Magnetic Properties of Heavy Rare-Earth Metallofullerenes M@C82

The fittings to the Curie−Wiess law and to the Brillouin function for the heavy ... and the interactions between the metal centers were proposed to ...
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J. Phys. Chem. B 2000, 104, 1473-1482

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Magnetic Properties of Heavy Rare-Earth Metallofullerenes M@C82 (M ) Gd, Tb, Dy, Ho, and Er) Houjin Huang and Shihe Yang* Department of Chemistry, The Hong Kong UniVersity of Science and Technology, Clear Water Bay, Kowloon, Hong Kong

Xixiang Zhang Department of Physics, The Hong Kong UniVersity of Science and Technology, Clear Water Bay, Kowloon, Hong Kong ReceiVed: September 16, 1999; In Final Form: December 8, 1999

We have conducted a comprehensive study on the magnetic properties of five heavy rare-earth metallofullerenes M@C82 (M ) Gd, Tb, Dy, Ho, Er) in the temperature range of 1.8 and 300 K at a magnetic field up to 5 T. The isothermal magnetization curves of the endohedral metallofullerenes follow the Brillouin function only above certain temperatures. The fittings to the Curie-Wiess law and to the Brillouin function for the heavy rare-earth metallofullerenes both result in effective magnetic moments that are significantly smaller than those of the corresponding free M3+ ions. The magnetic moment reduction and the imperfect paramagnetic behavior of M@C82 were found to be related to the orbital angular momentum of entrapped M3+ ions. The fullerene cage crystal field splitting, the partial hybridization of the orbitals of the entrapped metal atom and the carbon cage, and the interactions between the metal centers were proposed to account for the peculiar magnetic behaviors of the endohedral metallofullerenes.

Introduction Although the electronic structure of the rare-earth ions embedded in diamagnetic host lattices has been investigated extensively, the magnetic properties of rare earth-containing molecular compounds have been studied much less.1 This is due partly to the limited number of well-characterized compounds of this kind and partly to the difficulty in the precise interpretation of the experimental data in most cases. It is recognized that in dealing with magnetism of lanthanide metalcontaining compounds, the orbital angular momentum plays an important role.2 Endohedral metallofullerenes represent a novel type of molecular compounds, in which rear-earth metal atoms are completely shielded by a robust carbon cage. This type of molecular compound has been the subject of much scientific as well as technological interest for the past few years.3,4 Scientifically, the formation mechanism,5 framework stability,6,7 electronic structure,7 and dynamic behavior8,9 of metallofullerenes have attracted special attention. Practically, this type of novel material promises a variety of important applications such as superconductors, organic ferromagnets, laser medium, and ferroelectrics.3 The well-established molecular nature of the rare-earth endohedral metallofullerenes offers an excellent opportunity to understand the magnetic properties of rare-earth-containing molecular compounds in general. Such perfect supermolecules can be used as a model system to test some of the theories concerning the magnetic behavior of rare-earth-containing molecular compounds.1 Reports on magnetic properties of metallofullerenes have started to appear.10-14 For example, the average magnetic moment of La@C82 has been measured to be * E-mail: [email protected].

0.38 µB by Funasaka et al.11 This value is apparently larger than the magnetic moment of the free La3+ ion, and therefore was attributed to an incomplete electron transfer, as observed by Kessler et al.15 Previous studies on the electronic structure and magnetic properties of metallofullerenes primarily concentrated on lanthanide elements with their 4f shells half-filled (Gd),12 nearly full (Tm),16 and empty or nearly empty (La).11,15 In those cases, the orbital contribution to the total magnetic moment of the ion is small or negligible owing to the small or zero orbital angular momentum L of the magnetic orbitals. Consequently, the electron configuration, orbital hybridization, and energy level scheme of these lanthanide ions inside the carbon cage are anticipated to be much simpler than those of their homologues with a large L (e.g., Ho, Nd, Dy). We have reported our preliminary comparative study on the magnetic properties of Ho@C82 and [email protected] A significant reduction of magnetic moment of Ho@C82 was revealed in comparison with that of the free ion Ho3+. To get a deeper insight into the magnetic properties of the metallofullerenes, we have systematically studied the magnetic behavior of another three heavy rare-earth metallofullerenes with L * 0, including Tb@C82 (L ) 3), Dy@C82 (L ) 5) and Er@C82 (L ) 6), in conjunction with their spectroscopic measurements. This article gives a full account of the magnetic properties of a series of all the five heavy rare-earth metallofullerenes we have studied. We begin with the description of the experimental methods used in this work, the presentation of our results on the metallofullerene preparation, electronic structural characterization, and magnetic measurements, followed by the discussion on the novel magnetic properties of the metallofullerenes. Finally, we present our conclusions.

