Volume 60A, number 3
21 February 1977
THE NORMAL HALL-EFFECT OF RANPOM CLOSE PACKED COBALT G. BERGMANN Institut für Festkorperforschung, Kernforschungsanlage Jalich, D-51 70 Jülich, Germany Received 17 December 1976 The Hall resistivity of amorphous ferromagnetic Co consists of an anomalous and a normal Hall-effect. They have been separated using their different behaviour in a magnetic field. The normal Hall-constant is negative, R 3/As, and agrees with recent measurements on liquid Co. 0 = —15.9 x 10_il m
The Hall-effect of liquid metals with an atomic magnetic moment does not follow the free electron model and can even be positive . This is in contrast to iiquid simple metals which fulfill besides a few exceptations the free electron model very well [2j. The structure of liquid metals is well represented by the model of random close packed hard spheres . The same model applies for amorphous metals . And —
indeed, the Hall-constant of amorphous metals agrees with that of liquid metals [5—8].The Hall-effect of amorphous metals with an atomic magnetic moment yielded the key for the understanding of the positive Hall-effect of these metals in the liquid state . The Hall-effeôt consists of two different parts, the normal part R0B5 and the anomalous contribution which is given R5J5 where J = B ~ H is the magnetization of theby sample, R B +R ~ —
In amorphous alloys one can separate the normal and the anomalous Hall-effect in two ways. First, one can saturate the magnetization at low temperatures where the alloy is ferromagnetic and second, above the Curietemperature where J = xB B/(T Tc) one can extrapolate the total Hall-constant as a function of (T TcY’ towards infmite temperature to obtain R 0. Both procedures give nearly the same value for R0 . Recently GUntherodt et al.  were able to plot the total high temperature Hall-constant of liquid Co, RH = (Ro+R5X) versus the susceptibility x. Under the condition that the resistivity is temperature independent because R5 depends on the resistivity an extrapolation to x 0 is possible. They obtained for the3/As. normal Hall-constant the value in R0the = —16.2 X 10—11 Co can be prepared amorphous statemby
quenched condenstation. The anomalous Hall-effect is positive . In fig. 1 the Hall-resistivity is plotted as a function of the magnetic field. The linear increase on the left hand side of the curve is due to the anomabus Hall-effect. Because of the high demagnetization factor of the film, the z-component of the magnetization increases linearly with the applied magnetic field B 5 according to = B5 until the whole magnetization points into the z-direction. Then the magnetization is saturated and the further decrease at the Hall-resistivity is according to our present knowledge due to the normal Hall-effect. The expanded scale on the right hand side demonstrates the linearity between Hallresistivity and field. The corresponding Hall-constant obtained from three different samples —15.8,value —15.0 3 /As yielding theare averaged and —17.0 X 10—11 m R 3/As.The agreement with the extrapolated for liquid Co is better than we ex0 = —15.9 Xvalue l0~m pected. —
‘N N Co
“N—” ‘N N,
B (w,m] Co as Fig. 1. The Hall-resistivity of amorphous ferromagnetic function of the applied field. The right scale is expanded.
Volume 60A, number 3
In ferromagnetic materials below Tc the spin up and down conduction electrons experienôe a different scattering probability because the magnetization yields a spin dependent potential. This effect is present in amorphous Co, too, as indicated by the rather large difference in resistivity of amorphous Co with Pa = 0.41 XlO6~2mandliquid Co withp1= l.15X l06&~m . In non-ferromagnetic metals the resistivities agree quite well in the liquid and amorphous phase. If the difference in resistivity is due’ to a different mean free path of spin up and spin down conduction electrons the Hall-constant measures a smaller number of conduction electrons, in the most extreme case smaller by a factor of two. We obtain for the effective number of conduction electrons in amorphous Co the value Zeff
The experiments have been generously sponsored by the Deutsche Forschungsgemeinschaft.
References  H.-J. Gtlntherodt and H.U. Kunzi, Phys. Kondens. Materie 16(1973)117.  G. Busch and H.-J. GUntherodt, Sol. State Phys. 29 (1974) 235.  J.L. Finney, Proc. Roy. Soc. Lond. A319 (1970) 479. [41 Cargill,Z.J.Physik Appi. Phys. 41(1970)  G.S. W. Buckel, 154 (1959) 474. 2248.
 1. Fortmann and W. Buckel, Z. Physik 162 (1961) 93.  G. Bergmann, Z. Physik 255 (1972) 76.  A. Comberg, S. Ewert and G. Bergmann, Z. Physik 231 (1974) 317.
—(~l 0/eR0)= 0.5
For the atomic volume ~ we choose a 10% larger value than in the crystalline case because the random close packed structure is less dense packed than the crystalline structure .
21 February 1977
 G. Bergmann, Sol. State Commun. 18 (1976) 897.  H.-J. GUntherodt, I-LU. KUnzi, M. Liard, R. MUller, R. Oberle, and H. Rudin, Proceedings of the Third International Conference on Liquid Metals, Bristol, 1976. iiii P. Whymann and R.V. Aidridge, S. Phys. F4 (1974) L6.  H.-J, GUntherodt et al., Phys. Lett. 54A (1975) 291.