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A possible mechanism for uniaxial anisotropy in ferromagnetic films is the magnetoelastic energy Wλ which results from the constraint imposed on the film by the substrate. Below some temperature T′ at which the mobility of the film atoms on the substrate is sufficiently low, the constraint prevents the film from deforming in magnetostriction. An increase in the magnetoelastic energy, therefore, occurs when the film is magnetized in a direction other than that in which the film was deposited.This paper examines this constraint energy in detail and shows that earlier calculations which have been based on the average polycrystalline magnetostriction are not correct in principle, since the correct calculation requires averaging the magnetoelastic energy over a polycrystalline aggregate. For the maximum value of Wλ at room temperature the correct calculation gives 4.2, 1.8, and 42 (103 erg cm−3) in nickel, iron, and cobalt, respectively. The value for iron is an order of magnitude larger than that given by ear...

In low saturating magnetic field, the magnetoresistive effect in a polycrystalline ferromagnet is described by the relation Δρ/Δρ0 = cos2α where Δρ is the resistivity change which occurs when the saturation magnetization Ms is oriented first normal then at an angle α to the electric current i. The maximum change Δρ0 is characteristic of the material. The uniform rotation model of a uniaxially anisotropic film in a transverse magnetic field H⊥ leads to a dependence of Δρ on H⊥ of the form Δρ/Δρ0 = h⊥2 when i is normal to the anisotropy axis (K axis) and of the form Δρ/Δρ0 = 1−h⊥2 when i is parallel to the K axis. In these expressions h⊥ is the ratio of H⊥ to HK, where HK = 2K/Ms, and K is the anisotropy energy constant. The present paper treats the transverse magnetization process in Ni-Fe alloy films on the basis of a simple model in which the K axes in local regions of the film are dispersed in direction about an average 〈K〉 axis. For a single numerical value of the dispersion angle β the transverse magn...

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.T...

The temperature dependence of the difference between the demagnetized and saturation ultrasonic absorptions has been measured between 77° and 650°K. From 77° to above 400°K, at 10 mc sec−1, this difference is found to be inversely proportional to the first‐order magnetocrystalline anisotropy constant K1 to approximately the first power. This result shows the inadequacy of present theories of absorption based on microeddy current losses accompanying domain wall motion and domain rotation. Further evidence is presented which seems to definitely exclude the rotation mechanism for this frequency range in nickel.

The partition function which describes the thermal equilibrium behavior of an aligned assembly of uniaxially anisotropic particles in a field H applied along the direction of alignment is: Z = 2π ∫ 0π sinθ exp(−a sin2θ+b cosθ)dθ. In this expression a = KV/kT; and b = μH/kT, where K is the anisotropy energy density;V the particle volume; μ the particle magnetic moment; k the Boltzmann factor; and T the absolute temperature. It is shown that the tabulated function y = exp(−x2) ∫ 0x exp(l2)dt can be used to obtain the fractional magnetization m∥ along the direction of alignment for general values of a and b. Numerical results for m∥ have been obtained for a = 0.01, 0.1, 1, 2, 5, 10, 100; and 0.01≤b≥100. Curves of m∥ vs b with a as a parameter are presented. For a