Magnetotransport measurements

Magnetotransport measurements provide a sensitive tool to study magnetic anisotropy and magnetization reversal in low-dimensional magnetic structures. They also provide information on transport-related phenomena such as the spin-dependent scattering mechanism of carriers. One important advantage of magnetotransport, particularly for the case of FM/SC hybrid structures, is its relative insensitivity to a semiconducting or insulating substrate. For thin films, it is difficult to subtract the magnetic contribution of the substrate in traditional magnetometry techniques like vibrating sample magnetometry or SQUID magnetometry. In magnetotransport, only the metallic portion of the sample (the thin film) is measured. Another advantage of magnetotransport is the simplicity of the experimental set-up and the relative low cost of the equipment.

Figure 0.1: The geometry of magnetotransport measurements. (a) Magnetic field is applied in-plane. The longitudinal magnetoresistance is referred to as anisotropic magnetoresistance (R_xx) and the transverse magnetoresistance (R_xy) as planar Hall effect. (b) Magnetic field is applied perpendicular to the film plane and the transverse resistance is measured. This is the usual Hall effect geometry. For ferromagnets this is sum of ordinary and extraordinary Hall effect.

The subject of galvanomagnetism is rather vast. One of the most important type of electrical resistance change in ferromagnetic metals, which is to be studied in this work, is the one associated with the direction of magnetization relative to the current. Magnetotransport measurements can be performed in several applied magnetic field geometries as defined schematically in Fig. 1. When the magnetic field is applied in-plane [Fig. 1 (a)], the longitudinal resistance R_xx is referred to as anisotropic magnetoresistance (AMR), and the transverse resistance R_xy as the planar Hall effect (PHE). For perpendicular magnetic field [Fig. 1 (b)], two contributions arise in the transverse resistance of ferromagnets. The ordinary Hall effect (OHE) arises from the Lorenz force while the Anomalous Hall effect (AHE) (also called extraordinary Hall effect) is related to the magnetization of the thin film. The electric field E for arbitrary orientations of the external magnetic field H and magnetization M for a polycrystalline and single domain ferromagnetic sample is often written in the following way [1,[2]:

where J is the current density and [^(a)] is a unit vector in the direction of the magnetic moment of the single domain sample. r_^ and r_|| are the longitudinal resistivities parallel and perpendicular to [^(a)], respectively. r_AHE is the transverse resistivity for the magnetization perpendicular to the film plane. Thus the last term denotes the AHE. The first two terms represent both AMR and PHE. When the magnetic field is applied in the film plane with a current along the x-axis, we can find from Eq. (1) [1,[2]:

where q_M represents the angle between J (or x-axis) and [^(a)]. These Eqs. (2) and (3) are conventionally used to describe the AMR and PHE, respectively. It may be pointed out that the above three equations are simplified form for polycrystalline samples and do not necessarily describe the behavior of single crystalline samples. When a saturating field H with components H_i=Ha_i, is applied to a crystal, the relationship between the electric field E and current density J is defined through the relation:

where r_ij(a) is a second-rank magnetoresistivity tensor and E_i (J_j) are components of E (J). Here, the Einstein summation convention is understood. The tensor r_ij(a) depends on the direction cosines, a_i. Since r_ij(a) is a second-rank tensor it can be divided into its symmetrical and antisymmetrical parts:

and

The Onsager's theorem [3] applied to a magnetically saturated crystal implies that:

so that r_ij^s is an even function of the a_i and r_ij^a is an odd function of the a_i. In fact it can be easily shown that AMR originates from the symmetric part of the resistivity tensor whereas the AHE originates from the antisymmetric part of the resistivity tensor. Though there is very few literature examining the exact origin of PHE, usually the PHE is also attributed to the symmetric part of the resistivity tensor.

Bibliography

[1]

T. McGuire and R. Potter, IEEE Trans. Magn. 11, 1018 (1975).

[2]

J. P. Jan, in Solid State Physics, edited by F. Seitz and D. Turnbull (Academic Press Inc., New York, 1957), vol. 5, pp. 1-96.

[3]

R. R. Birss, Symmetry and Magnetism (North-Holland Publishing Company, Amsterdam, 1964), p. 70.

File translated from T_EX by T_TH, version 3.68.
On 20 Oct 2005, 17:23.

Last Updated Wednesday October 26, 2005