THE precise manner in which quantum-mechanical behaviour at the microscopic level underlies classical behaviour at the macroscopic level remains unclear, despite seventy years of theoretical investigation. Experimentally, the crossover between these regimes can be explored by looking for signatures of quantum-mechanical behaviour—such as tunneling—in macroscopic systems1. Magnetic systems (such as small grains, spin glasses and thin films) are often investigated in this way2–12 because transitions between different magnetic states can be closely monitored. But transitions between states can be induced by thermal fluctuations, as well as by tunnelling, and definitive identification of macroscopic tunnelling events in these complex systems is therefore difficult13. Here we report the results of low-temperature experiments on a single crystal composed of super-paramagnetic manganese clusters (Mn12-ac), which clearly demonstrate the existence of quantum-mechanical tunnelling of the bulk magnetization. In an applied magnetic field, the magnetization shows hysteresis loops with a distinct 'staircase' structure: the steps occur at values of the applied field where the energies of different collective spin states of the manganese clusters coincide. At these special values of the field, relaxation from one spin state to another is enhanced above the thermally activated rate by the action of resonant quantum-mechanical tunnelling. These observations corroborate the results of similar experiments performed recently on a system of oriented crystallites made from a powdered sample4.

Macroscopic quantum tunnelling of magnetization in a single crystal of nanomagnets

Magnetic Relaxation in Fine‐Particle Systems

The quantum dynamics of mesoscopic or macroscopic systems is always complicated by their coupling to many `environmental' modes. At low T these environmental effects are dominated by localized modes, such as nuclear and paramagnetic spins, and defects (which also dominate the entropy and specific heat). This environment, at low energies, maps onto a `spin bath' model. This contrasts with `oscillator bath' models (originated by Feynman and Vernon) which describe delocalized environmental modes such as electrons, phonons, photons, magnons, etc. The couplings to N spin bath modes are independent of N (rather than the ~O(1/(N )1/2 ) dependence typical of oscillator baths), and often strong. One cannot in general map a spin bath to an oscillator bath (or vice versa); they constitute distinct `universality classes' of quantum environment. We show how the mapping to spin bath models is made, and then discuss several examples in detail, including moving particles, magnetic solitons, nanomagnets, and SQUIDs, coupled to nuclear and paramagnetic spin environments. We then focus on the `central spin' model, which couples a central two-level system to a background spin bath. It is the spin bath analogue of the famous `spin-boson' oscillator model, and describes, e.g., the tunnelling dynamics of nanoscopic and mesoscopic magnets and superconductors. We show how to average over (or `integrate out') spin bath modes, using an operator instanton technique, to find the central spin dynamics. The formal manouevres involve four separate averages - each average corresponds physically to a different `decoherence' mechanism acting on the central spin dynamics. Each environmental spin has its own topological `spin phase', which by interacting with the phase of the central system, decoheres it - this can happen even without dissipation. We give analytic results for the central spin correlation functions, under various conditions. We then describe the application of this theory to magnetic and superconducting systems. Particular attention is given to recent work on tunnelling magnetic macromolecules, where the role of the nuclear spin bath in controlling the tunnelling is very clear; we also discuss other magnetic systems in the quantum regime, and the influence of nuclear and paramagnetic spins on flux dynamics in SQUIDs. Finally, we discuss decoherence mechanisms and coherence experiments in superconductors and magnets. We show that a spin bath environment causes decoherence even in the T 0 limit. Control of this decoherence will be essential in the effort to construct `qubits' for quantum computers.

