F.-C. Pu

Quantum phase interference for quantum tunneling in spin systems

The point-particle-like Hamiltonian of a biaxial spin particle with external magnetic field along the hard axis is obtained in terms of the potential field description of spin systems with exact spin-coordinate correspondence. The Zeeman energy term turns out to be an effective gauge potential which leads to a nonintegrable phase of the Euclidean Feynman propagator. The phase interference between clockwise and anticlockwise under barrier propagations is recognized explicitly as the Aharonov-Bohm effect. An additional phase which is significant for quantum phase interference is discovered with the quantum theory of spin systems in addition to the known phase obtained with the semiclassical treatment of spin. We also show the energy dependence of the effect and obtain the tunneling splitting at excited states with the help of periodic instantons.

ENHANCEMENT OF QUANTUM TUNNELING FOR EXCITED STATES IN FERROMAGNETIC PARTICLES

A formula suitable for a quantitative evaluation of the tunneling effect in a ferromagnetic particle is derived with the help of the instanton method. The tunneling between nth degenerate states of neighboring wells is dominated by a periodic pseudoparticle configuration. The low-lying level-splitting previously obtained with the Lehmann-Symanzik-Zimmermann method in field theory in which the tunneling is viewed as the transition of n bosons induced by the usual (vacuum) instanton is recovered. The observation made with our result is that the tunneling effect increases at excited states. The results should be useful in analyzing results of experimental tests of macroscopic quantum coherence in ferromagnetic particles.

Quantum-classical phase transition of escape rates in biaxial spin particles

By using a stereographic projection of the unit sphere of magnetization vector onto a complex plane for the equations of motion, the effect of an external magnetic field for integrability of the system is discussed. The properties of the Jest solutions and the scattering data are then investigated through introducing transformations other than the Riemann surface in order to avoid double-valued functions of the usual spectral parameter. The exact multisoliton solutions are investigated by means of the Binet-Cauchy formula. The results showed that under the action of an external magnetic field nonlinear magnetization depends essentially on two parameters: its center moves with a constant velocity, while its shape changes with another constant velocity; its amplitude and width vary periodically with time, while its shape is also dependent on time and is unsymmetric with respect to its center. The orientation of the nonlinear magnetization in the plane orthogonal to the anisotropy axis changes with an external magnetic field. The total magnetic momentum and the integral of the motion coincident with its z component depend on time. The mean number of spins derivated from the ground state in a localized magnetic excitations is dependent on time. The asymptotic behavior of multisoliton solutions, the total displacement of center, and the phase shift of the jth peak an also analyzed. [S0163-1829(99)07121-0].

Macroscopic quantum coherence in mesoscopic ferromagnetic systems

Fe/Sb multilayer films with various Fe and Sb layer thicknesses were prepared by vapor deposition. A metastable rhombohedral Fe phase was formed in the Fe/Sb multilayered films, when the Fe layer thickness was of 1.7 nm and the Sb layer thickness was of 10 nm. In an opposite condition, a metastable bcc Sb phase was obtained, when the Fe layer was thicker than 4 nm and the Sb layer was thinner than 2.5 nm. Interestingly, the metastable rhombohedral Fe exhibited ferromagnetic behavior and its average magnetic moment was as high as 1.52 mu(B). The magnetic behavior and electronic and magnetic structures of the rhombohedral Fe were calculated by the first-principles all-electron linearized augmented plane-wave method (LAPW) within the local spin-density functional approximation. The difference between the calculation of the Fe magnetic-moment amplitude (3.32 mu(B)) and the experimental determination (1.52 mu(B)) was discussed in terms of the presence of dead layers at the Fe/Sb interfaces. [S0163-1829(99)02017-2].

Macroscopic quantum coherence in small antiferromagnetic particles and quantum interference effects

Abstract Starting from the Hamiltonian of the uncompensated two-sublattice model of a small antiferromagnetic particle, we derive the effective Lagrangian of a biaxial antiferromagnetic particle in an external magnetic field with the help of spin-coherent-state path integrals. Two unequal level-shifts induced by tunneling through two types of barriers are obtained using the instanton method. The energy spectrum is found from Bloch theory regarding the periodic potential as a superlattice. The external magnetic field indeed removes Kramers degeneracy, however, a new quenching of the energy splitting depending on the applied magnetic field is observed for both integer and half-integer spins due to the quantum interference between transitions through two types of barriers.

CROSSOVER FROM THERMAL HOPPING TO QUANTUM TUNNELING IN MN12AC

The crossover from thermal hopping to quantum tunneling is studied. We show that the decay rate Gamma with dissipation can accurately be determined near the crossover temperature. Besides considering the Wentzel-Kramers-Brillouin (WKB) exponent, we also calculate contribution of the fluctuation modes around the saddle point and give an extended account of a previous study of crossover region. We deal with two dangerous fluctuation modes whose contribution cannot be calculated by the steepest descent method and show that higher-order couplings between the two dangerous modes need to he taken into consideration. At last the crossover from thermal hopping to quantum tunneling in the molecular magnet Mn12Ac is studied. [S0163-1829(99)03409-8].

TEMPERATURE DEPENDENCE OF MACROSCOPIC QUANTUM TUNNELING IN ANTIFERROMAGNETIC PARTICLES

Abstract By explicit calculation of quantum tunneling at the level of excited states in a model of an antiferromagnetic particle, it is demonstrated that the transition through the potential barrier may be subdivided into three distinct regions: the ground state tunneling region, the thermally assisted tunneling region and the thermal activation region. The numerical result that the tunneling rate is independent of temperature in the first region agrees with the experimental observation reported by Tejada and Zhang [J. Phys. Condens. Matt. 6 (1994) 263].

Macroscopic quantum phase interference in antiferromagnetic particles

The tunnel splitting in biaxial antiferromagnetic particles is studied with a magnetic field applied along the hard anisotropy axis. We observe the oscillation of tunnel splitting as a function of the magnetic field due to the quantum phase interference of two tunnelling paths of opposite windings. The oscillation is similar to the recent experimental result with Fe8 molecular clusters.

Periodic Instanton Calculations of Quantum-Classical Transitions in Spin Systems

The quantum-classical transitions of the escape rates in the molecular magnet Mn12Ac and a biaxial anisotropic ferromagnetic spin model are investigated by applying the periodic instanton method. The effective free energies are expanded around the top of the potential barrier in analogy to the Landau theory of phase transitions. We show that the first-order transitions occur below the critical external magnetic field hx = 1/4 for Mn12Ac and beyond the critical anisotropy constant ratio λ = 1/2 for the biaxial ferromagnetic grains, which is in good agreement with earlier studies.

Completeness of Bethe type eigenfunctions for the 1D N-body system with δ-function interactions

Abstract By extending the original domain of definition for the wavefunctions to the whole space periodically so that the translation symmetry can be applied, a rigorous proof is given for the completeness of the “Bethe type” eigenfunctions in the 1D N -body systems with δ-function interactions proposed by Lieb and Liniger, and Yang.