerenes. This property of the magnetization is wellcharacterized [18] by the Brillouin function BJðxÞ as

M ¼ ngJlBBJðxÞ ð2Þ

with

BJðxÞ ¼2J þ 1

2Jcoth

2J þ 12J

x� �

� 12J

coth12J

x� �

; ð3Þ

where J is the total angular momentum, n is the number of mag-netic ions per unit mass, and x ¼ gJlBH=ðkBTÞ. For a free rare-earthion where the spin-orbit coupling is small, the total orbital angularmomentum, J, is a good quantum number [19].

From these equations, the magnetization can be derived as aunique function of the parameters g and J for an ideal paramagneticmaterial. By fitting the isothermal magnetization data in Fig. 2 tothe Brillouin function BJðxÞ, the effective magnetic moment canbe obtained using

leff ¼ gffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiJðJ þ 1Þ

plB: ð4Þ

In ErSc2N@C80, Er2ScN@C80 and Er3N@C80, the Brillouin functionwas not found to be a unique function of g- and J-values. As both gand J can take various values, the effective magnetic moment can-not be derived from the fit. However, a comparison of the magne-tization curves of ErSc2N@C80, Er2ScN@C80 and Er3N@C80 has beenperformed. Fig. 3a shows the magnetization as a function of ap-plied magnetic field normalized by the temperature at 2 K forErSc2N@C80, Er2ScN@C80 and Er3N@ C80. The figure shows that as

Fig. 2. Magnetization versus applied magnetic field normalized with temperatureranging from 2 to 300 K for ErSc2N@C80 powder.

the number of Er3þ ions inside the cage decreases, the curve bendsmore steeply. In Fig. 3b and c, a normalized magnetization as afunction of H/T is plotted using Eq. (2) for constant J-value of 4.5and for a constant g-value of 2, respectively. For the constant J-va-lue, the g-value is varied from 2 to 6 in a step of 2. Similarly, for theconstant g-value, the J-value is varied from 3/2 to 11/2. Hence fromFig. 3a, one can infer that an increase in number of Er3þ ions insidethe cage induces a reduction in the values for g and J. This indicatesthat the magnetic moment which is proportional to g- and J-values(Eq. (4)) decreases with increase in the number of Er3þ ions. Theobserved trend for the effective magnetic moments of the ion inErSc2N@C80, Er2ScN@ C80 and Er3N@C80 from the isothermal mag-netization is in a good agreement with the evolution obtained fromCurie–Weiss law.

Hysteresis measurements were also performed for ErSc2 N@C80,Er2ScN@C80 and Er3N@C80. They show no trace of the residual fieldor magnetization in any of the fullerenes. This indicates that none ofthese fullerenes exhibits any ferro- or ferri-magnetic interactions.

5. Discussion

The magnetic moment of Er3þ in Er3�x ScxN@C80 fullerenes, con-sisting of a planar cluster enclosed in an Ih-symmetry C80 cage[20,21], decreases with increase in the number of Er3þ ions. Nadaïet al. have reported a similar decrease in the magnetic moment ofthe Er3þ and Dy3þ ions with increase in number of ions from one totwo inside the cage. Such a decrease in the moment has beenattributed to the crystal-field interactions between the 4f orbitalof the ion and the cage [22,23]. This effect is known to quenchthe angular momentum of the ion in a non-degenerate groundstate resulting in the decrease in the effective magnetic momentof the ion. Our photoluminescence studies reveal that Er3þ ion inErSc2N@C80, Er2ScN@ C80 and Er3N@C80 is subjected to slightly dif-ferent cage crystal–field effects [24,25]. The small differences inthe crystal–field effects could be responsible for a variation ofEr3þ moments in ErSc2N@C80, Er2ScN@C80 and Er3N@ C80. To

some extent orbital hybridization, which causes the back donationof electrons between the metal ion and the cage, can also decreasethe moment of the ion with an increase in the number of Er3þ in-side the cage [9,22]. The hybridization among the orbitals of the

158 A. Tiwari et al. / Chemical Physics Letters 466 (2008) 155–158

cage and the ion can quench the total angular momentum J of theion due to the partial quenching of the spin quantum number S.

Unlike Er@C82, the magnetic moment of ErSc2N@C80 is compa-rable to that of a free Er3þ. Er@C82 exhibits strong antiferromag-netic interactions between the unpaired electron on the cage andon the Er3þ. This interaction quenches the magnetic moment ofthe ion inside the cage [9,26,27]. ErSc2N@C80 has no unpaired elec-trons on the cage and has negligible possibility of quenching of themagnetic moment due to antiferromagnetic interactions. A weakantiferromagnetic coupling between molecules in the powderwas evident from the small and negative Weiss temperature, h,for all three fullerenes. As the 4f orbital of Er3þ is well shieldedby the outer s- and p-orbitals, an increase in the number of ionswould not mediate any antiferromagnetic interactions [11].

6. Conclusions

The observed magnetic moment of the Er3þ ion in ErSc2N@C80

is similar to that of a free Er3þ ion. As the number of Er3þ ion in-creases inside the C80 cage, the magnetic moment decreases. Thisbehavior is attributed due to the crystal-field effect from the Er3þ

ion due to the local direction of the incarcerated cluster insidethe C80 cage which quenches the angular momentum of the incar-cerated ions. The small and negative values for the Weiss temper-ature in all the three fullerenes demonstrates the presence of weakantiferromagnetic interactions between molecules in the powder.No trace of ferromagnetic interactions was observed in any of thesefullerenes.

Acknowledgements

This research is part of the QIP IRC http://www.qipirc.org (GR/S82176/01). GADB thanks EPSRC for a Professorial Research Fel-lowship (GR/S15808/01). AA is supported by the Royal Society.AT is supported by Felix Scholarship. GD is supported by QIP IRC,Oxford. Raw samples were obtained from Luna NanomaterialsInc. The authors acknowledge Dr. D. Prabhakaran and Dr. P. Bakerfor their assistance with the Clarendon SQUID magnetometer, andDr. M. Carmen for the useful discussions.

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