TEMPERATURE DEPENDENCE OF THE EXTRAORDINARY HALL EFFECT IN AMORPHOUS ( FeCoNi)78B12Si10 ALLOYS

Temperature dependences of the extraordinary Hall coeficient R, and resistivity p, yield a m p 2 (arising from the side-jump mechanism) for the majority of investigated FeCoNi-based alloys. The deviation from p2 variation in Co-rich alloys is probably due to the temperature dependence of the magnetic anisotropy in these alloys. One of the characteristic features of amorphous ferromagnetic alloys, as compared to the crystalline ones, is large extraordinary Hall effect. This is a direct consequence of the high resistiGty p of these alloys. It is generally accepted [l, 21 that in strongly disordered transition metal alloys the main contribution to the extraordinary Hall effect comes from the sidejump mechanism [3] that leads to the p2 dependence of the extraordinary Hall coefficient R,. The experimental confirmation of this dependence is somewhat difficult in amorphous alloys because their resistivity, that is already large, changes only slightly with temperature, and the same holds for R, too. Therefore very accurate determination of R, is required in order to deduce the correlation between R, and p. Here we report this correlation for amorphous FexNi.ra-xBlzSilo, FexCo78-xB12Si1~ and C0~Ni78-~B12Si10 alloys. All our alloys are ferromagnetic with the Curie temperature Tc above 420 K except for Fe23Ni~~B12Si10 and alloys (Tc=410 and 390 K respectively). The Hall resistivity p~ (in magnetic field up to 1 T) and electrical resistivity have been measured from 77 to 420 K. The details concerning the sample preparation and the measurement technique were reported earlier [4, 51. The temperature variations of the resistivity were reported in reference [6]. The rather small cross section of our samples (typically 0.8 x 0.018 mm2) resulted in an uncertainty of about 10 % in the absolute value of OH. The initial slopes of the Hall resistivity as a function of magnetic field RH= ( A ~ H / A B ) ~ = ~ for all our alloys are of the order m3 A-' s. At the same time the n~rmal Hall coefficient & of the amorphous alloys is equal to or lower than the free electron value and is practically temperature independent. For our s and alloy systems & is of the order 10-lo m3 A-' therefore we neglect its contribution to RH. Hence RH is practically equal to R. (po AM/AB)B=, where M is the magnetization of the sample. In the case of a thin Hall sample and isotropic material RH is then equal to the extraordinary Hall coefficient R,. The concentration dependence of R, for our alloys at room temperature is shown in figure 1. The data for amorphous FeXNi8o-,BlsSi2 alloys from references [4, 51 are included in the same figure. We note a similar size and practically the same concentration dependence of R, in two FeNi-based systems. The variation of R, with x in FeCo-based alloys is also similar to that observed for homogeneous ferromagnetic FeNibased alloys (a: 2 15). For ferromagnetic CoNi-based alloys we have not enough data to deduce the yariation of R. with x in this system. It would be misleading to correlate R, and p values for different alloys because the differences in the band structure may influence R, more than the resistivity does [3]. Therefore one has to investigate the temperature variations of p and R. in order to deduce the actual dependence of R, on p. Fig. 1. Concentration dependence of RH in FeCoNi-based alloys. '~e~artement of Physics, Faculty of Science, Zagreb, Yugoslavia. '~nstitute "Rudjer BoSkoviZn, Zagreb, Yugoslavia. Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19888593 C8 1302 JOURNAL DE PHYSIQUE The temperature dependence of R, in four alloys is shown in figure 2. A continuous increase of R. with temperature was observed for all alloys. We note that the relative change of R. in the temperature inteval from 77 to 420 K is ranging from 10 to 15 % only. The behaviour of R. in Fe23NiS6B12Si~o and Co39Ni39B12Si10 alloys as well as our previous data [4, 51 indicate that the extraordinary Hall coefficient does not change on passing through T,. We consider that such behaviour of l& is characteristic for FeCoNibased amorphous alloys and possibly extends to other amorphous ferromagnets as well. In order to obtain the correlation between R. and p we plotted ln(& (T) 1% (77 K)) vs. In (p (T) /p (77 K)) and the results for three alloys are presented in figure 3. We note that the correlation systematically depends on the concentration of the alloys. In most of FeCoNi alloys l& varies, through the explored temperature interval, as the square of the resistivity as predicted by theory [3]. In Co-rich alloys R, increases with temperature significantly faster than p2 and cannot be described by a single power law of p. However the deviation from the predicted p2 dependence becomes smaller with increasing temperature and in the case of Co39Ni39B12Si12 alloy (Fig. 3) R, varies almost as p2 when temperature approaches T,. The observed behaviour indicates that the assumptions of the same temperature dependence and equality between R, and RH may not be quite correct for Co-rich alloys. Although we have no detailed explanation for this observation we note that for magnetically anisotropic material (,uoAM/AB)~=, value is expected to be different from unity and temperature dependent. Even small temperature variation of (poAM/AB) ,,, values can influence the determination of the actual R, values from the PH data only. In this case in order to obtain the exact correlation between R. and p a detailed knowledge of the temperature and field dependences of magnetization is required. In conclusion, an average P2 dependence of R, (consistent with the side-jump mechanism [3]) has been obtained for the majority of amorphous FeCoNi-based alloys. For Co-rich alloys R, vs. p dependence cannot be described by a single power law. This behaviour is tentatively ascribed to the temperature dependence of the magnetic anisotropy which affects the determination of actual R, values. [I] Hurd, C. M., J. Appl. Phys. 50 (1979) 7526. [2] McGuire, T. R., Gambino, R. J. and O'Handley, R. C., The Hall Effect and its Applications, Eds. C. L. Chien and C. R. WF (New York, Plenum) 1980. Fig. 2. Variation of RH with tempera~ture for four alloys. Fig. 3. In RH vs. In p variation for three alloys. [3] Berger, L., Phys. Rev. B 2 (1970) 4559. [4] Ivkov, J., Marohnit, Z., Babit, EL, Miljak, M. and Liebermann, H. H., J. Phys. F 13 (1983) 2173. [5] Ivkov, J., Marohnik, Z., Babid, E. and Dubcek, P., J. Phys. F 14 (1984) 3023. [6] Babit, E., Ocko, M., Marohnit, Z., Davies, H., A. and Donald. I. W., Proc. 4th Int. Conf. RQM, Eds. T. Masumoto and K. Suzluki (Japan Institute of Metal, Sendai) 1982, p. 857.