MAGNETIC PROPERTIES NEAR THE METAL INSULATOR TRANSITION IN Si:P

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1 MAGNETIC PROPERTIES NEAR THE METAL INSULATOR TRANSITION IN Si:P H. Alloul, P. Dellouve To cite this version: H. Alloul, P. Dellouve. MAGNETIC PROPERTIES NEAR THE METAL INSULATOR TRANSITION IN Si:P. Journal de Physique Colloques, 1988, 49 (C8), pp.c c < /jphyscol: >. <jpa > HAL Id: jpa Submitted on 1 Jan 1988 HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

2 JOURNAL DE PHYSIQUE Colloque C8, Supp16ment au no 12, Tome 49, d6cembre 1988 MAGNETIC PROPERTIES NEAR THE METAL INSULATOR TRANSITION IN Si:P H. Alloul and P. Dellouve Laboratoire de Physique des Solides, Universite' Paris-Sud, 91/05 Orsay, France Abstract NMR ~ data allow to demonstrate that Coulomb interactions induce spin localisation in slightly metallic Si:P. The observed nuclei are associated with delocalised electrons (weak xion enhanced Pauli susceptibility, nuclear Korringa relaxation). The fraction of Iocalised spins, which wipe out 3 1 nuclei ~ from the observed signal, increases through the transition. 1. Introduction The respective role of intra atomic Coulomb interaction and disorder for the occurence of metal insulator transitions (MIT) [I, 21 is far from being clarified and might be somewhat dependent on the actual properties of the investigated system. In doped semiconductors, for which model Hamiltonians are well established, and for which the limiting metallic and insulating regimes are nearly perfectly understood, the difference of critical exponent of the conductivity at the concentration n, for the MIT, a = (n - n,)", CY = 1 or =1/2 respectively for uncompensated and compensated semi-conductors, has led to conclude that the role of electron-electron correlations is quite important in systems with a single scattering site per electron [3]. These results have led many workers to examine again carefully the magnetic properties at the transition, which had been already studied for more than 20 years [46]. The main feature discovered recently has been the large increase of the magnetic susceptibility at low T on the metallic side of the MIT 17, The behaviour of the macroscopic susceptibility x,, which is usually obtained from ESR data, is summarized in figure 1, where it can be seen that X, has a low T behaviour which is often fitted with a T - law, ~ where p N 0.7 and slightly depends on n. Such results, obtained by techniques which only probe the q = 0 modes of X, might be explained either by a large density of excitations in a highly correlated electron gas [9], or by spin localisation. In this paper we show that NMR techniques, which probe the local susceptibilities do allow us to demonstrate unambiguously that spin localization occurs in Sip already for n, < n < 2nc, from 3 1 NMR ~ data taken with an optimized sensitivity. The paper will be organized as follows. In section 2 we shall recall some essential informations which can be obtained by NMR on the magnetic properties of metals and local moments. The NMR data in Si:P in the good metallic state (n > 2nc, Sect. 3) and near the MIT (n < 2nc, Sect. 4) will be presented then. These results will be discussed in section 5 together with ESR and 29~i NMR data. Some open questions, on both the metallic and the insulating side of the transition, will then be summarized in section NMR in metals and local moment systems A nuclear spin I located at R is coupled to electronic moments S through a bilinear coupling AIA (R) S. In the most simple cases, it is dominated by a contact scalar coupling A (R), and the nuclear spins sense a static local field HL(R)=A(R)(S)/~=A(R) M(R)l k e ~ n (1) where ye and 7, are the electronic and nuclear gyromagnetic ratios and M (R) is the magnetization at site R. The fluctuations of the electron spins induce transitions between nuclear spin levels and yield a nuclear spin lattice relaxation I I l l,, I I 10" 10'~ ", 1019 ton Concentration (c1n-~1 Fig Concentration dependence of the electronic susceptibility X, in Si:P at 4.2 K and 1.1 K (respectively full and empty symbols). The data are taken from various sources: (A) reference [4], (0) reference 151, (0) reference [6], (o) reference [&]. The limiting Curie and Pauli behaviour are given by straight lines. T;' = [A' (R) I 21 J (s+(t) S- (0)) exp (iwnt) dt, where the spin correlation function is directly linked to the electronic dynamic susceptibility through fluctuation dissipation theorem, and w,, is the Larmor frequency of the nuclei. In simple cases the autocorrelation function decays as exp - t / T, which yields Article published online by EDP Sciences and available at

