Permanent magnet and rotary electrical machine

A permanent magnet expressed by a composition formula:

• RpFeqMrCutCo100-p-q-r-t
• where R is at least one element selected from the group consisting of rare earth elements, M is at least one element selected from the group consisting of Zr, Ti, and Hf, p is a number satisfying 11.05≤p≤12.4 atomic %, q is a number satisfying 28≤q≤29.18 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 permanent magnet comprising:
• a metal structure including cell phases and Cu-rich phases provided to divide the cell phases, each cell phase having a Th2Zn17 crystal phase, and each Cu-rich phase having a Cu concentration higher than that of the Th2Zn17 crystal phase,
• wherein an Fe concentration of the Th2Zn17 crystal phase is not less than 30 atomic % nor more than 45 atomic %,
• wherein the Cu concentration of each Cu-rich phase is 30 atomic % or more,
• wherein each Cu-rich phase is defined by a plate region on a Cu-mapped image of a cross section of the metal structure by transmission electron microscope energy dispersive x-ray spectroscopy, the cross section including a c-axis of the Th2Zn17 crystal phase, the plate regions being provided between the cell phases and having a width of 50 nm or less,
• wherein an average length of the Cu-rich phases is not less than 179 nm nor more than 243 nm,
• the average length of the Cu-rich phases being defined by an average value of five average lengths, the five average lengths being defined by a remainder excluding a maximum average length and a minimum average length from seven average lengths, and each of the seven average lengths being defined by an average length of the plate regions in each Cu-mapped image,
• each length of the plate regions being defined by
• a length from an intersection point between one end of one of the plate regions in a longitudinal direction and another one of the plate regions to an intersection point between another end of one of the plate regions in the longitudinal direction and another one of the plate regions,
• a length from one end of one of the plate regions in the longitudinal direction to another end of one of the plate regions in the longitudinal direction, or
• a length from an intersection point between one end of one of the plate regions in the longitudinal direction and another one of the plate regions to another end of one of the plate regions in the longitudinal direction,
• wherein the number of the Cu-rich phases is 20 or more in a region having an area of 1 μm2 in the cross section, and
• wherein a coercive force of the permanent magnet is 1530 kA/m or more and 1850 kA/m or less.