<p>This study provides a comprehensive exploration of various localized wave structures in a higher-order Heisenberg ferromagnetic equation, with potential implications for understanding the dynamics of magnetic vectors in isotropic ferromagnetic materials. We start by constructing an iterative generalized Darboux transformation, which allows us to obtain diverse localized wave solutions, such as rogue wave, higher-order rational soliton, and their hybrid wave solutions on periodic and zero/non-zero constant backgrounds. Compared with the classical Heisenberg ferromagnetic equation, the higher-order Heisenberg ferromagnetic equation similarly possesses rogue wave solutions, but they additionally exhibit rational soliton solutions that are not found in the classical counterpart. Particularly, we successfully derive the hybrid interaction structures of rational soliton and periodic wave on vanishing and periodic backgrounds. Intriguingly, we also analyze the magnetic moment distribution and directional shifts of magnetic vectors for rogue wave and rational soliton, revealing that the magnetic vector of rogue wave cannot be distributed throughout the entire sphere. Finally, numerical simulations are conducted to illustrate the evolutions of certain rogue wave and rational soliton solutions. Compared to the classical Heisenberg ferromagnetic equation, the higher-order extension displays a richer diversity of wave structures under periodic and vanishing/non-vanishing backgrounds, which may contribute to a deeper understanding of the motion of magnetic vectors in ferromagnetic materials.</p>