Permanent magnet and rotary electrical machine

A permanent magnet expressed by a composition formula:

• (R1-xAx)pFeqMrCutCo100-p-q-r-t
• where A is at least one element selected from the group consisting of Ce, Pr, and Nd, R is at least one element selected from the group consisting of rare earth elements except for the element A, M is at least one element selected from the group consisting of Zr, Ti, and Hf, x is a number satisfying 0.02≦x≦0.2, p is a number satisfying 10.5≦p≦12.4 atomic %, q is a number satisfying 28≦q≦40 atomic %, r is a number satisfying 0.88≦r≦4.3 atomic %, and t is a number satisfying 3.5≦t≦13.5 atomic %,
• the magnet comprising:
• a metal structure including a plurality of crystal grains which constitutes a main phase having a Th2Zn17 crystal phase,
• wherein an Fe concentration of each of the crystal grains is 28 atomic % or more, and
• a concentration difference of the element A among the crystal grains is not less than 0.2 atomic % nor more than 3.0 atomic %.