Permanent magnetic moment in mesoscopic metals with spin–orbit interaction

We argue that at zero temperature an isolated metal particle (or an AB ring) with spin–orbit interaction and odd number of electrons will have a permanent magnetic moment, even in zero magnetic field (flux). In a zero-field-cooled state both the direction and the magnitude of the moment varies from particle to particle and averages to zero. In a field-cooled state it averages to ∼μB(kFℓ)1/2. We argue that the permanent moment is due to an uncompensated electron in the last occupied (Fermi) level. We introduce an effective single-electron Hamiltonian which accounts for spin–orbit coupling.