Fig. 2: Illustration of various spin generation mechanisms in FMs.
From: Spin current and spin-orbit torque induced by ferromagnets
a jAH,↑ and jAH,↓ denote the majority and minority spin current flows induced by the anomalous Hall (AH) effect. The negative sign is introduced for jAH,↓ because its direction is opposite to jAH,↓. The spin anomalous Hall current is given by jAH,↑ − jAH,↓. b A similar mechanism applied for the planar Hall (PH) effect. The spin planar Hall current is given by jPH,↑ − jPH,↓. Here the direction of jPH,↓ is illustrated as the same direction of jPH,↑ because the planar Hall effect mainly originates from anisotropic charge transport. c The spin Hall effect generated in a FM. The magnetization direction is illustrated arbitrarily since the spin Hall effect may occur regardless of the direction of the magnetization. d Precession of spins of the spin Hall current (translucent orange spheres) around the magnetization direction generates a spin current with another spin component, providing an example of the magnetization-dependent spin Hall effect.
