Spin flips in cyclotron emission by an electron

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The spin dependence of cyclotron emission is treated using the non-relativistic limit of the Dirac equation; the Schrodinger–Pauli theory is inadequate because of the importance of spin–orbit coupling, which is an intrinsically relativistic effect. Only the choice of the magnetic moment as the spin operator is physically acceptable; all other spin operators precess at a rate comparable with or in excess of cyclotron transition rates. The spin-flip (s = 1 → −1) transition rate is smaller than the non-spin-flip of the order B/Bc (Bc = 4.4 × 109 T), and the reverse spin-flip (s = −1 → +1) transition rate is smaller by a further factor of order (B/Bc)2, implying that it is strongly forbidden. It is shown that there is a preference for electrons with spin s = 1 initially in a high Landau level, n 1, to relax to the ground state, s = −1, n = 0, by stepwise jumps to the lowest Landau level for s = 1 and then making the spin-flip transition to s = −1, rather than making the spin-flip transition from a higher Landau level, and that this preference increases with decreasing B/Bc.