10.1021/jp9933166 CCC: $19.00 © 2000 American Chemical Society Published on Web 01/27/2000

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Experimental Section Carbon soot containing metallofullerenes was produced by the standard arc vaporization method using a composite anode, which contained graphite powder and lanthanide metal oxides in an atomic ratio metal/C ≈ 0.02. These two components were uniformly mixed with graphite cement (GC grade, Dylon Inc.). The mixture was pressed into the center of a 6-mm-diameter graphite rod (inner diameter, 4.5 mm; length, 12 cm). These rods were baked under a vacuum at 1100 °C for more than 3 h and then were subjected to a direct current discharge under a He atmosphere of 125 Torr. The raw soot was collected and extracted for 24 h using dimethylformamide (DMF) as the solvent.18,19 The extract was filtered using a slow-rate filter paper, and a brownish green solution was obtained. After removal of DMF by vacuum evaporation, a black powder was collected and redissolved in toluene. The solution was filtered with a 0.2-µm disk filter (Rubbermaid Inc.) before highperformance liquid chromatography (HPLC) separation. For HPLC separation, a PYE Cosmosil column (10 × 250 mm, Nacalai Tesque Inc.) was used with toluene as the mobile phase. The injection volume was 5 mL, and the elution rate was 4.0 mL/min. Desorption chemical ionization (DCI) negative ion mass spectrometry (Finnigan TSQ 7000) was used to characterize the composition of the samples. X-ray photoelectron spectroscopy (XPS) measurements were performed with monochromatized Al KR radiation (hυ ) 1486.6 eV) with an instrumental energy resolution of ∼0.5 eV (Perkin-Elmer PHI 5600). Electron paramagnetic resonance (EPR) spectra were recorded using a JEOL JES200 spectrometer with the option of liquid nitrogen cooling. An X-band frequency of 9.437 GHz was used with a field modulation frequency of 100 kHz. Before measurements, the metallofullerene solutions were degassed by at least three freeze-pump-thaw cycles to remove any trace amount of paramagnetic impurities (e.g., O2). Mn2+ in MgO was used as an EPR marker for the calibration of the g values. The metallofullerenes were purified immediately before the magnetic measurements to avoid oxidation. Special caution was taken in handling the metallofullerene samples. For example, the sample transfer was usually performed under a nitrogen atmosphere. However, our experience shows that the exposure of the metallofullerene solutions to air for a few days did not cause significant oxidation of the species. The metallofullerene samples for the magnetic characterization were dried and in powder form. They weighed 2.5 mg for Gd@C82, 1.1 mg for Tb@C82, 3.4 mg for Dy@C82, 2.8 mg for Er@C82, and 1.0 mg for Ho@C82, as determined using a precision balance (Autobalance model AD-6). The powder samples were wrapped in a very small, thin Teflon tape for the magnetic measurements. The magnetic characterizations of the pure metallofullerene samples were performed on a Quantum-Design SQUID magnetometer equipped with 5 T magnet in the temperature range between 1.8 and 300 K. A blank experiment on the Teflon tape was performed, and its magnetic response was found to be negligible in comparison with that of the metallofullerene samples. Results Metallofullerene Purification. Some of the metallofullerenes studied in this work have been isolated previously.11,12,20-24 We only present our experimental data on the isolation of the metallofullerenes that have never been reported before. Figure 1a shows an HPLC trace of the crude extract of fullerenes and Tb-containing metallofullerenes redissolved in

Figure 1. HPLC chromatograms of a crude terbium@fullerene extract redissolved in toluene (a) and a purified Tb@C82 sample (b).

