  Starting from a phenomenological standard energy functional to describe the
condensation of a dilute gas of bosonic quasiparticles in magnetic insulators,
we find that the inclusion of a perturbation term that explicitly violates the
axial symmetry significantly modifies the details of the resulting Bose
Einstein condensation. Systems with an originally axial symmetry must show an
intrinsic tendency to spontaneously violate this symmetry as soon as the
condensation sets in, and the phase transition at the respective critical field
may even become of first order. We can explain a number of features in the
experimental data of various insulating spin systems, such as a slightly
nonlinear magnetization near the critical field as well as hysteresis effects
and peculiarities in the energy-level scheme of TlCuCl3. We also offer a
consistent explanation for certain anomalies in the magnetocaloric effect and
in the magnetization of BaCuSi2O6 by assuming a spontaneous violation of axial
symmetry at the magnetic phase transition on an energy scale of about 1
micro-eV. The resulting anisotropy gap in the magnetic excitation spectrum,
that inevitably forms at the critical field of all such systems, lifts the
linear Goldstone mode and is therefore seriously limiting the lifetime of
magnetic condensates to a few nanoseconds at most.