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Theory of the spin bath

Alternating current (ac) magnetic susceptibility data are presented for six distorted cubane complexes of the composition [MnIVMnIII3O3X] Each of these complexes has a well isolated S = 9/2 ground state There is zero-field splitting (ZFS) in the ground states where D, the axial ZFS parameter, is found to be in the range of −027 to −038 cm-1 As a result of the big spin ground state and appreciable magnetic anisotropy, an out-of-phase ac magnetic susceptibility signal is seen for each of the six Mn4 complexes The out-of-phase ac susceptibility signal reflects slow magnetization relaxation which is taken to indicate that individual molecules are acting as magnets Alternating current susceptibility data are presented for a frozen glass of one of the Mn4 complexes to confirm that the out-of-phase ac signal is associated with isolated molecules The factors that influence whether a given complex can function as a single-molecule magnet are described The above Mn4 complexes represent only the second type

Distorted MnIVMnIII3 Cubane Complexes as Single-Molecule Magnets

For many years physicists thought small structures would be nearly ideal systems in which to explore and manipulate magnetic interactions. On a small enough length scale the interactions between individual atomic spins cause their magnetic moments to align in the ordered pattern of a single domain, without the complication of domain walls separating regions of varying orientation. For particle sizes at or below that of a single domain, many theoretical models of dynamical behavior predict simple, stable magnets with controllable classical properties. However, as with advances in semiconductor physics, the process of miniaturizing magnetic materials has unexpectedly revealed fascinating new classical and quantum mechanical phenomena. Even the simplest magnetic system, the isolated single‐domain particle, exhibits a wealth of exotic behavior that pushes us to the limits of our present understanding of the fundamentals of magnetism.

Complex dynamics of mesoscopic magnets

Macroscopic Quantum Tunneling in ferromagnetic particles

The time decay of the zero field cooled diamagnetic magnetization of superconducting Bi(Pb)2Sr2Ca2Cu30y and YBa~CU~O~- ~ ceramics has been measured and analyzed in terms of a mean activation energy f. We find f cc H~(T)jH~ ' Hi ') where H~(T) is the themlodynamic critical field, H the applied one and Ho a constant. The proportionality coefficient as well as the characteristic field Ho depend sensitively on the level of diamagnetic susceptibility P~ 4 WM~H at which experiments are performed. Our experiments show below 10K the existence of an anomaly on the mean activation energy. Different possible altematives to explain this phenomenon are considered, the most probable being a (thermally assisted) quantum tunneling of vortex lines.

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Field and temperature dependence of the mean penetration rate of fluxons in the mixed state of high-Tc superconductors

Publisher Summary This chapter presents the observation of quantum tunnelling of the magnetization vector in small particles with and without domain walls. The chapter describes an experiment and discusses the results obtained on the magnetic viscosity in Fe/Cu, Dy/Cu, Fe/Sm, and SmCo multilayers in low fields and temperatures above 1.7 K. All the systems were magnetically characterized in certain temperature range by applying low and high magnetic fields. By using this procedure, all the variations with temperature were obtained for the saturation magnetization, remanence saturation, and coercive field and information on the freezing phenomena occurring in the zero field cooled (ZFC) and field cooled (FC) processes. The relaxation experiments were done by measuring the time dependence of the sample magnetization. The magnetic measurements were performed by using a SHE SQUID magnetometer. The Fe/Cu, Dy/Cu, Fe/Sm, and Co/Sm multilayer systems were prepared by using two electron beam evaporators and a high vacuum chamber. The chapter illustrates dependence of magnetization on temperature for the samples for FC and ZFC processes when the field is applied parallel to the film plane. The main features of these measurements are the presence of a large irreversibility in the ZFC–FC processes and a broad maximum in the ZFC state. The onset of the irreversibility starts before the cusp of the peak, indicating the existence of clusters of spins involved in the freezing phenomena. During the process of relaxation, the direction of the magnetization vector changes because of the coherent rotation in single domain particles and the motion of domain walls.

M. Uehara

Papers

Macroscopic Quantum Tunneling in ferromagnetic particles

Field and temperature dependence of the mean penetration rate of fluxons in the mixed state of high-Tc superconductors

OBSERVATION OF QUANTUM TUNNELING OF THE MAGNETIZATION VECTOR IN SMALL PARTICLES WITH AND WITHOUT DOMAIN WALLS: Part I