Figure 2. DCI methane negative ion mass spectrum of a purified Tb@C82 sample. The inset shows the observed and calculated isotope distributions of Tb@C82.

toluene after evaporation of DMF. A prominent peak appears at ∼24.5 min, which is absent for samples produced from arc discharge of a pure carbon electrode. This peak is apparently from Tb@C82, as identified by the mass spectrum shown in Figure 2. Because the peak of Tb@C82 is somewhat overlapped with that of C88 right after it, we collected only the eluate fraction before the C88 shoulder. The mass spectrum shown in Figure 2 was obtained for the purified Tb@C82 sample. As shown in Figure 2, the observed isotope distribution is consistent with the expected isotope distribution for Tb@C82. The intensities of empty fullerenes are significantly smaller than that of Tb@C82, and the purity of our sample is estimated to be ∼95% based on the analysis of the HPLC profile and mass spectrum. However, we cannot exclude the possibility of some residual solvent molecules being trapped in the interstices of the metallofullerene samples. Ground-State Electronic Structure of M@C82 (M ) Gd, Tb, Dy, Ho, and Er). UV-visible-near-infrared absorption spectra of these metallofullerenes have been reported previously.19 These spectra show similar absorption peaks characteristic of this type of metallofullerenes, which are likely derived from electronic transitions in the carbon cage. The similarity in the absorption spectra of these metallofullerenes indicates that they have similar electronic structure, namely, the metal atom is trapped inside the carbon cage and it donates roughly three electrons to the carbon cage. This is corroborated by the XPS spectra of these metallofullerenes. Typical XPS patterns

Magnetic Properties of Heavy Rare-Earth M@C82

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Figure 3. X-ray photoelectron spectra of Tb@C82 and TbCl3 in the 3d core level region of Tb.

Figure 5. EPR spectrum of Tb@C82 at room temperature. The g factor is 2.00235.

Figure 4. X-ray photoelectron spectra of Tb@C82 (a) and TbCl3 (b) in the 4d core level region of Tb. The solid lines represent the fitting results.

of Tb@C82 in the 3d and 4d core level regions are shown in Figures 3 and 4, respectively, along with those of TbCl3. The striking similarity between XPS patterns of Tb@C82 and those of TbCl3 in terms of both the peak positions and their intensity ratios suggests that the oxidation state of Tb is roughly 3+. XPS of Ho@C82, Dy@C82, and Er@C82 also showed a similar oxidation state of the corresponding rare-earth ions in the fullerene cage.17,22 Further evidence is from the EPR spectrum of Tb@C82 (Figure 5), which shows a single resonance peak with a g factor of 2.00235. This g value is consistent with an unpaired electron spin from the carbon cage. The line splitting due to 159 65 Tb (I ) 3/2) was not observed, and this may be attributed to the broadening of the spectral peaks perhaps owing to the interactions between the spin on the carbon cage and that centered on the metal atom. A similar situation was encountered in the EPR of Er@C82, which also lacks hyperfine splitting.25 Temperature-Dependent Magnetic Susceptibility. To characterize the magnetic behavior of the endohedral metallofullerenes, the temperature-dependent magnetization in a low applied magnetic field of 50 Oe was measured in zero-fieldcooled and field-cooled processes. No blocking or freezing of magnetic moments was observed down to 1.8 K for all the metallofullerenes studied in this work. Plotted in Figure 6 is the reciprocal of the magnetic susceptibility of the metallofullerene Gd@C82 as a function of temperature measured in a magnetic field of 0.1 T and in the temperature range between 1.8 and 250 K. Clearly, the reciprocal

Figure 6. The reciprocal magnetic susceptibility as a function of temperature obtained at H ) 0.5 T for Gd@C82. A straight line is drawn based on the fitting to the Curie-Weiss law.

susceptibility data can be well fitted to a straight line in almost the whole temperature range we studied. The nice fitting of the reciprocal susceptibility data in Figure 6 to a straight line shows that the magnetization follows the Curie-Weiss law

χ - χ0 ) C/(T - θ),

(1)

where C ) nN0µ2eff/(3AkB) ) N0g2J(J + 1)µ2B/(3AkB), θ () CγF) is the Weiss temperature which reflects the strength of the interactions between the particles, N0 is the Avogadro constant, n is the number of moles of the metallofullerene sample, and A is molecular weight per mole. γ is the molecular field constant, and F is the density. A least-squares fitting of the susceptibility data to the equation above gives a Curie constant C ) 0.00519 emu‚K/(g‚Oe), a Weiss temperature of θ ) -1.8 K, and a constant term χ0 ) -2.65 × 10-6 emu/ (g‚Oe). The Curie constant for Gd@C82 corresponds to an effective magnetic moment of 6.90 µB. It is gratifying that the effective magnetic moment of Gd@C82 estimated from our data (e.g. 6.90 µB) is consistent with that measured by Funasaka et al. (6.9 µB).12 This value is, however, somewhat smaller (by ∼13%) than the magnetic moment of

