Thermal spike in muon implantation

R. C. Vilão, H. V. Alberto, J. M. Gil, and A. Weidinger

Phys. Rev. B 99, 195206 – Published 29 May 2019

Abstract

In muon spin rotation experiments, the diamagnetic fraction observed at low temperatures is a consequence of the muon interaction with the lattice during the incorporation process and depends on the properties of the material. An increase in the diamagnetic fraction with decreasing temperature is observed in some cases, which we attribute to a thermal spike at the end of the muon trajectory. The thermal spike is due to energy liberated not only during the muon stopping process but also as a consequence of the stress release when the electron bound to a muon in an unrelaxed configuration jumps to a neighboring lattice site. The magnitude and time extension of this effect are more significant for highly disturbed lattices which exhibit very low thermal conductivities at low temperatures. A phenomenological description of some selected examples is presented, together with a discussion of heat transport, using existing models for the thermal spike.

Received 31 January 2019
Revised 4 April 2019

DOI:https://doi.org/10.1103/PhysRevB.99.195206

Physics Subject Headings (PhySH)

Impurities Thermal conductivity

Muonium Semiconductors

Ion implantation Muon spin resonance

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

R. C. Vilão^1,*, H. V. Alberto¹, J. M. Gil¹, and A. Weidinger²

¹CFisUC, Department of Physics, University of Coimbra, P-3004-516 Coimbra, Portugal
²Helmholtz-Zentrum Berlin für Materialien und Energie, Institute for Nanospectroscopy, D-12489 Berlin, Germany

^*ruivilao@uc.pt

Comments & Replies

Comment on “Role of the transition state in muon implantation” and “Thermal spike in muon implantation”

Jess H. Brewer, Vyacheslav G. Storchak, Gerald D. Morris, and Dmitry Eshchenko

Phys. Rev. B 101, 077201 (2020)

Reply to “Comment on ‘Role of the transition state in muon implantation’ and ‘Thermal spike in muon implantation”’

R. C. Vilão, H. V. Alberto, R. B. L. Vieira, J. M. Gil, and A. Weidinger

Phys. Rev. B 101, 077202 (2020)

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Original Article

Role of the transition state in muon implantation

R. C. Vilão, R. B. L. Vieira, H. V. Alberto, J. M. Gil, and A. Weidinger

Phys. Rev. B 96, 195205 (2017)

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Vol. 99, Iss. 19 — 15 May 2019

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Images

Figure 1
Temperature dependence of the diamagnetic fraction of ${Lu}_{2} O_{3}$ at a transverse field of $B = 10$ mT (data from Ref. [19]). The black line fit was obtained using a two-component Boltzmann recovery function [19]. The red line is a fit with an effective thermal spike temperature (see text).
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Figure 2
Temperature dependence of the diamagnetic fraction $f_{dia}$ of CZTS (data from Ref. [17]). The designation film at 14 keV refers to measurements in which the muons stop in a CZTS film, with an implantation energy of 14 keV, whereas the junction at 22 keV refers to measurements in a CdS/CZTS junction where a muon implantation energy of 22 keV forces the muon to stop in CZTS, near the interface with CdS. The black curves describe the increase in the diamagnetic fraction above 150 K as a thermally activated process. The red line is a fit with an effective spike temperature (see text) for the junction sample.
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Figure 3
Temperature dependence of the asymmetry in a longitudinal field experiment on ${Si}_{0.09} {Ge}_{0.91}$ . Slow, moderate, and fast refer to different relaxation rates. Total asymmetry, as shown, is calculated by summing the individual components. The low-temperature part looks like a mirror image of the high-temperature part with a compressed temperature scale. The dashed orange line was added by us and indicates the approximate inversion point. Reprinted from Ref. [22], with permission from Elsevier.
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Figure 4
Simulation of the total asymmetry in the ${Si}_{0.09} {Ge}_{0.91}$ experiment of Ref. [22] (Fig. 3). Top: The effective temperature at the muon site is a sum of the lattice temperature $T$ and a local, temperaturelike effect $T_{spike}$ : $T_{eff} = T_{spike} + T$ . The spike temperature is given by Eq. (1) with the parameters shown in the legend. Bottom: Total asymmetry obtained from Fig. 3. The red line is a simulation of the asymmetry using a total fraction as described in Eq. (2) with the effective temperature $T_{eff}$ shown in the top frame. The corresponding parameters describing the thermal recovery above 100 K are shown in the legend.
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Figure 5
Suggested schematic potential profile for muonium in the unrelaxed lattice. The energy associated with the compact atomlike configuration around $μ^{+}$ is higher than the energy of a configuration, which we named a transition state, where the electron is some distance away from the muon (transition state). Note that the transition state energy minima exist in all three spatial directions and also at larger distances, but the nearest positions are favored by the Coulomb attraction and correspond to the formation of a weakly bound state.
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