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Unformatted text preview: 7 – 10 Three main mechanisms have been proposed for AHE, including intrinsic deflection, side jump, and skew scattering. The AHE in an intrinsic homogeneous mag- netic material is related to spin polarization due to different states of spin up and spin down at the Fermi energy level, which matches the Berry phase theory. 11 In the case of inhomogeneous magnetic materials, however, the AHE implies the presence of the spin-dependent scattering mechanism. The skew scattering dominates at low temperature, while the side jump becomes im- portant at high temperature. 7 Interestingly, the observation of AHE in inhomogeneous ferromagnets, especially in ferromag- netic clusters embedded in a non-magnetic material matrix, pro- vides evidence for interaction between spin-carriers and localized magnetic clusters. However, it is difficult to distin- guish these two intrinsic and extrinsic phenomena. The Hall effect in magnetic materials is commonly described by the phenomenological equation (1) , where q H is the Hall resistivity, H the magnetic induction, and M the magnetization in the z-direction. 12 q H ¼ R o H þ R AHE M : (1) A specific feature of ferromagnetic materials is that their Hall resistivity possesses two components, one of which is due to the Lorentz force and is proportional to the magnetic induc- tion B (the normal part), while the other is proportional to the magnetization M (the anomalous part). The latter is related to the influence of the SOI on the scattering of spin-polarized carriers and is much greater than the normal component. In addition, it has been experimentally confirmed that ferromagnetic materials follow the law of approach to satura- tion (2) , where M S is the saturation magnetization, and a , b , and v are constants. 13 M ¼ M s 1 ÿ a H ÿ b H 2 þ v H : (2) By plugging M identified from Eq. (2) into Eq. (1) , we have q H ¼ R o H þ R AHE M s 1 ÿ a H ÿ b H 2 þ v H : (3) From Eq. (3) , it is clear that the Hall resistance is dependent on a , b , and v . We note that the first term of b / H 2 is contrib- uted of magnetocrystalline, 14 , 15 stress, 16 and shape anisot- ropy. 17 The second term of a / H is known as the magnetic hardness but it still remains theoretically controversial because this term is impossible or only effective in a certain field range because it can lead to an indefinite energy of magnetization. 18 The v H term is often referred to as the so- call paramagnetism-like term proportional to H 1/2 , whose or- igin may lie in the defects present in ferromagnetic materials. 19 – 21 Furthermore, Zhang et al. reported that the a / H , b / H 2 , and v H terms all originate from the magnetocrys- talline anisotropy....
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- Fall '13
- Magnetism, Magnetic Field, Magnetic moment, Magnetic anisotropy, out-of-plane magnetic anisotropy, in-plane magnetic anisotropy