Magnon softening in metals at quantizing magnetic fields

Diamagnetic phase transition is shown to be associated with the instability of the three-dimensional electron gas against a temperature dependent magnon soft mode whose frequency vanishes at the phase transition point. Temperature and sample size softening of the magnon mode of an orbital nature is considered at quantizing magnetic fields under conditions of the non-linear de Haas-van Alphen effect in bulk metals and confined metallic samples.