Refined spin Hamiltonian on the Cairo pentagonal lattice of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>Bi</mml:mi> <mml:mn>2</mml:mn> </mml:msub> <mml:msub> <mml:mi>Fe</mml:mi> <mml:mn>4</mml:mn> </mml:msu

The frustrated magnet Bi2Fe4O9 has been reported to exhibit complex spin dynamics coexisting with conventional spin wave excitations. The magnetic Fe3+ (S = 5/2) ions are arranged into a distorted two-dimensional Cairo pentagonal lattice with weak couplings between the layers, developing long-ranged noncollinear antiferromagnetic order below 245 K. In order to enable studies and modeling of the complex dynamics close to TN, we have reexamined the magnetic excitations across the complete energy scale (0 &lt; h&lt;overline&gt;omega &lt; 90 meV) at 10 K. We discover two distinct gaps, which can be explained by introducing, respectively, easy axis and easy plane anisotropy on the two unequivalent Fe sites. We develop a refined spin Hamiltonian that accurately accounts for the dispersion of essentially all spin-wave branches across the full spectral range, except around 40 meV, where a splitting and dispersion are observed. Polarization analysis shows that the system has magnetic anisotropic fluctuations, consistent with our model. A continuum of scattering is observed above the spin wave branches and is found to principally be explained by an instrumental resolution effect. The full experimental mapping of the excitation spectrum and the refined spin Hamiltonian provides a foundation for future quantitative studies of spin waves coexisting with unconventional magnetic fluctuations in this frustrated magnet found at higher temperatures.