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.

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Under ambient condition PdSe2 has the PdS2-type structure. The crystal structure of PdSe2 under pressure (up to 30 GPa) was investigated at room temperature by X-ray diffraction in an energy-dispersive configuration using a diamond anvil cell with a mixture of water/ethanol/methanol as a pressure transmitting medium. A reversible structural transition from the PdS2-type to the pyrite-type structure occurs around 10 GPa, and the applied pressure reduces the spacing between adjacent 2/proportional to [PdSe2] layers of the PdS2-type structure to form the three-dimensional lattice of the pyrite-type structure. First principles and extended Hückel electronic band structure calculations were carried out to confirm the observed pressure-induced structural changes. We also examined why the isoelectronic analogues NiSe2 and PtSe2 adopt structures different from the PdS2-type structure on the basis of qualitative electronic structure considerations.

ConspectusFor most chemists and physicists, electron spin is merely a means needed to satisfy the Pauli principle in electronic structure description. However, the absolute orientations of spins in coordinate space can be crucial in understanding the magnetic properties of materials with unpaired electrons. At a low temperature the spins of a magnetic solid may undergo a long-range magnetic ordering, which allows one to determine the directions and magnitudes of spin moments by neutron diffraction refinements. The preferred spin orientation of a magnetic ion can be predicted on the basis of density functional theory (DFT) calculations including electron correlation and spin-orbit coupling (SOC). However, most chemists and physicists are unaware of how the observed and/or calculated spin orientations are related to the local electronic structures of the magnetic ions. This is true even for most crystallographers who determine the directions and magnitudes of spin moments because, for them, they are merely the parameters needed for the diffraction refinements. The objective of this article is to provide a conceptual framework of thinking about and predicting the preferred spin orientation of a magnetic ion by examining the relationship between the spin orientation and the local electronic structure of the ion. In general, a magnetic ion M (i.e., an ion possessing unpaired spins) in a solid or a molecule is surrounded with main-group ligand atoms L to form an MLn polyhedron, where n is typically 2 -6, and the d-states