Fully self-consistent band-structure calculations have been performed for palladium and platinum. The effective Hamiltonian contains exchange, correlation, and relativistic effects as well as the external magnetic field. The anisotropy of the cyclotron-orbit Zeeman splitting agrees well with experimental data from de Haas-van Alphen measurements. The calculated total susceptibilities also agree with the experimental values.PACS numbers: 71.70.Ej, 71.25.Jd, 75.20.En The Zeeman splitting of cyclotron orbits has been thoroughly investigated by means of the de Haas-van Alphen (dHvA) effect. In the alkali metals [1] the Zeeman splitting is found to be isotropic, but the g factor deviates from the free-electron value of 2. On the other hand, in Rh [2], Pd [3,4], Ir [5], and Pt [6,7] the cyclotron-orbit g factor (g c ) is found to be strongly anisotropic, and it is also known that in Pd and Pt the average g factor is large. The g c factor in the noble metals [8] also shows a strong anisotropy. Previous experience indicates that simple band-structure models with the magnetic field taken into account by first-order perturbation theory cannot explain this behavior.To our knowledge, no calculations aiming at a total picture of the Zeeman splitting have been performed. MacDonald [9] has calculated average g factors for the transition metals including spin-orbit coupling, but without exchange and correlation effects. Jarlborg and Freeman [10] have calculated g factors for certain k points on the Fermi surface of Pd, neglecting spin-orbit coupling. For comparison with dHvA experiments, cyclotron-orbit values must be calculated. This has been done, including spin-orbit coupling but without enhancement of the Zeeman splitting from exchange and correlation, for the platinum group metals [11], noble metals [12], and alkali metals [13]. These studies show that spin-orbit coupling is the dominant source of the anisotropy for most Fermisurface sheets and indicate that exchange and correlation enhancement must be included in the model in order to also get the right order of magnitude of the Zeeman splitting. In the present paper results for Pd and Pt are presented using a calculational scheme where the external magnetic field is included in the self-consistent cycle, which allows the spin-dependent exchange-correlation potential and the spin-orbit coupling to affect the Zeeman splitting.In an external magnetic field, a Fermi-surface sheet in a paramagnetic or diamagnetic metal is split into two slightly different surfaces. The interference between the two dHvA signals of these sheets will then appear as a modulation of the amplitude, according to a cosine function with argument xR, where A\ and A 2 are the extremal cross-sectional areas of the two split surfaces perpendicular to the magnetic field, and B is the applied field strength. In moderate fields (i.e., for small splittings) R can be approximated bywhere m c is the effective cyclotron mass in units of the free-electron mass. In this paper, R is calculated and compared to exp...