Trinity College Dublin

Within density functional theory (DFT) the complicated quantum mechanical many-body problem of interacting electrons and nuclei is mapped exactly, without introducing empirical parameters, onto an effective single particle problem. The single particle problem can then be solved very efficiently using highly parallelized computer codes and thus allows the accurate ab initio calculation of a large variety of materials properties. The huge impact of DFT on today's understanding of materials properties was recognized by the Nobel Prize in chemistry for Walter Kohn in 1998 (see Figure on the right).

The ultimate goal for the development of such a "first principles" method is to be able to calculate all properties of an arbitrary material using as input only its chemical composition. This is obviously an extremely ambitious goal, but achieving this goal would be a tremendous achievement with huge impact on both materials science and engineering. Modern first principles methods are already extremely powerful in accurately determining many properties for a large variety of materials, and the improvement of currently used methods to include larger classes of materials and formerly unaccessible quantities is therefore a very active and important field of research.

In addition, first principles calculations provide an ideal environment where atoms can be accurately placed at certain positions, defects can be excluded and then re-introduced in a controlled way, and even certain interactions can be "switched off" to see the resulting effect on the physical properties. The insights gained by such "computer experiments" are extremely useful for guiding modeling efforts and interpreting/understanding experimental observations.

Even though the possibility to calculate the values of all observables for an arbitrary material would be a tremendous achievement, it would not necessarily lead to further physical insights. To gain such insights, one has to develop models that explain a certain effect in relatively simple terms. First principles methods represent a very useful tool for such model development, since it is possible to analyze in detail how a certain result comes about. After a model has been developed, the corresponding input parameters can be calculated by first principles methods to see whether the model leads to physically reasonable results.

Furthermore, a very promising way to improve the description of "correlated electron materials" (such as most of the complex oxides that are decribed below) is to combine DFT with numerical many-body techniques. These techniques are usually applied to very simplified models with only a few number of bands, but can describe effects that are not captured by current DFT methods. However, recent progress in "dynamical mean-field theory" (DMFT) has now opened up the possibility for many-body calculations based on realistic materials-specific band-structures.

Complex transition metal oxides are fascinating materials both from a basic science perspective as well as from a technological viewpoint (see Figures on the right for some examples). The unique electronic structure of these materials leads to a very strong coupling between structural, electronic, and magnetic properties. To understand this complex interplay between the various degrees of freedom is a great challenge for modern condensed matter physics. In addition, the same interplay leads to a tremendous variety of physical properties, such as for example metallic, semiconducting, or insulating behavior, high dielectric constants, piezoelectricity, ferroelectricity, ferromagnetism, metal-insulator transitions, and high temperature superconductivity. These functional properties are extremely attractive for use in modern electronic devices such as nonvolatile memory, integrated circuits, or new types of sensors and actuators, and in addition offer great prospects for the development of future technologies.

The unique features of transition metal oxides are a result of the partial occupation of the electronic d shell on the transition metal cation. The corresponding electronic orbitals are intermediate between being atomic-like and band-like, i.e. between being localized at the cation sites and being delocalized throughout the crystal by the formation of covalent chemical bonds. The extent to which these d electrons form chemical bonds crucially depends on volume, transition metal-oxygen bond length, bond angle (the angle formed by a transition metal-oxygen-transition metal structural unit), and the symmetry of the crystal-field, which is caused by the anion polyhedra surrounding the metal cation. One very common and probably the most studied crystal structure of complex transition metal oxides, the perovskite structure, is depicted on the left. In the perovskite structure the transition metal cations form a simple cubic lattice and are surrounded by octahedra of oxygen anions; additional (non-transition metal) cations occupy the space in between these octahedra. Small distortions from the perfect perovskite structure or small changes in volume or electron count (i.e. doping) can tip the balance toward either more localized or more covalent, thereby eventually changing the system from insulating to metallic or fundamentally affecting the degree and overall character of the magnetic ordering.

Multiferroic materials are materials that combine two or more of the primary forms of ferroic order, i.e. ferroeleasticity, ferroelectricity, ferromagnetism, and ferrotoroidicity. However, most of the recent research on multiferroics has focused on materials that combine some form of magnetic order (ferromagnetic, antiferromagnetic, non-collinear, ...) with ferroelectricity, so that the term "multiferroics" is now often used synonymous with "magnetic ferroelectrics".

Due to the combination of magnetic and dielectric properties, with eventual cross-coupling between these properties, multiferroics have immense potential for technological device applications and at the same time they pose very interesting and rich fundamental physics problems. It is probably this combination of applied and fundamental research that is partly responsible for the strong attraction that these materials have developed in recent years (in December 2007 Science Magazine listed multiferroic materials as one out of ten "Areas to watch in 2008", the only entry from the Materials Science/Condensed Matter area that was included in this list).

If you are interested in further details, you can also have look at this lecture I gave at the 2008 APCTP winter school on multiferroics in Pohang, South Korea (pdf-format, 5.1MB).