Hypert'meInteractions 85 (1994) 59-65 MUON LEVEL CROSSING ALUMINIUM 59 RESONANCE IN S.F.J. C O X 1, G.H. E A T O N 1, D.S. SIVIA 1, M.S. W A T T 1, D.W. C O O K E 2, M. L E O N 2, M.A. P A C I O T T I ~, J.L. S M I T H 2, W.L. H U L T S ~, T.L. E S T L E 3, B. H I T T I 3, C. B O E K E M A 4, J L A M 4, A. M O R R O B E L - S O S A S, R.L. L I C H T I ~, J. O O S T E N S T, C. S C H W A B s, E.A. DAVIS 9, A. S I N G H 9, N. A Y R E S DE C A M P O S lo, j. A Y R E S D E C A M P O S 1~ P.J. M E N D E S 1~ J.M. GIL 1~ K. C H O W 11, R. D U V A R N E Y 12 and P.F. M E I E R 13, 1ISIS, Rutherford Appleton Laboratory, Oxfordshire, UK,~ Los Alamos National Laboratory, Los Alamos, NM 87545, USA,aRice University, Houston, T X 77251, USA,4San Jose State University, San Jose, CA 95192, USA,SCalifornia Polytechnic State University, San Luis Obispo, CA 95192, USA,6Texas Tech University, Lubbock, TX 79409, USA,TLindsey Wilson College, Columbia, K Y 42728, USA, s CRN Universitd Louis Pasteur, Strasbourg, France, 9Department of Physics, University of Leicester, LE1 7RH, I/If, l~Departamcnto de Fisica da Universidade, 3000 Coimbra, Portugal, 11TRIUMF, Vancouver BC, V6T 2A3, Canada, 12Emory University, Atlanta, GA 30322, USA, laPhysik-Institut der Universitfft, 8057 Z~rich, Switzerland). Cross relaxation between implanted positive muons and ~TAI nuclei in A1 metal, lightly doped with Cu to impede the muon diffusion, shows weak resonances at 2.3 and 4.0 roT. Assignment of these to polarization transfer via the 89~ ~ and ~ ,--, transitions of the (J = 5/2) spins leads to a quadrupole coupling constant e2qQ/h -1.8(1)Mttz, i.e. an electric field gradient on A1 nuclei immediately adjacent to the muon site q = 0.048(3) a.u., with a small departure from axial symmetry. D e t e c t i o n of the q u a d r u p o l a r level crossing resonances ( Q L C R ) in alum i n i u m m e t a l is reported, providing a direct m e a s u r e of the electric field gradient created at 2rA1 nuclei by interstitial positive muons. Surprisingly, this appears to be only the second metallic s y s t e m to be studied in this way, following the m u c h acclaimed publication of the level crossing proposal [1] and its successful d e m o n s t r a t i o n in copper [2,3]. For the J = 3/2 nuclei of Cu, t h e level crossing s p e c t r u m shows a single m a i n resonance. T h e weak o r i e n t a t i o n - d e p e n d e n t satellite resonances which should also a p p e a r [4, 5] 9 J.C. Baltzer AG, Science Publishers 60 S.F.J. C o x et al. / Muon level crossing resonance in AI have not been resolved in practice - no doubt they are smeared by the contribution of the two Cu isotopes as well as some broadening due to muon motion. For A1, there is only one abundant quadrupolar isotope (2rA1, 100%), with J = 5/2. Two main resonances are expected in such a system, as illustrated in Figure 1. In common with Cu, A1 has a face-centred cubic lattice. Unlike the behaviour in Cu, however, there is no temperature r4gime for A1 where interstitial muons are quasi-static: muon diffusion is remarkably rapid at all temperatures. This motion would efface the level crossing resonances in pure aluminium, since their detection relies on a reasonably coherent polarization transfer between the muon and neighbouring metal nuclei. Muon diffusion breaks the coherence at each jump, broadening the resonances beyond detection for high jump rates. For the purposes of these experiments our A1 samples are therefore doped with Cu, which is known to impede the diffusion [6, 7]. According to simulations due to Dalmas de R4otier et al [8], the resonances are expected to appear as deviations from the low-field repolarisation curve representing non-resonant cross relaxation. Such a feature, centred near 4 roT, was first observed in high statistics data taken at L A M P F using the newly commissioned integral-counting spectrometer [9, 10]. The spectrum recorded