Electronic Properties of (NH 3 ) x NaK 2 C 60

Transcription

1 Electronic Properties of (NH 3 ) x NaK 2 C 60 M. Riccò a, T. Shiroka a, A. Sartori a, F. Bolzoni b and M. Tomaselli c a Dipartimento di Fisica and Istituto Nazionale di Fisica della Materia, Università di Parma, Parco Area delle Scienze 7/a, Parma ITALY b Istituto Maspec-CNR, Parco Area delle Scienze Loc. Fontanini, Parma, ITALY c Laboratory of Physical Chemistry, ETH Zurich CH-8092 Zurich, Switzerland Corresponding author : Tel : ; fax : Mauro.Ricco@fis.unipr.it Abstract The superconducting fulleride (NH3)xNaK 2 C 60 has a cubic structure with lattice parameter (a) and transition temperature (T c ) depending on x. The relation between these two parameters was found, however, to be opposite to what is expected from the BCS theory (and observed in the other fullerides). To better understand the origin of this anomaly we have measured the electronic spin susceptibility with SQUID magnetometry and NMR in two differently doped samples. The relation between T c and the density of states at the Fermi energy is found to be opposite to the Migdal-Eliashberg prediction. The 13 C-MAS measurement of the isotropic part of the 13 C Knight shift qualitatively confirms this result. 13 C NMR relaxation measurements validate the interpretation of the spin susceptibility in terms of density of states and rules out the presence of strong antiferromagnetic correlations in the Fermi liquid. PACS: Tx Electronic states of fullerenes and related materials and intercalation compounds Ha Magnetic properties of superconductors k Nuclear magnetic resonance and relaxation 1

2 The intercalation of ammonia in the C 60 based superconductors can induce a relevant increase in T c as it is observed in Na 2 CsC 60 [1] which, after ammoniation, gives (NH 3 ) 4 Na 2 CsC 60 with an increase in transition temperature from 10.5 to 29.6K. However, the same process yields a transition to an insulating (magnetic) state in K 3 C 60 [2]. In NH 3 K 3 C 60 superconductivity can be restored only by the application of external pressure [3]. The ammonia molecule in these systems is supposed to act simply as a molecular spacer so that it merely induces a change in lattice parameters and an increase of unit cell volume. As a consequence, the t 1u conduction band of the compound narrows and the density of states at the Fermi energy (N(ε F )) increases. According to Migdal- Eliashberg theory, an increase in N(ε F ) would yield an increase in superconducting transition temperature. This can explain the increase in T c observed in (NH 3 ) 4 Na 2 CsC 60 while, an increase of electron spin correlation could induce a Mott- Hubbard transition to the insulating (magnetic) state in the case of NH 3 K 3 C 60. In this work we report on ammonia intercalated fullerides which do not behave like this simple picture suggests. NaK 2 C 60 and NaRb 2 C 60 do not exist as a single phase but the insertion of ammonia in their lattice gives (NH 3 ) x NaK 2 C 60 and (NH 3 ) x NaRb 2 C 60 [4] which are both stable compounds. X-ray diffraction shows that [4] the NH 3 -Na groups occupy the large octahedral sites of the fcc lattice with a consequent off-centering of the Na ions. A particularly appealing feature of these compounds is the possibility of a continuous change in lattice parameter achieved by the progressive removal of NH 3. The decrease of the lattice parameters is however accompanied by an increase of the superconducting transition temperature, a trend opposite to that previously described. To better understand the origin of this anomaly we have determined N(ε F ) from DC magnetometry for two different ammonia doping x=0.85 (referred to as sample a) and x=0.75 (sample b) with transition temperature T c =9K (sample a) and T c =11.8K (sample b). Furthermore, we have performed 13 C spin-lattice relaxation and Knight shift measurements which allow to probe the existence of electron spin correlations. The samples were prepared following the procedures outlined in Ref. [4] in which stoichiometric amounts of alkali metals and C 60 were dissolved in anhydrous 2

