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International Journal of Modern Physics B

SPIN DYNAMICS OF MOLECULAR MAGNET INTERACTING WITH INJECTED ELECTRONS

DONG-SHENG HU, Shi‐Jie Xiong

Published Mar 20, 2003• 2 citations
Publisher

Abstract

We investigate the time evolution of the local spin in a molecular magnet interacting with injected electrons. By solving the time-dependent Schrödinger equations, we find that the variation in the magnetization of the molecular magnet and the electron spin crucially depends on the strength of the exchange interaction. We calculate the time evolution of the entanglement between the injected electron and the molecular magnet. It is found that the entanglement oscillates in time and the oscillations are closely related to the changes in the spins. The study provides an estimation of the feasibility of the encoding and read-out by using the polarization of the molecular magnets and the injected electrons.

DOI
10.1142/s0217979203015930

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Quantum dynamics time evolution of a molecular magnet Fe 8 interacting with an electron nuclear spin is studied by solving the time-dependent Schrödinger equations. It is found that the variation of Fe 8 magnetization and the nuclear spin crucially depends on the interaction strength. The time evolution of the entanglement between the injecting electron and Fe 8 is evaluated. It is observed that the entanglement oscillates in time and is tightly related to the spin variation of the injecting electron. From these characteristics, the technique for the reversing and read-out of Fe 8 spin states is suggested.
A new family of the supramolecular antiferromagnetically exchange-coupled dimer of single-molecules magnets, [Mn 4 ] 2 , really behave as a quantum mechanical coupled system and can be used for quantum computation [Tiron et al (2003) Phys. Rev. Lett . 91 227203]. We study the time evolution of [Mn 4 ] 2 dimer interacting with an injected electron by solving the time-dependent Schrödinger equations. We find that the variations of [Mn 4 ] 2 dimer magnetization and the electron spin crucially depend on the exchange interaction strength. Time evolution of the entanglement between the injected electron and supramolecular dimer [Mn 4 ] 2 is evaluated. It is observed that entanglement oscillates in time and is closely related to the spin variation of injected electron. From these characteristics the technique for the reversing and read-out of supramolecular dimer [Mn 4 ] 2 spin states is suggested.
We investigate the dynamics of spin and charge in an interacting system consisting of impurity and conducting electrons. The time evolution of spin and charge in the impurity is given by solving the time-dependent Schrödinger equations for the many-body states of the interacting system. By switching on the interaction between impurity and conducting electrons, the spin and charge of the impurity begin oscillations with frequencies that reflect the elementary excitations of the interacting system. The dynamics reflects the basic picture of the Kondo effect.
We consider the time evolution of entanglement in a finite two-dimensional transverse Ising model. The model consists of a set of seven localized spin-12\frac{1}{2}21​ particles in a two-dimensional triangular lattice coupled through nearest-neighbor exchange interaction in the presence of an external time-dependent magnetic field. The magnetic field is applied in different function forms: step, exponential, hyperbolic, and periodic. We found that the time evolution of the entanglement shows an ergodic behavior under the effect of the time-dependent magnetic fields. Also, we found that while the step magnetic field causes great disturbance to the system, creating rapid oscillations, the system shows great controllability under the effects of the other magnetic fields where the entanglement profile follows closely the shape of the applied field even with the same frequency for periodic fields. This follow-up trend breaks down as the strength of the field, the transition constant for the exponential and hyperbolic forms, or the frequency for periodic field increase leading to rapid oscillations. We observed that the entanglement is very sensitive to the initial value of the applied periodic field: the smaller the initial value is, the less distorted the entanglement profile is. Furthermore, the effect of thermal fluctuations is very devastating to the entanglement, which decays very rapidly as the temperature increases. Interestingly, although a large value of the magnetic field strength may yield a small entanglement, the magnetic field strength was found to be more persistent against thermal fluctuations than the small field strengths.
We study the time evolution of entanglement of two spins in an anisotropically coupled quantum dot interacting with the unpolarised nuclear spins environment. We assume that the exchange coupling strength in the z direction J z is different from the lateral one J l . We observe that the entanglement decays as a result of the coupling to the nuclear environment and reaches a saturation value, which depends on the value of the exchange interaction difference J = ‖J l − J z ‖ between the two spins and the strength of the applied external magnetic field. We find that the entanglement exhibits a critical behaviour controlled by the competition between the exchange interaction J and the external magnetic field. The entanglement shows a quasi-symmetric behaviour above and below a critical value of the exchange interaction. It becomes more symmetric as the external magnetic field increases. The entanglement reaches a large saturation value, close to unity, when the exchange interaction is far above or below its critical value and a small one as it closely approaches the critical value. Furthermore, we find that the decay rate profile of entanglement is linear when the exchange interaction is much higher or lower than the critical value but converts to a power law and finally to a Gaussian as the critical value is approached from both directions. The dynamics of entanglement is found to be independent of the exchange interaction for an isotropically coupled quantum dot.
Quantum computation in molecular magnets is studied by solving the time-dependent Schr\"odinger equation numerically. Following Leuenberger and Loss [Nature (London) 410,410,410, 789 (2001)], an external alternating magnetic field is applied to populate and manipulate a superposition of single-spin states in molecular magnet Mn12.{\mathrm{Mn}}_{12}.Mn12​. The conditions to realize parallel recording and reading databases of Grover algorithms in molecular magnets are discussed in detail. It is found that an accurate time duration of the magnetic pulse as well as the discrete frequency spectrum and the amplitudes are required to design a quantum computing device.