In this article, we resolve the apparent contradiction between recent experiments and earlier theoretical studies predicting strongly asymmetric condensates resulting in an attractive interaction between condensate magnons. We show that the relaxation time required to achieve equilibrium of the two condensates at the two energy minima exceeds the experiment duration. Therefore, the system is inherently out of balance and must be described by Boltzmann’s kinetic equations. We develop an appropriate kinetic theory and derive the relation between the critical pumping power and the effective temperature of over-condensate magnons.

Abstract This book is an introduction to explicitly time-dependent physics. We describe the theory of the dynamic regime that we refer to as “quasi-adiabatic”. It pertains to time-dependent evolution that, while slow, is not genuinely adiabatic. It is rich in effects that can be understood even in quantum systems with complex many-body interactions. Examples from research in quantum computing, phase transitions, Bose-Enstein condensates, and quantum control will be used to illustrate these effects. Prerequisites include undergraduate introductory courses in quantum and classical mechanics, as well as complex analysis. Our book aims to fill the gap in the literature by providing an accessible, for early graduate and advanced undergraduate students, introduction to both geometric phases and nonadiabatic transitions at a level sufficient to consider numerous applications.

Two recent articles of the Munster University experimental team led by S.O. Demokritov displayed several important facts related to the Bose-Einstein condensation of magnons (BECM) under permanent pumping first discovered in 2006. They contradicted existing theories of this phenomenon, which predict the attractive interaction between magnons and strong spontaneous violation of the reflection symmetry. In this article, we show that these theories implicitly assumed all relaxation processes to be fast compared with the lifetime of the magnons, whereas one of them -- relaxation between two minima of energy -- is slow. We classify processes responsible for the inter-minima relaxation and present their analytic theory. We analyze how the slow inter-minima relaxation modifies the anticipated properties of a ferromagnet with the magnon condensate.

the U.S. Department of Energy (from the early 1980s to the present time). Taken all together, these offices have provided nearly continuous support for our research for nearly 50 years. As we have said on many occasions, this research support has been the best we have ever had, by far. As we look back on the nearly five decades of support from the Division of Materials Sciences and the predecessor offices, we find that the continuity of support that we have enjoyed has allowed us to be most productive and terms of papers published, doctoral students graduated and influence on the field of materials science. This report will, of course, cover the three-year period of the present grant, in summary form, but will also make reference to the output that resulted from support of previous grants from the Division of Materials Sciences and its predecessor offices.

The new class of phenomena described in this review is based on the interaction between spatially separated, but closely located ferromagnets and superconductors, the so-called ferromagnet-superconductor hybrids (FSH). Typical FSH are: coupled uniform and textured ferromagnetic and superconducting films, magnetic dots over a superconducting film, magnetic nanowires in a superconducting matrix, etc. The interaction is provided by the magnetic field generated by magnetic textures and supercurrents. The magnetic flux from magnetic structures or topological defects can pin vortices or create them, changing the transport properties and transition temperature of the superconductor. On the other hand, the magnetic field from supercurrents ( vortices) strongly interacts with the magnetic subsystem, leading to formation of coupled magnetic - superconducting topological defects.The proximity of ferromagnetic layer dramatically changes the properties of the superconducting film. The exchange field in ferromagnets not only suppresses the Cooper-pair wavefunction, but also leads to its oscillations, which in turn leads to oscillations of observable values: the transition temperature and Josephson current. In particular, in the ground state of the Josephson junction the relative phase of two superconductors separated by a layer of ferromagnetic metal is equal to p instead of the usual zero ( the so-called pi-junction). Such a junction carries a spontaneous supercurrent and possesses other unusual properties. Theory predicts that rotation of magnetization transforms s-pairing into p-pairing. The latter is not suppressed by the exchange field and serves as a carrier of long-range interaction between superconductors.

We explore the precessional motion of the magnetization vector in a model magnetic element. We find that the Landau–Lifshitz equation governing this motion allows trajectories of the magnetization vector to bifurcate. This yet unknown phenomenon is accompanied by a slowing down of the precessional motion and an abrupt shrinking of the size of the trajectory of the precessing magnetization. We discuss the implication of bifurcation for future devices using precessional switching and suggest how magnetic elements showing the classical phenomenon of bifurcation can be tuned to act as quantum bits.

We discuss a new class of phenomena based on strong interaction between magnetic superstructures and vortices in superconductors in combined heterogeneous structures. An inhomogeneous magnetization can pin vortices or create them spontaneously changing drastically properties of the superconductor. On the other hand, the interaction between magnetic moments mediated by vortices can result in specific types of magnetic ordering. The same interaction can create coupled magnetic-superconducting defects. We discuss possible experimental observation of magnetism controlled vortex matter in superconducting films with magnetic nanoscale dots or stripes and layered systems with alternating superconducting and magnetic layers.

We discuss a new class of phenomena based on strong interaction between magnetic superstructures and vortices in superconductors. A local variation of the magnetic moment can pin and create vortices spontaneously, changing drastically properties of the superconductor. At the same time, magnetic moments can be changed and strongly interact via coupling with vortices. This highly inhomogeneous mechanism of interaction between superconductivity and magnetism is totally different from the traditional mechanism based on competition of homogeneous order parameters. This mechanism can be realized in a broad class of systems. We discuss the case of superconducting films with magnetic nanoscale dots and recent experiments with rare-earth-nickel-borocarbide magnetic superconductors.

We propose two statistical models for description the metal-insulator phase transition coupled with paramagnetic-ferromagnetic phase transition in manganites of the type La_{1-x}Sr_xMnO_3. The first one based on the competition of small polarons and delocalized carriers. In the second one the conductivity appears as a result of overlapping of large polarons. We compare our models with the experimental data.