Keren

Description

Keren’s generalization of the Abragam relaxation function to a longitudinal field, for fitting the time-dependent muon polarization.

The function is derived in *Phys Rev B, vol. 50, 14, 10039-42 (1994)* and is given by

P_z(t) = A\exp\left[-\Gamma(t)t\right]

where the relaxation rate \Gamma(t) is

\Gamma(t)t = 2\Delta^2 \frac{\left\{\left(\omega_L^2 + \nu^2\right)\nu t + \left(\omega_L^2-\nu^2\right)\left(1-e^{-\nu t}\cos(\omega_L t)\right) - 2\nu\omega_L e^{-\nu t}\sin(\omega_L t)\right\}}{\left(\omega_L^2 + \nu^2\right)^2}

A = P_z(0) is the polarization at time zero, \nu is the fluctuation rate (inverse correlation time), \Delta is the distribution width of the local fields and \omega_L is the Larmor frequency (longitudinal field times muon gyromagnetic ratio).

Properties (fitting parameters)

Name Default Description
A 1.0 Polarization at time zero
Delta 0.2 Distribution width of local fields (MHz)
Field 50.0 Longitudinal field (Gauss)
Fluct 0.2 Hopping rate (inverse correlation time, MHz)

Categories: FitFunctions | Muon

Source

C++ source: Keren.cpp

C++ header: Keren.h