ABSTRACT
Contents 1.1 Introduction..................................................................................................... 2 1.2 Some Historical Notes .................................................................................... 3 1.3 Magnetoelectric Eect; Symmetry Considerations ................................... 4 1.4 Multiferroics .................................................................................................... 8
1.4.1 General Considerations .................................................................... 8 1.5 Dierent Types of Multiferroics ................................................................. 10 1.6 Type-I Multiferroics ..................................................................................... 12 1.7 Type-II Multiferroics .................................................................................... 17 1.8 Beyond Multiferroics .................................................................................... 22
1.8.1 Electric Activity of Magnetic Domain Walls .............................. 22 1.8.2 Spiral Magnetic Structures on Metal Surfaces ............................ 22 1.8.3 Magnetoelectric Eects in Magnetic Vortices and Skyrmions ......................................................................................... 25 1.8.4 Electric Activity of Spin Waves ..................................................... 26
1.9 Conclusions .................................................................................................... 27 References ................................................................................................................. 27
1.1 Introduction e intrinsic coupling of electricity and magnetism is one of the cornerstones of modern physics. It goes back to the famous Maxwell equations, or even earlier, to Michael Faraday, and one can even nd earlier reports pointing in that direction. is coupling plays crucial roles in all modern physics, and it is one of the foundations of modern technology, for example, in the generation of electricity in electric power stations, and in electric transformers. Recently this eld acquired new life in spintronics-the idea of being able to use not only charge but also spin of electrons for electronic applications. In this eld, one predominantly deals with the inuence of magnetic eld and/or magnetic ordering on transport properties of materials; for example, the well-known magnetoresistance or the work of magnetic tunnel junctions. But very interesting such eects can also exist in insulators. ese are, for example, the (linear) magnetoelectric eect, or the coexistence and mutual inuence of two types of ordering, magnetic and ferroelectric ordering in multiferroics. Such phenomena are very interesting in terms of its physical features, and are very promising for practical applications, such as for addressing magnetic memory electrically without the use of currents, or as very e cient magnetic sensors. ese factors probably are reasons for creating such a signicant interest in this eld. It is now one of the hottest topics in condensed matter physics, and in addition to magnetoelectrics and multiferroics per se, the study of these has many spin-os in the related elds of physics, such as the study of magnetoelectric eects in dierent magnetic textures (domain walls, magnetic vortices, skyrmions, etc.).