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TABLE 1: Electronic Structures of Some Relevant Lanthanide Ions and Experimental Magnetic Data of the Corresponding Metallofullerenes µeff of M@C82 ions Gd3+ Tb3+ Dy3+ Ho3+ Er3+ b

ground-state 8

S7/2 7 F6 6H 15/2 5 I8 4 I15/2

percentage of reduction in µeff

Weiss temp.

gxJ(J + 1)

Brillouina

Curie-Weissb

Brillouin

Curie-Weiss

θ (K)

7.94 9.72 10.64 10.60 9.58

6.95 6.80 8.48 5.55 6.37

6.91 7.51 9.25 6.33 7.06

12.5 30.0 20.3 47.6 33.5

13.0 22.7 13.1 40.3 26.3

-1.8 -6.6 -10.4 -5.9 -20.7

a From fitting to the Brillouin function, µeff is taken to be the value at 40 K for Ho@C82 and the maximum values for others (see Figure 11). From fitting to the Curie-Weiss law, µeff is taken to be the value at 0.1 T for Gd@C82, 0.2 T for Ho@C82, and 0.5 T for others.

Figure 7. The reciprocal magnetic susceptibility as a function of temperature obtained at H ) 0.5 T (or 0.2 T) for Tb@C82, Dy@C82, Ho@C82, and Er@C82. In each curve, a straight line is drawn based on the fitting to the Curie-Weiss law.

the free Gd3+ ion (7.94 µB) perhaps because the C823- cage possesses roughly one unpaired electron. One could imagine an antiparallel arrangement between the spin localized on Gd and that on the carbon cage, giving approximately S ) 3. The resulting magnetic moment can be calculated to be 6.93 µB, a value remarkably close to what we obtained for Gd@C82. This antiferromagnetic coupling between the cage spin and metalcentered spin, if present, is likely to be mediated through the 5d orbitals of the lanthanide ion.26 Another possibility is related to the possible presence of a small amount of solvent molecules. A ∼13% reduction in the effective magnetic moment corresponds to an existence of ∼26% solvent molecules by weight in the metallofullerene sample. This seems unreasonable considering that the intermetallofullerene interaction is relatively strong and the volume fraction of the interstices is small. The Weiss temperature estimated above is -1.8 K, which is lower than that of Funasaka et al. (-0.65 K). We notice that the estimated Weiss temperature depends on the temperature range of the data used for the fitting. Therefore, the difference is thought to be within the experimental uncertainty. Figures 7a-d show the reciprocal of the magnetic susceptibility for the metallofullerenes Tb@C82, Dy@C82, Ho@C82, and Er@C82, respectively, as a function of temperature measured in a magnetic field of 0.5 T (or 0.2 T) and in the temperature range of 1.8-300 K. For all the four metallofullerenes, the reciprocal susceptibility data can be nicely fitted to the Curie-

