Effect of spin-orbit coupling on the conduction-electron Zeeman splitting in platinum-group metals

Abstract

Local g factors, cyclotron effective masses, and cyclotron-orbit g factors (g, ) for rhodium, palladium, iridium, and platinum have been calculated using a relativistic linear muffin-tin orbital method, including perturbation of a magnetic field. These calculations are compared with experimental results from de Haasvan Alphen measurements. Both measurements and calculations give an anisotropic g, factor for the I -centered electron sheet and the X pocket while they give a rather isotropic one for the o. orbit existing on the open-hole sheet. This indicates that the spin-orbit coupling is a major source of the anisotropic behavior of the g, factor in these metals.

Zeeman splitting in Pd and Pt calculated from self-consistent band structure including an external magnetic field

“…In the present calculations the value of g c in [001] is larger than around the "waist" of the pocket, in contrast to Ref. [11], indicating that the exchange-correlation enhancement of the Zeeman splitting is strongly anisotropic, with a larger effect near [001] than in the (001) plane. This is in line with experimental studies, in which a small amount of Ni in Pd has been used in order to increase the exchange-correlation effects [18].…”

“…As for all studied orbits, the Zeeman splitting is several times larger than the values presented in Ref. [11]. Regarding the g c factor on the X4 pocket in Pd, the differences in anisotropic behavior are larger (Fig.…”

“…Figure 2 presents calculated and experimental [3] R values for the a5 orbit in Pd. Comparison with Ohlsen and Calais [11], where spin-orbit interaction is included but no exchange-correlation effects are enhancing the Zeeman splitting, shows that the improvement in agreement with respect to anisotropic behavior, when comparing to experiment, is small but significant. As for all studied orbits, the Zeeman splitting is several times larger than the values presented in Ref.…”

“…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.…”

The electron g factor for one-band and two-band extended models of the electron energy spectrum

“…On the other hand, in many papers, see, e.g., Refs. [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26], the so-called local g factors g( ) k introduced by De Graaf and Overhauser [27] for points k on the Fermi surface were calculated, and the g factor of the orbit was obtained by integration of g( ) k over the orbit. In this symplified approach the dynamics of the electron spin is neglected completely.…”