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From small magnets to big magnets,
and what pool balls and superconductors have in common

Anders Vestergren
Theoretical Physics
Royal Institute of Technology (KTH), Sweden
April 2003

Theoretical physics is about describing nature in the simplest possible way, but not any simpler. I am studying high temperature superconductivity and certain types of magnetism, phenomena involving a large number of particles at temperatures several hundred centigrades below zero. This is done by using descriptions and explanations that only are valid at these temperatures. In the future, research from high temperature superconductivity can revolutionize electronics, power transmission and medical technologies. A deep understanding of magnets and quantum magnets is important for data storage and in the future, maybe, for new types of information processing.

What high-temperature superconductivity and certain types of magnetism have in common is that they arise from what many things do together. An example is a magnet, which consists of a very large number of atoms, where each atom is acting as a small magnet. The small magnets are generally acting together in a way that cannot be understood by studying just one small magnet. We need to describe all the small magnets to understand and explain the one magnet. This is very difficult due to their large number. The trick is to create a simpler description by keeping only important information. When non-important information is discarded, the new description will only be good in certain situations, such as a low temperature. From this description, one can draw conclusions and deeper understanding of different phenomena. I have applied this technique to complicated systems such as high temperature superconductors and quantum spin glasses (a fancy magnet) to get important information about how they work.

A superconductor is a material which has no resistance to electrical current. If a superconductor is placed in a magnetic field, the magnetic field will not go through the superconductor. This is in strong opposition to other materials, where a magnetic field will go through. If the magnetic field is strong enough, it will start to penetrate a high temperature superconductor. However, it will not go through in a uniform way, as it does through an ordinary material. It will penetrate as tubes of magnetic field, with each tube carrying the smallest possible piece of magnetic field. The tubes move around very easily. Think of pool balls on a hard floor - they roll easily. Superconductivity is lost when the magnetic field tubes move around. To keep the magnetic field tubes from moving, one can introduce defects in the superconductor that pin the tubes. In the floor example, the defects would be small holes or craters where the balls will stick.

I have studied how different types of defects change the way a high temperature superconductor turns superconducting from just conducting, if it does it at all. For example, I have studied if it is better to have a few large or many small defects? Should defects be long and thin or point-like? When speaking about high temperature superconductors, high temperature is not very hot: high temperature superconductors start to work below approximately -150 Co. This is high compared to ordinary superconductors that work at approximately -260 Co .

Another part of my research is concerned with quantum spin glasses. A quantum spin glass is a disordered magnet, which means that the very small magnets in it want to have positions that look completely random. If we observe a certain small magnet in a certain direction, it always points up or down with respect to that direction. In a quantum spin glass, the preferred state of a certain small magnet is a combination of up and down, but we always observe up or down. If we observe the small magnet at different times, we will see it sometimes up and sometimes down. We will see a movement. Because the total magnetization is the sum of how all the small magnets point, this quantum movement can be measured by measuring the total magnetization. This quantum movement makes the quantum spin glass very different compared to an ordinary disordered magnet.

I have performed calculations that can explain how the small magnets are moving together at very low temperatures. Hopefully this new method can lead to many more insights in dynamics of disordered quantum systems.