at 20 K is reproduced in Figure 2, where this feature is enhanced by subtraction of a Lorentzian function fitted to the repolarization behaviour at low field. This is a phenomenological fit, in that analytical expressions for the low-field (non-resonant) cross relaxation functions P(t), and their time-average r21. f P(t).e-t/r".dt as measured by the integral counting technique, are impossible to derive. Numerical simulations demonstrate that the Lozentzian form is remarkably accurate, however [11]. The sample for this experiment was polycrystalline All_~Cu~ with z = 0.1 atomic percent, as cast. Further experiments were performed at ISIS on this sample and one with x = 0.45% at a lower temperature close to 10 K. The level crossing resonances are stronger for the more heavily doped sample, indicating a longer effective residence time for the muon at a given interstitial site. The spect r u m is shown in Figure 3. A resonance at 4.1(2)mT is confirmed by the ISIS time-resolved data and its expected partner identified, centred on 2.3(2)mT: roughly stated, the two lines correspond to polarisation transfer frorn the implanted muons via the 3 s and 1 a transitions of the 27A1nuclei, respectively, as illustrated in Figure 1. Use of delayed time windows in the analysis of the ISIS data demonstrates the slow development of the polarization transfer and the expected signal enhancement [8, 12]. A very weak feature near 8roT may 61 S.F.J. Cox et al. / M u o n level crossing resonance in A I Energy (arb.units) ~ 5/2 hi~l ~ 3 ] / 2 h~ 12 ~, B j = 5/2 i = 1/2 M a g . field (arb. u n i t s ) Fig. 1. Energy level scheme for a muon (I = 1/2) in dipolar interaction with a single ~TA1 nucleus (J = 5/2). This is drawn for the case of axial symmetry of the quadrupole interaction on Al, and with the vector joining Al and/~+ (assumed to be the symmetry axis) in line with the applied magnetic field. Resonant polarization transfer occurs at the avoided crossings, corresponding to cross relaxation via the individual spin transitions depicted in the insert. (The spin states become mixed, and other crossings weakly avoided, for arbitrary orientation.) 62 S.F.J. Cox et aL / Muon level crossing resonance in AI ~J V._/ QJ i -15 -I0 I -5 I i 0 5 I 10 I 15 Mag. field (roT) Fig. 2. QLCR spectrum of interstitial #+ in AI(Cu: 1000ppm) at 20K, recorded at LAMPF. The integral positron count in forward detectors was normalised to the proton beam current. Here the residue of this ratio is plotted after subtraction of a Lorentzian function fitted to the low-field data (deleted). Note the symmetric field sweep. indicate that some muons are trapped immediately adjacent to Cu d o p a n t atoms. The positions of the resonances (Hres "~ 27ru/(Tu - "YAt)) imply zero field splittings on 2TA1 (Figure 1, insert) of ul -~ 285(25)kHz and v2 510(25) kHz. Pending the the fitting of a simulated polycrystalline s p e c t r u m to extract more precise values, and ignoring the small anisotropy parameter, these may be written [13] u2 = 2ul = ~e2qQ/h, giving a preliminary value for the quadrupole coupling constant of e2qQ/h = 1.80(10)MHz. This m a y be compared with values deduced from the field dependence of the transverse-field #SR linewidths in earlier experiments by H a r t m a n n et al. using different dopants [14]: for instance, for tetrahedral-site trapping, the "electric frequency" reported by these authors (0a~/27r = e2qQ/h.4J(2J- 1) = 56(4)kHz in AI(Mn, 1300ppm) at 15K) corresponds to e2qQ/h = 2.2(2) MHz. Interestingly, their value for octahedral-site trapping (w~/27r = 41(7)kHz; i.e. e2qQ/h = 1.64(28)MHz in AI(Mn, 50 ppm) at 40 inK) appears closer to our present result. This may reflect an anticipated influence of the d o p a n t in favouring one or other site [15]. Our resulting value for the electric field gradient, q = 0.048(3)atomic 63 S.F.J. Cox et al. I Muon level crossing resonance in A I (a) Integral (b) 