Observation of a molecular muonium polaron and its application to probing magnetic and electronic states

M. Rogers, T. Prokscha, G. Teobaldi, Leandro Liborio, S. Sturniolo, E. Poli, D. Jochym, R. Stewart, M. Flokstra, S. Lee, M. Ali, B. J. Hickey, T. Moorsom, and O. Cespedes

Phys. Rev. B 104, 064429 – Published 17 August 2021

Abstract

Muonium is a combination of first- and second-generation matter formed by the electrostatic interaction between an electron and an antimuon ( $μ^{+}$ ). Although a well-known physical system, their ability to form collective excitations in molecules had not been observed. Here, we give evidence for the detection of a muonium state that propagates in a molecular semiconductor lattice via thermally activated dynamics: a muonium polaron. By measuring the temperature dependence of the depolarization of the muonium state in $C_{60}$ , we observe a thermal narrowing of the hyperfine distribution that we attribute to the dynamics of the muonium between molecular sites. As a result of the time scale for muonium decay, the energies involved, charge and spin selectivity, this quasiparticle is a widely applicable experimental tool. It is an excellent probe of emerging electronic, dynamic, and magnetic states at interfaces and in low dimensional systems, where direct spatial probing is an experimental challenge owing to the buried interface, nanoscale elements providing the functionality localization and small magnitude of the effects.

Received 30 January 2021
Revised 3 June 2021
Accepted 21 July 2021

DOI:https://doi.org/10.1103/PhysRevB.104.064429

Physics Subject Headings (PhySH)

Magnetism Polarons

Functional materials Multilayer thin films Muonium

Muon spin resonance

Condensed Matter, Materials & Applied PhysicsAccelerators & BeamsAtomic, Molecular & Optical

Authors & Affiliations

M. Rogers ^1,*, T. Prokscha ², G. Teobaldi ^3,4,5, Leandro Liborio ³, S. Sturniolo ³, E. Poli ³, D. Jochym ³, R. Stewart^6,†, M. Flokstra⁶, S. Lee⁶, M. Ali¹, B. J. Hickey¹, T. Moorsom^1,‡, and O. Cespedes^1,§

¹School of Physics and Astronomy, University of Leeds, Leeds LS2 9JT, United Kingdom
²Laboratory for Muon Spin Spectroscopy, Paul Scherrer Institute, 5232 Villigen, Switzerland
³Scientific Computing Department, Science & Technology Facilities Council, Rutherford Appleton Laboratory, Didcot OX11 0QX. United Kingdom
⁴Stephenson Institute for Renewable Energy, Department of Chemistry, University of Liverpool, Liverpool L69 3BX, United Kingdom
⁵School of Chemistry, University of Southampton, Highfield, Southampton SO17 1BJ, United Kingdom
⁶School of Physics and Astronomy, SUPA, University of St Andrews, St Andrews KY16 9SS, United Kingdom

^*M.D.Rogers@leeds.ac.uk
^†Current address: Laboratory for Mesoscopic Systems, Department of Materials, ETH Zurich, 8093 Zurich, Switzerland and Laboratory for Multiscale Materials Experiments, Paul Scherrer Institute, 5232 Villigen PSI, Switzerland.
^‡Current address: Kelvin Building; University of Glasgow, Glasgow, G12 8QQ, United Kingdom.
^§O.Cespedes@leeds.ac.uk

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Vol. 104, Iss. 6 — 1 August 2021

