Quantum description of spin tunneling in magnetic molecules

Abstract

Abstract.A new approach is used that allows to describe the magnetic molecules main properties in a direct and simple way. Results obtained for the F e 8 cluster show good agreement with the experimental data.PACS numbers: 03.65. Ca, 75.45+j, 75.60Jp Submitted to: J. Phys. C: Solid State Phys.In recent years, with the experimental advances in the measurement of magnetic molecular clusters properties, it has emerged a new frontier in this area. One of the interesting aspects that came out of these studies is the possibility of measuring spin tunneling in mesoscopic systems what corresponds, in a standard quantum description, to the tunneling of the collective degree of freedom corresponding to the magnetization direction through a potential barrier separating two minima of an effective potential associated with the spatial orientation [1,2,3,4,5,6,7,8].From the theoretical point of view, spin tunneling has been treated mainly by the use of a WKB method adapted to spin systems [9,10], by using Feyman's path integral treatment of quantum mechanics [11,12], and also by using su(2) coherent states [13] in order to establish a correspondence between the spectrum of the spin system with the energy levels of a particle moving in an effective potential [14].In the present letter we intend to show that still another approach may be used for describing spin tunneling -in angle representation -in such a way that analytic expressions for the characteristic parameters of the magnetic molecular clusters can be obtained; in particular, the results for the spectrum and energy barrier heights are directly obtained and the spin tunneling process can be easily interpreted.The starting point of the present approach is the introduction of a quantum phenomenological Hamiltonian describing the spin system, written in terms of angular momentum operators obeying the standard commutation relations, and that reflects

Quantum spin tunneling of magnetization in small ferromagnetic particles

“…In fact, the formalism also embodies the possibility of describing high spin systems because it is given in terms of expressions that are not a priori restricted to a particular range of the spin value. As shown elsewhere [6], the proposed approach gives a reliable description for physical systems with spin S ≥ 5. It does not require new commutation relations connecting pairs of new canonical operators specially constructed for high spin systems; in this way, the usual commutation relations associated with the angular momentum operators is the basic algebraic tool for treating systems of any spin value (S ≥ 5).…”

“…(2) has been already shown elsewhere and will not be repeated here [6,10]. In fact, as it was proved there, the variational generator coordinate method can in this case be used to rewrite the Hamiltonian from which we start in an exact and discrete representation which can then be conveniently treated in order to give an approximate Hamiltonian in the polar angle representation.…”

“…Hamiltonian is akin to that one suggested to describe the Fe 8 magnetic cluster (also with an external magnetic field) and that has been treated elsewhere [6,7]. Now, carrying out all the steps of the approach as mentioned before, we obtain the approximate Hamiltonian in the angle representation, namely…”

“…In the present paper we intend to apply a new quantum description originally proposed to treat magnetic molecules of low and intermediate spins [6,7] to ferromagnetic particles. We will show that it can be used in such a way that the energy level splitting in ferromagnetic particles can also be obtained in a direct and simple way.…”

“…The paper is organized as follows. In Section 2 we use the formalism [6] to discuss a phenomenological Hamiltonian associated with a ferromagnetic particle submitted to an external magnetic field. In Section 3, selected properties of ferromagnetic particles will be discussed, namely the energy spectrum and the saturation magnetic field.…”