Griffiths phase manifestation in disordered dielectrics

We predict the existence of Griffith phase in the dielectrics with concentrational crossover between dipole glass (electric analog of spin glass) and ferroelectricity. The peculiar representatives of above substances are $KTaO_3:Li$, $Nb$, $Na$ or relaxor ferroelectrics like $Pb_{1-x}La_xZr_{0.65}Ti_{0.35}O_3$. Since this phase exists above ferroelectric phase transition temperature (but below that temperature for ordered substance), we call it "para-glass phase". We assert that the difference between paraelectric and para-glass phase of above substances is the existence of clusters (inherent to "ordinary" Griffiths phase in Ising magnets) of correlated dipoles. We show that randomness play a decisive role in Griffiths (para-glass) phase formation; this phase does not exist in a mean field approximation.Comment: 5 pages, 4 embedded postscript figure

Role of dimensionality in spontaneous magnon decay: easy-plane ferromagnet

We calculate magnon lifetime in an easy-plane ferromagnet on a tetragonal lattice in transverse magnetic field. At zero temperature magnons are unstable with respect to spontaneous decay into two other magnons. Varying ratio of intrachain to interchain exchanges in this model we consider the effect of dimensionality on spontaneous magnon decay. The strongest magnon damping is found in the quasi-one-dimensional case for momenta near the Brillouin zone boundary. The sign of a weak interchain coupling has a little effect on the magnon decay rate. The obtained theoretical results suggest possibility of experimental observation of spontaneous magnon decay in a quasi-one-dimensional ferromagnet CsNiF$_3$. We also find an interesting enhancement of the magnon decay rate for a three-dimensional ferromagnet. The effect is present only for the nearest-neighbor model and is related to effective dimensionality reduction in the two-magnon continuum.Comment: 6 pages, 6 figure

Spontaneous magnon decays in planar ferromagnet

We predict that spin-waves in an easy-plane ferromagnet have a finite lifetime at zero temperature due to spontaneous decays. In zero field the damping is determined by three-magnon decay processes, whereas decays in the two-particle channel dominate in a transverse magnetic field. Explicit calculations of the magnon damping are performed in the framework of the spin-wave theory for the $XXZ$ square-lattice ferromagnet with an anisotropy parameter $\lambda<1$. In zero magnetic field the decays occur for $\lambda^*<\lambda<1$ with $\lambda^*\approx 1/7$. We also discuss possibility of experimental observation of the predicted effect in a number of ferromagnetic insulators.Comment: 6 pages, 6 figures, to appear in Europhysics Letter