3 ammonia. After the reaction had taken place the ammonia was slowly evaporated and the successive pumping at different temperatures (RT gave sample a, 120C gave sample b in our case) afforded samples with different ammonia content. The samples were successively annealed at 100C for 10 days. The manipulation of the samples was done in oxygen and moisture free Ar atmosphere (O 2 <1 ppm, H 2 O<1 ppm) and the use of metallic tools was accurately avoided to minimize contamination with ferromagnetic impurities. DC magnetometry measurements (performed by a Quantum Design SQUID magnetometer) showed the onset of superconductivity at 9K for sample a and 11.8K for sample b. The shielding fractions were 22.5% and 25% respectively, indicative of bulk superconductivity. The ammonia concentration (x=0.85 and 0.75 respectively) was determined from the superconducting transition temperature by interpolating the T c vs. x data reported in Ref. [4]. Figure 1 represents the DC magnetization curve for sample b for the applied field value of H=2T. Three contributions to the static magnetic moment are clearly distinguishable: a Curie contribution from paramagnetic impurities (being always present in fullerides), a diamagnetic contribution from the superconducting phase below T c and a temperature independent positive contribution. The subtraction of the fitted Curie term in the normal state yields a precise determination of the temperature independent contribution (dotted line in the figure) which has been determined at different applied fields. Its field dependence is shown in Figure 2. The departure from the expected linear dependence observed below 1.5 T is attributed to the presence of ferromagnetic impurities whose effect saturates at fields H>1.5 T (even few ppm can give an appreciable effect). This suggests that the correct value for the normal state susceptibility χ must be derived from the slope of the high field linear behaviour rather than from the simple M/H ratio. The measured quantity is indeed the sum of three contributions: a Pauli term due to the spin susceptibility of conduction electrons (χ S ), a Landau term due to their orbital susceptibility (χ Landau ) and a core contribution (χ Core ). χ Landau in fullerides is strongly diminished due to the high value of the effective mass (see below) or even completely quenched by molecular rotational disorder as claimed in Ref.[5]. χ Core (diamagnetic + Van Vleck), on the other hand, must be evaluated by summing the contributions of the single components reported in 3

4 Table 1. The χ Core value listed for C 60 is that of the neutral molecule and could be different from that of C 3-60 because of a different Van Vleck contribution. Although this could introduce a systematic error in the final absolute determination of N(ε F ), it 3- should not, however, invalidate the comparison of N(ε F ) values from different C 60 compounds. The results of the outlined analysis are summarized in Table 2 where it appears evident that χ S is ~3 times larger than χ Core. In a free electron metal, the value of χ S is related to the density of electron states at the Fermi energy by N(ε F )=χ S /2µ 2 B, (note that the density of electron spin states is sometimes reported as twice this value). The values obtained in our case are shown in Table 3 where the same quantities for Rb 3 C 60 and K 3 C 60 are also reported for comparison. The most relevant feature is that N(ε F ) decreases with increasing T c, a trend opposite to that predicted by the Migdal-Eliashberg theory. The effective mass m eff can also be derived from the free electron expression of the Pauli susceptibility: S 4µ = m 3 B eff π h 2 n χ (1) where n is the conduction electron density. The calculated values are also reported in Table 3. This striking result may, however, be the consequence of the wrong free electron assumption as the antiferromagnetic (AF) spin fluctuations would decrease the measured spin susceptibility by a Stoner factor α: χ S =2αµ 2 B N(ε F ), α=1/(1- IN(ε F )) where I represents the exchange coupling constant. In other words we need to exclude the possibility that the observed effect is due to spin correlations or better to show that the influence of spin antiferromagnetic correlations is not stronger in these systems than in other superconducting fullerides. 13 C NMR Knight shift and spinlattice relaxation measurements can be employed for this purpose. In metals where the conduction band has a mixed s-p character (like intercalated graphite or fullerides) the Knight shift tensor K is related to the spin lattice relaxation time T 1 by the modified Korringa relation [6]: 1 T T 1 1 βs 2 2 ( 2 K + ) 11 K iso = (2) 4

5 where S is the Korringa constant (S= sec K for 13 C) [7], K 11 is a component of the traceless anisotropic part of K and K iso is its isotropic value; the refers to the average over the three non equivalent carbon sites in the fcc lattice. The exact relation where β=1 is valid for a free electron gas, while electron correlations change the β value since K is proportional to the generalized spin susceptibility at q=0 and ω=0 (referred to as χ(0,0)) while 1/T 1 is proportional to Σ q χ(q,ω). β can be expressed as [8]: β = 2 4πhω χ(0,0) 0 Im( χ( q, ω )) q 0 where ω 0 is the Larmor frequency. AF spin fluctuations, in particular, give a q=q AF 0 contribution to χ decreasing its q=0 value thus yielding β<1. A rough estimation of the K tensor from the 13 C lineshape was performed following the procedure outlined in Ref. [7]. In detail the following assumptions were made: 1- both Knight and chemical shift tensors were supposed cylindrical with coincident principal axes. 2- the chemical shift value is: σ iso =143 ppm (charge effects are neglected) and σ aniso =( ) ppm [9] (neglecting the 0.28 asymmetry present in pristine C 60 ). 3- there are three inequivalent carbon sites with intensity ratio 1:2:2 with different local density of states. The available band calculations [10] give ratios of these values for K 3 C 60 ~(4:7:12) or Rb 3 C 60 and Rb 2 CsC 60 ~(3:4:7). The Knight shift anisotropy should be proportional to the local density of states. Due to their similarity (the largest difference is related to the less intense carbon) and in absence of similar calculations for our system we tried to fit our data with both these values. The difference between the two obtained average K values is however within the reported error. 4- to reproduce the observed spectrum, the three carbon powder lineshapes are convoluted with Gaussian functions to account for tensor deviations from axial symmetry, nuclear-dipolar interactions and other possible broadening sources. (3) 5

