On zero-field anisotropic static Kubo-Toyabe relaxation functions |
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Authors: | R E Turner |
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Institution: | (1) TRIUMF, 4004 Wesbrook Mall, V6T 2A3 British Columbia, Vancouver, Canada |
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Abstract: | For muons which have thermalized in the allowed stopping sites of a given crystal, zero-field static Kubo-Toyabe spin dynamics
is expressed in terms of the crystal frame spherical harmonic coefficients of the local classical random magnetic field distributions
associated with each stopping site. The resulting muon spin polarization involves nine observable relaxation functions which
are the counter frame spherical tensor expansion coefficients of the second-rank dynamic motion tensor. These relaxation functions
can be measured simultaneously using the skewed field technique for the same experimental conditions, that is, with a single
apparatus and with a single crystal-counter frame orientation. The local field distributions of, in general, arbitrary symmetry
are classical approximations to the magnetic field interactions between the spin of the muon and the spins of the nuclei associated
with each site at which the muon has stopped. They are characterized by equating their moments with the quantal moments generated
by the quantal magnetic fields. The observable consequences of the anisotropic second-order moments associated with the planar
sites of hexagonal crystals are used as an illustration. |
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Keywords: | |
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