Model Exact Low-Lying States and Spin Dynamics in Ferric Wheels; Fe6_6 to Fe12_{12}

Using an efficient numerical scheme that exploits spatial symmetries and spin-parity, we have obtained the exact low-lying eigenstates of exchange Hamiltonians for ferric wheels up to Fe$_{12}$. The largest calculation involves the Fe$_{12}$ ring which spans a Hilbert space dimension of about 145 million for M$_s$=0 subspace. Our calculated gaps from the singlet ground state to the excited triplet state agrees well with the experimentally measured values. Study of the static structure factor shows that the ground state is spontaneously dimerized for ferric wheels. Spin states of ferric wheels can be viewed as quantized states of a rigid rotor with the gap between the ground and the first excited state defining the inverse of moment of inertia. We have studied the quantum dynamics of Fe$_{10}$ as a representative of ferric wheels. We use the low-lying states of Fe$_{10}$ to solve exactly the time-dependent Schr\"odinger equation and find the magnetization of the molecule in the presence of an alternating magnetic field at zero temperature. We observe a nontrivial oscillation of magnetization which is dependent on the amplitude of the {\it ac} field. We have also studied the torque response of Fe$_{12}$ as a function of magnetic field, which clearly shows spin-state crossover.Comment: Revtex, 24 pages, 8 eps figure

Macroscopic quantum coherence in mesoscopic ferromagnetic systems

In this paper we study the Macroscopic Quantum Oscillation (MQO) effect in ferromagnetic single domain magnets with a magnetic field applied along the hard anistropy axis. The level splitting for the ground state, derived with the conventional instanton method, oscillates with the external field and is quenched at some field values. A formula for quantum tunneling at excited levels is also obtained. The existence of topological phase accounts for this kind of oscillation and the corresponding thermodynamical quantities exhibit similar interference effects which resembles to some extent the electron quantum phase interference induced by gauge potential in the Aharonov-Bohm effect and the $\Theta$-vacuum in Yang-Mills field theory..Comment: 12 pages, 4 figures, to appear in Phys. Rev.

Quantum-Classical Phase Transition of Escape rate in Biaxial Spin Particles

The escape rates of the biaxial single domain spin particles with and without an applied magnetic field are investigated. Using the strict potential field description of spin systems developed by Ulyanov and Zaslavskii we obtain new effective Hamiltonians which are considered to be in exact spin-coordinate correspondence unlike the well studied effective Hamiltonians with the approximate correspondence. The sharp first-order transition is found in both cases. The phase diagram of the transitions depending on the anisotropy constant and the external field is also given.Comment: 15 pages, 8 figure

Crossover from thermal hopping to quantum tunneling in Mn_{12}Ac

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 can't be calculated by the steepest descent method and show that higher order couplings between the two dangerous modes need to be taken into considerations. At last the crossover from thermal hopping to quantum tunneling in the molecular magnet Mn_{12}Ac is studied.Comment: 10 pages, 3 figure

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 n-th degenerate states of neighboring wells is dominated by a periodic pseudoparticle configuration. The low-lying level-splitting previously obtained with the LSZ 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 new 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.Comment: 18 pages, LaTex, 1 figur

Nonadiabatic Pauli susceptibility in fullerene compounds

Pauli paramagnetic susceptibility $\chi$ is unaffected by the electron-phonon interaction in the Migdal-Eliashberg context. Fullerene compounds however do not fulfill the adiabatic assumption of Migdal's theorem and nonadiabatic effects are expected to be relevant in these materials. In this paper we investigate the Pauli spin susceptibility in nonadiabatic regime by following a conserving approach based on Ward's identity. We find that a sizable renormalization of $\chi$ due to electron-phonon coupling appears when nonadiabatic effects are taken into account. The intrinsic dependence of $\chi$ on the electron-phonon interaction gives rise to a finite and negative isotope effect which could be experimentally detected in fullerides. In addition, we find an enhancement of the spin susceptibility with temperature increasing, in agreement with the temperature dependence of $\chi$ observed in fullerene compounds. The role of electronic correlation is also discussed.Comment: Revtex, 10 pages, 8 figures include

