We report that the Kondo effect exerted by a magnetic ion depends on its chemical environment. A cobalt phthalocyanine molecule adsorbed on an Au(111) surface exhibited no Kondo effect. Cutting away eight hydrogen atoms from the molecule with voltage pulses from a scanning tunneling microscope tip allowed the four orbitals of this molecule to chemically bond to the gold substrate. The localized spin was recovered in this artificial molecular structure, and a clear Kondo resonance was observed near the Fermi surface. We attribute the high Kondo temperature (more than 200 kelvin) to the small on-site Coulomb repulsion and the large half-width of the hybridized d-level.

The magnetic energy levels of a given magnetic solid are closely packed in energy because the interactions between magnetic ions are weak. Thus, in describing its magnetic properties, one needs to generate its magnetic energy spectrum by employing an appropriate spin Hamiltonian. In this review article we discuss how to determine and specify a necessary spin Hamiltonian in terms of first principles electronic structure calculations on the basis of energy-mapping analysis and briefly survey important concepts and phenomena that one encounters in reading the current literature on magnetic solids. Our discussion is given on a qualitative level from the perspective of magnetic energy levels and electronic structures. The spin Hamiltonian appropriate for a magnetic system should be based on its spin lattice, i.e., the repeat pattern of its strong magnetic bonds (strong spin exchange paths), which requires one to evaluate its Heisenberg spin exchanges on the basis of energy-mapping analysis. Other weaker energy terms such as Dzyaloshinskii–Moriya (DM) spin exchange and magnetocrystalline anisotropy energies, which a spin Hamiltonian must include in certain cases, can also be evaluated by performing energy-mapping analysis. We show that the spin orientation of a transition-metal magnetic ion can be easily explained by considering its split d-block levels as unperturbed states with the spin–orbit coupling (SOC) as perturbation, that the DM exchange between adjacent spin sites can become comparable in strength to the Heisenberg spin exchange when the two spin sites are not chemically equivalent, and that the DM interaction between rare-earth and transition-metal cations is governed largely by the magnetic orbitals of the rare-earth cation.

A novel general method of describing the spin-lattice interactions in magnetic solids is proposed in terms of first-principles calculations. The spin exchange and Dzyaloshinskii-Moriya interactions, as well as their derivatives with respect to atomic displacements, can be evaluated efficiently on the basis of density-functional calculations for four ordered spin states. By taking into consideration the spin-spin interactions, the phonons, and the coupling between them, we show that the ground-state structure of a representative spin-frustrated spinel, MgCr${}_2$O${}_4$, is tetragonally distorted, in agreement with experiments. However, our calculations find the lowest energy for the collinear spin ground state, in contrast to previously suggested noncollinear models.

Magnetic anisotropy is crucially important for the stabilization of two-dimensional (2D) magnetism, which is rare in nature but highly desirable in spintronics and for advancing fundamental knowledge. Recent works on CrI₃ and CrGeTe₃ monolayers not only led to observations of the long-time-sought 2D ferromagnetism, but also revealed distinct magnetic anisotropy in the two systems, namely Ising behavior for CrI₃ versus Heisenberg behavior for CrGeTe₃. Such magnetic difference strongly contrasts with structural and electronic similarities of these two materials, and understanding it at a microscopic scale should be of large benefits. Here, first-principles calculations are performed and analyzed to develop a simple Hamiltonian, to investigate magnetic anisotropy of CrI₃ and CrGeTe₃ monolayers. The anisotropic exchange coupling in both systems is surprisingly determined to be of Kitaev-type. Moreover, the interplay between this Kitaev interaction and single ion anisotropy (SIA) is found to naturally explain the different magnetic behaviors of CrI₃ and CrGeTe₃. Finally, both the Kitaev interaction and SIA are further found to be induced by spin–orbit coupling of the heavy ligands (I of CrI₃ or Te of CrGeTe₃) rather than the commonly believed 3d magnetic Cr ions.

The origin of ferromagnetism in $d^0$ semiconductors is studied using first-principles methods with ZnO as a prototype material. We show that the presence of spontaneous magnetization in nitrides and oxides with sufficient holes is an intrinsic property of these first-row $d^0$ semiconductors and can be attributed to the localized nature of the $2p$ states of O and N. We find that acceptor doping, especially doping at the anion site, can enhance the ferromagnetism with much smaller threshold hole concentrations. The quantum confinement effect also reduces the critical hole concentration to induce ferromagnetism in ZnO nanowires. The characteristic nonmonotonic spin couplings in these systems are explained in terms of the band coupling model.