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arXiv:cond-mat/0108063 · Progress of Theoretical Physics

Quantum Tunneling in Half-Integer Spin Systems

Seiji Miyashita, Naoto Nagaosa

Published Sep 1, 2001• 41 citations
arXivHTMLPDF

Abstract

Motivated by the experimental observation of resonant tunneling in systems of half-integer spin, such as V15 and Mn4, we study the mechanism of the adiabatic change of the magnetization in systems with time-reversal symmetry. Although tunneling between the degenerate ground states is suppressed in a simple Kramers doublet, some types of perturbational interactions cause an avoided level crossing structure in the energy level structures when the system possesses additional degeneracy of the ground state. We show that a nonadiabatic transition governed by the Landau-Zener-Stückelberg mechanism occurs in many cases, and also find more general cases of adiabatic change of the magnetization in which LZS mechanism cannot be applied directly.

DOI
10.1143/ptp.106.533

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Motivated by the experimental observation of resonant tunneling in systems of half-integer spin, such as V15 and Mn4, we study the mechanism of the adiabatic change of the magnetization in systems with time-reversal symmetry. Although tunneling between the degenerate ground states is suppressed in a simple Kramers doublet, some types of perturbational interactions cause an avoided level crossing structure in the energy level structures when the system possesses additional degeneracy of the ground state. We show that a nonadiabatic transition governed by the Landau-Zener-Stückelberg mechanism occurs in many cases, and also find more general cases of adiabatic change of the magnetization in which LZS mechanism cannot be applied directly.
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Half-integer spin systems are characterized by a degenerate ground state. Here, the authors show that the chiral interactions of a spin-\textonehalf{} qubit with the vacuum fluctuations may spontaneously break both the time-reversal and the time-translation symmetries. In the former case, the electron spin becomes anchored along some particular direction of space determined by a geometrical symmetry. In contrast, the latter situation occurs when the intrinsic spin magnetic moment undergoes a cyclic oscillation in the ground state, realizing a time crystal.
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We investigate the transfer between spin quantum bit (qubit) states and study the Landau–Zener–Stückelberg–Majorana (LZSM)-like dynamics of tunneling spin qubits in a multiband two-state magnetic quantum wire. Indeed, within the framework of an optical parabolic potential in a three-dimensional (3D) heterostructure quantum wire and under the influence of an external time-varying magnetic field, a model for a multiband two-state magnetic quantum wire is developed. Here, the external magnetic field is used to coherently manipulate and control spin qubit states. By driving the system through an avoided crossing, we consider the associated effective quantum two-level system (TLS) related to the spin qubit states in each band, driving by an external coherent magnetic field in which the related Hamiltonian is Hermitian, and which generally paves a way to LZSM interferometry. Thus, we establish the analytical expressions of the energy eigenvalues in each band and derive the analytical solution of the dynamical evolution of the tunneling probabilities of the associated TLS. Accordingly, nonadiabatic and adiabatic tunneling probabilities (survival and transition) are calculated for each band of the multiband TLS. In this respect, the nonadiabatic and adiabatic dynamical evolutions of the tunneling probabilities of spin qubit populations in the first four bands, with band quantum numbers n = 0, 1, 2 and 3 are analyzed. As a result, depending on the amplitude strength of the driven magnetic field and the magnitude of the driving frequency, we report two striking nonadiabatic and adiabatic scenarios in each band for both the diabatic and adiabatic states. In this context, driving the two states of each band of the multiband TLS related to the spin qubit states through an avoided level crossing can result in nontrivial and incoherent dynamics at certain phases, resulting to apparent inaccurate probabilities, especially in the case of strong driven magnetic field and high driving frequency.