Weiss equation except at temperatures below 20 K. Based on the least-squares fitting, the effective magnetic moments and Weiss temperatures of the four metallofullerenes were all obtained and listed in Table 1. Although magnetic moments of Gd@C82 and Ho@C82 have been documented previously, this is the first report on the magnetic moments of Tb@C82, Dy@C82, and Er@C82. In the least-squares fitting, we deliberately used only the susceptibility data above 20 K, because magnetic properties of the metallofullerenes deviated from the Curie-Weiss law below 20 K. The estimated Weiss temperatures of the metallofullerenes are all negative, including Gd@C82, which suggests antiferromagnetic interactions among metallofullerenes and between the metal ions and the fullerene cage. Overall, the Weiss temperature appears to increase with increasing orbital angular momentum. For example, θ ) -1.8 K for Gd@C82 (Gd3+, L ) 0), whereas θ ) -20.69 K for Er@C82 (Er3+, L ) 6). Therefore, the difference in the Weiss temperature of the metallofullerenes is likely due to the magnetic anisotropy effect, which becomes more important as the orbital angular momentum increases. A closer look at the Weiss temperatures of different metallofullerenes reveals that the decreasing trend of the Weiss temperatures from Gd@C82 to Er@C82 mentioned above is not monotonic, and this indicates that the detailed interactions involved may be more subtle. Careful examination of the reciprocal magnetic susceptibility plot versus temperature shows that at the temperature close to 0 K, there is a discernible deviation from the fitted straight line for all the metallofullerenes we studied except Gd@C82. This suggests that Gd@C82 can be well described as a paramagnetic system even at low temperatures. This is because Gd3+ has a half-filled 4f shell with no orbital angular momentum, and consequently its electron distribution is more spherical. On the other hand, the curves for M@C82 (M ) Dy, Er, Tb, and Ho) all fall below the straight lines below ∼20 K, which suggests ferromagnetic interactions between the metal centers. More extensive investigations on the magnetic behavior of these metallofullerenes below 1.8 K should be a worthwhile endeavor. The constant term χ0 in eq 1 was negative for all the metallofullerenes we examined. Because the diamagnetic contribution from the sample vessel is quite small (Mvessel ) ∼10-7 emu/g), we believe that the metallofullerenes have substantial diamagnetic components, perhaps mainly because of the electrons in the carbon cage. We also fitted our susceptibility data to the Curie-Weiss law at different magnetic fields. Although similar magnetic moments and Weiss temperatures were obtained, the χ0 values were quite different at different magnetic fields. Specifically, χ0 became more negative with increasing magnetic fields for all the mellofullerenes; its magnitude may double when the magnetic field increases to a certain extent. Take Gd@C82 as an example, χ0 ) -2.65 × 10-6 emu/(g‚Oe) at 0.1 T, whereas it decreases to χ0 ) -5.76 × 10-6 emu/

Magnetic Properties of Heavy Rare-Earth M@C82

J. Phys. Chem. B, Vol. 104, No. 7, 2000 1477 Isothermal Magnetization. Additional information on the peculiar magnetic behavior of the metallofullerenes comes from the isothermal magnetization as a function of the applied magnetic field at different temperatures. Figures 8-10 show isothermal magnetization curves for different metallofullerenes M@C82 (M) Gd, Tb, Dy, Ho, and Er). Because the diamagnetic component is very small compared with the paramagnetic signal at temperatures below 40 K, we ignored the contribution from χ0 in Figures 8-10. No hysteresis loop was observed down to 1.8 K for all the five metallofullerenes. Instead, the isothermal magnetization curves display typical paramagnetic characteristics. If the magnetic interaction between the metallofullerene particles and between the lanthanide ion and the carbon cage are negligible, the isothermal magnetization should be described by the Brillouin function,

Figure 8. The isothermal magnetization as a function of H/T at different temperatures for Gd@C82. The inset shows the enlargement in the low H/T range. Note that the magnetization curves almost overlap at temperatures above 8 K.

(g‚Oe) at 0.5 T. The physics about this field dependence is not presently fully understood.

M ) ngJµBBJ(x)

(2)

BJ(x) ) [(2J + 1)/(2J)] coth[(2J + 1)x/(2J)] [1/(2J)] coth[x/(2J)] (3) where n is the number of magnetic ions per unit mass, and x )

Figure 9. The isothermal magnetization as a function of H/T at different temperatures for Tb@C82 and Dy@C82. The insets show the enlargement in the low H/T range. Note that the magnetization curves almost overlap at temperatures above 20 K for Tb@C82 and 30 K for Dy@C82.

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Figure 10. The isothermal magnetization as a function of H/T at different temperatures for Ho@C82 and Er@C82. The insets show the enlargement in the low H/T range. Note that the magnetization curves almost overlap above 40 K for Ho@C82 and 50 K for Er@C82.

gµBH/(kBT). From the equations above, the magnetization is a unique function of the parameter x for a given ideal paramagnetic material if J and g are constant, regardless of the temperature and the applied magnetic field. In other words, if we plot the measured magnetization M as a function of H/T using the isothermal magnetization data obtained at different temperatures, all the isothermal magnetization data points should collapse on the master curve expressed in eqs 2 and 3. Thus, by fitting the isothermal magnetization data to the Brillouin function BJ(x), one would hope to obtain the effective magnetic moments of metallofullerenes. The scenario described above appears to be applicable to Gd@C82 because Gd3+ has a zero orbital angular momentum and a spherical electron distribution. However, this works only at temperatures above ∼8 K (see Figure 8). Below ∼8 K, the isothermal magnetization curves deviate significantly from the master curve. For other metallofullerenes, the deviation of the isothermal magnetization data from the master curve is even more severe at low temperatures, as shown in Figures 9 and 10. The magnetization curves nearly collapse into a master curve above ∼20 K for Tb@C82, ∼30 K for Dy@C82, ∼40 K for Er@C82, and ∼40 K for Ho@C82. In other words, the magnetization curves of the metallofullerenes conform to their

