Spin Exchanges between Transition Metal Ions Governed by the Ligand p-Orbitals in Their Magnetic Orbitals

Abstract

In this review on spin exchanges, written to provide guidelines useful for finding the spin lattice relevant for any given magnetic solid, we discuss how the values of spin exchanges in transition metal magnetic compounds are quantitatively determined from electronic structure calculations, which electronic factors control whether a spin exchange is antiferromagnetic or ferromagnetic, and how these factors are related to the geometrical parameters of the spin exchange path. In an extended solid containing transition metal magnetic ions, each metal ion M is surrounded with main-group ligands L to form an MLn polyhedron (typically, n = 3–6), and the unpaired spins of M are represented by the singly-occupied d-states (i.e., the magnetic orbitals) of MLn. Each magnetic orbital has the metal d-orbital combined out-of-phase with the ligand p-orbitals; therefore, the spin exchanges between adjacent metal ions M lead not only to the M–L–M-type exchanges, but also to the M–L…L–M-type exchanges in which the two metal ions do not share a common ligand. The latter can be further modified by d0 cations A such as V5+ and W6+ to bridge the L…L contact generating M–L…A…L–M-type exchanges. We describe several qualitative rules for predicting whether the M–L…L–M and M–L…A…L–M-type exchanges are antiferromagnetic or ferromagnetic by analyzing how the ligand p-orbitals in their magnetic orbitals (the ligand p-orbital tails, for short) are arranged in the exchange paths. Finally, we illustrate how these rules work by analyzing the crystal structures and magnetic properties of four cuprates of current interest: α-CuV2O6, LiCuVO4, (CuCl)LaNb2O7, and Cu3(CO3)2(OH)2.

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“…Consequently, the overlap density between the magnetic orbitals of Cu1 and Cu2 becomes nonzero due to a nonzero overlap density between the x 2 − y 2 and 3 z 2 − r 2 orbitals of the Cu2 site. 33–35 As a consequence, the spin exchange between the adjacent Cu 2+ sites becomes ferromagnetic in AMP[CuCl 4 ].…”

Absence of Spin Frustration in the Kagomé Layers of Cu2+ Ions in Volborthite Cu3V2O7(OH)2·2H2O and Observation of the Suppression and Re-Entrance of Specific Heat Anomalies in Volborthite under an External Magnetic Field

“…The present work makes it clear that the use of a correct spin lattice is critical in describing the properties of a magnetic material. As a criterion for finding a proper spin lattice, the geometrical pattern of magnetic ion arrangement can be grossly misleading because a spin lattice is decided by the geometrical pattern of the strong spin exchange paths [3,4,19]. If volborthite were to be treated as a spin-frustrated kagomé lattice model, the S = 1/2 antiferromagnetic uniform Heisenberg chain behaviors of its magnetic susceptibility and magnetization are exotic and novel, as are its specific heat anomalies below 1.5 K. By the same token, all other magnetic properties of volborthite not explained by a spin-frustrated kagomé lattice model would be novel and surprising.…”

“…However, our work showed that each kagomé layer of Cu 2+ ions consists of very-weakly interacting two-leg spin ladders, so the seemingly exotic magnetic properties previously attributed to magnetic frustration are simply explained by a well-studied S = 1/2 antiferromagnetic uniform Heisenberg chain model. To find a correct spin lattice for any given magnetic material, it is necessary to evaluate the relative strengths of various possible spin exchanges of a given magnetic system by using an unbiased and straightforward method such as the energy-mapping analysis, based on first principles DFT calculations [3,4,19,33].…”

“…The two-leg spin ladder model as the spin lattice of volborthite described above is also supported by Janson et al's spin exchanges (Table 1), although their spin exchanges differ considerably from ours in magnitude. In general, a spin exchange J between two magnetic ions located at sites i and j can be written as the sum of the FM and AFM components (J F and J AF , respectively), namely, J = J F + J AF [3,4,19]. With the magnetic orbitals describing the spin sites i and j as ψ i and ψ j , respectively, the overlap density ρ ij = ψ i ψ j gives rise to the exchange repulsion K ij , while the overlap integral <ψ i |ψ j > leads to an energy split ∆e between the two states described by the magnetic orbitals.…”

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“…They reflect that the magnetic orbitals of a cation M forming an ML n polyhedron with surrounding ligands are given by d-states of ML n , in which the p-orbitals of L are combined out-of-phase with the d-orbitals of M, and that all types of spin exchanges are governed largely by the ligand p-orbitals of the magnetic orbitals. The qualitative aspects of spin exchanges were reviewed by Myung-Hwan Whangbo, Hyun-Joo Koo and Reinhard K. Kremer [2], in which they discuss how the qualitative trends in spin exchanges are related to the arrangements of the magnetic orbitals, providing the structure-property relations with which to understand the magnetic properties of complex magnetic solids.…”