Rotating-Field Technique for Galvanomagnetic Measurements

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⊥)+ρH(n×j),relating the electric field E to the current density j. 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 Ẽx=12jx(ρ∥−ρ⊥) cos2ωt,Ẽy=12jx(ρ∥−ρ⊥) sin2ωt.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 Ẽy=ρHjxsinωt. 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 measuring Ẽx 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.