On the Hall Effect in Ferromagnetics

LETTE RS TG THE ED I TOR 2. The energy calibration was carried out by means of the E-radiation from Te. Figure 3 shows oscilloscope traces of the pulse distribution obtained from( Pa~' in the proportional counter in comparison with the E x-rays emitted from Te's'. Critical absorption of the nuclear gamma-ray from Pa~' also showed that its energy lies between the absorption edges of Cd and In (26. 7 and 27. 9 kev) (Fig. 4). For this experiment, Cd, In, and Sn absorbers were placed between the sample and the beryllium window, and the discriminator voltage of the proportional counter was kept constant at the peak-value for the y-ray. Teillac, ' by means of a Wilson chamber technique, had observed at least 3 conversion electron groups from this isotope. The most intense group, at 24 kev, may be identi6ed with the M-electrons from in Fig. the 27-kev gamma-ray. Low energy gamma-rays have hitherto received only scant attention. A systematic study of their occurrence is now in progress. Our thanks are due to M. Studier of Argonne National Labora- tory and G. Harbottle of this laboratory for the preparation of Pa ' samples, and to E. der Mateosian for valuable help. The experimental data of Smith are reproduced in Fig. 1. Here e~ has been plotted against B, the magnetic induction. It is clear that above technical saturation the slopes of e~ oersls B curves are constant with increasing 8 and are essentially the same for different temperatures, except for the temperatures in the neighborhood of the Curie point where a sharp increase of these slopes with temperature is apparent. In (A), Rp was computed from these data with the assumption that above technical satura- tion M = constant with increasing 8 or H, so that; Rp= Be~/BH The values of Rp thus computed from Smith's data are shown in Fig. 2, which corresponds to Fig. 3A of (A), and the spike in the neighborhood of the Curie point is very pronounced. However, it has been discovered that, when the change in intrinsic magnetization with IJ after technical saturation is taken I I 0SIope ~e„/be — R, ox peeented — R. camaa4 * Research carried out under contract with AEC. R. L. Macklin and G. B. Knight, Phys. Rev. 72, 435 (1947). ~ Schar8-6oldhaber, der Mateosian, McKeown, and Sunyar, Phys. Rev. Compton and Allison, X-Rays in Theory and Keperirlent (D. Van Nostrand Company, Inc. , Net York, 1934). 4 Theory predicts only ~1L x-ray per 104 a-particles for this effect. Recent experiments on polonium show that this e8ect is of the order of 1 per 10II alphas fW. Rubinson and W. Bernstein, Bull. Am. Phys. Soc. 26, No. 1, 4V (1951)). ' J. Teillac, Compt. rend. 239, 1056 (1950). 6 J. Teillac, Compt. rend. 229, 650 (1949). = Be~/BB. for I Oboxe bcbncOI oolrfIOFon, I t4). etnnec xuecepbIxIIty. 'a ot g Q x 4QQQQPE TENxER4TURE / CURIE TEMPER4TURE FIG. 2. Temperature dependence of the Hall constant Ra for nickel. On the Ha11 ESect in Ferromagnetics N. RosT0KER AND EMERsoN M. PUGH of Physks, Cornegie Institute of TechnoLogy, Departmcptt Pittsblrgh, Penssyh ania (Received January 18, 1951) N a recent referred to as (A), Hall effect . . measurements paper, for nickel were presented. The following relation hereafter to describe the Hall effect on the basis of these was proposed measurements and previous measurements made by Smith' em~ R p(&+4~0tM), where eIt is the Hall electric Geld per unit current density, Rp is the Hall constant which should depend chiefly on the numbers of electrons and holes and be substantially independent of tempera- ture, H is the magnetizing force, M is the magnetization, and 0. is a Geld parameter which increases with temperature. (a varies from cE 1 at low temperatures to a~100 in the neighborhood of the Curie point. ) into consideration, the Rp versus T/8 curve is altered as shown in Fig. 2 and the anomalous behavior in the neighborhood of the Curie point disappears. The behavior of the intrinsic magnetiza- tion for high 6eld strengths in the case of nickel has been studied by Weiss and Forrer' over temperatures ranging from room tem- perature to well above the Curie point. A susceptibility x; due to change in intrinsic magnetization at high field strengths can be estimated from their data: x;= B3f/BH. Rp= P(1+4m x;)/(1+4xnx;) )Bert/BB. I 8 E4 T 4bxobrle temp, 8 Cone bxnp. I x IL' kl/~w~ l2 I M46NETIc l6 IE InfoUcTobI sxo e yahoo FtG. $. Hall effect in nickel after A. W. Smith. At room temperature, we find x;~2. 7X10 ', which is so small that it does not significantly alter our previously computed value of Rp. The only significant change occurs near the Curie point, where x; is much larger. For example, in the neighborhood of the paramagnetic Curie point 8, x; 3.7X10 '. From Eq. (1) Be~/BII = Rp(1+4Trnx;) and, since Be~/BH = (1+4~x;) BeIt/BB, Equation (2. 1) reduces to Eq. (2) when x; is small, which is the case in the neighborhood of the Curie point. When Rp was computed by the more correct Eq. (2.1), using the experimental data of Weiss and Forrer, it was found that Eq. {1) is consistent with the experimental data of Smith and Schindler presented in (A), with Rp a constant independent of both temperature and magnetic 6elds, and with EE a parameter dependent on tempera- ture only. It was previously suggested4 by one of us that Eq. {1) might be applicable to paramagnetic as well as ferromagnetic substances, but that it might be difficult to detect the contribution to the Hall effect from the magnetization in most paramagnetic sub- stances, because the magnetization is proportional to II and very small. The above discussion indicates an observable paramagnetic contribution to the Hall effect in nickel in the neighborhood of the Curie point where the nickel is strongly paramagnetic.