An R-T-B based permanent magnet including a rare earth element R, a transition metal element T, B, and Ga,
- wherein the R-T-B based permanent magnet includes at least Nd as R,
- the R-T-B based permanent magnet includes at least Fe as T,
- the R-T-B based permanent magnet comprises a plurality of main phase grains containing Nd, T, and B;
- and grain boundaries surrounded by a plurality of the main phase grains,
- at least a portion of the grain boundaries contains a first T rich phase,
- at least a portion of the grain boundaries contains a second T rich phase,
- at least a portion of the grain boundaries contains a T poor phase,
- the first T rich phase is a phase containing Nd, Ga, and at least one of Fe and Co and satisfying the following Formula 1,
- the second T rich phase is a phase containing Nd, Ga, and at least one of Fe and Co and satisfying the following Formula 2,
- the T poor phase is a phase containing Nd and satisfying the following Formula 3,
- the first T rich phase, the second T rich phase, and the T poor phase satisfy the following Formula 4, and
- the first T rich phase and the second T rich phase satisfy the following Formula 5:
- 1.7≤[T]/[R]≤3.0 (1)
- 0.8≤[T]/[R]≤1.5 (2)
- 0.0≤[T]/[R]≤0.6 (3)
- wherein [T] in the Formula 1 represents the sum of the concentrations of Fe and Co in the first T rich phase;
- [R] in the Formula 1 represents the sum of the concentrations of Nd, Pr, Tb, and Dy in the first T rich phase;
- [T] in the Formula 2 represents the sum of the concentrations of Fe and Co in the second T rich phase;
- [R] in the Formula 2 represents the sum of the concentrations of Nd, Pr, Tb, and Dy in the second T rich phase;
- [T] in the Formula 3 represents the sum of the concentrations of Fe and Co in the T poor phase;
- [R] in the Formula 3 represents the sum of the concentrations of Nd, Pr, Tb, and Dy in the T poor phase;
- and the respective units of [T] and [R] in the Formula 1, the Formula 2, and the Formula 3 are atom %,
- 0.30≤(S1+S2)/(S1+S2+S3)≤0.80 (4)
- 0.20≤S2/(S1+S2)≤0.80 (5)
- wherein S1 in the Formula 4 and the Formula 5 represents the sum of the areas of the first T rich phase exposed at a cross-section of the R-T-B based permanent magnet;
- S2 in the Formula 4 and the Formula 5 represents the sum of the areas of the second T rich phase exposed at the cross-section of the R-T-B based permanent magnet;
- and S3 in the Formula 4 represents the sum of the areas of the T poor phase exposed at the cross-section of the R-T-B based permanent magnet.