0.3-16/zs (c) 4-16#s o (d) 8-16/zs o AP ] 0 t t t I [ 5 I .t , ) = 10% . .I 10 Mag. field (mT) Fig. 3. Muon repolarization and QLCR in polycrystalline AI(Cu: 4500 ppm) at 10K, recorded at ISIS. The forward-backward asymmetry data is analysed to give r; 1. f P(t).e -qT. .dr as though for integral counting in (a) and (t2 -tl)-a.ftt~ P(t).dt for various delayed time windows in (b-d). The vertical scales are offset for clarity. units, induced at A1 nuclei adjacent to a muon, could in principle be used to test theoretical calculations of the electronic screening and elastic interaction of this defect, which models the screened proton state of interstitial hydrogen. The precise ratio of the quadrupole splittings is described by an anisotropy parameter, given by u2/2ua -"~ (1 - ~'13'5-2"~)[13], for which we obtain a preliminary value r/2 ~ 0.08(7). Some small departure from axial symmetry is indeed expected if the muons trap at strain fields in the vicinity of the copper impurity atoms (present calculations of the trapping potential do not, however, take account of this pre-existent distortion) [15, 16]. 64 S.F.J. Cox et al. / Muon level crossing resonance in AI T h e effect of t e m p e r a t u r e in d e t e r m i n i n g the distance of a p p r o a c h to the s u b s t i t u t i o n a l a t o m m a y be i m p o r t a n t here [17]. A survey of Q L C R s p e c t r a with different d o p a n t s and at different t e m p e r a t u r e s would be valuable in clarifying some of these issues. Acknowledgments This work benefits by s u p p o r t f r o m the Science and Engineering Research Council, the C o m m i s s i o n of the E u r o p e a n C o m m u n i t i e s Large I n s t a l l a t i o n s Plan, t h e R o b e r t A. Welch F o u n d a t i o n (grant D-1053), t h e National Science F o u n d a t i o n (grant DMR-8917639) and a N A T O Collaborative Research Grant. References [1] A. Abragam, Compt. Rend. Acad. Sci. (Paris) 299 (1984) 95. [2] S.R. Kreitzman, J.H. Brewer, D.R. Harshman, R. Keitel, D.L. Williams, K.M. Crowe and E.J. Ansaldo, Phys. Rev. Lett. 56 (1986) 181. [3] G. Luke, J.H. Brewer, S.R. Kreitzman, D.R. Noakes, M. Celio, R. Kadono and E.J. Ansaldo, Proc. pSR'gO: Hyp. Int. 65 (1990) 721; Phys. Rev. B 56 (1991) 3284. [4] S.F.J. Cox, Z .Fiir Naturforschung 47a (1992) 371. [5] T.L. Estle (unpublished simulations). [6] B. Hitti, W.J. Kossler, J.R. Kempton, C.E. Stronach and W.F. Lankford, Proc. ~SR'86: Hyp. Int. 31 (1986) 211. [7] J.H. Brewer, E. Koster, A. Schenck, H. Schilling and D.L. Williams, Proc. #SR'80: Hyp. Int. 8 (1981) 671. [8] P. Dalmas de R~otier, A. Yaouanc and J.P. Boucher, Proc. I~SR '90: Hyp. Int. 65 (1990) 1121; P Dalmas de l~otier, thesis (INP Grenoble, 1990). [9] D.W. Cooke, M. Leon, M.A. Paciotti, C. Pillai, B.L. Bennett, O. Rivera, J.L. Smith, W.L. Hults, S.F.J. Cox, T.L. Estle, B. Hitti, C. Boekema, J. Lam, R.L. Lichti, A. Morrobel-Sosa, E.A. Davis, A. Singh, P.F. Meier and J. Oostens, Muon level crossing resonance results from LAMPF, Proc. LEMS'93 (Low Energy Muon Science Workshop, Santa Fe, April 4-8, 1993). [10] M.A. Paciotti, D.W. Cooke, M. Leon, B.L. Bennett, B. Hitti, T.L. Estle, S.F.J. Cox, R.L. Lichti, T.R. Adams, C.D. Lamp, A. Morrobel-Sosa, O. Richter, C. Boekema, J. Lam, S. Alves, J. Oostens and E.A. Davis, Development of a I~SR Facility at LAMPF, these proceedings. [11] M. Leon (unpublished simulations). [12] M. Leon, Phys. Rev. B46 (1992) 6603. [13] A. Abragam, Principles of Nuclear Magnetism (OUP Oxford,1961). [14] O. Hartmann, E. Karlsson, B. Lindgren, E. Ws D. Richter, R. Hempelmann and J.M. Welter, Proc. I~SR'83: Hyp. Int. 17-19 (1984) 197. [15] S. Estreicher and P.F. Meier, Proc #SR'83: Hyp. Int. 17 (1984) 241. S.F.J. Cox et al. / Muon level crossing resonance in Al 65 [16] B. Lindgren and E. W~ckelg~rd, Proc. #SR'86: Hyp. Int. 31 (1986) 99. [17] N.V. Prokof'ev, Inhomogeneous quantum diffusion of muons in solids, these proceedings.