6 The isotropic Knight shift K iso of both samples was measured in the temperature range K. The static line width of ~18 ppm (FWHM at 300K) prevented its precise determination with a conventional experiment therefore a MAS experiment has been used. The results are shown in Figure 3: the values found for K iso is 45.9 ppm for sample a and 44.6 ppm for sample b, no temperature dependence was observed within the 153K-300K range. Figure 4 represents the 13 C NMR spectrum of sample b at T=14K just above T c. The simulated powder pattern following the above mentioned assumptions is shown before (continuous line) and after (dotted line) the convolution with the Gaussian functions. The value obtained for the Knight shift anisotropy averaged over the three non-equivalent carbons is K 33 -K 11 =285± 5 ppm for sample b (i.e. <K aniso > = ( ) ppm). Both K 33 -K 11 and K iso values are comparable to those obtained for other fullerides: K 33 -K 11 =300 ppm, K iso =43 ppm for Rb 2 CsC 60 [11], K 33 -K 11 =286 ppm, K iso =41 ppm for Rb 3 C 60 and K 33 -K 11 =259 ppm, K iso =37 ppm for K 3 C 60 [7]. The spin susceptibility χ S is related to the isotropic/anisotropic value of K by: K a γ γ = ii χ (i=1,2,3), ii h S e n K a γ γ = iso χ (4) iso h S where a ii is the anisotropic traceless components of the hyperfine coupling tensor and a iso is its isotropic part. It is relevant to note that: a) both N(ε F ) (from χ S ) and K in our case are slightly larger or comparable to the values measured in other fullerides with higher transition temperatures, in contrast to the Migdal predictions; b) the values of K iso measured in the two samples (a and b) qualitatively confirm the anti-migdal behaviour indicated by magnetometry. The 13 C spin lattice relaxation time T 1 was measured below 35K with an inversion recovery sequence with Hahn echo detection. The observed recovery was fitted with a single exponential function although it poorly fits especially at longer recovery times as expected from 1- the anisotropic nature of the Knight shift [8] and 2- the presence of three non equivalent carbons [7]. A more detailed analysis is however beyond the scope of the present work. Figure 4 illustrates the temperature dependence of 1/T 1 T. e n 6

7 Above T c this quantity looks reasonably temperature independent as predicted by the Korringa law, the average value being 1/T 1 T =7.2± sec -1 K -1. If we insert the values for 1/T 1 T, K iso and K 11 in eq. 2 we obtain β=0.74 which is higher than the values determined for other fullerides (see Table 3). Similar NMR measurements performed on sample a gave the same qualitative results and the comparison of the Knight shift tensor anisotropies requires a more accurate data analysis based on specific band calculations. Nevertheless the high value of β rules out the presence of strong AF correlations in the Fermi liquid corroborating the N(ε F ) values obtained from the spin susceptibilities. As originally shown in Ref. [4] and confirmed by our double resonance NMR result [12], the presence of ammonia induces a Å off-centering of the octahedral cation (Na). This could resolve the t 1u level degeneracy and give a broader bandwidth with respect to other fullerides. This effect could have two consequences: 1) the decrease of N(ε F ), 2) the removal of electron (AF) correlations and a consequent increase in χ S. The latter is supported by NMR and the high value of χ S (validated by the high value of K) demonstrates that it is the dominant effect. This simple mechanism, however, does not explain the observed non-migdal relation between N(ε F ) and T c (also corroborated by NMR) which remains one of the most striking features of these compounds. While it is not clear why this effect was observed only in the present systems (the weak electronic correlation could play a role), its origin could reside in the non adiabatic nature of C 60 based superconductivity. Recent theoretical studies [13] predict that the spin susceptibility is reduced, with respect to the purely electronic value, if the electron-phonon coupling is taken into account in the non-adiabatic regime. Since this reduction is shown to increase as the electronphonon coupling increases, it could yield an anti-migdal correlation between the observed χ S and T c. 7

