Muon Spin Rotation in Ferromagnetic Hosts as a Probe of Electron-Sourced Torsion

Muon spin rotation implants a perfectly polarised positive muon into a material and watches its spin precess in the local fields until the muon decays — a probe that begins life with unit polarisation inside the source matter itself. Placing that probe in a ferromagnetic host makes it, in principle, a torsion sensor sitting at the exact location where electron-sourced Einstein-Cartan torsion exists. This paper computes what it sees. In magnetised iron, with a polarised electron density of 1.9e29 per cubic metre, the torsion at the muon site is 6.24e-40 per metre; the muon's spin splitting is 1.23e-46 eV, an extra precession of 1.87e-31 radians per second, accumulating a phase of 4.11e-37 radians over the 2.2 microsecond muon lifetime. Expressed as an equivalent magnetic field the torsion contributes 4.39e-40 tesla, against internal fields of tenths of a tesla that the technique measures routinely. A fractional frequency resolution of 1e-06 on a 4e07 Hz internal precession bounds any multiplier of the torsion coupling at 1.34e+33 — the weakest fence in this programme's contact family, recorded here because the muon is the one probe whose polarisation, lifetime, and implantation are all ideal in every respect except the one that matters, which is the size of the coupling. Computed from stated assumptions, not measured.