In this paper, we review some of the key concepts in ultrathin film magnetism which underpin nanomagnetism. We survey the results of recent experimental and theoretical studies of well characterized epitaxial structures based on Fe, Co and Ni to illustrate how intrinsic fundamental properties such as the magnetic exchange interactions, magnetic moment and magnetic anisotropies change markedly in ultrathin films as compared with their bulk counterparts, and to emphasize the role of atomic scale structure, strain and crystallinity in determining the magnetic properties. After introducing the key length scales in magnetism, we describe the 2D magnetic phase transition and survey studies of the thickness dependent Curie temperature and the critical exponents which characterize the paramagnetic–ferromagnetic phase transition. We next discuss recent experimental and theoretical results on the determination of the exchange constant, followed by an overview of measurements of the magnetic moment in the elemental 3d transition metal thin films in the various crystal phases that have been successfully stabilized, thereby illustrating the sensitivity of the magnetic moment to the local symmetry and to the atomic environment. Finally, we discuss briefly the magnetic anisotropies of Fe, Co and Ni in the fcc crystalline phase, to emphasize the role of structure and the details of the interface in influencing the magnetic properties. The dramatic effect that adsorbates can have on the magnetic anisotropies of thin magnetic films is also discussed. Our survey demonstrates that the fundamental properties, namely, the magnetic moment and magnetic anisotropies of ultrathin films have dramatically different behaviour compared with those of the bulk while the comparable size of the structural and magnetic contributions to the total energy of ultrathin structures results in an exquisitely sensitive dependence of the magnetic properties on the film structure.

https://iopscience.iop.org/article/10.1088/0034-4885/71/5/056501/pdf

Magnetism in ultrathin film structures

Systematic evaluation of the accuracy of exchange-correlation functionals is essential to guide scientists in their choice of an optimal method for a given problem when using density functional theory. In this work, accuracy of one Generalized Gradient Approximation (GGA) functional, three meta-GGA functionals, one Nonseparable Gradient Approximation (NGA) functional, one meta-NGA, and three hybrid GGA functionals was evaluated for calculations of the closest interatomic distances, cohesive energies, and bulk moduli of all 3d, 4d, and 5d bulk transition metals that have face centered cubic (fcc), hexagonal closed packed (hcp), or body centered cubic (bcc) structures (a total of 27 cases). Our results show that including the extra elements of kinetic energy density and Hartree–Fock exchange energy density into gradient approximation density functionals does not usually improve them. Nevertheless, the accuracies of the Tao–Perdew–Staroverov–Scuseria (TPSS) and M06-L meta-GGAs and the MN12-L meta-NGA approac...

Bulk Properties of Transition Metals: A Challenge for the Design of Universal Density Functionals

Manganese is an element with outstanding structural and magnetic properties. While most metallic elements adopt a simple crystal structure and order magnetically---if at all---in a simple ferromagnetic or antiferromagnetic configuration, the stable phase of manganese at ambient conditions, paramagnetic $\ensuremath{\alpha}\ensuremath{-}\mathrm{Mn},$ adopts a complex crystal structure with 58 atoms in the cubic cell. At a N\'eel temperature of ${T}_{N}=95\mathrm{K},$ a transition to a complex noncollinear antiferromagnetic phase takes place. The magnetic phase transition is coupled to a tetragonal distortion of the crystalline structure. In this paper we present an ab initio spin-density functional study of the structural and magnetic properties of $\ensuremath{\alpha}\ensuremath{-}\mathrm{Mn}.$ It is shown that the strange properties of Mn arise from conflicting tendencies to simultaneously maximize according to Hund's rule the magnetic spin moment and the bond strength, as expected for a half-filled d band. Short interatomic distances produced by strong bonding tend to quench magnetism. The crystal structure of $\ensuremath{\alpha}\ensuremath{-}\mathrm{Mn}$ is essentially a consequence of these conflicting tendencies---it may be considered as a topologically close-packed intermetallic compound formed by strongly magnetic (MnI, MnII) and weakly magnetic (MnIII) or even nearly nonmagnetic (MnIV) atoms. The noncollinear magnetic structure is due to the fact that the MnIV atoms arranged on triangular faces of the coordination polyhedra are not entirely nonmagnetic---their frustrated antiferromagnetic coupling leads to the formation of a local spin structure reminiscent of the N\'eel structure of a frustrated triangular antiferromagnet. Consequently, also the other magnetic moments are rotated out of their collinear orientation. The calculated crystalline and magnetic structures are in good agreement with experiment. However, it is suggested that the magnetism leads to a splitting of the crystallographically inequivalent sites into a larger number of magnetic subgroups than deduced from the magnetic neutron diffraction data, but in accordance with NMR experiments. In a companion paper, the properties of the other polymorphs of Mn and their relative stability will be discussed.

