Some variations provide a permanent-magnet structure comprising: a region having a plurality of magnetic domains and a region-average magnetic axis, wherein each of the magnetic domains has a domain magnetic axis that is substantially aligned with the region-average magnetic axis, and wherein the plurality of magnetic domains is characterized by an average magnetic domain size. Within the region, there is a plurality of metal-containing grains characterized by an average grain size, and each of the magnetic domains has a domain easy axis that is dictated by a crystallographic texture of the metal-containing grains. The region has a region-average easy axis based on the average value of the domain easy axis within that region. The region-average magnetic axis and the region-average easy axis form a region-average alignment angle that has a standard deviation less than 30° within the plurality of magnetic domains. Many permanent-magnet structures are disclosed herein.