Small ferrite-disk particles with magnetostatic (magneto-dipole) oscillations are characterized by the topological-phase states - the vortex states. In a recently published paper (Kamenetskii et al 2010 Phys. Rev. A 81 053823), it was shown that such magnetic vortices act as traps, providing purely subwavelength confinement of electromagnetic fields. The symmetry properties of magnetostatic-vortex ferrite disks allow one to propose new-type subwavelength microwave structures. In this paper it is demonstrated that the unique topological properties of the fields in a ferrite disk are intimately related to the symmetry breaking effects of magnetostatic oscillations. This analysis is based on postulates about a physical meaning of the magnetostatic-potential function ψ(r→, t) as a complex scalar wavefunction, which presumes a long-range phase coherence in magnetic dipole-dipole interactions. The proper solutions are found based on an analysis of magnetostatic-wave propagation in a helical coordinate system. It is shown that while a composition of two helical waves may acquire a geometrical phase over-running of 2π during a period, every separate helical wave has a dynamical phase over-running of π and so behaves as a double-valued function. This results in the appearance of helical-mode magnetostatic resonances in quasi-2D ferrite disks. The solutions give magnetostatic-wave power-flow-density vortices with cores at the disk center and azimuthally running waves of magnetization. The near fields of magnetostatic-vortex ferrite-disk particles are characterized by space-time symmetry violation. For incident electromagnetic waves, such particles, with sizes much less than the free-space electromagnetic wavelength, appear as local singular regions. From the properties of a composition of magnetostatic-vortex ferrite-disk particles, one may propose novel metamaterials - singular metamaterials.