3 C JOURNAL DE PHYSIQUE TF~ ~BT r b e 1 + w:r2 = (R) - (SX) - where we is the electron Larmor frequency. The difference between localized and non localized electron spins might be seen in their respective contribution to the T dependence of Xe, but can usually be better understood from the fluctuating components. Indeed for conduction electrons the fluctuation time T is governed by the residence time of an electron on the atomic site h/ EF, the relaxation rate being then directly correlated to the Knight shift K = HL / HO of the NMR through the Korringa relation [ll] lows to demonstrate that the distributions of A (R) (2) and M (R)/ Ho, which cannot be separated n griori, are T and field independent. Although measurements of Tl and K at the peak position of the resonance lines have shown for long that a Korringa relation holds [13-151, we could rather on the broad 3 1 spectrum, ~ mea- sure TI in different fields all along the NMR line and do find out that equation (3) applies perfectly, with s = 1. This confirms that Si:P is a good free electron metal for n > 2nc, which implies that the electronic magnetization is not distributed, and therefore that the linewidth in figure 2 is, in this range due to a distribution of A (R). where s = 1 for free electrons and s > 1 in presence of ferromagnetic electron-electron interactions. For localized spins r is much longer and depends upon the scattering mechanisms which couple the electron spins to the lattice. 3. Metallic Si:P for n > 2nc For high P concentrations the impurity band is highly broadened and merges in the conduction band of Si. It is indeed found that both C, 1121 and X, [4] agree with calculated values for n electrons in the 6 ellipsoidal pockets in the minima of the Si conduction band. The expected n1i3 dependence of the Pauli susceptibility xe is indeed followed by the ESR data (Fig. 1). As for the NMR, we are dealing with a material which differs from standard elemental metals, as the density of conduction electrons is strongly non uniform ia space. Although the original hydrogenoid orbitals of Phosphous are screened by the conduction electrons, the wave functions are still peaked on the P atoms and become uniform only far from the P sites. Therefore A (R) a I$ (R)I~ is highly distributed on Si nuclei but also on P nuclei because of the dis- order in atomic positions [ The resulting 29~i and 3 1 lines ~ are broad, but the data of figure 2 al-.?, i 1 Q g'.t 0.0' '10 0.0' NMR SHIFT K=(H,-H)/& Fig Spin Echo intensity versus NMR shift for a metallic sample for two fields (arbitrarily normalized in intensity) and two temperatures (corrected for the Curie dependence of the nuclear magnetization). NMR SHIFT K= (Ho-Hl/Ho Fig (T~T)-~ values taken at different positions on the NMR line for two fields and temperatures in metallic samples. The straight lines are fits to a Korringa law (Eq. (3)), with s = 1.04 for n = 16 x 10' cm-3 and s = 0.63 for n = 4.5 x 10" ~m-~ L ~ NMR near the MIT We have taken 3 1 data ~ for samples with concentrations as low as 0.7 nc [16]. The raw data for the spectra, normalized to the number of phosphorus atoms are displayed in figure 4. There, it can be seen that the area of the signal decreases steadily with decreasing n, which shows that 3 1 spins ~ are progressively wiped out of the detected signal. Its NMR shift goes through a maximum for n N 1.2 nc and decreases sharply below nc. Apart from careful control of the spectrometer sensitivity, skin depth effect in the sample etc. we had to correct for variation of the spin echo decay time along the spectrum, to be able to deduce quantitative information from the data. The decrease of the fraction a: of detected nuclei (Fig. 5), the deviation of Xe with respect to X,, the appearance of a T dependence of X,, the deviation of the average measured shift (K) from

