Mesoscopic mixing of spin orientation phases in particles with Ising ions: Holmium: Yttrium iron garnets in strong magnetic fields

The paper presents a theoretical analysis of macroscopic quantum tunneling phenomena in small particles of a cubic ferromagnet of the Ho_xY_3?xFe₅O₁₂ type with strongly anisotropic (Ising) impurity ions present in a low concentration x ? 1 in the region of strong magnetic fields, at which many orientation phase transitions related to the competition of external and exchange field actions on the spin subsystem are observed. The theory of path integrals for the magnetic subsystem was used to calculate the instanton contributions to interphase tunneling amplitudes in the vicinity of first-order transitions for three principal orientations of an external magnetic field in a cubic crystal. It was shown that low-energy barriers separating angular phases could result in anomalously large mesoscopic volumes at which macroscopic spin tunneling effects could appear in the energy spectra of particles. The special features of spectral splitting caused by the mixing of azimuthally degenerate angular phases and phases with different polar angles of magnetization orientation were revealed.