The purpose of this critical review is to give a representative and comprehensive overview of the arising developments in the field of magnetic metal–organic frameworks, in particular those containing cobalt(II). We examine the diversity of magnetic exchange interactions between nearest-neighbour moment carriers, covering from dimers to oligomers and discuss their implications in infinite chains, layers and networks, having a variety of topologies. We progress to the different forms of short-range magnetic ordering, giving rise to single-molecule-magnets and single-chain-magnets, to long-range ordering of two- and three-dimensional networks (323 references).

Magnetic metal-organic frameworks.

“…. For the truth of the conclusions of physical science, observation is the supreme Court of Appeal….” (Sir Arthur Eddington, The Philosophy of Physical Science.) In this paper we shall review the theoretical and experimental results obtained on simple magnetic model systems. We shall consider the Heisenberg, XY and Ising type of interaction (ferro and antiferromagnetic), on magnetic lattices of dimensionality 1, 2 and 3. Particular attention will be paid to the approximation of these model systems in real crystals, viz. how they can be realized or be expected to exist in nature. A large number of magnetic compounds which, according to the available experimental information, meet the requirements set by one or the other of the various models are considered and their properties discussed. Many examples will be given that demonstrate to what extent experiments on simple magnetic systems support theoretical descriptions of magnetic ordering phenomena and contribute to their understanding. It will a...

Experiments on simple magnetic model systems

Systematic trends in the geometry of 149 oxide and 80 sulfide binary and ternary spinels have been examined from the standpoint of ionic radius and electronegativity. The mean ionic radii of the octahedral and tetrahedral cations, taken together, account for 96.9 and 90.5% of the variation in the unit cell parameter, a, of the oxides and sulfides, respectively, with the octahedral cation exerting by far the dominant influence in sulfides. The mean electronegativity of the octahedral cation exerts an additional, but small, influence on the cell edge of the sulfides. The equation a=(8/3√d)d
tet+(8/3)d
oct, where d
tet and d
oct are the tetrahedral and octahedral bond lengths obained from the sum of the ionic radii, accounts for 96.7 and 83.2% of the variation in a in the oxides and sulfides, respectively, again testifying to the applicability of the hard-sphere ionic model in the case of the spinel structure. Comparison of observed and calculated u values for 94 spinels indicates that up to 40% of the experimentally measured anion coordinates may be significantly in error. In addition to these compounds, u values are given for 52 spinels for which no data have previously been determined. Diagrams are presented for the rapid interpretation of the internal consistency of published data and the prediction of the structural parameters of hypothetical or partially studied spinels.

Systematics of the spinel structure type

The co-operative Jahn-Teller effect is a phase transition which is driven by the interaction between localized orbital electronic states and the crystal lattice. The possible origins, symmetries and properties of the electron-lattice interactions and how they lead to possible hamiltonians for the coupled system are discussed. The relation of these interactions with quadrupolar interactions and magnetostriction is included. The methods of solution of the hamiltonians lead to an understanding of the electronic states, the phonon spectrum and the mixed normal modes. The wide variety of experimental techniques used on this problem are reviewed in detail and the results are compared with theoretical expressions whenever possible. The application of external stress and magnetic field is of particular significance in the case of the rare earth compounds, because they can product effects which are larger than the low-temperature spontaneous effects.

http://iopscience.iop.org/article/10.1088/0034-4885/38/1/001/pdf

Co-operative Jahn-Teller effects

A review is given of the formation, the crystal structure and the magnetic properties of several classes of rare earth based intermetallic compounds that lend themselves as starting materials of permanent magnets. These compounds include R2Fe14B, R2Fe14C and R2Co14B and the large class of ternary rare earth compounds having the tetragonal ThMn12 structure. Special emphasis is given to the changes in magnetic properties of R2Fe17 compounds observed after interstitial solution of C or N atoms. The magnetic properties of all these compounds are discussed in terms of current models based on intersublattice and intrasublattice exchange and the interplay between the rare earth sublattice anisotropy and 3D sublattice anisotropy. A substantial portion of the review is devoted to manufacturing routes of permanent magnets and a description of the coercivity mechanisms operative in the magnets. A comparison is made of the performance and economic costs of various types of magnets and novel applications are briefly discussed.

https://iopscience.iop.org/article/10.1088/0034-4885/54/9/001/pdf

New developments in hard magnetic materials

The Faraday rotation of yttrium, gadonlinium, and terbium iron garnets at 1.15 \ensuremath{\mu} is presented as a function of temperature between 100 and 450\ifmmode^\circ\else\textdegree\fi{}K. The rotation is analyzed in terms of electric and magnetic dipole contributions from the various magnetic sublattices (${\mathrm{Fe}}^{3+}$ octahedral, ${\mathrm{Fe}}^{3+}$ tetrahedral, R${\mathrm{E}}^{3+}$), and the contributions are separated by a least-squares fit to magnetization data. The similarities and differences in the electric dipole contributions are discussed, and it is suggested that charge-transfer processes are important. The effect of a knowledge of the electric dipole contributions at 1.15 \ensuremath{\mu} on published results at longer wavelengths is investigated, and deductions of $g$ factors in this region are shown to be probably in error. In an Appendix, theoretical derivations are given for the form of the electric dipole rotation due to magnetic ions in various circumstances.

