Existing values of the magnetoresistance (ρ∥−ρ⊥)/ρ0 for crystalline Ni1−xFex, Ni1−xCox, Ni1−xMnx, Fe1−xCrx, and Fe1−x‐Vx alloys depend on x in a way which disagrees with the traditional Smit theory, based on the Born approximation. The reasons are related to the variation of the 3d wave‐function amplitude between chemically different atoms and, in turn, to a variation of s‐d scattering intensity. Experimental atomic moments indicate that this 3d amplitude variation is large. The variation is related to the fact that d‐d scattering is strong and resonant. We predict large deviations from Nordheim’s rule ρ↓∝ x(1−x) where ρ↓ is the spin‐down resistivity, similar to the deviations found experimentally. Correspondingly, (ρ∥−ρ⊥)/ρ0 is much larger for x≂0 than for x≂1.

Theory of magnetoresistance in concentrated ferromagnetic alloys (invited)

This article reviews the Hall effect in amorphous metals and amorphous metallic alloys from an experimental point of view. The theory of the Hall effect in amorphous materials is similar to that in liquid metals which is covered in the article by Ballentine (1980) in this volume. Some theoretical papers directed specifically at disordered metals are Samoilovitch and Kon’kov (1950) and Kondorskii et al. (1975 a, b).

Hall Effect in Amorphous Metals

The saturation magnetization, 4πMs, and the magnetostriction constant, λs, of Ni81Fe19, Ni81Fe19/Ta, and Ni72Fe17Rh11/Ta thin films were studied as a function of film thickness before and after annealing at 250 °C in vacuum for 2 h. For films of thickness t<200 A, 4πMs and λs were found to be strongly dependent on film thickness with an even larger variation after annealing. For all films, at t=60A, 4πMs decreases by 20%–30% compared to bulk value. The value of λs is in the range of 10−6 for all films and shows a complex behavior, including a change of sign, depending on film composition as well as Ta capping. Auger depth profiling of uncapped films has shown the presence of an Fe‐rich surface oxide layer whose composition changed and thickness increased after annealing. The composition and thickness of the Ta‐film interface layer in the Ta‐capped films did not change with annealing. The presence of such layers, at the film surface, Ta‐film interface, and film‐substrate interface, of different composition...

Effect of surface composition observed by Auger electron spectroscopy on magnetization and magnetostriction of NiFe and NiFeRh thin films

The electrical resistivity of Pd‐Fe alloys has been measured in magnetic fields parallel and perpendicular to the current, for a wide range of alloy compositions. The influence of atomic ordering on the magnetoresistance has been investigated. The ferromagnetic anisotropy of resistance Δρ/ρ0 reaches a maximum value of +9% in the ordered state between 30 and 35 at. % Fe, and +6% in the disordered state between 40 and 60 at. % Fe, at 4.2 K. At 295 K, Δρ/ρ0 never exceeds +1%. Similar measurements have been done on (Pd50 Ni50)100−x Fex for x≤30 at. % Fe. The maximum Δρ/ρ0 value of +7% is obtained for 10 at. % Fe at 4.2 K.

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Magnetoresistance of Pd‐Fe and Pd‐Ni‐Fe alloys

The ferromagnetic anisotropy of resistivity Δρ/ρ0=(ρ∥−ρ⊥)/ρ0 depends strongly on the nature of the dominant electron scattering centers, and is usually larger for impurity scattering than for phonon scattering. This explains why Δρ/ρ0 decreases with increasing temperature T in crystalline transition‐metal alloys. Parker has proposed an expression for Δρ/ρ0 as a function of T, based on Matthiessen’s rule. It contains the parameters (Δρ/ρ0)im and (Δρ/ρ0)ph, representing the Δρ/ρ0 values for impurity scattering and phonon scattering, respectively. In an alloy series with weak electron scattering, such as Fe‐Co, (Δρ/ρ0)ph is found experimentally to be positive and equal to a fixed fraction ≂ (1)/(4) of (Δρ/ρ0)im. On the other hand, in crystalline alloy series with strong, resonant electron scattering, such as Ni‐Fe, Fe‐Cr, Fe‐V, (Δρ/ρ0)ph is found to be negative and has a minimum at the composition where (Δρ/ρ0)im is maximum.

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On the temperature dependence of the magnetoresistance of ferromagnetic alloys

In concentrated alloys where the nuclear charges or exchange fields of the components differ sufficiently, the coherent potential approximation predicts that each alloy component has its own 3d band, having minimal overlap with the 3d bands of other components. As we pointed out earlier, this “split‐band model” applies well to the spin‐down bands of f.c.c. Ni‐Fe, Ni‐Fe‐Cu, etc., and explains many of their properties. For example, several physical quantities exhibit anomalies when the Fermi level eF crosses the boundary T between nickel and iron bands. A systematic search for b.c.c. iron‐base alloy series where the spin‐up band might be split, and where eF might cross a boundary T between bands, yields Fe‐V. As expected, the electronic specific heat coefficient γ of Fe‐V has a minimum when eF is at T, around 15 at % V. The electrical resistivity ρ, the slope ρ−1 dρ/dH, and the anomalous Hall coefficient Rs have sharp anomalies close by. The magnetoresistance Δρ/ρo is unusually large in Fe‐V. A scattering r...

L. Berger

Papers

Evidence for split bands from electronic specific heat and electrical transport data in Fe--V and in other iron and nickel alloys