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Images

Figure 1
(a) Schematic of the $END O_{f}$ formation via ionization, charge hopping, and trapping then coupled with molecular rotations. Its oscillation frequency is sensitive to, e.g., the electron transfer and emergent magnetism at interfaces. (b) Fourier transform of the time domain asymmetry data at ZF for a 210-nm- thick amorphous $C_{60}$ film on a thermally oxidized Si substrate. The EXO muonium at 1.2, 7.4, and 8.6 MHz is observable at 40 K. At 300 K, only the $END O_{f}$ muonium is observed. Inset: (∼keV) muon-beam generated free carriers remain delocalized in the conduction band (CB) of the $C_{60}$ film, leaving the e-acceptor state of the $μ^{+}$ empty. (c) The temperature dependence of the asymmetry attributed to the low-frequency $END O_{f}$ together with the calculated spin-density using the PBE exchange-correlation (XC) functional (yellow: $10^{- 6} μ_{B} Å^{- 3}$ ). A semiempirical model has been used to fit the temperature dependence leading to an activation energy (equivalent to $- E_{POL}$ ) for $END O_{f}$ of $E_{A} = 300 \pm 100 meV$ [30]. (d) Temperature dependence of the EXO signal fraction, also with the calculated PBE spin-density (yellow: $10^{- 6} μ_{B} Å^{- 3}$ ). The EXO state becomes more apparent as we cool the system through the glass transition and the molecular rotations are frozen.
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Figure 2
Muonium dynamics and activation energies. (a) Time evolution of the Mu- and C- rotational dynamics in $END O_{f}$ , as calculated by the angles between the instantaneous Mu (closest C-atom) radial distance from the $C_{60}$ ’s center of mass and the $x (θ_{x}), y (θ_{y})$ and $z (θ_{z})$ axes. The C-trace reports the rotational evolution of the C-atom closest (∼3 Å) to the Mu at the start of the BOMD trajectory. (b) As in a, but for the EXO muonium state. The C-atom closest to the Mu does not change during the whole BOMD trajectory. Note that for the $END O_{f}$ state the dynamics of molecule and muonium are decoupled, whereas in the EXO state the muonium follows the molecular rotation. (c) Ab initio path integral molecular dynamics (AI-PIMD) distribution of the muon particle in the $END O_{f}$ at 50 and 300 K. For each of the 16 beads used in the simulations, 1000 frames (2 fs apart) were extracted from the production run and superimposed in the same image. The initial position of the $C_{60}$ is used to provide a better visualization of the quantum spread of the muonium inside the molecule. C: cyan, Mu: pink. (d) Temperature dependence of the depolarization rate associated with $END O_{f}$ state, showing the two thermal activation regimes above (red line fit) and below (blue) the glass transition $T_{g}$ .
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Figure 3
The magnetic field dependence of the $END O_{f}$ and EXO muonium oscillation frequencies as measured in the crystalline sample. (a) Observed experimental frequencies (circles) vs simulations (color map) for $END O_{f}$ at 250 K. (b) 20 K experiments (circles) and simulations (color map) for the $END O_{f}$ state, modeled with a hyperfine isotropic coupling $A_{iso} = 9.65 MHz$ . (c) Observed experimental frequencies (circles, squares, and triangles) vs simulated intensities (color map) for the EXO state. The dipolar part of the tensor was chosen to match the observations at zero field and the Fermi contact term is in the high limit ( $A_{iso} ≫ 100 MHz$ ). Since the middle peaks become very broad and low at high field, the color map here is logarithmic in order to enhance their visibility. This decay with field is observed experimentally [22].
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Figure 4
ZF-LE-μSR measurements of the Mu@ $C_{60}$ frequency, $υ_{Mu}$ , and depth profile in a thin film heterostructure. (a) The simulated implantation profile for a structure of [Si(Sub)/Ta(3)/Cu(5)/ $C_{60}$ (114)/ Cu(5)/Au(14)], where the thicknesses in brackets are in nm. At the 4 and 18 keV implantation energies, a considerable percentage (57% and 34%, respectively) of muons stop in the metal layers. As the measurement was performed in ZF, these are not expected to contribute to the oscillating signal. (b) The obtained depth dependence of the relative change in the $END O_{f}$ oscillation frequency, $Δ υ_{Mu}$ , for the initial state measurement and following a degauss; lines are a guide for the eye. The corresponding change in the local field, $Δ B_{Local}$ , calculated from the measured calibration curve in the crystalline $C_{60}$ sample is also shown. Inset shows the highly anisotropic spin density (red: $10^{- 6} μ_{B} Å^{- 3}$ ) for the endohedral muonium polaron state with an additional electron $END O_{f}$ (-) calculated using screened-hybrid DFT (HSE06, see Supplemental Material).
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