Orbital Magnetism and Magnetic Anisotropy Probed with Ferromagnetic Resonance

Abstract

Via ferromagnetic resonance both the magnetic anisotropy energy (MAE) and the spectroscopic splitting tensor (g tensor) for a bcc Fe 2 ͞V 5 ͑001͒ superlattice are measured independently. The theoretically proposed proportionality between the anisotropy of the orbital moment m L and the MAE is quantitatively checked and its limitations are discussed. From layer-resolved first-principles calculations we find a reduced spin moment m S 1.62m B for Fe and m V S 20.67m B in the first V layer. The g-tensor elements reveal a 300% enhanced ratio m L ͞m S 0.133 in comparison to bulk Fe. The MAE and the orbital moment anisotropy is found to be unusually small for Fe monolayers.[S0031-9007 (99)08741-4] PACS numbers: 75.70.Ak, 75.30.Gw, 75.30.PdFor a long time the magnetism of 3d metals has been described only in terms of spin magnetism. The relativistic spin-orbit interaction which leads to orbital magnetism and is manifested in the existence of magnetic anisotropy energy (MAE) was neglected. This has been justified by reasoning that due to the high symmetry of bulk crystals the orbital contribution is nearly completely quenched. Later in extending the localized models of ionic crystals to band ferromagnets Bruno [1] calculated within second-order perturbation theory at T 0 K that the MAE is related to the difference Dm L m Ќ L 2 m k L of orbital moments with respect to the symmetry axis of the crystallographic lattice,with the spin-orbit coupling parameter l 20.054 eV [1] for Fe. More recent first-principles calculations [2-5], on the other hand, have shown that a strict proportionality between MAE and Dm L does not exist (see, for example, Fig. 5 of [2]). Thus it is questionable to deduce the magnitude of MAE from a determination of anisotropic orbital moments. In ultrathin films the MAE and orbital moment anisotropy are enhanced, since tetragonally distorted lattices with partially unquenched m L [2,6] are stabilized. Both orbital m L and spin m S moments have been determined in x-ray magnetic circular dichroism (XMCD) experiments [7] by applying the sum rules. In this analysis which uses a localized picture the results have been interpreted as an enhancement or anisotropy of the orbital moment-that is, of the expectation value of L z [8,9]. The correct comparison to low temperature measurements ͑T ! 0 K͒ of the MAE according to Eq. (1) could not be performed.In this work we will measure in a new way via only one experimental technique, that is, frequencyand angular-dependent ferromagnetic resonance (FMR), independently both MAE at T ഠ 0 K and the orbital moment anisotropy for Fe monolayers. We find an about 300% increase of the ratio of orbital to spin moment m L ͞m S 0.133 in comparison to bulk Fe and a small anisotropy of the orbital momentum which is correlated with the experimental MAE at T 0 K. Both sides of Eq. (1) are experimentally measured. It is pointed out that our FMR provides comparable information on the orbital magnetic moment as XMCD experiments, however, with the advantage that FMR can be measured in the...

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