corresponding master curves only above a certain temperature, which increases from Gd, Tb, and Dy to Ho and Er. This may be caused by carbon cage crystal field splitting and magnetic interactions between the metallofullerene particles. In fact, the validity of the Brillouin function may be questionable because the substantial, negative Weiss temperature of M@C82 already indicated antiferromagnetic interactions among the metallofullerene particles and between the metal ions and the carbon cage in the temperature range between ∼25 K and ∼300 K. Because the isothermal magnetization curves depend sensitively on temperature at low temperatures as opposed to the Brillouin function, we performed many tedious fittings for all the measured magnetization curves as a function of temperature to discover any systematic behaviors among different metallofullerenes through meaningful comparisons. The least-squares fittings were performed based on eq 2 for a series of temperatures with both J and g as fitting parameters. The effective magnetic moment was then calculated according to µeff ) g[(J(J + 1)]1/2µB. Two approaches were performed in the fittings to eq 2: (1) Fix g (take the theoretical value) and vary J; and (2) vary both g and J. Both procedures gave comparable results for the magnetic moments at different temperatures. Another conceivable procedure is to fix S and vary L, and set J ) L +

Magnetic Properties of Heavy Rare-Earth M@C82

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Figure 11. Effective magnetic moments of M@C82 (M ) Gd, Tb, Dy, Ho, and Er) as a function of temperature. The effective magnetic moments were obtained from the fitting described in the text. χ0 contribution to the magnetization was subtracted in the fitting. Note that the temperature corresponding to the maximum µeff (Tµ) is in the order of Gd < Tb < Dy < Er. The inset shows Tµ as a function of the orbital angular momentum of the lanthanide ions.

S and g ) 3/2 + (1/2)[{S(S + 1) - L(L + 1)}/{(L + S)(L + S + 1)}]. The resulting effective magnetic moments from the first fitting procedure as a function of temperature for all the five metallofullerenes are shown in Figure 11. The fitting result for Ho@C82 is presented for T < 50 K because the measurement was not extended to higher temperatures. In general, the effective magnetic moment increases with temperature and levels off at certain temperature (Tµ) to, more or less, a constant value. In the fitting process, we took into account the contribution from χ0. When it was not considered, the effective magnetic moment rose with temperature to a maximum and fell gradually at high temperatures. Although χ0 depends on the magnetic field, we used a typical value for the fitting simply aiming to get an idea about the diamagnetic contribution. The leveling-off temperature (Tµ) is different for different metallofullerenes and is in the order of Gd < Tb < Dy < Er, which agrees with the increase of the orbital angular momentum of the lanthanide ions (Figure 11, inset). The Tµ data for Ho@C82 is not available owing to the limited temperature range we studied. The effective magnetic moments of all the five metallofullerenes estimated from the plateaus of Figure 11 at high temperatures are listed in Table 1. The results are comparable with reported values when they are available. For example, the effective magnetic moment estimated from the plateau of Figure 11 at high temperature for Gd@C82 is 6.95 µB. Although this value is somewhat smaller than that estimated by Funasaka et al. (7.7 µB) by fitting to the Brillouin function,12 it is in excellent accord with that from fitting to the CurieWeiss law. In general, the effective magnetic moments estimated from the fittings to the Brillouin function are generally consistent with those estimated from the fittings to the Curie-Weiss law as shown in Table 1. Discussion Magnetic Moment Reduction. As can be seen in Table 1, all the metallofullerenes studied in the present work exhibit effective magnetic moment reduction based on the fittings to both the Curie-Weiss equation and the Brillouin function. The

