Bose-Einstein condensation of magnons in magnets with predominant ferromagnetic interaction

We discuss Bose-Einstein condensation of magnons (BEC) in magnets with predominant ferromagnetic (FM) interaction in magnetic field $H$ near saturation ($H_c$). Because $H_c$ is independent of FM couplings, magnetic materials of this type can have small $H_c$ that makes them promising candidates for experimental investigation of BEC. Ferromagnets with easy-plane anisotropy and antiferromagnets (AFs) containing weakly coupled FM planes or chains are discussed in detail. We observe small effective interaction between magnons near the QCP in such magnets, in contrast to AFs with strong AF coupling previously discussed. In particular, this smallness allows us to find crossovers in the critical temperature $T_c(H)\propto (H_c-H{)}^{1\mathrm{/}\varphi }$ from $\varphi =3\mathrm{/}2$ to $\varphi =1$ in quasi-1D magnets, and from $\varphi =3\mathrm{/}2$ to $\varphi \approx 1$ ($T_c\ln T_c\propto H_c-H$) in quasi-2D ones.