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We present a mean-field theory describing the influence of long-range dipolarforces on the temperature transition from the paramagnetic to ordered phases infrustrated Heisenberg spiral magnets. It is shown that the dipolar interactionproduces a cascade of first- and second- order phase transitions between theparamagnetic and the spiral states upon temperature decreasing. Depending onsystem parameters, the following intermediate phases can arise: anincommensurate and a commensurate sinusoidally modulated states, spiral phasesin which perpendicular spin components have different amplitudes and aremodulated with the same and with different wave vectors. We distinguish sixpossible sequences of phase transitions upon temperature decreasing at leastfour of which were observed before experimentally in specific compounds. It isfound that the action of dipolar forces cannot always be modeled evenqualitatively by small one-ion anisotropic spin interactions. We demonstratethat the dipolar interaction is responsible for successive phase transitions inthe triangular-lattice multiferroic MnI$_2$: almost all available experimentalfindings are described quantitatively within the mean-field theory by takinginto account the exchange, the dipolar and small symmetry-allowed anisotropicspin interactions.

Cascades of phase transitions in spiral magnets caused by dipolar forces