The recently discovered oscillating exchange effect in iron–chromium multilayers can best be studied on an epitaxial iron sandwich with a wedge shaped chromium interlayer. Domain patterns are analyzed as well as magnetization curves on such samples using magnetooptical techniques. Unusual domains are found in zones around the transitions between ferromagnetic and antiferromagnetic exchange. Also the magnetization curves for larger chromium thickness show some peculiar features. The interpretation of these patterns invokes coupling between the iron layers which favours a right angle between the magnetization directions in both layers. Such a non-collinear interaction can be derived phenomenologi-cally from a biquadratic coupling as introduced earlier in the analysis of spin structures in oxides. A biquadratic coupling can be understood either as a second order Heisenberg or a second order Dzyaloshinskii interaction. In the course of these investigations domain observations proved to be a useful and sensitive method to detect locally the nature of interactions between ferromagnetic layers.



Die kiurzlich entdeckte oszillierende Wechselwirkung in Eisen–Chrom-Vielfachschichten kann am besten an einer epitaxialen Schichtanordnung mit einer keilformigen Chromzwischenschicht studiert werden. Die auf solchen Proben beobachtbaren Domanenstrukturen sowie die Magnetisierungskurven werden mit magnetooptischen Verfahren untersucht. Im Bereich der Ubergange zwischen ferroma-gnetischer und antiferromagnetischer Kopplung werden Zonen ungewohnlicher Muster entdeckt. Auch die Magnetisierungskurven fur grosere Chrom-Schichtdicken zeigten eigentumliche Zuge. Die Beobach-tungen lassen sich erklaren, wenn eine zusatzliche Kopplung der Schichten angenommen wird, die einen rechten Winkel zwischen den Magnetisierungsrichtungen in beiden Schichten begunstigt. Phanomenologisch ergibt sich eine solche nicht-kollineare Kopplung aus der Annahme einer biquadrati-schen Wechselwirkung, wie sie fruher in der Analyse von Spinstrukturen magnetischer Oxide eingefuhrt wurde. Eine biquadratische Kopplung Iast sich entweder als Heisenberg- oder Dzyaioshinskii-Wechselwirkung zweiter Ordnung interpretieren. Domanenbeobachtungen erwiesen sich im Laufe dieser Untersuchung als empfindliche Methode zur Untersuchung des Charakters der Kopplung in Vielfachschichten.

https://onlinelibrary.wiley.com/doi/pdf/10.1002/pssa.2211250225

Domain Observations on FeCrFe Layered Structnres. Evidence for a Biquadratic Coupling Effect

Unusual phases in quantum spin-1 systems

Recent results on the effect of the nanocrystalline state on the mechanical, thermal, and magnetic properties and microscopic structure of metals and solid-phase compounds are reviewed Basic methods for preparing compact nanocrystalline materials are briefly discussed Size effects in such materials are discussed in detail and the importance of interfaces in determining the structure and properties of compact nanomaterials is demonstrated Models explaining the structural features and anomalous properties of nanocrystalline solids are analyzed

https://iopscience.iop.org/article/10.1070/PU1998v041n01ABEH000329/pdf

Effects of the nanocrystalline state in solids

As the pnictide superconductors have metallic ground states, the Heisenberg model has not been successful in describing the magnetic behaviour. But the addition of a biquadratic interaction term to the usual Heisenberg Hamiltonian leads to a description of many experimental observations.

/pdf/consistent-model-of-magnetism-in-ferropnictides-3jpy6njc5p.pdf

Consistent model of magnetism in ferropnictides

Magnetism in recently discovered van der Waals materials has opened several avenues in the study of fundamental spin interactions in truly two-dimensions. A paramount question is what effect higher-order interactions beyond bilinear Heisenberg exchange have on the magnetic properties of few-atom thick compounds. Here we demonstrate that biquadratic exchange interactions, which is the simplest and most natural form of non-Heisenberg coupling, assume a key role in the magnetic properties of layered magnets. Using a combination of nonperturbative analytical techniques, non-collinear first-principles methods and classical Monte Carlo calculations that incorporate higher-order exchange, we show that several quantities including magnetic anisotropies, spin-wave gaps and topological spin-excitations are intrinsically renormalized leading to further thermal stability of the layers. We develop a spin Hamiltonian that also contains antisymmetric exchanges (e.g., Dzyaloshinskii–Moriya interactions) to successfully rationalize numerous observations, such as the non-Ising character of several compounds despite a strong magnetic anisotropy, peculiarities of the magnon spectrum of 2D magnets, and the discrepancy between measured and calculated Curie temperatures. Our results provide a theoretical framework for the exploration of different physical phenomena in 2D magnets where biquadratic exchange interactions have an important contribution.

/pdf/biquadratic-exchange-interactions-in-two-dimensional-magnets-2ezftoiaxw.pdf

Biquadratic exchange interactions in two-dimensional magnets

This review is primarily devoted to a discussion of isotropic magnetic materials with localized magnetic moments between which the exchange interaction is more complex than in the usual Heisenberg model. They include insulators for which the biquadratic or multispin exchange mechanisms are comparable with the bilinear exchange, conductors which do not satisfy the conditions of validity of the RKKY indirect exchange theory, and the nuclear magnetic material solid helium. Additionally, an analysis is made of high-anisotropy magnetic materials behaving similarly to isotropic non-Heisenberg materials. These anisotropic materials have anomalous properties, compared with the Heisenberg case. Experimental data on these materials and their theoretical interpretation are given. The following topics are discussed: 1) the conditions for a strong non-Heisenberg exchange and non-Heisenberg Hamiltonians; 2) quadrupole ordering and order-proper disorder phase transitions; 3) order-order and order-improper disorder phase transitions; 4) metamagnetism of isotropic materials; 5) normal sequences and "devil's ladders" of phase transitions between commensurable structures; 6) canted antiferromagnetism of high-symmetry crystals which do not obey the condition for the existence of relativistic Dzyaloshinskiĩ-type interactions.

É L Nagaev

Papers

Anomalous magnetic structures and phase transitions in non-Heisenberg magnetic materials