Static Longitudinal Field Relaxation

Relaxonomy --> here

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

[math]\displaystyle{ g_{zz}(t) \; \equiv \; \langle P_z(0) \, P_z(t) \rangle }[/math]

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

In the limit where [math]\displaystyle{ 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]\displaystyle{ \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:

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