CriticalPeakRelaxationRate

Description

The Critical Peak Relexation Rate is defined as:

\[y = \frac{B_1}{(|x - T_c|)^a} + B_1\Theta(x < T_c) + B_2\Theta(x >= T_c)\]

where: - \(S_c\) - Scaling - \(T_c\) - Critical temperature - \(a\) - Critical exponent - \(B_1\) - is a non-critical background when \(x < T_c\) - \(B_2\) - is a non-critical background when \(x >= T_c\)

When fitting users should set \(T_c\) as the temperature at which the peak occurs. Users are also asked to supply two values for \(B_g\). The first should be the value of y when x is at it’s minimum. The second should be the value of y when x is at its maximum, minus the first background value.

Examples

An example of when this might be used is for examining the Chiral-like critical behaviour in antiferromagnet Cobalt Glycerolate [1] or in muon spin relaxation studies of critical fluctuations and diffusive spin dynamics in molecular magnets [2].

Attributes (non-fitting parameters)

Name	Type	Default	Description
Delta

Properties (fitting parameters)

Name	Default	Description
Scaling	1.0	coefficient for scaling
CriticalTemp	0.01	coefficient for critical temperature
Exponent	1.0	coefficient for critical exponent
Background1	0.0	coefficient for non-critical background when x < Critical Temperature
Background2	0.0	coefficient for non-critical background when x > Critical Temperature

References

[1]

Pratt, F.L, Baker, P.J., Blundell, S.J., Lancaster, T., Green, M.A., and Kurmoo, M. (2007). Chiral-Like Critical Behaviour in the Antiferromagnet Cobalt Glycerolate. Phys. Rev. Lett., Vol 99 Issue 1, 017202 doi: 10.1103/PhysRevLett.99.017202.

[2]

Pratt, F. et al (2009) Muon spin relaxation studies of critical fluctuations and diffusive spin dynamics in molecular magnets. Physica B: Condensed Matter, Volume 404 Issues 5–7, pp585-589 doi: 10.1016/j.physb.2008.11.123.

Categories: FitFunctions | Muon\MuonModelling\Magnetism

Source

C++ header: CriticalPeakRelaxationRate.h

C++ source: CriticalPeakRelaxationRate.cpp