The normal Hall-effect of random close packed cobalt

The normal Hall-effect of random close packed cobalt

Volume 60A, number 3 PHYSICS LETTERS 21 February 1977 THE NORMAL HALL-EFFECT OF RANPOM CLOSE PACKED COBALT G. BERGMANN Institut für Festkorperforsc...

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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 [1]. 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 [3]. The same model applies for amorphous metals [4]. 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 [9]. 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 ~ —


0 z


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 [9]. Recently GUntherodt et al. [10] 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 [11]. 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. —




/ I






/ /


‘N N Co

“N—” ‘N N,

________________________________________ 00

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 [12]. 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 [1] H.-J. Gtlntherodt and H.U. Kunzi, Phys. Kondens. Materie 16(1973)117. [2] G. Busch and H.-J. GUntherodt, Sol. State Phys. 29 (1974) 235. [3] J.L. Finney, Proc. Roy. Soc. Lond. A319 (1970) 479. [41 Cargill,Z.J.Physik Appi. Phys. 41(1970) [5] G.S. W. Buckel, 154 (1959) 474. 2248.

[6] 1. Fortmann and W. Buckel, Z. Physik 162 (1961) 93. [7] G. Bergmann, Z. Physik 255 (1972) 76. [8] 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 [3].


21 February 1977

[9] G. Bergmann, Sol. State Commun. 18 (1976) 897. [10] 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. [12] H.-J, GUntherodt et al., Phys. Lett. 54A (1975) 291.

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