Spin Exchanges between Transition Metal Ions Governed by the Ligand p-Orbitals in Their Magnetic Orbitals
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 el...
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| Format: | Article |
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MDPI AG
2021-01-01
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| Series: | Molecules |
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| Online Access: | https://www.mdpi.com/1420-3049/26/3/531 |
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| author | Myung-Hwan Whangbo Hyun-Joo Koo Reinhard K. Kremer |
| author_facet | Myung-Hwan Whangbo Hyun-Joo Koo Reinhard K. Kremer |
| author_sort | Myung-Hwan Whangbo |
| collection | DOAJ |
| description | 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 ML<sub>n</sub> 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 ML<sub>n</sub>. 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 d<sup>0</sup> cations A such as V<sup>5+</sup> and W<sup>6+</sup> 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-CuV<sub>2</sub>O<sub>6</sub>, LiCuVO<sub>4</sub>, (CuCl)LaNb<sub>2</sub>O<sub>7</sub>, and Cu<sub>3</sub>(CO<sub>3</sub>)<sub>2</sub>(OH)<sub>2</sub>. |
| first_indexed | 2024-03-09T04:11:05Z |
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| institution | Directory Open Access Journal |
| issn | 1420-3049 |
| language | English |
| last_indexed | 2024-03-09T04:11:05Z |
| publishDate | 2021-01-01 |
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| spelling | doaj.art-ddd9f39f981a4cfd805862b6d943225d2023-12-03T14:00:55ZengMDPI AGMolecules1420-30492021-01-0126353110.3390/molecules26030531Spin Exchanges between Transition Metal Ions Governed by the Ligand p-Orbitals in Their Magnetic OrbitalsMyung-Hwan Whangbo0Hyun-Joo Koo1Reinhard K. Kremer2Department of Chemistry and Research Institute for Basic Sciences, Kyung Hee University, Seoul 02447, KoreaDepartment of Chemistry and Research Institute for Basic Sciences, Kyung Hee University, Seoul 02447, KoreaMax Planck Institute for Solid State Research, Heisenbergstrasse 1, D-70569 Stuttgart, GermanyIn 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 ML<sub>n</sub> 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 ML<sub>n</sub>. 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 d<sup>0</sup> cations A such as V<sup>5+</sup> and W<sup>6+</sup> 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-CuV<sub>2</sub>O<sub>6</sub>, LiCuVO<sub>4</sub>, (CuCl)LaNb<sub>2</sub>O<sub>7</sub>, and Cu<sub>3</sub>(CO<sub>3</sub>)<sub>2</sub>(OH)<sub>2</sub>.https://www.mdpi.com/1420-3049/26/3/531<b>Keywords</b>: spin exchangemagnetic orbitalsligand p-orbital tailsM–L–M exchangeM–L…L–M exchangeα-CuV<sub>2</sub>O<sub>6</sub> |
| spellingShingle | Myung-Hwan Whangbo Hyun-Joo Koo Reinhard K. Kremer Spin Exchanges between Transition Metal Ions Governed by the Ligand p-Orbitals in Their Magnetic Orbitals Molecules <b>Keywords</b>: spin exchange magnetic orbitals ligand p-orbital tails M–L–M exchange M–L…L–M exchange α-CuV<sub>2</sub>O<sub>6</sub> |
| title | Spin Exchanges between Transition Metal Ions Governed by the Ligand p-Orbitals in Their Magnetic Orbitals |
| title_full | Spin Exchanges between Transition Metal Ions Governed by the Ligand p-Orbitals in Their Magnetic Orbitals |
| title_fullStr | Spin Exchanges between Transition Metal Ions Governed by the Ligand p-Orbitals in Their Magnetic Orbitals |
| title_full_unstemmed | Spin Exchanges between Transition Metal Ions Governed by the Ligand p-Orbitals in Their Magnetic Orbitals |
| title_short | Spin Exchanges between Transition Metal Ions Governed by the Ligand p-Orbitals in Their Magnetic Orbitals |
| title_sort | spin exchanges between transition metal ions governed by the ligand p orbitals in their magnetic orbitals |
| topic | <b>Keywords</b>: spin exchange magnetic orbitals ligand p-orbital tails M–L–M exchange M–L…L–M exchange α-CuV<sub>2</sub>O<sub>6</sub> |
| url | https://www.mdpi.com/1420-3049/26/3/531 |
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