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Journal ArticleDOI

Anisotropic Superexchange Interaction and Weak Ferromagnetism

Tôru Moriya1
01 Oct 1960-Physical Review (American Physical Society)-Vol. 120, Iss: 1, pp 91-98
TL;DR: In this paper, the Anderson theory of superexchange was extended to include spin-orbit coupling and the antisymmetric spin coupling suggested by Dzialoshinski from purely symmetry grounds and the symmetric pseudodipolar interaction were derived.
Abstract: A theory of anisotropic superexchange interaction is developed by extending the Anderson theory of superexchange to include spin-orbit coupling. The antisymmetric spin coupling suggested by Dzialoshinski from purely symmetry grounds and the symmetric pseudodipolar interaction are derived. Their orders of magnitudes are estimated to be ($\frac{\ensuremath{\Delta}g}{g}$) and ${(\frac{\ensuremath{\Delta}g}{g})}^{2}$ times the isotropic superexchange energy, respectively. Higher order spin couplings are also discussed. As an example of antisymmetric spin coupling the case of Cu${\mathrm{Cl}}_{2}$\ifmmode\cdot\else\textperiodcentered\fi{}2${\mathrm{H}}_{2}$O is illustrated. In Cu${\mathrm{Cl}}_{2}$\ifmmode\cdot\else\textperiodcentered\fi{}2${\mathrm{H}}_{2}$O, a spin arrangement which is different from one accepted so far is proposed. This antisymmetric interaction is shown to be responsible for weak ferromagnetism in $\ensuremath{\alpha}$-${\mathrm{Fe}}_{2}$${\mathrm{O}}_{3}$, MnC${\mathrm{O}}_{3}$, and Cr${\mathrm{F}}_{3}$. The paramagnetic susceptibility perpendicular to the trigonal axis is expected to increase very sharply near the N\'eel temperature as the temperature is lowered, as was actually observed in Cr${\mathrm{F}}_{3}$.
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Journal ArticleDOI
TL;DR: Spintronics, or spin electronics, involves the study of active control and manipulation of spin degrees of freedom in solid-state systems as discussed by the authors, where the primary focus is on the basic physical principles underlying the generation of carrier spin polarization, spin dynamics, and spin-polarized transport.
Abstract: Spintronics, or spin electronics, involves the study of active control and manipulation of spin degrees of freedom in solid-state systems. This article reviews the current status of this subject, including both recent advances and well-established results. The primary focus is on the basic physical principles underlying the generation of carrier spin polarization, spin dynamics, and spin-polarized transport in semiconductors and metals. Spin transport differs from charge transport in that spin is a nonconserved quantity in solids due to spin-orbit and hyperfine coupling. The authors discuss in detail spin decoherence mechanisms in metals and semiconductors. Various theories of spin injection and spin-polarized transport are applied to hybrid structures relevant to spin-based devices and fundamental studies of materials properties. Experimental work is reviewed with the emphasis on projected applications, in which external electric and magnetic fields and illumination by light will be used to control spin and charge dynamics to create new functionalities not feasible or ineffective with conventional electronics.

9,158 citations


Additional excerpts

  • ...86 The anisotropic exchange interaction of the DzyaloshinskiiMoriya form, S1 × S2 (Dzyaloshinskii, 1958; Moriya, 1960) appears as a result of spin-orbit coupling in semiconductors lacking 0 1 2 3 4 5 6 B (tesla) 10 1 10 2 10 3 10 4...

