Volume 109A, number 1,2 PHYSICS LETTERS 6 May 1985 PRECISE MEASUREMENT OF LOW TEMPERATURE DIFFUSION OF POSITIVE MUONS IN Cu: "EVIDENCE FOR THE EFFECT OF MUON-ELECTRON INTERACTION IN METALS R. KADONO, J. IMAZATO, K. NISHIYAMA, K. NAGAMINE, T. YAMAZAKI Meson Science Laboratory and Department of Physics, Faculty of Science, University of Tokyo, Hongo, Bunkyo-ku, Tokyo 113, Japan D. RICHTER and J.-M. WELTER Institut ffir Festk&perforschun~ Kernforschungsanlage, J~lich GmbH, Jf~lich, Fed. Rep. Germany Received 13 September 1984; revised manuscript received 19 February 1985; accepted for publication 20 February 1985 The diffusion rate of positive muons in high purity Cu was measured by means of the zero field muon spin relaxation method for temperatures from 69 mK to 135 K. We found that with decreasing temperature the rate reaches a minimum at around 20 K and increases down to 0.5 K, where it clearly levels off. The origin of the observed temperature dependence is discussed in the light of recently developed theories taking into account the bt+-conduction electron interaction in metals, where the basic coupling constant K is determined to be 0.32. The problem of light particle diffusion in metals has been one of the most interesting subjects in the fundamental physics of condensed matter. Many kinds of materials have been investigated to understand the diffusion and trapping mechanisms for the hydrogen isotopes and positrons. Compared to them, positive muon (/a +) has the following advantages: because of the unique mass (m r "~ mp/9), its diffusion is domi- nated by various types of quantum mechanical effects, e.g., phonon-assisted tunneling, band-like diffusion, etc. Also the/a + diffusion can be studied in a comple- tely dilute concentration. In the last decade many experiments have been done for/a+ in metals with the/aSR method by utiliz- ing the motional narrowing of the transverse/~+ spin relaxation (TF-/aSR) due to the nuclear dipolar field at the interstitial/a +. Although particularly interesting results were obtained for the/a + in Cu at low temper- atures [1,2], their implications were not unique. On the other hand, ZF-/aSR has an important advantage over TF-/aSR [3]: the zero field (ZF) relaxation func- tion Gz(t) has a "recovered" component (~1/3) at later time whose decay is directly given by the dynam- ical correlation time r c of the local field [3]. This feature is quite helpful for the study of/~+ in Cu in the temperature region below 100 K where the hopping rate v (=l/re) of/a+ is expected to be small compared with the static width A of the local field and the TF- /~SR method loses sensitivity to such a small v. In this slow modulation regime(At c > 1) the A can be readily determined independently of r c and thus the ZF-/aSR method is capable of detecting even a change of the/a + site. Recently this ZF method was applied to the study of/l + diffusion in Cu down to 0.5 K and evidence was found for enhanced muon diffusion at lower tempera- ture [4]. In this paper we present the first systematic data on the temperature dependence of v obtained by ZF-/aSR in a wide regime from 69 mK to 135 K. The new features of the present work are: (1) a precise determination of the slow hopping rate v by means of the pulsed/aSR method which enables us to discuss the functional form of the temperature dependence of v; (2) extension of the temperature range down to 69 mK and the measurement of the/a + hopping rate below 0.5 K where the line width in TF-/~SR becomes tem- 61