Features of spin waves focusing in ferromagnets

Features of focusing spin waves in ferromagnets with magnetic moment exchange interaction with the closest neighbors and second neighbors are explored. It is shown that in the long-wave approximation, no spin wave focusing occurs: it is observed only in the wavevectors in the second half of the Brillouin zone (at $aq\ge\pi/2$, where $a$ is the lattice constant, $q$ is the value of wavevector). Additionally, it is shown that magnons in such system are focused along directions [110], and are defocused in directions [100]. It is found that the external magnetic field and the magnetic anisotropy field do not cause changes in directions of magnon focusing. When the parameter of exchange interaction with the second neighbors near directions [110] and [111] is negative, magnons form a caustic, near which the intensity of the spin-wave field surges.