Stern--Gerlach Spin Sorting in Relativistic Magnetic Reconnection

We introduce a Stern--Gerlach (SG) spin-kinetic control parameter for magnetic reconnection. The fully projected branch parameter, $\Xi_0=<Z>/r_L$ compares the SG cross-sheet displacement accumulated during a diffusion-region transit with the relativistic Larmor radius. For an ensemble or partially participating population the relevant effective parameter is $\Xi_{\rm Eff}=P_{eff}\Xi _0$, where $P_{eff}$ represents the surviving branch weight or effective spin/moment projection. Evaluating $\Xi_{\rm Eff}$ across representative space and astrophysical environments reveals a robust hierarchy: SG transport is negligible in the magnetotail, solar corona, active galactic nuclei (AGN)/blazar jets, and pulsar-wind nebulae, but becomes transitional to strong in magnetar current sheets and extreme near magnetar surfaces. We further show, using electron--positron particle-in-cell simulations, that the SG force sorts particles by magnetic-moment projection into opposite sides of a Harris current sheet without measurably changing the global reconnection rate in the tested regime. This identifies magnetars as the clearest natural target for strong-field spin-kinetic reconnection ($\Xi_{\rm eff}\gg 1$) near the surface; transitional in the outer magnetosphere), while SG transport is safely negligible ($\Xi_{\rm eff}\ll 1$) in all heliophysical and jet environments considered, and provides a falsifiable framework for assessing where SG physics is relevant.