8 Figure Captions Figure 1: Magnetization curve of (NH 3 ) 0.85 NaK 2 C 60 (sample b) with T c =11.8K. The continuous line represents a fit to a Curie contribution (attributed to paramagnetic impurities), the dotted line is the residual magnetization after its subtraction. Figure 2: Field dependence of the temperature independent magnetization of (NH 3 ) 0.85 NaK 2 C 60 (sample b) in its normal state. At low fields, ferromagnetic impurities give a non linear contribution. Figure 3: 13 C-MAS determination of K iso (referenced with respect to pristine C 60 ) for both samples [ν r = 2.5 khz, ν Larmor = MHz].The 1 H decoupling field strength was 0.8 mt (8G), a 13 C π/2 pulse of 7 µs was used. The observed broadening at 213K and more pronounced at 153K can be attributed to the slowdown of the C 60 molecular reorientations, with correlation times τ c ~ 1/ν r. The shift scale is referenced with respect to tetramethylsilane (TMS). Figure 4: Comparison of the observed 13 C-NMR spectrum of sample b at T=14K (ν Larmor =75 MHz, the shift is measured with respect to TMS) with its simulation. K n (n=1,2,3) are the traceless Knight shift tensors for the three non-equivalent carbons taken with ratio (3:4:7); σ n are the applied Gaussian broadenings, both are expressed in ppm units. Figure 5: Temperature dependence of 1/T 1 T (T 1 = 13 C spin lattice relaxation time) for (NH 3 ) 0.85 NaK 2 C 60 (sample b). 8

9 Table Captions Table 1. Core (diamagnetic + Van Vleck) contributions to the susceptibility from the single components of (NH 3 ) x NaK 2 C 60. Table 2. Results of the analysis of magnetometry data. The ferromagnetic impurities are expressed in equivalent molar fraction of Fe (M sat =218 emu/g) while for the paramagnetic ones, the number of electronic spins per mole is reported. Table 3. The values for the density of states at the Fermi energy N(ε F ), the effective mass m eff and the correction factor of the modified Korringa relation β determined in this work for (NH 3 ) x NaK 2 C 60 are here compared with those of more common superconducting fullerides K 3 C 60 and Rb 3 C 60 (a represents the lattice parameter). 9

10 Table 1. χ Core [ 10-6 emu/mole ] C [14] K [15] Na [15] NH 3-18[16] Table 2. Sample a Sample b Units χ measured emu/mole χ Core emu/mole χ S emu/mole Ferromagn. Impur Fe molar fraction Paramagn. Impur Electronic spin/mole Table 3. Comp. T c a [Å] N(ε F ) m eff [m e ] β [states/ev spin C 60 ] K 3 C ±1[5,17] 6.4±1.5[17] 0.58[7] Rb 3 C ±0.6[5] 0.48[7] (NH 3 ) 0.75 NaK 2 C ± ± (NH 3 ) 0.85 NaK 2 C ± ±0.2 10

11 M [emu/g] Paramagn. Impurities H=2 T Temperature [K] Figure 1 11

12 T indep. Magnet. [emu/g] χ= emu/g T Ferromagnetic impurities H [T] Figure 2 12

13 sample a (T c ~ 9 K) sample b (T c ~ 11.8 K) 300 K K = 45.9 ppm iso 300 K K = 44.6 ppm iso 253 K 253 K 213 K 213 K 153 K 153 K Shift [ppm] Shift [ppm] Figure. 3 13

14 15 10 experimental simulation theoretical K 1 =( ), σ 1 =76 K 2 =( ), σ 2 =45 K 3 =( ), σ 3 =70 Intensity Shift [ppm] Figure 4. 14

15 0.012 (NH 3 ) 0.75 NaK 2 C / T T 1 [sec. 1 K 1 ] T c Temperature [K] Figure 5. 15

16 References [1]O. Zhou et al., Nature, 362 (1993) [2]Y. Iwasa et al., Phys. Rev. B, 53 (1996) R [3]O. Zhou et al., Phys. Rev. B, 52 (1995) [4]H. Shimoda et al., Phys. Rev. B, 54 (1996) R [5]A. P. Ramirez et al., Phys. Rev. Lett., 69 (1992) [6]Y. Maniwa et al., J. Phys. Soc. Jpn., 54 (1985) 666. [7]N. Sato et al., Phys. Rev. B, 58 (1998) [8]M. Mehring, F. Rachdi, and G. Zimmer, Philos. Mag. B, 70 (1994) 787. [9]R. Tycko et al., Science, 253 (1991) [10]D. L. Novikov, V. A. Gubanov, and A. J. Freeman, Physica C, 191 (1992) 399. [11]C. H. Pennington et al., Phys. Rev. B, 53 (1996) R [12]M. Ricco et al., Physica C, 306 (1998) [13]C. Grimaldi and L. Pietronero, Europhysics Letters, 47 (1999) [14]R. C. Haddon et al., Nature (London), 350 (1991) [15]N. W. Ashcroft and N. D. Mermin, Solid State Physics HRW International Editions, Philadelphia PA, (1976). [16]P. Lazzeretti, R. Zanasi, and B. Cadioli, J. Chem. Phys., 67 (1976) 382. [17]W. H. Wong et al., Europhysics Letters, 18 (1992)