In ferromagnetic materials atoms having unpaired electrons act as individual magnets. Their magnetism is mostly caused by the magnetic moments of the uncompensated electron spins. Since these atomic magnets tend to be oriented in the same direction due to quantum-mechanical exchange interaction, a macroscopic magnetic moment appears. As the atoms strongly interact, a reversal of a single atomic magnetic moment is not spatially localized but spreads through the solid as a wave of discrete magnetic momentum transfer. This wave is known as a spin wave, and in frame of second quantization it is associated with a quasi-particle named magnon. Weakly interacting magnons can be considered as a gas of magnetic bosonic quasi-particles and, therefore, this is referred to as a magnon gas.

Nowadays magnon gases are recognized as an excellent model environment for the experimental investigation of collective classical and quantum macroscopic properties of bosonic systems. Its potential is due to the wide controllability of the magnon density as well as of the spectral properties influencing the magnon-magnon interaction. For example, the dispersion branch of a magnon gas can be frequency shifted or otherwise modified by change in the strength or orientation of a bias magnetic field. The magnon population density can be effectively controlled by means of electro-magnetic parametric pumping (see Gurevich and Melkov, Magnetization Oscillation and Waves, CRC, Cleveland, 1996). In the simplest case one photon of the pumping electromagnetic field excites two magnons with half the energy/frequency that propagate in opposite directions. Such a mechanism creates a huge quantity of phase correlated magnons, which are called a condensate of photon-coupled magnon pairs. The behavior of parametrically created magnon condensates, of gaseous magnon phases, and of Bose-Einstein condensates (BEC), which can be formed at the lowest energy state of a magnon gas, constitutes a hot research topic. The main goal of our work is to study the phase transition processes resulting in the formation of quantum macroscopic states of a magnon gas and to understand the role of magnon-magnon and magnon-phonon interactions in the properties of these correlated states of matter in comparison with the dynamics of ultra-cold quantum gases and quantum spin systems. We investigate the dynamics of the magnon system in a low-damping magnetic insulator (yttrium-iron-garnet, YIG) using wavevector- and time-resolved Brillouin light scattering (BLS) spectroscopy with special attention on the pump-free evolution of the magnetic medium after pumping. A focus lies on transport phenomena in magnon condensates including phase induced supercurrents.