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arXiv:quant-ph/0603183

Quantum description of spin tunneling in magnetic molecules: a new view

D. Galetti

Published Mar 21, 2006• 0 citations
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Abstract

Starting from a phenomenological Hamiltonian originally written in terms of angular momentum operators we derive a new quantum angle-based Hamiltonian that allows for a discussion on the quantum spin tunneling. The study of the applicability of the present approach, carried out in calculations with a soluble quasi-spin model, shows that we are allowed to use our method in the description of physical systems such as the Mn12-acetate molecule, as well as the octanuclear iron cluster, Fe8, in a reliable way. With the present description the interpretation of the spin tunneling is seen to be direct, the spectra and energy barriers of those systems are obtained, and it is shown that they agree with the experimental ones.

DOI
10.48550/arxiv.quant-ph/0603183

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Starting from a phenomenological Hamiltonian originally written in terms of angular momentum operators we derive a new quantum angle-based Hamiltonian that allows for a discussion on the quantum spin tunneling. The study of the applicability of the present approach, carried out in calculations with a soluble quasi-spin model, shows that we are allowed to use our method in the description of physical systems such as the Mn12-acetate molecule, as well as the octanuclear iron cluster, Fe8, in a reliable way. With the present description the interpretation of the spin tunneling is seen to be direct, the spectra and energy barriers of those systems are obtained, and it is shown that they agree with the experimental ones.
We have used an angle-based description and the quantum discrete phase space formalism to characterize Fe8 cluster properties. Through the angle-based approach we have calculated the the ground state barrier height, the energy splitting of the two lowest levels, the crossover temperature, the matching and the saturation magnetic field intensities. With the quantum phase space approach we also have used the energy splitting in order to study the spin tunneling of the lowest energy levels, a qualitative and a quantitative way to show the correlations between the angle and angular momentum variables via the Wigner and Husimi functions
Discrete quantum phase space formalism is used to discuss some basic aspects of the spin tunneling occurring in Fe8 magnetic cluster by means of Wigner functions as well as Husimi distributions. Those functions were obtained for sharp angle states and symmetric combinations of the lowest energy doublet with the application of an external magnetic field. The time evolution of those functions carried out numerically allows one to extract valuable information about the dynamics of the states under consideration, in particular, the coherent oscillations associated with the spin tunneling. It is also shown that an entropy functional constructed out of the discrete Husimi distribution function allows to characterize the spin tunneling.
A discrete quantum phase space formalism is used to discuss some basic aspects of the spin tunnelling which occurs in Fe8 magnetic clusters by means of Wigner functions as well as Husimi distributions. Those functions were obtained for sharp angle states and symmetric combinations of the lowest energy doublet—the particular tunnelling energy doublet—with the application of an external magnetic field. The time evolution of those functions carried out numerically allows one to extract valuable information about the dynamics of the states under consideration, in particular, the coherent oscillations associated with the particular energy doublet.
In this thesis we present the results of calculations of the properties of quantum spin systems. \nThe majority of the work is concerned with one dimensional spin chains and the particular \neffects that reduced dimensionality produce. The final chapter describes some earlier work on \nmixed valence manganite compounds. \nWe demonstrate one derivation of the Heisenberg Hamiltonian and discuss its applicability to \nmodelling magnetic systems both in three and one dimension. We discuss systems that are \nexactly soluble and the failure of spin wave theory in I-D. The Density-Matrix \nRenormalisation Group (DMRG) method is discussed in detail as is the extension to finite \ntemperature (TMRG). \nWe show results of calculations on a number of S=1/2 and S=l models and fundamental \ndifferences in their excitation spectra is observed. The thermodynamics of these systems have \nbeen obtained over a wide temperature range. In addition, excellent agreement with \nexperiment is shown for a number of quasi one dimensional compounds. The DMRG and \nTMRG are shown to be very competitive and accurate methods of studying such systems, \nespecially in the case of gapped systems. \nThe final chapter discusses the role of correlated magnetic clusters in determining the magnetic \nproperties of mixed valence manganites at temperatures near the Curie temperature. Our \nresults are supported by recent direct experimental observation of the formation of these \nclusters. We also briefly discuss some preliminary results regarding the effect of an interface \non the electronic and magnetic properties of these compounds.
This thesis is about the tunneling dynamics of the Fe8 molecule in the presence of an environment. Although a lot of progress has been made experimentally to determine among many things the extremely small tunnel splitting energies of this macromolecule, the question of how the environment affects the molecule has still not been properly understood. It is the purpose of this thesis to put forward a coherent model for the decoherence processes that affect the Fe8 molecule. The decoherence allows us to treat the Fe8 molecules as classical objects and we can write down rate equations that determine the relaxation dynamics of the entire Fe8 solid. The theoretical predictions are in very good agreement with Monte-Carlo simulations of spherical samples. We believe that the model developed can be generalized to different geometries and also improvised to tackle the different experimental protocols that have been undertaken on these macroscopic molecules.