III. What is quasi equilibrium?

Now the way is clear: With an electromagnetic microwave field we can create magnons nearly instantly. The number of magnons that are additionally created is determined through the amplitude of the electromagnetic field. The higher the amplitude, or in other words the higher the microwave power, the more magnons are created in the ferromagnet.

I already mentioned that magnons created through a microwave field have a very narrow energy distribution. Under the experimental conditions we normally use to create an mBEC these magnons are ultra-cold. This means that their energy is much lower than the mean energy of all magnons in the thermal magnon gas. Due to magnon-magnon scattering events this magnons are heated up very quickly. We already saw, that the magnon-magnon interaction is much faster than the destruction of magnons through dissipation into the lattice.

We can compare this situation to a glass of water with a temperature of let’s say 20°C into which we throw an ice cube. Now the energy distribution of water molecules in the glass is also NOT thermal anymore because the quantity of cold atoms rose significantly. But we all know that this energy distribution won’t last forever. Ice cubes melt after a certain time and the energy distribution becomes thermal again. The time until a system reaches thermal equilibrium after it is brought out of it is called thermalization time.

This means that within a short time period the energy distribution of the magnon gas becomes thermal again. During this process magnons cannot dissipate into the crystalline lattice as it takes a longer time.

Consequently the magnon gas is not able to minimize its free energy by magnon destruction. So for a short time period we have a magnon gas with thermal energy distribution and a chemical potential that is greater than zero. This state is called quasi-equilibrium.

I would like to point out the terms quasi-equilibrium and thermal-equilibrium more precisely.

It might sound strange that we make such huge efforts in order to get a special phase of matter for at best one microsecond. And there is also the question whether the concept of quasi equilibrium is a real physical concept or not. I would therefore like to connect the concept of quasi equilibrium with something that is more familiar to the reader.

Let us consider a shelter in a cold winter’s night. Let’s further assume that there is a heater in this shelter and the shelter is thermally well isolated. A poor family lives in this shelter. The family can only effort to let the heater run for one hour before the night. When they do so, the heater produces warmth very quickly. So within one hour the shelter is warmed up to let’s say 25°C.

As the house is thermally good insulated, it takes a very long time until the heat is radiated into the environment of the shelter. So if the shelter is sufficiently insulated, it will keep a more or less constant temperature over time, before the heat gets dissipated into the environment. We can consider the inside of the shelter as being in a thermal equilibrium, as it can be labeled with a temperature which is ONLY defined in thermal equilibrium, but it is not in thermal equilibrium with its environment, as the dissipation of heat takes a long time due to the good isolation. The shelter can then be considered as being in quasi-equilibrium.

This system bears some analogy to the magnon gas in a YIG film in quasi equilibrium. We just have to identify the shelter as the magnon gas, the heater as the microwave field, the environment of the shelter as the crystalline lattice and the thermal insulation as the conversion efficiency between spin- and lattice vibrations.

We see that quasi equilibrium is a real physical concept which we encounter in everyday life. The difference between the magnon gas and the shelter are the different time scales on which a quasi equilibrium can be maintained.

For the shelter the time span was about a few hours, which is a sufficiently long time to do a lot of things like cooking washing, hanging around or sleeping. In the magnon system the time span was only up to one microsecond. This seems to be a very short time. If we on the other hand take a look on the time scales which are important in microelectronics, especially in CPU-Units this time span appears large. Normal CPUs work at a clock rate of a few GHz, which essentially means that the chip can perform one operation within one nanosecond. So within one microsecond a normal CPU can perform up to 1000 operations, so several operations can be done with the mBEC until it is destroyed.

A quasi equilibium is not the only form of equilibrium, that can support a Magnon Bose Einstein Condensate. Another one is the, so called, flow equilibrium. The next section treats the question:

What is flow equilibrium?

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