4 H. Allotrl and P. Dellouve C '-.. Si: P. H,=20 kg p-.** *. T=4.2 k ~ ~ ~ l * 'i oooo 0. ul o 0 o O 0 0 O L: 0 ooo0 0 n 0%- *-***. -; * *a e**.- 3: oocp*oo ooo~~o~~om 0 U) O B 6 & **.C. ** ** n (r 10'~ cm-3) % ',, = C * * : - &oa. d m mo ooo o 0 oo0oooooo C o-o-oao O 0-0- cn 8. o o 5; e - e - e '* **- e r -. ~ ~ ~! o-o- 1 1 f i I H - H, (Gauss 1 H - H,(Gauss) Fig NMR spectra observed in a series of Si:P samples through the MIT (n, = 3.4x lo1' ~m-~). The signal intensities are normalized to the number of phosphorus atoms. I Id a 10 ' =! E K"' n ' : *, a 't. v - '. 8 / e:.., - 6 f oms: J' b I,.A*., 0 - V) 1 \? + - : 2 + e ; -. l l a. n, n (XIO'* crn 3) Fig Concentration dependence of the average NMR shift (K ). Our data (0) differ from the results of previous authors for n > n,. Brown and Holcomb (+) 4.2 K; (O) 1.1K) find smaller values [14], presumably because they do not get enough sensitivity to follow the resonance far in the wings. Their apparant T variation might result from the temperature dependence of the spin echo decay time for large shifts. The double resonance result of JBrome et al. [17] at low T is also plotted (n). The NMR data can be compared with Xe of reference [4] taken at 4.2 K (A) and 1.1 K (A). its monotonous high concentration variation (Fig. 6), all occur simultaneously at about n 2 n,, which confirms that the system departs then from simple free electron behaviour. In spite of the loss of signal intensity, we could perform TI measurements down to n = 4.5 x 1018 ~ m-~, that is n 1.32 n,. The data in this sample still follows a Korringa relation, as for larger n, although a slightly smaller value s x 0.63 is obtained (Fig. 3). We could not detect any significant change of the spectrum down to 1.65 K on this sample, while the macroscopic susceptibility Xe increases at low T. However a small decrease of the number of detected spins with decreas- Fig Variation with concentration of the fraction x of detected nuclei in Ho = 20 kg, at two temperatures.

5 C JOURNAL DE PHYSIQUE ing T is observed (Fig. 7). Finally, we did not detect any signal for n = 2.4 x 10'' cm-3 at the Knight shift position given by Jerome et al. [17], which points out that these authors observed less than 3 % of the 3 1 ~ nuclear spins, in their very sensitive double resonance experiments. the wave functions, and therefore in the distribut'ion of A (R), the increase of the normalized linewidth points out a corresponding increase of the distribution of X for the observed sites, mainly for n = n,. In order to perform a crude analysis of the data we might neglect this distribution and assume that xo and XI are the susceptibility per electron sensed respectively by the detected and lost nuclei, so that I-. &. : a a. I h Temperature (K) Fig Variation of z with T for metallic samples. 5. Discussion All these experimental observations indicate that the electronic states associated with the increase of X, near the MIT are not detected in the present experiment, and are rather associated with the 3 1 nuclei ~ which are wiped out from the NMR signal. As for the observed nuclei, they sense conduction band electron states with a T independent susceptibility and undergo a well behaved Korringa relaxation. We are therefore dealing with a situation for which both A (R) and X are spatially distributed. This is even true for the detected NMR signal, as the ratio of the NMR width to its average shift (K) is found to increase abruptly below n, (Fig. 8). As we don't expect a marked change in With such an equality, we can deduce Xo from the measurement of (K), if we estimate the average hyperfine field (A (R)). We could, as in reference [lo] assume that, for these low concentrations, (A (R)) is unchanged with respect to Ao / 2n = MHz, de- termined for the isolated donor [18]. This value is indeed found to hold, up to n = 10'' ~m-~[19]. We can as well obtain (A (R)) in the metallic range from the ratio (K)/ X,. An interpolation between these two limiting regimes [20], allows then the estimates of Xo and XI from equations (1) and (4), which are plotted in figure 9. We find that Xo decreases with respect to both x, and X,. This indicates that the band electrons correspond then for n < 2 n, to a low density of states as expected for an impurity band tail. Such a result is I!I!! 1 IkIfi I I Ill 2 nc Concentration (x10'~cm-3) Fig Variation with concentration of the ratio of the NMR half intensity width to the average NMR field shift (K) Ho. It is seen that this quantity increases abruptly below n,. Fig The data for X, at 4.2 K are plotted with the same symbols as in figure 1 together with the average Pauli susceptibility Xo and the localised spin susceptibility nl per electron deduced from the NMR data, with the rough analysis sketched in the text.