Resonant Magnetization Tunneling in Mn12 Acetate: The Absence of Inhomogeneous Hyperfine Broadening

We present the results of a detailed study of the thermally-assisted-resonant-tunneling relaxation rate of Mn12 acetate as a function of an external, longitudinal magnetic field and find that the data can be fit extremely well to a Lorentzian function. No hint of inhomogeneous broadening is found, even though some is expected from the Mn nuclear hyperfine interaction. This inconsistency implies that the tunneling mechanism cannot be described simply in terms of a random hyperfine field.Comment: Some minor revisions, title changed, updated figures, two added notes, one added reference. RevTeX, 4 pages, 3 postscript figures. Submitted to Rapid Communication

Magnetic Field Dependence of Macroscopic Quantum Tunneling and Coherence of Ferromagnetic Particle

We calculate the quantum tunneling rate of a ferromagnetic particle of $\sim 100 \AA$ diameter in a magnetic field of arbitrary angle. We consider the magnetocrystalline anisotropy with the biaxial symmetry and that with the tetragonal symmetry. Using the spin-coherent-state path integral, we obtain approximate analytic formulas of the tunneling rates in the small $\epsilon (=1- H/H_c)$-limit for the magnetic field normal to the easy axis ($\theta_H = \pi/2$), for the field opposite to the initial easy axis ($\theta_H = \pi$), and for the field at an angle between these two orientations ($\pi/2 << \theta_H << \pi$). In addition, we obtain numerically the tunneling rates for the biaxial symmetry in the full range of the angle $\theta_H$ of the magnetic field ($\pi/2 < \theta_H \leq \pi$), for the values of \epsilon =0.01 and 0.001.Comment: 25 pages of text (RevTex) and 4 figures (PostScript files), to be published in Phys. Rev.

Tunneling of a large spin via hyperfine interactions

We consider a large spin \bf S in the magnetic field parallel to the uniaxial crystal field, interacting with N >> 1 nuclear spins \bf I_i via Hamiltonian \cal H = -DS_z^2 - H_zS_z+ A{\bf S}\cdot \sum_{i=1}^N {\bf I}_i with A << D, at temperature T. Tunneling splittings and the selection rules for the resonant values of H_z are obtained perturbatively. The quantum coherence exists at T << ASI while at T >= ASI the coherence is destroyed and the relaxation of \bf S is described by a stretched dependence which can be close to log t under certain conditions. Relevance to Mn-12 acetate is discussed.Comment: 5 PR pages, 4 figures, submitted to PR

Thermally Activated Resonant Magnetization Tunneling in Molecular Magnets: Mn_12Ac and others

The dynamical theory of thermally activated resonant magnetization tunneling in uniaxially anisotropic magnetic molecules such as Mn_12Ac (S=10) is developed.The observed slow dynamics of the system is described by master equations for the populations of spin levels.The latter are obtained by the adiabatic elimination of fast degrees of freedom from the density matrix equation with the help of the perturbation theory developed earlier for the tunneling level splitting [D. A. Garanin, J. Phys. A, 24, L61 (1991)]. There exists a temperature range (thermally activated tunneling) where the escape rate follows the Arrhenius law, but has a nonmonotonic dependence on the bias field due to tunneling at the top of the barrier. At lower temperatures this regime crosses over to the non-Arrhenius law (thermally assisted tunneling). The transition between the two regimes can be first or second order, depending on the transverse field, which can be tested in experiments. In both regimes the resonant maxima of the rate occur when spin levels in the two potential wells match at certain field values. In the thermally activated regime at low dissipation each resonance has a multitower self-similar structure with progressively narrowing peaks mounting on top of each other.Comment: 18 pages, 8 figure