Faraday Rotation in Rare-Earth Iron Garnets

Magnetic properties, conductivity and ionic ordering in Fe1−xCuxCr2S4

Magnetic and electrical properties of copper containing sulphides and selenides with spinel structure

Exchange interactions of nearest-neighbor ${\mathrm{Cr}}^{3+}$ pairs in Zn${\mathrm{Ga}}_{2}$${\mathrm{O}}_{4}$ have been studied in detail. An analysis of the emission, absorption, and luminescence excitation spectra yield the ($^{4}A_{2}$, $^{4}A_{2}$) ground-state level splittings and the ($^{4}A_{2}$, $^{2}E$) excited-state splittings. The first are described by $\ensuremath{-}J{\stackrel{\ensuremath{\rightarrow}}{\mathrm{S}}}_{1}\ifmmode\cdot\else\textperiodcentered\fi{}{\stackrel{\ensuremath{\rightarrow}}{\mathrm{S}}}_{2}+j{({\stackrel{\ensuremath{\rightarrow}}{\mathrm{S}}}_{1}\ifmmode\cdot\else\textperiodcentered\fi{}{\stackrel{\ensuremath{\rightarrow}}{\mathrm{S}}}_{2})}^{2}$, with ${S}_{1}={S}_{2}=\frac{3}{2}$, $J=\ensuremath{-}22.2\ifmmode\pm\else\textpm\fi{}0.5$ ${\mathrm{cm}}^{\ensuremath{-}1}$, and $j=\ensuremath{-}1.7\ifmmode\pm\else\textpm\fi{}0.3$ ${\mathrm{cm}}^{\ensuremath{-}1}$. The ($^{4}A_{2}$, $^{2}E$) level splittings are compared with the values calculated from the orbital-dependent exchange Hamiltonian ${\mathcal{H}}_{\mathrm{ex}}=\ensuremath{-}{\ensuremath{\Sigma}}_{j}{J}_{\mathrm{ij}}{\stackrel{\ensuremath{\rightarrow}}{\mathrm{s}}}_{i}\ifmmode\cdot\else\textperiodcentered\fi{}{\stackrel{\ensuremath{\rightarrow}}{\mathrm{s}}}_{j}$, where ${s}_{i}={s}_{j}=\frac{1}{2}$ and the sum is over the ${t}_{2g}$ orbitals of the ${\mathrm{Cr}}^{3+}$ ion. In the local ${C}_{2\ensuremath{\nu}}$ symmetry of the pair, there are four independent ${J}_{\mathrm{ij}}$ parameters which have been determined as ${J}_{c}=+39$ ${\mathrm{cm}}^{\ensuremath{-}1}$, $J_{c}^{}{}_{}{}^{\ensuremath{'}}=+117$ ${\mathrm{cm}}^{\ensuremath{-}1}$, ${J}_{d}=\ensuremath{-}561$ ${\mathrm{cm}}^{\ensuremath{-}1}$, and ${J}_{\ensuremath{\pi}}=\ensuremath{-}105$ ${\mathrm{cm}}^{\ensuremath{-}1}$. The large value of ${J}_{d}$ is a consequence of the direct overlap between ${t}_{2}\ensuremath{\zeta}$ functions, which is possible in the 90\ifmmode^\circ\else\textdegree\fi{} exchange configuration of nearest-neighbor Cr pairs in the spinel structure. The relative intensities of the different pair lines are compared with values calculated from the mechanism of the exchange-induced dipole moment and reasonable agreement is found.

R. P. van Stapele

Papers

Faraday Rotation in Rare-Earth Iron Garnets

Magnetic properties, conductivity and ionic ordering in Fe1−xCuxCr2S4

Magnetic and electrical properties of copper containing sulphides and selenides with spinel structure

Optical Spectra of Cr 3 + Pairs in the Spinel Zn Ga 2 O 4

Anisotropy of hexagonal ferrites with M, W and Y structures containing Fe3+ and Fe2+ as magnetic ions