Magnetic structure and anisotropy of thin Fe films on Cu(001) substrates

We present a novel approach to the calculation of the spin structures and magnetic anisotropies in crystals and in thin films. Our technique is based on self-consistent real-space recursion calculations using a tight-binding-linear-muffin-tin-orbital (TB-LMTO) Hubbard Hamiltonian including spin-orbit coupling and allowing for arbitrary orientations of the local spin-quantization axes. It allows one to scan the magnetic energy continuously as a function of the direction of the magnetic moment and thus to avoid the computational problems that plague other techniques for the calculation of the magnetic anisotropy energies. The method also presents important advantages in determining the magnetic ground state in the presence of competing ferro- and antiferromagnetic interactions. Applications are presented for bulk iron, free-standing iron monolayers and for thin Fe overlayers on Cu(001) substrates. In the monolayer regime, we predict a perpendicular direction of the magnetic moment for free-standing fee Fe(001) monolayers and for fcc monolayers on Cu(001) (with free surfaces and covered by Cu overlayers), with anisotropy energies of the order of 1-2 meV. We also present a detailed investigation of the spin structures and of the change from perpendicular to in-plane anisotropy with increasing thickness of the Fe films. We find that stable low-moment and metastable high-moment spin structures coexist in films with more than four monolayers. With increasing thickness of the films the perpendicular anisotropy decreases and for an ideal fee geometry a transition to in-plane anisotropy can be expected around eight monolayers.