Rotating-Field Technique for Galvanomagnetic Measurements

Abstract

The isothermal galvanomagnetic behavior of an isotropic conductor in a magnetic field can be described by the vector equation E =ρ ⊥ j + n ( j · n ) (ρ ∥ −ρ ⊥ )+ρ H ( n × j ) ,relating the electric fieldE to the current densityj. The resistivities ρ ∥ and ρ ⊥ are those which result when the magnetic induction is parallel to j, and normal to j, respectively; ρH is the Hall resistivity. The vector n is a unit vector which has the direction of the induction. When j is directed along the x axis, and n is made to rotate in the x‐y plane with angular frequency ω, one obtains an electric field with ac components Ẽ x = 1 2 j x (ρ ∥ −ρ ⊥ ) cos 2ωt, Ẽ y = 1 2 j x (ρ ∥ −ρ ⊥ ) sin 2ωt. These equations describe the magnetoresistive effects in a rotating magnetic field. On the other hand, if n is allowed to rotate in the x‐z plane, the y component of the electric field becomes Ẽ y =ρ H j x sin ωt .This equation describes the Hall effect in a rotating field. By measuring the ac components of E having frequencies ω and 2ω when jx is known, ρ ∥ −ρ ⊥ and ρH can be determined. This rotating‐field technique is being used to study the galvanomagnetic properties of ferromagnetic films of rectangular geometry. The films are placed in the field of a magnet rotating at a frequency of 20 cps. When the magnetic field is in the plane of the film, the magnetoresistive equations apply, as has been verified by measuringẼx and Ẽy using a wave analyzer. No components having a frequency other than 2ω (40 cps) were detected. The absence of a component with frequency ω shows that no ``Umkehreffekt'' is present in the magnetoresistance. If the wave analyzer is replaced by a high‐gain amplifier having a narrow band‐pass at 40 cps, it is possible to detect a magnetoresistive change (ρ ∥ −ρ ⊥ )/ρ ∥ =10 −6 in a typical film of 10‐Ω resistance. A particular advantage of this method is that it is not susceptible to small variations in ρ∥ or ρ⊥ due to fluctuations in temperature. Thus, measurements as a function of temperature are easily and rapidly obtainable. The utility of the technique is demonstrated by measurements of ρ ∥ −ρ ⊥ as a function of composition in Ni‐Fe alloy films having fcc and bcc structures near 30% Ni. The effect of allotropic transformations (fcc→bcc) on magnetoresistance in these films is also presented. It has been found that this transformation occurs with greater difficulty in films on glass substrates than in the bulk alloys.