Certain aspects relate to topologies for an interior permanent magnet (IPM) electrical machine having increased saliency torque, increased flux-linkage, reduced magnet leakage flux, and reduced detrimental slotting effects compared to existing IPM electrical machines. The IPM electrical machine includes a rotor having a number of poles and a flux barrier formed along the edge of the rotor between poles. The flux barrier contains a magnet or set of magnets having a varying thickness, with a central thickest portion located along the d-axis of the rotor. A magnet retention structure, which may be formed integrally with the rotor or provided as a separate structure, surrounds the rotor and magnets. The rotor and magnets combine to form a smooth circular profile having no air gaps.