Three-Magnon Linewidth and Effective Exchange Constant in a Hexagonal Ferrite, Zn ₂ Y

The three-magnon linewidth in the ferromagnetic resonance absorption experiment of Zn 2 Y (Ba 2 Zn 2 Fe 12 O 22 ), which arises from destruction of a k =0 magnon with the simultaneous creation of two magnons having half the uniform mode frequency and having equal and opposite wavenumber vectors, is measured separately from the other linewidths. The theoretical three-magnon linewidth is calculated by the transition probability method for the anisotropy energy and demagnetizing energy. The complete agreement between the experimental three-magnon linewidth and the theoretical one is achieved when the effective exchange constants are D ⊥ =0.13×10 -9 Oe cm 2 and D || =6.8×10 -9 Oe cm 2 within and between the crystallographic c planes.