Static Longitudinal Field Relaxation - Revision history

Jess at 18:24, 17 September 2022

2022-09-17T18:24:41Z

Jess at 18:19, 17 September 2022

2022-09-17T18:19:46Z

Jess at 22:10, 15 September 2022

2022-09-15T22:10:28Z

WikiSysop: Created page with "Relaxonomy --> here ---- When the muon spin polarization $\vec{P}$ is initially in the same direction as the applied magnetic field $\vec{B}$ , we ca..."

2022-08-20T01:20:59Z

Created page with "Relaxonomy --> here ---- 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 ca..."

New page

[[Relaxonomy]] --> here
----

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 described by

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

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

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

@@ Line 20: / Line 20: @@
 |}
 </center>
+It is slightly ironic that the ZF/LF relaxation by nuclear dipole moments predicted by Kubo and Toyabe was first observed in MnSi at 285 K, since at lower temperatures MnSi exhibits a rich magnetic behavior due to the strong paramagnetic moments of the Mn ions.  At room temperature these huge moments fluctuate fast enough to decouple from both the muon and the Mn nuclei, leaving their spins to influence each other directly.

@@ Line 10: / Line 10: @@
 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 (<i>B</i> <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:
+<center>
+[[Image:MnSi-ZLF.png|300px|inline image (click to see full size)]]
+{| width="80%"
+! align="center" |
+<math>g^{\rm GKT}_{zz}(t)</math> in MnSi at 285 K for LF = 0, 10 and 30 Oe.
+|}
+</center>

@@ Line 2: / Line 2: @@
 ----
-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 described by
+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
 <center><math> g_{zz}(t) \; \equiv \; \langle P_z(0) \, P_z(t) \rangle </math></center>
 where the lower case <math>g</math> is used (instead of the more general <math>G</math>)
-to designate a '''''static''''' relaxation function.  ('''''Dynamic''''' cases will be treated later.)
+to designate a '''''static''''' relaxation function, just like in '''ZF'''.  ('''''Dynamic''''' cases will be treated later.)
-just like in '''ZF'''.  In the limit where <math>B</math> >> any random local magnetic fields ('''RLMF'''), this formulation is valid.  (At last, a "low-bogosity" case!)  However, in modest applied fields (<i>B</i> <math> \sim </math> RLMF) it is subject to the same ''caveats'' as the '''ZF''' case, which see.
+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 (<i>B</i> <math> \sim </math> RLMF) it is subject to the same ''caveats'' as the '''ZF''' case, which see.

Static Longitudinal Field Relaxation - Revision history

Jess at 18:24, 17 September 2022

Jess at 18:19, 17 September 2022

Jess at 22:10, 15 September 2022

WikiSysop: Created page with "Relaxonomy --> here ---- When the muon spin polarization \vec{P} is initially in the same direction as the applied magnetic field \vec{B}, we ca..."

WikiSysop: Created page with "Relaxonomy --> here ---- When the muon spin polarization $\vec{P}$ is initially in the same direction as the applied magnetic field $\vec{B}$ , we ca..."