I. What are the creation and destruction mechanisms for magnons?

There are mainly two ways to excite magnons. Thermal fluctuations are always a way to produce magnons. When atoms vibrate on their lattice sites due to thermal energy, their electron cloud vibrates along with them. But when the electron cloud vibrates the spin of these electrons also vibrates. In the manner described in section 2a these vibrations can propagate through the spin system forming a spin-wave or magnon. The problem is that this thermally excited magnon gas is always in absolute thermal equilibrium and has therefore zeroed chemical potential, so it doesn’t help us a lot.

Another possibility is to excite spin-waves through an alternating magnetic field. Spins on the lattice sites will try to follow the external magnetic field, like a compass in the earth’s magnetic field. Spin waves in YIG-films have typically frequencies in the GHz (Gigahertz) range. So we need alternating magnetic fields in the GHz regime to excite these spin-waves. The easiest way is to use electromagnetic radiation with GHz frequency. These are simply microwaves, the same ones that are used in the microwave ovens. An electromagnetic wave consists always of oscillating electric- and magnetic fields. For our purpose we utilize the magnetic field component of the electromagnetic wave in order to excite spin waves. This happens on an incredibly fast time scale. As soon as a microwave field is applied to the YIG film spin waves are generated nearly instantly. The energy and velocity distribution of this induced magnons depends strongly on the shape and frequency of the electromagnetic field. Especially the energy of excited magnons is proportional to the frequency of the electromagnetic field. When we excite magnons with an electromagnetic field of a single frequency all magnons excited by this field will have energy proportional to that frequency. This energy distribution is NOT thermal! It is now obvious that this is a mechanism that can produce a magnon gas that is out of thermal equilibrium.

Now let’s consider the possible mechanisms that destroy magnons. The main mechanism is dissipation into the crystalline lattice. This means that the vibration of spins excites vibrations of the atoms on the lattice sites which we percept as heat. Generally it takes some time till the spin vibrations induce lattice vibrations. The time scale for this process in YIG films is typically in the microsecond regime.

So now we know the main mechanisms that are responsible for the creation and destruction of magnons. And we know one mechanism with which it is possible to create an out of thermal equilibrium magnon gas. This sounds good, but there is a small problem. Bose-Einstein condensation is ONLY defined IN thermal equilibrium.

So the next question is:

How does a magnon gas reach a thermal energy distribution?

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