The Itinerant Limit of Metallic Anisotropy

I . I N T R O D U C T I O N Magnetic anisotropy caused by itinerant electrons in bulk materials and thin films has attracted considerable attention in recent years. Examples are the phenomenon of pcrpendicular thin-film anisotropy relevant to magnetooptical recording [ 11 and the 3d contribution to the magnetocrystalline anisotropy of permanent magnets such as SmCoj and Nd2Fel4B [2, 31. Apart from a magnetostatic contribution of order poMs2, magnetic anisotropy is of magneto-crystalline origin and involves relativistic spin-orbit coupl ing and electrostatic crystal-field interaction. Essentially, the orbital motion of the electrons is influenced by the electrostatic potential of the cr interaction couples the orbital motion of the electrons to spin and magnetization. However, the detailed anisotropy mechanism depends on the strengths of spin-orbit coupling and crystal-field interaction as well as on the degree of localization of the magnetic electrons. PROLATE OBLATE Magnetocrystalline anisotropy in modern rare-earth permanent magnets such as SmCoj 141, Nd2Fe13B 121, and Sm2Fc17N.i [ 51 largely originates from the rare-earth sublattice. In spite of the coinparatively low volume fraction of the rare earths, typical rare-earth anisotropy contributions are of order 10 MJ/m3 in these intermetallics 14, 6, 71. Tripositive rare-earth ions are reasonably well described by Hund's rules, so that rare-earth anisotropy may be interpreted in terms of the electrostatic interaction of well-localized 4f electron shells with the crystal environment 16-81. Figure 1 shows prolate and oblate 41 charge distributions in a crystal environment symbolized by positive charges above and below the ion. Since there, is a firm coupling between the 41 charge cloud and the magnetic moment, the preferrcd magnetization direction is obtained by minimizing the electrostatic energy of the ion. Compared to rare-earth anisotropy contributions, the anisotropy caused by itinerant d electrons tends to be rather low. However, anisotropies of order 1 M J h 3 are observed in thin films [ l ] as well as in layered intermetallics such as YCos and PtCo 191. A good example is the Llo compound PtCo, which can be regarded as a tetragonally distorted fcc derivate consisting of alternating layers of magnetic (34 and nonmagnetic elements. This makes it possible to treat itinerant interface, surface, and bulkanisotropies on a common basis. 3d anisotropy in metals is characterized by two basic features. First, as in nonmetallic magnets the orbital moment of the 3d electrons is largely suppressed by the crystal field. This quenching does not only affect Ihe spontaneous magnet izat ion but a l so reduces the magnetocrcrystalline anisotropy. Secondly, metallic 3 d electrons are itinerant, and the question arises to what extent the ionic anisotropy mechanism survives the delocalizatih of [he 3d electrons. From the point o f view of band-structure theory, anisotropy produced by itinerant 3d electrons can be regarded as a higher-order perturbation, and reasonable anisotropy predictions have been made in a number of cases [ 10131. Essentially, one includes spin-orbit interaction in addition to the energy terms appearing in the Stoner theory or in spin-polarized band-structure calculations. Since the charge density of the metallic 3d electrons remains, in some sense, reminiscent of that of free ions, band-structure calculations mix ionic and itinerant features. For instance, in the limit o f weakly overlapping tight-binding orbitals the problem retains its ionic charactcr, although the matrix elements between different orbitals are now wave-vector dependent [lo]. Here we discuss the nature of itinerant anisotropy in terms of analytical approaches. Fig. 1. Ionic prolaticity and anisotropy. In this example, prolate and oblate ions yield easy anisotropies parallel and perpendicular to the L axis, respectively. 0018-9464/96$05.00