Jess H. Brewer

Canadian Inst. for Advanced Research
and Dept. of Physics & Astronomy,
Univ. of British Columbia, Vancouver, BC, Canada V6T 1Z1

This page is under construction at     /~jess/musr/
First let's talk about the acronym: when these phenomena were first discovered in 1985-1986 at TRIUMF, the term ``level-crossing resonance'' (LCR) was used to describe the situation where the muon Zeeman splitting matches that of another spin system which can thus exchange polarization with the muon ensemble in a sort of ``flip-flop'' mutual transition.

Shortly thereafter, similar experiments were begun at PSI, where the proponents pointed out quite correctly that the levels never actually cross; this being an intrinsically quantum mechanical phenomenon, the energy eigenstates of the combined system avoid crossing, so that the proper terminology is ``avoided level crossing'' (ALC) [resonance].

In an effort to keep everyone relatively happy, I have adopted the acronym µALCR, the meaning of which I trust is obvious now to all concerned.

  1.   Nuclear Quadrupolar µALCR:
  2. The first such phenomenon observed in µSR was the resonant relaxation of muons in copper at the longitudinal field where the muon Zeeman splitting matches the splitting of the Cu nuclear quadrupole moment in the electric field gradient (EFG) due to the interstitial muon. This possibility was predicted by Anatole Abragam in 1984. Almost the same thing was suggested a few years earlier by Tom McMullen and Eugene Zaremba, but we misunderstood and looked for a resonance in transverse field.     ``Doh!''

  3.   Paramagnetic µALCR:
  4. In the case of a paramagnetic system, the unpaired electron couples to both the muon and a nearby nucleus via their respective hyperfine (HF) interactions, thus allowing the muon and nuclear spins to ``flip-flop'' much more strongly than through mere nuclear dipolar couplings. This picture may be a little oversimplified. . . .
    This was first observed in the ``muonated radical'' formed by addition of muonium (Mu) to a double C=C bond in the tetramethylethylene molecule. The time dependence of the muon polarization on and off a resonant LF was also observed at that time.
    Similar behaviour was seen in C6F6 µ., the muonated radical formed by addition of Mu to a C=C bond in hexafluorobenzene.

  5.   Applications of µALCR:
  6. Quadrupolar µALCR is often used to determine the muon site in diamagnetic solids or to confirm the formation of a diamagnetic molecule incorporating the muon, as in this example. (There are prettier cases, but I don't have the figures for them handy.)
    Paramagnetic µALCR has found many applications to the study of radicals in chemistry, many of which are difficult or impossible to detect by other means. Since the difference between the ``muonated'' radical and the analogous ``hydrogenated'' version (formed by addition of an H atom to a double bond) is mainly in the configuration of a single bond (due to the lighter mass of the muon), much can be learned about the behaviour and structure of such molecules using µALCR.
    Paramagnetic µALCR is also an important tool for determining the local electronic structure of the Mu* centre in various semiconductors, where the HF couplings to various nearby nuclei (and the orientation dependence of the µALCR spectrum) reveal minute details of the muon's location and environment. The examples shown are GaP and GaAs, the first materials studied by this method. Such measurements have since been extended to 29Si-enriched silicon and 13C-enriched diamond and well as many other systems.
    I include this pretty spectrum from copper chloride just for aesthetics.

      Jess H. Brewer
      Last modified: Fri Aug 14 17:08:46 PDT 1998