magnetic moment reduction observed in the metallofullerenes is in contrast to the magnetic property of some rare-earth organometallic compounds, which, at room temperature, give magnetic moments expected for uncoupled rare-earth ions plus the organic radicals.26 In addition, the extent of the reduction in effective magnetic moment is different for different metallofullerenes. The general trend is that, the higher the orbital angular momentum, the larger the magnitude of the reduction. However, even for Gd@C82 with L ) 0, some reduction occurs in the effective magnetic moment. There are several possible explanations for the observations above pertaining to the magnetic moment reduction of the rare-earth atoms in the carbon cage. First, magnetic moment reduction may be due to the intrametallofullerene magnetic properties. For example, the electron spins that localized on M3+ and on the carbon cage are likely to be coupled antiferromagnetically. This can only account for small magnetic moment reductions of such metallofullerenes as Gd@C82 and Dy@C82. Next, in the magnetic moment reduction of metallofullerenes, we notice that the carbon cage crystal field and orbital hybridization between the metal and the cage may partially quench the orbital angular momentum of the entrapped rareearth metal atom. Indeed, the antiferromagnetic coupling between the metal atom and the carbon cage already indicated a substantial orbital interaction between the metal atom and the carbon cage. Moreover, the larger L is, the more anisotropic the electron orbitals of M3+ will be, and the stronger the quenching effect will be. This mechanism for the magnetic moment reduction may be the most important one for the metallofullerenes we have studied among all possible causes. As shown in Table 1, the generally increasing magnitude of magnetic moment reduction for metallofullerenes with rare-earth metal ions of larger L corroborates such an assumption. The largest reduction in effective magnetic moment occurs to Ho@C82,10,17 which may be attributed to its relatively large zerofield splitting and many crystal field split levels. Similar reduction in effective magnetic moment was revealed previously for Ho2C3,27 and it was explained by the crystal field effect

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Figure 12. The magnetization (M) as a function of the applied magnetic field (H) at 40 K for Gd@C82 (a), Tb@C82 (b), Dy@C82 (c), Ho@C82 (d), and Er@C82 (e). The arrows show the points of deviation (Td) from the linear M-H relationship. The plot of Td vs L is presented in f.

based on a model calculation using the operator equivalent method.28 The calculation showed that the ground-state 5I8 of

Ho2C3 is split by the carbon cage crystal field Hamiltonian and the degree of reduction depends on the energy-level splitting.

Magnetic Properties of Heavy Rare-Earth M@C82 Erbium dimetallofullerenes have also shown crystal field splitting in the ground electronic states in fluorescence measurements by Ding et al.29 and Macfarlane et al.30 Imperfect Paramagnetic Behavior. In general, for the metallofullerenes, the 2S+1ΓJ free-ion ground state is likely to be partially split by the unique carbon cage crystal field. Because the carbon cage crystal field has very low symmetry (e.g. C2V),6 we expect the number of splitting angular momentum components to be 2J + 1 for integer J, and J + 1/2 for half-integer J. In the latter case, the components are Kramers doublets. The extent of magnetic moment reduction conceivably may be explained by the different multiplet widths, which are determined by the extent of zero-field splitting and the number of the splitting components. As temperature is lowered to a certain extent, the higher energy components start to be depopulated, and the free-ion approximation then becomes questionable. Consequently, both the Curie-Weiss law and the Brillouin function are not applicable anymore for the magnetic susceptibility data. Indeed, the isothermal magnetization data of all the five metallofullerenes cannot be well fitted to the Brillouin function below a certain temperature; this temperature is 8 K for Gd@C82 and 40 K for Er@C82. Aside from the fullerene cage crystal field splitting, intermetallofullerene magnetic interactions may also play a role in the failure of the Brillouin function for the low-temperature isothermal magnetization data of the metallofullerenes; at low temperatures, the interaction between the metallofullerene molecules becomes more and more evident. This type of magnetic coupling becomes important only at temperatures below 20 K because such coupling is expected to be a weak phenomenon. The interactions between the metal centers and between the metal ion and the fullerene cage cannot be fully understood without knowing the metallofullerene assembly structures. Scanning tunneling microscopy studies have shown that the monometallofullerenes M@C82 prefer the linear or ringshaped head-to-tail structures.31-33 We have also recently observed long-chain head-to-tail structures of M@C82 by transmission electron microscopy.34 These structures are favorable because of the sizable electric dipole moment along the symmetry axis of the metallofullerene molecules. The magnetic structure of these metallofullerenes would be one-dimensional, which involves the interaction between the encaged lanthanide ion and the carbon cage and between the metal centers. Although the distance between the lanthanide ions is quite large, such one-dimensional molecular magnetic materials have been studied for a long time, in which the distance between the lanthanide ions along the chain exceeds 1 nm.26 As temperature increases, the effective magnetic moment obtained from the fitting to the Brillouin function increases and levels off at a certain temperature (Tµ) to a roughly constant value (Figure 11). According to the discussion above, one would expect the leveling-off temperature (Tµ) to depend on the magnetic anisotropy of the metallofullerenes, which in turn is related to the orbital angular momentum of the rare-earth ions. The more anisotropic the metallofullerene is, the higher the leveling-off temperature will be. This is in accord with the Tµ - L correlation data described above. The different magnetic behavior among the metallofullerenes can be appreciated more directly by plotting the magnetization as a function of the applied magnetic field at a given temperature. Figure 12 shows the magnetization as a function of the applied field at a moderate temperature (40 K) for all five metallofullerenes. As shown in Figure 12a, the linear relationship of M-H for Gd@C82 persists at a magnetic field as large as 5

