Relativistic Linear Muffin-tin Orbital Method Research Articles

Relativistic LMTO method for systems of light elements

This paper reviews the theoretical background of an approximate treatment of relativistic effects within the tight-binding (TB) linear muffin-tin orbital (LMTO) method for ab-initio electronic structure calculations of solids. The formalism employs two-component spinors and an orbital basis set of the scalar-relativistic approximation. The developed theory is applied to selected metallic systems and its results are compared to those of a fully relativistic TB-LMTO method.

Experimental and ab initio theoretical study of optical and magneto-optical properties of Co/Cu multilayers

The polar Kerr rotation and ellipticity spectra were measured in the spectral range 0.8 - 5.5 eV for a set of Co/Cu multilayered structures (MLS). The magneto-optical (MO) response of Co/Cu MLS being related to the -part of the optical conductivity tensor was obtained from the Kerr spectra and tensor component , determined by spectroscopic ellipsometry. The self-consistent spin-polarized fully relativistic linear muffin-tin orbital method within the local spin-density approximation was used to calculate the electronic structure, optical, and MO properties of some model Co/Cu MLS. Good agreement between the measured and calculated optical and MO spectra is observed. The role of the spin - orbit coupling and exchange splitting at the Co and Cu sites, and the hybridization effects are examined and discussed. The spin-polarized Cu interface states appear to give a weak contribution to the - and Kerr spectra whereas the latter ones are strongly influenced by the Cu-dominated optical spectra structure. The results obtained demonstrate that the MO properties of real large-period multilayered structures can be quantitatively predicted from first-principles band-structure calculations.

First-principles study of the magnetic hyperfine field in Fe and Co multilayers.

We present ab initio calculations of the magnetic hyperfine field and magnetic moments in several Fe and Co multilayers (Fe(Co${)}_{2}$${\mathrm{Cu}}_{6}$ fcc (001), FeCu(Ag${)}_{5}$ fcc (001), bcc Fe/fcc ${\mathrm{Ag}}_{5}$ (001), bcc ${\mathrm{Fe}}_{\mathit{n}}$/fcc ${\mathrm{Au}}_{5}$ (001) (n=1,3,7), ${\mathrm{Co}}_{\mathit{k}}$${\mathrm{Pd}}_{1}$ fcc (111) [k(l)=1 (5), 2 (4), 3 (3)] and ${\mathrm{Co}}_{2}$${\mathrm{Pt}}_{\mathit{m}}$ fcc (111) (m=1,4,7)) as well as in bcc Fe and fcc (hcp, bcc) Co. The first-principles spin-polarized, relativistic linear muffin-tin orbital method is used. Therefore, both the orbital and magnetic dipole contributions as well as the conventional Fermi contact term are calculated. Calculations have been performed for both in-plane and perpendicular magnetizations. The calculated hyperfine field and its variation with crystalline structure and magnetization direction in both Fe and Co are in reasonable agreement (within 10%) with experiments. The hyperfine field of Fe (Co) in the interface monolayers in the magnetic multilayers is found to be substantially reduced compared with that in the corresponding bulk metal, in strong contrast to the highly enhanced magnetic moments in the same monolayers. It is argued that the magnetic dipole and orbital contributions to the hyperfine field are approximately proportional to the so-called magnetic dipole moment and the orbital moment, respectively.These linear relations are then demonstrated to hold rather well by using the calculated non-s-electron hyperfine fields, orbital and magnetic dipole moments. Unlike in the bulk metals and alloys, the magnetic dipole moment in the multilayers is predicted to be comparable to the orbital moment and as a result, the magnetic dipole contribution to the hyperfine field is large. The anisotropy in the hyperfine field is found to be very pronounced and to be strongly connected with the large anisotropy in the orbital moment and magnetic dipole moment. The induced magnetic moments and hyperfine fields in the nonmagnetic spacer layers are also calculated. The results for the multilayers are compared with available experiments and previous nonrelativistic calculations. \textcopyright{} 1996 The American Physical Society.

Band-theoretical investigation of the magneto-optical Kerr effect in Fe and Co multilayers.

A band theory of the magneto-optical (MO) properties of solids, based on the first-principles spin-polarized, relativistic linear muffin-tin orbital method, is described. Two expressions of the relativistic electron-photon-interaction matrix elements are implemented and their accuracies are investigated. It is found that the spin-polarized, relativistic band theory, together with the expression of the photon-absorption matrix elements, is able to give reliable optical conductivity and MO Kerr rotation spectra of bcc Fe that agree well with both experiments and recent calculations using a different method. The MO properties of several Fe and Co multilayers [Fe(Co${)}_{2}$${\mathrm{Cu}}_{6}$ fcc-(001), FeCu(Ag${)}_{5}$ fcc-(001), bcc-Fe/fcc-${\mathrm{Ag}}_{5}$ (001), bcc-${\mathrm{Fe}}_{\mathit{n}}$/fcc-${\mathrm{Au}}_{5}$ (001) (n=1,3), ${\mathrm{Co}}_{2}$${\mathrm{Pd}}_{4}$ fcc-(111), and ${\mathrm{Co}}_{2}$${\mathrm{Pt}}_{\mathit{m}}$ fcc-(111) (m=1,4,7)] are then investigated theoretically. The calculated MO Kerr effect in all the multilayers except ${\mathrm{Co}}_{2}$${\mathrm{Pt}}_{1}$ fcc-(111) is not larger than in bulk Fe and Co. Nevertheless, the results suggest that materials with larger Kerr rotations can be achieved by making Fe (Co) superlattices with ultrathin layers (few monolayers thick) of heavy elements possessing a partially filled d band (e.g., Pt and Os).Kerr rotation spectra for Fe(Co)/Cu(Ag, Au, Pd, Pt) bilayers [i.e., a thin layer of Fe (Co) on the Cu (Ag, Au, Pd, Pt) substrate] are also obtained from the calculated optical conductivity tensors of Fe, Co, Cu, Ag, Au, Pd, and Pt. It is found that the MO Kerr effect in the Fe (Co)/noble-metal bilayers is considerably enhanced near the plasma edge of the substrate. This indicates that one can obtain good MO materials by fabricating Fe (Co) bilayers using nonmagnetic metals with a sharp plasma edge (e.g., Ag and Al) as substrates. Calculated Kerr rotation spectra of the Fe and Co multilayers as well as bilayers are in satisfactory agreement with available experiments. The spin and orbital magnetic moments in the Fe and Co multilayers are also calculated, and possible correlations between these and MO properties of the Fe and Co multilayers are discussed.

