Static Longitudinal Field Relaxation

Relaxonomy --> here

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When the muon spin polarization <math>\vec{P}</math> is initially in the same direction as the applied magnetic field <math>\vec{B}</math>, we call that the <math>z</math> direction. This is called the longitudinal field (LF) geometry. The relaxation of <math>\vec{P}</math> is then usually described by

<math> g_{zz}(t) \; \equiv \; \langle P_z(0) \, P_z(t) \rangle </math>

where the lower case <math>g</math> is used (instead of the more general <math>G</math>) to designate a static relaxation function, just like in ZF. (Dynamic cases will be treated later.)

In the limit where <math>B \gg </math> any random local magnetic fields (RLMF), this formulation is valid. (At last, a "low-bogosity" case!) However, in modest applied fields (B <math> \sim </math> RLMF) it is subject to the same caveats as the ZF case, which see.

The "decoupling" effect of LF was observed in the same experiment where ZF "Kubo-Toyabe relaxation" was first observed:

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<math>g^{\rm GKT}_{zz}(t)</math> in MnSi at 285 K for LF = 0, 10 and 30 Oe.