Structure and magnetism of homometallic ludwigites:<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mtext>Co</mml:mtext></mml:mrow><mml:mn>3</mml:mn></mml:msub><mml:msub><mml:mtext>O</mml:mtext><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mrow><mml:mtext>BO</mml:mtext></mml:mrow><mml:mn>3</mml:mn></mml:msub></mml:mrow></mml:math>versus<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mtext>Fe</mml:mtext></mml:mrow><mml:mn>3</mml:mn></mml:msub><mml:msub><mml:mtext>O</mml:mtext><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mrow><mml:mtext>BO</mml:mtext></mml:mrow><mml:mn>3</mml:mn></mml:msub></mml:mrow></mml:math>

We present an extensive study of the structural, magnetic, and thermodynamic properties of the oxyborate ${\text{Co}}_{3}{\text{O}}_{2}{\text{BO}}_{3}$. This is carried out through x-ray diffraction, static and dynamic magnetic susceptibilities, and specific heat experiments in single crystals in a large temperature range. The structure of ${\text{Co}}_{3}{\text{O}}_{2}{\text{BO}}_{3}$ is composed of subunits in the form of three-leg ladders where Co ions with mixed valency are located. The magnetic properties of this Co ludwigite are determined by a competition between superexchange and double-exchange interactions in the low-dimensional subunits. We discuss the observed physical properties in comparison with the only other known homometallic ludwigite, ${\text{Fe}}_{3}{\text{O}}_{2}{\text{BO}}_{3}$. The latter presents a structural distortion in the ladders and two magnetic transitions. Both features are not found in the present study of the Co ludwigite. The reason for these differences in the structural and magnetic behavior of two apparently similar compounds is discussed.