Model exact low-lying states and spin dynamics in ferric wheels: Fe<SUB>6</SUB> to Fe<SUB>12</SUB>

Using an efficient numerical scheme that exploits spatial symmetries and spin parity, we have obtained the exact low-lying eigenstates of exchange Hamiltonians for ferric wheels up to Fe12. The largest calculation involves the Fe12 ring which spans a Hilbert space dimension of about 145&#215;106 for the MS=0 subspace. Our calculated gaps from the singlet ground state to the excited triplet state agree well with the experimentally measured values. Study of the static structure factor shows that the ground state is spontaneously dimerized for ferric wheels. The spin states of ferric wheels can be viewed as quantized states of a rigid rotor with the gap between the ground and first excited states defining the inverse of the moment of inertia. We have studied the quantum dynamics of Fe10 as a representative of ferric wheels. We use the low-lying states of Fe10 to solve exactly the time-dependent Schr&#246;dinger equation and find the magnetization of the molecule in the presence of an alternating magnetic field at zero temperature. We observe a nontrivial oscillation of the magnetization which is dependent on the amplitude of the ac field. We have also studied the torque response of Fe12 as a function of a magnetic field, which clearly shows spin-state crossover