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Submitted on 1 Jan 1971
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NON LINEAR MAGNETIZATION IN Pd METAL AND A Pd-Rh ALLOY, MEASURED IN
SEMI-CONTINUOUS FIELDS UP TO 350 kOe
R. Gersdorf, F. Muller
To cite this version:
R. Gersdorf, F. Muller. NON LINEAR MAGNETIZATION IN Pd METAL AND A Pd-Rh ALLOY, MEASURED IN SEMI-CONTINUOUS FIELDS UP TO 350 kOe. Journal de Physique Colloques, 1971, 32 (C1), pp.C1-995-C1-996. �10.1051/jphyscol:19711354�. �jpa-00214390�
JOURNAL DE PHYSIQUE Colloque C 1, supplkment au no 2-3, Tome 32, Fkvrier-Mars 1971, page C 1
-
995NON LINEAR IMAGNETIZATION IN Pd METAL AND A I'd-Rh ALLOY,
MEASURED IN SEMI-CONTINUOUS FIELDS UP TO 350 kOe
R. GERSDORF and F. A. MULLER
Natuurkundig Laboratorium der Universiteit van Amsterdam, the Netherlands
RBsum6. - L'installation de l'universitk #Amsterdam, creant des champs magnktiques intenses semi-continus, permet de mesurer t r h sensiblement les deviations eventuelles de la linearitk de la relation entre le moment magnetique et le champ applique (jusqu'a 350 kOe) des echantillons paramagnktiques.
L'aimantation du Pd pur montre une courbe positive significative, cependant des changements de seulement 0.001 de l'aimantation maximum porteraient les points expkrimentaux sur une ligne droite ; pour l'alliage de Pd-Rh les deviations sont plus grandes et de signe n6gatif.
Puisqu'on n'aperqoit pas une structure fine, une explication dans le cadre d'une bande rigide avec une singularit6 dans la densit6 d'ktats au-dessous du niveau de Fermi de Pd n'est pas possible.
Abstract. - The installation for semi-continuous high magnetic fields at the University of Amsterdam permits a very sensitive test of the linearity of the relation between magnetic moment and field strength up to 350 kOe in parama- gnetic samples. The magnetization of pure Pd at 4 OK shows a significant upward curvature. However, changes of only 0.001 times the maximum magnetization would bring the points on a straight line. In Pd-Rh alloys the deviation is much larger and of opposite sign. Fine structure is not observed, therefore an explanation based on the rigid band model and a singularity in the density of states just below the Fermi level of Pd is not possible.
The high field installation at the University of Amsterdam [l, 21 is able to generate a magnetic field pulse, rising quickly from zero to 35 T (350 kOe), then remaining for 60 ms at that value with an accuracy of better than 1 : 1 000, descending to 30 T and remain- ing there an other 60 ms, and so on until in seven steps zero is reached again. The total pulse has a duration of about one second. The periods of constant field allow the eddy currents to decay. Therefore accurate measurements of magnetic moments of metallic specimens are possible. The voltage of a pick-up coil system [3] is integrated in order to measure the magnetic moment ; the linear part of this moment as a function of the field can be compensated with a fraction of the signal of a larger coil in the magnetic field. A few details have been published earlier 141.
The slope of the magnetization curve can therefore not be determined as accurately as its non-linearity. Pure Pd and a Pd-Rh alloy were investigated at 4 OK. The pure metalwas obtained from Johnson Matthey and labelled {( Spectrographically Standarized >>, the sample of the alloys was made by spark-cutting an arc-melted button, made from the pure elements. Chemical ana- lysis of the composition of part of the bytton was in fair agreement with the starting percentage of Rh.
The non linearity of the relation found between the magnetic moment o and the field B can be presented in several ways. One method is to show the deviations from the best fitted straight line through the data points. This method was followed in [4], but the disadvantage is that the deviations in that case strongly depend on the field range. A second method is to show the deviation from the tangent in the origin of the o(B) curve. This is done in practice by fitting the measuring points to a polynomial :
o = a , B
+
a , B3+ +
a,, B n ,determination of a , , are perturbed by the very large susceptibility in low fields of impurities of Fe and Co in the Pd-metal. A few ppm of these impurities, which occur even in the best purified metals, show a clearly visible effect [5]. It appeared that, at 40K, these moments are saturated above 3 T. We can therefore eliminate this perturbation if we consider only points measured above 3 T, and try to fit them to a poly- nomial a = a,
+
a , B+
a , B~+ +
a, Bn. a. being equal to the saturation moment of the impurities.time
-
1 second ---t
FIG. 1. - Upper curve : magnetic moment of Pd, with compen- and giving the as Ao = Orneas - In sation of the linear part, as a function of time. The large peaks reality this method has the disadvantage that the are due to eddy currents in the specimen. Lower curve : magnetic low-field points, which are most important for the field versus time.
