A PURE QUANTUM-MECHANICAL THEORY OF PARITY EFFECT IN TUNNELING AND EVOLUTION OF SPINS

In recent years, the spin parity effect in magnetic macroscopic quantu m tunneling has attracted extensive attention. Using the spin coherent -state path-integral method it is shown that if the Hamiltonian (H) ov er cap of a single-spin system has M-fold rotational symmetry around z -axis, the tunneling amplitude (-S\e(-i (H) over cap t)\S) vanishes wh en S, the quantum number of spin, is not an integer multiple of M/2, w here \ m) (m = -S, -S + 1,..., S) are the eigenstates of (S) over cap( z). Not only is a pure quantum mechanical approach adopted to the abov e result, but also is extended to more general cases where the quantum system consists of N spins, the quantum numbers of which can take any values, including the single-spin system, ferromagnetic particle and antiferromagnetic particle as particular instances, and where the stat es involved are not limited re the extreme ones. The extended spin par ity effect is that if the Hamiltonian (H) over cap of the system of N spins also has the above symmetry, then (m'(N)...m'(2)m'(1)\e(-i (H) o ver cap t)\m(1)m(2)...m(N)) vanishes when Sigma(i=1)(n)(m(i)-m'(i)) is not an integer multiple of M, where \m(1)m(2)...m(N)) = Pi(a=1)(N)\m( a)] and \ m(a))] are the eigenstates of (S) over cap(a)(z). In additio n, it is argued that for large spin the above result, the so-called sp in parity effect, does not mean the quenching of spin tunneling from t he direction of +/-z to that of -/+z.