Tunneling in magnetic nanoparticles

Date of Award




Degree Name

Doctor of Philosophy (Ph.D.)

First Committee Member

Stewart E. Barnes, Committee Chair


Monodomain ferromagnetic particles have an energy function which up to second order can be written as H=K∥S 2z- K⊥S2x ; with K⊥, K ∥ > 0. The hard and the easy axes are z and x, respectively. Two types of experiments can be performed on such systems:MQT (macroscopic quantum tunneling). The experiment typically consists of applying a magnetic field along the easy axis and measuring the magnetization of the sample while the field is being swept at a constant rate. Peaks in the relaxation rate indicate tunneling between minima on opposite sides of the anisotropy barrier. In the limit K∥/ K⊥ << 1, levels are ordered by their Sx quantum number, with deviations from -K⊥S2x coming from perturbative couplings given by K∥S2z . An example of this sort is the molecule Mn12O12 with K∥ = 0.MQC (macroscopic quantum coherence). The field is applied along the hard axis. Interference between the two possible symmetric tunneling paths around the hard axis lead, for particular values of the applied field, to the absence of splitting.The standard approach to MQC, as well as to MQT when K ∥ is not small enough to allow for a perturbative treatment, is path integrals in semi-classical approximation. In Chapter 2 it is shown how this method produces the correct tunneling exponent between ground states in the absence of longitudinal field. It is also shown how, for particular values of the transverse field, the Berry phase associated with the tunneling paths of opposite winding leads to "topological quenching" of tunneling between ground states.Chapter 3 introduces a new method, different from path integrals, to compute exactly (in the semi-classical limit) both the exponent and the prefactor of the tunneling matrix element. It shows that the level structure for an easy-plane ferromagnet is similar to the level structure of a double well potential. The applied magnetic field shifts the two wells with respect to one another. A model for tunneling with a spin-phonon assisted relaxation mechanism is shown to have relaxation peaks whenever two levels in the two wells cross.In Chapter 4 it is shown that a hidden symmetry (quasi-time-reversal) underlies the topological quenching of integer spins levels, explaining a massive degeneracy between pairs of states (the ground states being a particular case). A "Quasi-Kramer's" operator is defined and shown to act on degenerate pairs of states the same way the Kramer's operator acts on the degenerate pair of states | +/- 1/2 > of the spin 1/2.


Physics, Electricity and Magnetism; Physics, Condensed Matter

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