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We describe the Bose-Einstein condensate of magnetic bosonic quasiparticlesin insulating spin systems using a phenomenological standard functional methodfor T = 0. We show that results that are already known from advancedcomputational techniques immediately follow. The inclusion of a perturbativeanisotropy term that violates the axial symmetry allows us to remarkably wellexplain a number of experimental features of the dimerized spin-1/2 systemTlCuCl3. Based on an energetic argument we predict a general intrinsicinstability of an axially symmetric magnetic condensate towards a violation ofthis symmetry, which leads to the spontaneous formation of an anisotropy gap inthe energy spectrum above the critical field. We, therefore, expect that a trueGoldstone mode in insulating spin systems, i.e., a strictly linearenergy-dispersion relation down to arbitrarily small excitations energies,cannot be observed in any real material.

U(1)-Symmetry breaking and violation of axial symmetry in TlCuCl3 and other insulating spin systems