I have always thought, it would be nice to make a series notes of essential toolkits for everyone to know in the field of magnetism/spintronics. Sure, I am talking about theroetical tools — I am quite ignorant of any experimental tools, even rudimentary ones like x-ray diffraction and Hall measurements. One of the main motivations behind this project is that unlike other established fields, in magnetism/spintronics, there is no single textbook that makes you prepare for real research projects.

For example, when I was beginning my graduate study, everyone on the condensed matter theory track was studying one of famous many-body physics books; Mahan, Coleman, Altland&Simons, Bruus&Flensberg, etc. I was not an exception. I studied some of them, and I even read all chapters of Altland&Simons and Bruus&Flensburg thorougly. Practically, Bruus&Flensburg was the most helpful, on the practical side. I understood the main ideas and detailed procedures for calculating transport coefficeints by the Kubo formalism and incorporating many-body effects (quenched disorders, electron-electron interaction, etc.). Well, Altland&Simons is an excellent textbook for an overview of research topics involving many-body physics, but it was mostly for my own intellectual pleasure (I am quite sure that the concepts and ways of thinking really helped me, but what I mean here is I do not practically use functional integral methods in my own research).

I think it was from the second and third year of my graduate study, when I started to feel what I learn from the textbooks is quite far from what I was duing in my research project. Now, looking back previous years and gaining more experience, I start to see that in the field of magnetism/spintronics, you really need the T-shape knowledge: Together with a strong core methodology (the vertical line of “T”), a diverse background (the horizontal line in “T”) is also necessary. When I observe how my fellow researchers and seniors do their research works, even if they are known for particular techniques, they also use many other techniques and knowledge.

In my case, the core methodology that I currently employ is large-scale simulation of real materials and analysis of the electronic structure. But at the same time, I often need knowledge of symmetry analysis, quantum transport theory, Berry phase physics, and spin dynamics.

So, what topics I have in mind for the little side project? I still need to think more about it, to be honest. For the moment, I think of Kubo formula (and many different versions that appear in papers), symmetry analysis of response functions (also known as the Neumann’s principle), what people mean by Berry phase and topology, simple python programming for calculating band structures, producing high-quality figures with matplotlib — I think they are what I use “everyday”.

Yes, you don’t really need a lot of techniques to do research. But I want to emphasize that what is more important is developing ideas and setteling those ideas by simple but concrete calculations. In this regard, discussion with colleagues is invaluable!