Model Exact Low-Lying States and Spin Dynamics in Ferric Wheels; Fe₆ to Fe₁₂

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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 million for Mₛ=0 subspace. Our calculated gaps from the singlet ground state to the excited triplet state agrees well with the experimentally measured values. Study of the static structure factor shows that the ground state is spontaneously dimerized for ferric wheels. Spin states of ferric wheels can be viewed as quantized states of a rigid rotor with the gap between the ground and the first excited state defining the inverse of 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 Schrödinger 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 magnetization which is dependent on the amplitude of the ac field. We have also studied the torque response of Fe₁₂ as a function of magnetic field, which clearly shows spin-state crossover.