J. Phys. Chem. B, Vol. 104, No. 7, 2000 1481 T. The M-H curves of other metallofullerenes, however, start to diverge from the straight lines at lower magnetic fields (i.e. ∼3.6 T for Tb@C82, ∼2.5 T for Dy@C82, ∼1.6 T for Ho@C82, and ∼2.2 T for Er@C82 as shown in Figures 12b-e). This is understandable because the orbital angular momentum L of Gd3+ is zero, and therefore its electron density distribution is relatively more isotropic owing to its spherical electron distribution. On the other hand, the orbital angular momenta of M3+ (M ) Tb, Dy, Ho, Er) are nonzero, which induces magnetic anisotropy and results in the deviation from the expected linear M-H relationship. A cursory look at the data shows that the point of deviation, for example, the magnetic field (Hd) at which deviation from the linear M-H curve occurs, is again related to the orbital angular momentum of the lanthanide ions. Figure 12f presents the result (Hd vs L), which exhibits a nearly linear relationship between the applied magnetic field and the angular momentum of the lanthanide ions. This can be understood by noting that a larger orbital angular momentum is associated with a larger magnetic anisotropy, which would cause a larger deviation from the linear M-H relationship. As a result of this deviation from the linear M-H relationship above a critical magnetic field Hd, the determination of the effective magnetic moment of M@C82 must be performed in a sufficiently low magnetic field (gµBH , kBT); measuring µeff in a higher field will underestimate the effective magnetic moment. Summary and Conclusions We have measured the magnetic properties of the metallofullerenes M@C82 (M ) Gd, Tb, Dy, Er, and Ho) in the temperature range of 1.8 and 300 K with an applied magnetic field up to 5 T. No hysteresis loop was found down to 1.8 K. The magnetic susceptibility data for all five metallofullerenes obey the Curie-Weiss law quite nicely in all the temperature ranges we studied except at very low temperatures (i.e. ∼20 K < T < ∼300 K). At low temperatures (below 20 K), deviation from the Curie-Weiss law occurs because of the intermetallofullerene ferromagnetic couplings. We found the Weiss temperature θ to be -1.8 K for Gd@C82, -6.61 K for Tb@C82, -10.4 K for Dy@C82, -5.88 K for Ho@C82, and -20.7 K for Er@C82. The isothermal magnetization curves of M@C82 (M ) Gd, Tb, Dy, Er, and Ho) follow the Brillouin function above a certain temperature, which is different for different metallofullerenes. These temperatures and the fitting results were found to be related to the orbital angular momentum of the lanthanide ions. In addition, the effective magnetic moments of M@C82 obtained from both the Curie-Wiess law and the Brillouin function are significantly smaller than those of the free M3+ ions, but with a different extent of reduction for different metallofullerenes (13.0% for Gd@C82, 22.7% for Tb@C82, 13.1% for Dy@C82, 40.3% for Ho@C82, and 26.3% for Er@C82). The correlation of the magnetic moment reduction to the orbital angular momentum of the lanthanide ions entrapped in the carbon cage has been demonstrated. The magnetic moment reduction and the imperfect paramagnetic behavior of M@C82 are ascribed to the antiferromagnetic coupling between the rare-earth ions and the fullerene cages, the carbon cage crystal field splitting of the metal orbital angular momentum states, the partial hybridization of the electron orbitals of the metal ion and the carbon cage, and the interactions between the metal centers. Acknowledgment. This work was supported by the UGC of Hong Kong (RGC HKUST 601/95P and RGC HKUST 6111/ 98P).

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