Field-induced metamagnetic transitions and two-dimensional excitations in ludwigite <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi mathvariant="bold">Co</mml:mi><mml:mrow><mml:mn mathvariant="bold">4</mml:mn><mml:mo>.</mml:mo><mml:mn mathvariant="bold">76</mml:mn></mml:mrow></mml:msub><mml:msub><mml:mi mathvariant="bold">Al</mml:mi><mml:mrow><mml:mn mathvariant="bold">1</mml:mn><mml:mo>.</mml:mo><mml:mn mathvariant="bold">24</mml:mn></mml:mrow></mml:msub><mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi mathvariant="bold">O</mml:mi><mml:mn mathvariant="bold">2</mml:mn></mml:msub><mml:msub><mml:mi mathvariant="bold">BO</mml:mi><mml:mn mathvariant="bold">3</mml:mn></mml:msub><mml:mo>)</mml:mo></mml:mrow><mml:mn mathvariant="bold">2</mml:mn></mml:msub></mml:mrow></mml:math>

This paper presents an extensive study of the structural, magnetic, and thermodynamic properties of the heterometallic ludwigite ${\mathrm{Co}}_{4.76}{\mathrm{Al}}_{1.24}{({\mathrm{O}}_{2}{\mathrm{BO}}_{3})}_{2}$. This material orders ferrimagnetically at 57 K. Despite the fact that, in ${\mathrm{Co}}_{4.76}{\mathrm{Al}}_{1.24}{({\mathrm{O}}_{2}{\mathrm{BO}}_{3})}_{2}$, one quarter of the Co ions of the parent compound ${\mathrm{Co}}_{3}{\mathrm{O}}_{2}{\mathrm{BO}}_{3}$ is replaced by nonmagnetic ${\mathrm{Al}}^{3+}$ ions, the ${T}_{C}$ of the former (57 K) is larger than that of the latter (42 K). We obtain the phase diagram of ${\mathrm{Co}}_{4.76}{\mathrm{Al}}_{1.24}{({\mathrm{O}}_{2}{\mathrm{BO}}_{3})}_{2}$ in an external magnetic field. We find a line of second-order phase transitions where the system presents a metamagnetic transition (from 57 to 25 K). This line ends at a tricritical point at 25 K and 4.3 T, below which the transition to the paramagnetic phase is first order (from 25 to 3 K). In the magnetic phase at low temperatures specific heat measurements in zero and finite magnetic fields show that the low-energy excitations are magnetic (magnons) and elastic (phonons) excitations with two-dimensional character. These measurements also reveal the magnetocaloric properties of this material.