Magnetic domains in non-ferromagnetic metals: The non-linear de Haas-van Alphen effect

This review is devoted to an exposition of the principles of the physics of magnetic domains in non-ferromagnetic metals and diamagnetic phase transitions, which lead to the formation of the so-called Condon domains during magnetic oscillations in a three-dimensional electron gas. One of the goals of the review is to provide a deeper insight into the nature of this instability of the electron gas in normal metals and improve the understanding of this type of non-spin magnetism. We discuss theoretical aspects of the physics underlying magnetic ordering of conduction electrons in bulk metals and in thin films, and describe the behaviour of the susceptibility, thermal expansion, specific heat, compressibility, sound velocity, magnetic induction bifurcation, the order parameter, domain formation, wetting of domain walls, nucleation and kinetics of diamagnetic phase transitions. In the vicinity of diamagnetic phase transitions the results obtained coincide with those following from the Landau theory of phase transitions. The existence of the critical sample size for the diamagnetic phase transition in thin films is considered. We place special emphasis on the problem of the order of diamagnetic phase transitions. The survey is partly motivated as complementary to the recent review by G. Solt and V. Egorov describing the experimental situation in the field. Contents PAGE 1. Introduction 386 2. Diamagnetic phase transitions and Condon domains 390 2.1. Shoenberg's and Condon's consideration of the phenomena 390 2.2. Phase diagrams for one de Haas-van Alphen cycle 395 3. Critical phenomena at second-order diamagnetic phase transitions in three-dimensional metals 397 3.1. Introduction 397 3.2. Order parameter and susceptibility 397 3.3. Specific heat jump 403 3.4. Phase diagrams 407 3.5. Finite-size effects 410 3.6. Compressibility, thermal expansion and sound velocity 414 4. Condon domains and resonance methods of their investigation 417 4.1. Introduction 417 4.2. Nuclear magnetic resonance and Condon domains 418 4.3. Muon spin resonance spectroscopy and Condon domains 420 4.4. Critical exponents at diamagnetic phase transitions in silver and beryllium 426 4.5. Helicon resonance and Condon domains 428 4.6. Critical dynamics of the diamagnetic phase transition in aluminium 430 5. First-order diamagnetic phase transitions 431 5.1. Introduction 431 5.2. Domain formation 433 5.3. Kinetics 436 5.4. Wetting 441 5.5. Nucleation 442 5.6. Order of diamagnetic phase transitions 444 5.7. Hysteresis and Condon domains 445 6. Summary 446 7. Some open issues 448 Acknowledgements 450 References 451.