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Journal ArticleDOI
Abstract: Recent research activities on the linear magnetoelectric (ME) effect?induction of magnetization by an electric field or of polarization by a magnetic field?are reviewed. Beginning with a brief summary of the history of the ME effect since its prediction in 1894, the paper focuses on the present revival of the effect. Two major sources for 'large' ME effects are identified. (i) In composite materials the ME effect is generated as a product property of a magnetostrictive and a piezoelectric compound. A linear ME polarization is induced by a weak ac magnetic field oscillating in the presence of a strong dc bias field. The ME effect is large if the ME coefficient coupling the magnetic and electric fields is large. Experiments on sintered granular composites and on laminated layers of the constituents as well as theories on the interaction between the constituents are described. In the vicinity of electromechanical resonances a ME voltage coefficient of up to 90?V?cm?1?Oe?1 is achieved, which exceeds the ME response of single-phase compounds by 3?5 orders of magnitude. Microwave devices, sensors, transducers and heterogeneous read/write devices are among the suggested technical implementations of the composite ME effect. (ii) In multiferroics the internal magnetic and/or electric fields are enhanced by the presence of multiple long-range ordering. The ME effect is strong enough to trigger magnetic or electrical phase transitions. ME effects in multiferroics are thus 'large' if the corresponding contribution to the free energy is large. Clamped ME switching of electrical and magnetic domains, ferroelectric reorientation induced by applied magnetic fields and induction of ferromagnetic ordering in applied electric fields were observed. Mechanisms favouring multiferroicity are summarized, and multiferroics in reduced dimensions are discussed. In addition to composites and multiferroics, novel and exotic manifestations of ME behaviour are investigated. This includes (i) optical second harmonic generation as a tool to study magnetic, electrical and ME properties in one setup and with access to domain structures; (ii) ME effects in colossal magnetoresistive manganites, superconductors and phosphates of the LiMPO4 type; (iii) the concept of the toroidal moment as manifestation of a ME dipole moment; (iv) pronounced ME effects in photonic crystals with a possibility of electromagnetic unidirectionality. The review concludes with a summary and an outlook to the future development of magnetoelectrics research.

4,315 citations

Journal ArticleDOI
TL;DR: It is found that even a weak magnetoelectric interaction can lead to spectacular cross-coupling effects when it induces electric polarization in a magnetically ordered state.
Abstract: Magnetism and ferroelectricity are essential to many forms of current technology, and the quest for multiferroic materials, where these two phenomena are intimately coupled, is of great technological and fundamental importance. Ferroelectricity and magnetism tend to be mutually exclusive and interact weakly with each other when they coexist. The exciting new development is the discovery that even a weak magnetoelectric interaction can lead to spectacular cross-coupling effects when it induces electric polarization in a magnetically ordered state. Such magnetic ferroelectricity, showing an unprecedented sensitivity to ap plied magnetic fields, occurs in 'frustrated magnets' with competing interactions between spins and complex magnetic orders. We summarize key experimental findings and the current theoretical understanding of these phenomena, which have great potential for tuneable multifunctional devices.

3,683 citations


Additional excerpts

  • ...It involves the antisymmetric Dzyaloshinskii–Moriya (DM) interaction, D n,n+1 · S n × S n+1 , where D n,n+1 is the Dzyaloshinskii vecto...

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Journal ArticleDOI
TL;DR: Novel device paradigms based on magnetoelectric coupling are discussed, the key scientific challenges in the field are outlined, and high-quality thin-film multiferroics are reviewed.
Abstract: Multiferroic materials, which show simultaneous ferroelectric and magnetic ordering, exhibit unusual physical properties — and in turn promise new device applications — as a result of the coupling between their dual order parameters. We review recent progress in the growth, characterization and understanding of thin-film multiferroics. The availability of high-quality thin-film multiferroics makes it easier to tailor their properties through epitaxial strain, atomic-level engineering of chemistry and interfacial coupling, and is a prerequisite for their incorporation into practical devices. We discuss novel device paradigms based on magnetoelectric coupling, and outline the key scientific challenges in the field.

3,472 citations


Cites background from "Anisotropic Superexchange Interacti..."

  • ..., the symmetry also permits a canting of the antiferromagnetic sublattices resulting in a macroscopic magnetization — 'weak ferromagnetism...

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Journal ArticleDOI
TL;DR: From this description, potential applications of skyrmions as information carriers in magnetic information storage and processing devices are envisaged.
Abstract: Magnetic skyrmions are particle-like nanometre-sized spin textures of topological origin found in several magnetic materials, and are characterized by a long lifetime. Skyrmions have been observed both by means of neutron scattering in momentum space and microscopy techniques in real space, and their properties include novel Hall effects, current-driven motion with ultralow current density and multiferroic behaviour. These properties can be understood from a unified viewpoint, namely the emergent electromagnetism associated with the non-coplanar spin structure of skyrmions. From this description, potential applications of skyrmions as information carriers in magnetic information storage and processing devices are envisaged.

3,132 citations