*

The high precision time domain terahertz spectroscopy has uncovered exceptionally strong and unconventional Ho-Mn spin interactions in hexagonal HoMnO₃, manifesting as the mysterious asymmetrical splitting of antiferromagnetic resonance modes under weak external magnetic field along c-axis. The asymmetry indicates substantially different g-factors for the high and low energy branches of this excitation. To understand this, we studied the spin excitations on the Mn sublattice, focusing on the interaction between Mn ions and their nearest neighbor Ho layers. We propose a scenario including the simultaneous presence of Dzyaloshinskii-Moriya interaction between Mn ions and 2a Ho ions, and a quartic term possibly originating from high-order interaction. The significant renormalization of g-factors observed near the Ho ordering temperature is also explained.