6 in rather good agreement with a band structure calculation done by Serre and Ghazali [21]. Although these authors do not take into account properly the intraatomic Coulomb repulsion, their results give a reasonable estimate of the concentration n E 2 n, for which the density of states at the Fermi level recovers that of the Si conduction band. As for the localised susceptibility per electron, we obtain X1 N 0.26 Xc at 4.2 K, and XI 0.14 X, at 1.65 K, where Xc is the Curie susceptibility of free spins. Such large values for XI would correspond to an NMR shift (K) = 0.1 at 4.2 K, quite above our experimental range of observation. We believe that these spins are responsible for the large enhancement of "~i nuclear relaxation rate detected at low T near n, [22]. Indeed long correlation times T are expected, which should dominate the relaxation rate of the " ~i nuclei. The latter undergo very small NMR shifts [13], at least for those nuclei which are usually observed and are quite distant from the P atoms, 17C) (R)I~ being then quite small. In such a case, as in insulating solids, the dominant effects are associated with the dipole dipole coupling with localised moments [ll]. Further, the small line broadening allows spin diffusion among the " ~i nuclei, which have then a uniform relaxation driven by the local moments. Although the present situation is rather more complicated than the case of controlled magnetic impurities in metals, such as the classic situation of CuMn [23], the analogy is quite striking and the ETgl field dependence detected for T~-' both of 6 3 and ~ " ~i ~ nuclei [22], has been shown to be linked with nuclear spin diffusion in CuMn [23]. Such a possibility for the case of doped semiconductors has been already suggested [24] and is supported by new data, taken in high fields [25], for Si:P. 6. Conclusion Although a subdivision of the measured X, into Pauli and Curie terms has been proposed a long time ago [4], the present experiment allows us to establish a similar distinction from a local observation. Of course the quantitative analysis of figure 9 is somewhat crude and the numbers advanced are only reliable within a factor 2. However the qualitative information that localisation explains most of the anomalous low T susceptibility, while extended states correspond to a small Xo are important for the understanding of the MIT. This result excludes in disordered systems the description with a highly correlated electron gas which is valuable in ordered cases [9], while it favours the idea that the enhancement of X, is linked with a progressive decrease of the diffusion constant, which also explains the broadening of the ESR line at low T 181, Such features are now also proposed from renormalization group calculations [26, 271. H..~lllonl and P. Dellouve C Further issues concern the interplay between the two kind of electronic states. How do they interact together? From the similarity of the low T data for N, below and above n,, it seems reasonable to consider that the distribution of antiferromagnetic interactions between the localised spins which explains quite well [28, 291 the T-' dependence of X. below n,, does also somewhat describe that above, as long as XI dominates Xo, that is at low T. However, the exact picture might slightly differ. We do not know the localisation scale: groups or single P states? Are there also RKKY contributions to the interactions between localised states, and eventually a spin glass regime? As for the present experiment, it provides unique informations on the low susceptibility sites. For n, < n < 2nc the detected 3 1 NMR ~ signal is associated with electron states in a broad impurity band, with localised spin IeveIs in the band tail, the MIT being presumably due to a mobility edge rather than to the opening of a gap. Further work is needed to clarify whether the decrease of x at low T, and the slightly reduced value of s are again due to the Iocalised spins, which might progressively influence distant nuclei, or whether it is indeed associated with slowing down of spin diffusion for more and more spins. Also for n < n,, the weak observed signal, which has a small NMR shift, might still be due to spatially extended (but non conducting) electron states [17], or merely to antiferr~magneticall~ coupled P spin pairs. Finally, whether these magnetic properties are essential in the critical exponent problem of the conductivity is still a matter which needs further inquiries, and we are considering the possibility to perform similar studies of the magnetic properties of compensated systems. Acknowledgments The authors should like to thank M. T. BBal Monod, J. Friedel, D. Jbrome, N. F. Mott and H. Schulz for stimulating discussions all along this work. Partial financial support has been provided by the Centre National dyetudes des TBlBcommunications (contract No ). [I] Mott, N. F., Kaveh, M., Philos. Mag. B 52 (1985) 117. [2] Lee, P. A., Ramakrishnan, T. V., Rev. Mod. Phys. 57 (1985) 287. [3] Thomas, G. A., Philos. Mag. B 52 (1985) 579. [4] Quirt, J. D., Marko, J. R., Phys. Rev. B 5 (1972) 1716; 7 (1973) I51 Andres, K., Bhatt, R. N., Goalwin, P., Rice, T. M., Walstedt, R. E., Phys. Rev. B 24 (1981) 244.