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19711354
C 1
-
996 R. GERSDORF AND F. A. MULLERtesla -
x 1 0 - ~ V B TABLE
B 5 10 15 20 25 30 35
- -
-
-M (Pd) 6.72 13.25 19.80 26.36 32.95 39.56 46.21
M (Pd
+
2%
Rh) 10.79 21.18 31.31 41.04 50.35 59.18 67.72 a0(10-3PB)- bl(TIh) - b , ( ~ l P 3
-
Pd 0.19 765.9 - 2 700 f 500
Pd
+
2%
Rh 0.36 476.7 9 400 _+ 300Magnetic moments as a function of field strenght.
The absolute accuracy in the linear part of the magnetic moment is only about 2
%,
i. e. much worse than suggested above.This method was used by Foner and McNiff [6].
The disadvantage is that, if the power expansion does not converge very rapidly, the resulting deviations Ao = om,,, - a, - a, B depend on the number of terms of the polynomial. We shall use here a third method, in which the function u(Bj is inverted to a function B(o), which can be approximated by a poly- nomial :
B = bl(o - a,)
+
b,(o -+
f b,(o - a,)".The deviations from proportionality are now given by AB(o - a,) = B,,,, - bl(o - a,). It appears that this power expansion converges more rapidly so that the result depends less on the number of terms. Compa- rison of the results is simplified since theoreticians usually treat o as the independent variable [7]. In processing our data, we now first determine a,.This is most easily done by measuring, with a different high field pulse, the moment in several fields between 3 and 7 T (here the impurity moments are saturated, and the deviations from linearity are negligible) and extrapoling this result linearly to zero field. Then the high field points, measured a t a B of 5, 10, 15, 20, 25, 30, and 35 T, are fitted to the polynomial given above. The results are given in the table and in figure 2.
On comparing these data with the rigid-band cal- culations of Andersen [7], it appears that the measured curves are much smoother than the theoretical ones, although the order of magnitude is the same. Assuming that the rigid band model is valid in these - Pd-Rh alloys, we must conclude that the electron band density of states varies much more smoothly a sa func- tion of energy than suggested by Andersen, and that no singularity exists near the Fermi level. This agrees
qualitatively with band calculations from Lipton and FIG. 2. - Upper curves : magnetic moments of Pd Jacobs [8]. and Pd
+
2 % Rh as a function of field strength.It is possible to treat these alloys on the basis of a Lower curves : AB, defined as B-bl(a-ao), as a function of o.
some what more localized effect of the Rh-atoms ; the The solid lines are third power curves.
maxima in the specific heat and susceptibility near
5
%
Rh have, in that case, nothing to do with a gnetic susceptibility, all data can be qualitatively corresponding maximum or singularity in the Pd-band. understood. Future high field measurements 'on If we assume that a complex, consisting of a Rh-atom different Pd-Rh, Pd-Ag and Pd-Rh-Ag alloys will surrounded by 12 Pd-atoms, has a very high parama- perhaps decide which model is better applicable here.References ROELAND (L. W.), MULLER (F. A.) and GERSDORF
Coll. Int. CNRS, 1967, 166, 175.
GERSDORF (R.), MULLER (F. A.) and ROELAND (L.
Rev. Sci. Instr., 1965, 36, 1100.
GERSDORF (R.), MULLER (F. A.) and ROELAND (L.
Coll. Int. CNRS, 1967, 166, 185.
MULLER (F. A.), GERSDORF (R.) and ROELAND (L.
Physics Letters, 1970, 31A, 424.
MANUEL (A. J.) and ST QUINTON (J. M. P.), Proc.
Roy. Soc.. 1963. A 273, 412.
FONER (S.) and'Mc NIFF Jr (E. J.), Phys. Rev. Letters, 1967,19,1438, and Physics Letters, 1969, 29A, 28.
ANDERSEN (0. K.) Conf. on Magnetism and magnetlc materials. Philadeluhia. 1969.
LIPTON (D.) and JACOBS
