R-t-b-based magnet, motor, and generator

An R-T-B-based magnet comprising

• one or more of rare earth elements;
• one or more of transition metal elements, including iron, or two or more of transition metal elements, including iron and cobalt;
• boron;
• an element M that is gallium, or gallium and aluminum;
• and carbon,
• wherein a content ratio of the rare earth elements is set as “a”, a content ratio of the transition metal elements is set as “b”, a content ratio of boron is set as “c”, a content ratio of the element M is set as “d”, and a content ratio of carbon is set as “e” when the sum of elements contained in the R-T-B-based magnet is set to 100 at %, a, b, c, d, and e satisfy the following relationship,
• 14 at %≤a≤20 at %,
• 70 at %≤b≤82 at %,
• 4 at %≤c≤7 at %,
• 0.010≤d/b≤0.035, and
• 0.025≤e/b≤0.055,
• the R-T-B-based magnet includes main phase crystal grains composed of a compound having an R2T14B-type tetragonal structure, and a grain boundary phase existing between the main phase crystal grains,
• the grain boundary phase includes an R-T-M-C phase containing one or more of the rare earth elements, one or more of the transition metal elements or two or more of the transition metal elements, the element M, and carbon,
• the R-T-M-C phase satisfies relationships of RRC>RMP, TRC<TMP, MRC>MMP, and CRC>CMP, and RRC and MRC satisfy a relationship of 0.07≤MRC/RRC≤0.65, when content ratios of the rare earth elements, the transition metal elements, the element M, and carbon contained in the main phase crystal grains are respectively set as RMP, TMP, MMP, and CMP, and content ratios of the rare earth elements, the transition metal elements, the element M, and carbon contained in the R-T-M-C phase are respectively set as RRC, TRC, MRC, and CRC.