Magnetization ofMn12acetate in a slowly varying magnetic field: A quantum mechanical study

Abstract

Beginning with a Heisenberg spin Hamiltonian for the manganese ions in the M n 12 Ac molecule, we find a number of low-energy states of the system. We use these states to solve the time-dependent Schrödinger equation and find the magnetization of the molecule in the presence of a slowly varying magnetic field. We study the effects of the field sweep rate, fourth order anisotropic spin interactions and a transverse field on the weights of the different states as well as the magnetization steps which are known to occur in the hysteresis plots in this system. We find that the fourth order term and a slow field sweep rate are crucial for obtaining prominent steps in magnetization in the hysteresis plots.

Dzyaloshinskii-Moriya interactions and adiabatic magnetization dynamics in molecular magnets

“…[23][24][25][26][27] Thus, a minimal magnetic model Hamiltonian should contain (strong) Heisenberg inter-actions, DM interactions, and a coupling to the applied magnetic field. 11,[28][29][30][37][38][39][40][41][42] Experiments on Mn 12 suggest that the energy gaps related to the transition from a state with magnetization M Ϸ −10 to a state with magnetization M Ͻ 4 are of the order of 10 −9 K. 43 Such gaps are too small to detect with standard precision (13-14 digits) calculations, and therefore in this paper we present only the global energylevel diagram obtained from microscopic model calculations.…”

Numerically exact and approximate determination of energy eigenvalues for antiferromagnetic molecules using irreducible tensor operators and general point-group symmetries

“…It turns out that the aforementioned occurrence of steps can be understood and even be employed for a further reduction of the size of Hamilton matrices. The underlying reason is that the full Hamiltonian connects states belonging to different rotational-bands with very 0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0, 9…”

“…A possible compromise is to use only part of the spin-rotational symmetry (namely rotations about the z-axis) together with point-group symmetries 6 or to expand all basis states in terms of simpler product states. 7,8,9 To the best of our knowledge only two groups developed a procedure in which the full spinrotational symmetry is combined with point-group symmetries. O. Waldmann combines the full spin-rotational symmetry with those point-group symmetries that are compatible with the spin coupling scheme, i.e.…”

Exact and Approximate Theoretical Techniques for Quantum Magnetism in Low Dimensions

“…The methods discussed for spin clusters are directly relevant to areas of current interest such as quantum tunneling in the presence of time-dependent magnetic fields [17][18][19][20]95]. One-dimensional spin systems sometimes have unusual properties (such as a disordered ground state with an excitation gap above it) which are not observed in similar models in higher dimensions.…”