Theoretical investigation of the orientation dependence of the magneto-optical Kerr effect in Co.

The first-principles spin-polarized, relativistic linear muffin-tin orbital method has been applied to calculate electronic and magneto-optical properties of Co in both fcc and hcp structures. In particular, the magneto-optical properties have been calculated for several magnetization directions in order to study their magnetization orientation dependences. A pronounced anisotropy in the polar Kerr effect is found for hcp Co while the magneto-optical properties of fcc Co are predicted to be insensitive to the magnetization direction. Moreover, this magneto-optical anisotropy in hcp Co is found to be correlated with the presence of a large anisotropy in the orbital magnetic moment and orbital hyperfine field. Changing the structure from fcc to hcp gives rise to even greater changes in the magneto-optical properties of Co. Calculated Kerr angles and ellipticities are in reasonable agreement with the latest experiment.

A relativistic spin-polarised band theoretical study of magnetic properties of nickel and iron

In order to study the relativistic effects on the magnetic properties of transition metals, we have performed self-consistent relativistic spin-polarised electronic band structure calculations for two cubic systems: Ni and Fe. The spin-polarised fully relativistic linear muffin-tin orbital method is used. The calculated ground state spin and orbital magnetic moments and magnetic form factors for Ni and Fe are presented. The magneto-crystalline anisotropy in the band structure is studied, by rotating the magnetisation direction from (0 0 1) to (1 1 1) and then to (1 1 0). Finally, a computationally very intensive study of the magneto-crystalline anisotropy energy and moment has been carried out.

Theoretical study of magnetic and magneto-optical properties of Fe-based transition-metal alloys

Relativistic influences on the magnetic properties of transition-metal alloys manifest themselves for example by the occurrence of magnetocrystalline anisotropy, orbital contributions to the magnetic moment, and hyperfine fields. Among these effects, the magneto-optical Kerr effect is receiving much interest recently because of its application in the readout process of magneto-optical storage devices. We have studied the electronic structure of Fe-based transition metals by means of the spin-polarized version of the relativistic linear muffin-tin orbital method of band-structure calculation. By this way the mentioned consequences of relativistic effects, primarily the spin-orbit coupling, could be investigated without relying on the use of perturbational methods. Results for alloy systems, which were assumed to be of possible technical interest, are presented and discussed in comparison with experimental data as far as available.

Conduction-electron g factor on the X-pocket holes in iridium.

The conduction-electron Zeeman splitting on the ${\mathit{X}}_{3}$- and ${\mathit{X}}_{4}$-pocket holes in iridium has been measured by the de Haas--van Alphen technique. A large anisotropy in the cyclotron orbit g factor (${\mathit{g}}_{\mathit{c}}$) is found on both pockets. Calculations of the ${\mathit{g}}_{\mathit{c}}$ factor by a relativistic linear muffin-tin orbital method including an external magnetic field are also presented. The obtained results are compared with previous results on the X-pocket holes in palladium and platinum.

Theoretical investigations of the magneto-optical Kerr effect by means of the spin-polarized relativistic linear muffin-tin orbital method

During the last years the magneto-optical Kerr effect (MOKE) has received much interest because of its application to optical read-out of information stored in erasable magnetic media. Apart form this technical application it provides a helpful tool to study the electronic structure of magnetic materials. As is well known, the origin of MOKE is the simultaneous occurrence of spin-polarization in magnetic materials and of spin-orbit coupling giving rise to a non-diagonal optical conductivity tensor σ even for cubic lattices. Discussing experimental data until now one had to be content with the use of modified atomic models or with band structure calculations treating spin-orbit coupling by means of perturbation theory. To allow a reliable treatment, a description of MOKE has been developed that treats the electron-photon field interaction as well as the electronic structure of the spin-polarized system in a fully relativistic way. The approach has been implemented in connection with the recently developed spin-polarized relativistic version of the linear muffin-tin orbital (SPRLMTO) method of band structure calculation. Results of an application of our approach to ferromagnetic transition metals and alloys, as well as technical aspects of its implementation, are presented and discussed.

Spin-polarized relativistic LMTO method

A very simple and efficient version of the linear muffin tin orbital (LMTO) method of band-structure calculation is presented. It treats spin-polarization and relativistic effects on equal footing. As a result, it can be used to investigate the spin dependence of the electronic structure of magnetic materials containing heavy elements. The method is illustrated by explicit calculations on ferromagnetic Ni.

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

Local g factors, cyclotron effective masses, and cyclotron-orbit g factors (${g}_{c}$) 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 Haas--van Alphen measurements. Both measurements and calculations give an anisotropic ${g}_{c}$ factor for the \ensuremath{\Gamma}-centered electron sheet and the X pocket while they give a rather isotropic one for the \ensuremath{\alpha} orbit existing on the open-hole sheet. This indicates that the spin-orbit coupling is a major source of the anisotropic behavior of the ${g}_{c}$ factor in these metals.