Incomplete softening of the antiferromagnetic resonance mode at the spin-reorientation transition in multiferroic <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>GdF</mml:mi> <mml:msub> <mml:mi mathvariant="normal">e</mml

The multiferroic ferroborate $\mathrm{GdF}{\mathrm{e}}_{3}{(\mathrm{B}{\mathrm{O}}_{3})}_{4}$ with huntite-type structure exhibits magnetic ordering below ${T}_{\mathrm{N}}=38$ K and contains two magnetic subsystems associated with Gd and Fe ions. Competing anisotropies of these subsystems drive a spin-reorientation transition at ${T}_{\mathrm{SR}}=10.7$ K, switching the ground state from easy-axis to easy-plane. Using antiferromagnetic resonance, we investigate the spin dynamics across this transition. The observed incomplete softening of a magnon mode during both field- and temperature-induced spin-reorientation transitions indicates the first-order nature of the phase transition, which is accompanied by a discontinuous jump in the effective anisotropy field. We reproduce this behavior using a simple model that attributes the jump in the anisotropy field to the presence of an effective fourth-order anisotropy constant, responsible for the discontinuous character of the transition. Remarkably, for in-plane magnetic fields, we identify a new AFMR mode that persists from 12 K up to ${T}_{\mathrm{N}}$. This mode likely corresponds to the dynamics of a long-period incommensurate state, previously detected by resonant elastic x-ray scattering.