This is the first book presenting a coherent theoretical and experimental treatment of the rapidly developing field of macroscopic quantum tunneling of the magnetic moment. The theory is based on the concept of the magnetic instanton and its renormalization by the dissipative environment. The book includes discussions of the tunneling of magnetic moment in small ferromagnetic grains, tunneling of the Ne'el vector in antiferromagnetic grains, quantum nucleation of magnetic domains, and quantum depinning of domain walls. The experimental part collects the majority of recent data that are, or may be, relevant to spin tunneling. Among the topics described are low temperature magnetic relaxation and its interpretation in various systems, experiments on single particles and mesoscopic wires, and resonant spin tunneling in molecular magnets. This study of an important new field in condensed matter physics by two leading contributors to the subject will be of interest to theorists and experimentalists alike.

The dynamical theory of thermally activated resonant magnetization tunneling in uniaxially anisotropic magnetic molecules such as Mn 12 Ac (Sϭ10) 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 tunneling level splitting ͓D. A. Garanin, J. Phys. A 24, L61 ͑1991͔͒. There exists a temperature range ͑thermally activated tunneling͒ 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 tunneling͒. 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.

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We have found a novel feature of the bistable large-spin model described by the Hamiltonian H 2DS 2 z 2 H x S x . The crossover from thermal to quantum regime for the escape rate can be either first ͑H x , SD͞2͒ or second ͑SD͞2 , H x , 2SD͒ order, that is, sharp or smooth, depending on the strength of the transverse field. This prediction can be tested experimentally in molecular magnets like Mn 12 Ac. [S0031-9007(97)04645-0] PACS numbers: 75.45. + j, 75.50.Tt Transitions between two states in a bistable system can occur either due to the classical thermal activation or via quantum tunneling. A rigorous study of that problem was begun by Kramers [1] and WKB [2][3][4], and a review of the progress that followed can be found in Ref. [5]. At high temperature the transition rate follows the Arrhenius law, G ϳ exp͑2DU͞T͒, with DU being the height of the energy barrier between the two states. In the limit of T ! 0, the transitions are purely quantum, G ϳ exp͑2B͒, with B independent on temperature. Because of the exponential dependence of the thermal rate on T , the temperature T 0 of the crossover from quantum to thermal regime can be estimated as T ͑0͒ 0 DU͞B. For a quasiclassical particle in a potential U͑x͒, Goldanskii [6] noticed the possibility of a more accurate definition, T ͑2͒ 0 "͞t 0 , where t 0 is the period of small oscillations near the bottom of the inverted potential, 2U͑x͒. Below T ͑2͒ 0 , thermally assisted tunneling occurs from the excited levels, that reduces to the tunneling from the ground-state level at T 0. Above T ͑2͒ 0 quantum effects are small and the transitions occur due to the thermal activation to the top of the barrier. Affleck [7] demonstrated that the two regimes smoothly join at T T ͑2͒ 0 . Larkin and Ovchinnikov [8] called this situation the secondorder phase transition from classical to quantum behavior. This means that for G written as G ϳ exp͑2DU͞T eff ͒, the dependence of both T eff and its first derivative on T are continuous at T T ͑2͒ 0 . This situation is not generic, however. The transition between the two regimes can also be of the first order [8,9], i.e., more abrupt, with dT eff ͞dT discontinuous at a certain temperature T ͑1͒ 0 . T ͑2͒ 0 . Chudnovsky derived the criterion allowing one to establish whether first-or second-order transition takes place, based on the shape of the potential U͑x͒. Commonly studied potentials U 2x 2 1 x 4 and U 2x 2 1 x 3 yield the second-order transition. Physically relevant potentials which would exhibit the first-order transitions were not known. In this Letter we show that spin systems readily accessible in the experiment possess both first-and second-order transitions between the classical and quantum behavior of the escape rate. The order of the transition in these systems can be controlled by external magnetic field. Consider a spin system described by the Hamiltonianwhere S ¿ 1. This model is generic for problems of spin tunneling studied by different methods [10 -15]. It is believed to be a good approximation for the molecular magnet...

We argue that superconductor/ferromagnet multilayers of nanoscale period should exhibit strong pinning of vortices by the magnetic domain structure in magnetic fields below the coercive field when ferromagnetic layers exhibit strong perpendicular magnetic anisotropy. The estimated maximum magnetic pinning energy for single vortex in such a system is about 100 times larger than the pinning energy by columnar defects. This pinning energy may provide critical currents as high as 106−107 A/cm2 at high temperatures (but not very close to Tc) at least in magnetic fields below 0.1 T.

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