7 C JOURNAL DE PHYSIQUE [6] Sarachik, M. P., Roy, A., Turner, M., Levy, M., [17] Jbrome, D., Ryter, C., Schulz, 8. J., Friedel, J., He, D., Isaacs, L. L., Bhatt, R. N., Phys. Rev. B Philos. Mag. 52 (1985) (1986) 387. ' [18] Feher, G., Phys. Rev. 114 (1959) f7] Ikehata, S., Kobayashi, S., Solid State Commun. [I9] To~oda, Y-3 Morigaki, K., J. Phys. Sot. J P 43 ~ 56 (1985) 607. (1977) 118. [8] Paalanen; M. A., Sachdev, S., Bhatt, R. N., Ruckenstein, A. E., Phys. Rev. Lett. 57 (1986) [20] We find that (A (R)) decreases with decreasing n and reaches A012 for n - 5 n,. In order to interpolate between these two regimes we assumed that [9] Brinkman, W. F., Rice, T. M., Phys. Rev. B 2 (A (R)) goes through its minimum value around (1970) 1324; 2 (1970) n -- 3nc and increases to reach An at about [lo] Alloul, H., Dellouve, P., Phys. Rev. Lett. 59 (1987) 578. [ll] Slichter, C. P., Principles of magnetic resonance (Harper and Row) [12] Kobayashi, N., Ikehata, S., Kobayashi, S., Sasaki, W., Solid State Commun. 24 (1977) 67; 32 (1979) [13] Sasaki, W., Ikehata, S., Kobayashi, S., J. Phys. Soc. Jpn 36 (1974) [14] Brown, G. C., Holcomb, D. F., Phys. Rev. B 10 (1974) [15] Ikehata, S., Sasaki, W., Kobayashi, S., Phys. Soc. Jpn 39 (1975) [16] Since reference [lo], we have changed our scale for n versus the room T resistivity to the more recent one given by Thurber, W. R., Mattis, R. L., Liu, Y. M., Filliben, J. J., J. Electrochem. Soc. 127 (1981) The differences are only significant for n = n, = 3.4 x 10' ~rn-~. n N 0.3nc. This is quite equivalent to taking (A (R)) A012 for our experimental points below 2nc. [21] Serre, J., Ghazali, A., Phys. Rev. B 28 (1983) [22] Paalanen, M. A., Ruckenstein, A. E., Thomas, G. A., Phys. Rev. Lett. 54 (1985) [23] Bernier, P., Alloul, H., J.'Phys. F. 3 (1973) 869; 6 (1976) [24] Tunstall, D. P., Philos. Mag. 42 (1980) 735. [25] Hirsch, M. J., Holcomb, D. F., Phys. Rev. B 33 (1986) [26] Finkelshtein, A. M., Z. Phys. B 56 (1984) 189. [27] Castellani, C., Di Castro, C., Lee, P. A., Ma, M., Sorella, S., Tabet, E., Phys. Rev. B 33 (1986) [28] Rosso, M., Phys. Rev. Lett. 44 (1980) [29] Bhatt, R. N., Lee, P. A., J. Appl. Phys. 52 (1981) 1703; Phys. Rev. Lett: 48 (1982) 344.