de Haas-van Alphen Effect and Fermi Surface in Nickel

Abstract

takes place whenf(w) = (jOrr/sq, an equation that can be solved graphically to obtain the frequency wd where the acoustic and electromagnetic branches are degenerate. Ordinarily this transcendental equation possesses only one real root. However, there is a range of the magnetic field for which it can have up to three real roots. In this Letter we shall limit ourselves to the former situation. By treating the right-hand side of Eq. (5) as a perturbation, the solution for the eigenfrequencies at the crossover to first order in O 0 is For a metal such as sodium in a magnetic field of the order of 5xl0 4 G, the crossover frequency u) d is approximately equal to 3.6xl0 9 sec" 1 . The splitting at this point is about 12% of u^. The considerable admixture of acoustic and helicon modes in this region suggests the possibility of exciting transverse phonons in metals by means of electromagnetic radiation of the appropriate frequency. In Fig. 1 we give a graphical representation of the zeros of Eq. (5) in terms of the parameter w =qvQAV For tlie purpose of this calculation we have considered sodium at aThe Fermi surfaces of nonferromagnetic metals have been extensively investigated by de Haas-van Alphen (dHvA) and related techniques. Corresponding data on the magneto-oscillatory properties of ferromagnetic metals are much less complete, although preliminary dHvA effect results on Fe have been reported by Anderson and Gold, 1 and Shubnikov-de Haas oscillations have been detected in Co by Fawcett and Reed. 2 In this Letter we describe dHvA oscillations observed in nickel single crystals by means of a null deflection torsion balance in steady magnetic fields up to 40 kG. The dHvA oscillations were studied as a function of magnetic field orientation in the (001) and (11~0) crystallographic planes. The variation of the period of the oscillations in these planes suggests that at least one sheet of the Fermi surface of nickel is similar to that of the noble metals, in accord with a model of the Fermi surface proposed by magnetic field for which w at the crossover is Wfi = 2. Under this assumption £ 0 = 4.8 x 10 4 G i-and/(w^) = 0. 684. The foregoing results are, of course, only valid if CU 0 T » 1. Further details of this work will be the subject of a subsequent publication.The authors would like to thank J. Bok and D. N. Langenberg for communicating their results 6 prior to publication, M. Lampert for many helpful suggestions, and K. M. Brown for kindly assisting with the numerical calculations.Fawcett and Reed on the basis of magnetoresistivity studies.The torsion balance used for this study was modified so that the large steady torques exerted on the sample due to the ferromagnetic anisotropy of nickel could be nullified. Samples were cut from a single crystal nickel rod [p(300°K)/ p(4.2°K)*990] in the form of disks (0.20-in. diamx0.030 in. thick) and each was mounted with its axis of rotation vertical. In the first sample the [110] axis coincided with the disk axis, so that the magnetic field was located in the (1 TO) plane....

de Haas-van Alphen Effect in Ferromagnetic Nickel

“…9 It must also have one open sheet, similar to the copper Fermi surface, to satisfy the magnetoresistance experiments of Fawcett and Reed 10 and the dHvA experiments of Joseph and Thorsen (JT). 11 The dHvA data which we present here offer the first independent confirmation of this general approach to the ferromagnetic nickel band structure.…”

“…Of the two sets, the JT data should be the more reliable since they used a sample geometry for which D-0 (a thin cylindrical disk with H in the plane of the disk). 11 The excellent agreement between the two sets of data gives us some confidence that our corrections for D are right.…”

Electrical Resistivity and Screening in Some Dilute Ferromagnetic Nickel Alloys

“…Note that the radius, effectively the screen length, is of the same order of magnitude as that in many Cu DILUTE FERROMAGNETIC Ni ALLOYS 567 alloys, 12,13 in contrast to the over-all screening in transition metals occurring within the impurity site itself. 14 This is consistent with the recent band calculations [15][16][17][18][19] and Fermi-surface determinations [20][21][22][23][24] which suggest that the electronic structure for majority spin carriers in ferromagnetic nickel is very similar to that of copper, and also with the argument that the spin-f (minorityspin) electrons do the screening in Ni 11 .…”

Spin-Density-Wave Distributions in Chromium and Chromium Alloys

“…The resulting increase in modulus, which saturates at sufficiently high fields, has been observed. 7 The data plotted in Fig. 3 show that sufficiently large magnetic fields induce reversible transitions in the AF2 phase.…”

“…This has already been discussed in terms of SDW domain-boundary wall motion produced by applied stress which leads to an additional contribution to compliance. 7 Removal of domain-boundary walls, either by field cooling or the isothermal application of a field, partially or completely removes the anomalous compliance component, as may be seen in curves (b), (c), and (d) of Fig. 2.…”