Understanding the complex metallic element Mn. I. Crystalline and noncollinear magnetic structure of α-Mn

The binary Fe-Cr alloy is a system with a miscibility gap. The decomposition occurs either via the nucleation and growth mechanism or as spinodal decomposition, depending on the Cr content. However, at low chromium concentrations the alloys are anomalously stable. This is shown to be true only for the ferromagnetic body centered cubic (bcc) phase. The stability stems from the negative mixing enthalpy at low concentrations of chromium. We show that the effect has an electronic origin, that is, it is directly related to variations of the electronic structure in the alloy with concentration. We also demonstrate that the variation in the state density of the majority channel at the Fermi level in the concentration interval below $20\phantom{\rule{0.3em}{0ex}}\mathrm{at.}\phantom{\rule{0.2em}{0ex}}%$ Cr indicates increasing tendency of the system towards the spinodal decomposition in the system. Moreover, in the equimolar concentration region, significant deviations of the spin up band from its canonical shape are observed, which destabilize the bcc phase.

Electronic origin of the anomalous stability of Fe-rich bcc Fe-Cr alloys

It has been shown that concentrated solid solution alloys possess unusual electronic, magnetic, transport, mechanical and radiation-resistant properties that are directly related to underlying chemical complexity. Because every atom experiences a different local atomic environment, the formation and migration energies of vacancies and interstitials in these alloys exhibit a distribution, rather than a single value as in a pure metal or dilute alloy. Using ab initio calculations based on density functional theory and special quasirandom structures, we have characterized the distribution of defect formation energy and migration barrier in four Ni-based solid-solution alloys: Ni0.5Co0.5, Ni0.5Fe0.5, Ni0.8Fe0.2, and Ni0.8Cr0.2. As defect formation energies in finite-size models depend sensitively on the elemental chemical potential, we have developed a computationally efficient method for determining it which takes into account the global composition and the local short-range order. In addition we have compared the results of our ab initio calculations to those obtained from available embedded atom method (EAM) potentials. Our results indicate that the defect formation and migration energies are closely related to the specific atoms in the structure, which further determines the elemental diffusion properties. Different EAM potentials yield different features of defect energetics in concentrated alloys, pointing to the need for additional potential development efforts in order to allow spatial and temporal scale-up of defect and simulations, beyond those accessible to ab initio methods.

Defect energetics of concentrated solid-solution alloys from ab initio calculations: Ni0.5Co0.5, Ni0.5Fe0.5, Ni0.8Fe0.2 and Ni0.8Cr0.2

We present ab initio density-functional investigations of static long-period spin-density waves (SDWs) in chromium. Calculations were performed in the local-spin-density approximation with and without the generalized-gradient approximation, using both projector-augmented wave and muffin-tin-orbital techniques. The results show that for all cases the ground state of Cr is predicted to be of commensurate antiferromagnetic order, longitudinal SDWs lead to an increased total energy. The excitation energies associated with SDW formation are within the range of thermal energies even well below the N\'eel temperature. Structural relaxation of the SDW reveals that the stress relaxation has no significant effect on the energetics of the SDW phase. A possible scenario for the origin of the observed SDW state is developed.

Magnetic ground state of Cr in density-functional theory

The results of ab initio calculations for the electronic structure and the magnetic moments of unsupported hexagonal thin Ru and Fe films, bulk Ru and Fe metals, and ${\mathrm{Ru}}_{5}{\mathrm{Fe}}_{5}$ multilayer are presented with the focus on the crystallographic phase stability of the Fe layers. The calculated equilibrium lattice parameters of hcp Ru and Fe solids reproduce accurately the values found experimentally. For Ru/Fe multilayers it is demonstrated that in an Fe part of a multilayer an unusual hexagonal stacking with a distorted bcc-like local environment is more stable than the standard hexagonal close-packed stacking. The same result was obtained in thin Fe films and it is shown to be associated with band structure effects of Fe at the Fermi level. For thin films the ground state lattice parameters and magnetic states of films up to four monolayers were determined by total energy minimization. The faults in hexagonal planes stacking and interdiffusion do not lead to nonmagnetic Fe layers at the interfaces which were observed experimentally.

R. Lorenz

Papers

Magnetic ground state of Cr in density-functional theory

Structure and magnetism in thin films and multilayers of hexagonal ruthenium and iron

Ab initio local-spin-density study of the structural and magnetic properties of La1−xCaxMnO3 systems