Rotational motion of magnons and the thermal Hall effect

Matsumoto, Ryo; Murakami, Shuichi

doi:10.1103/physrevb.84.184406

Cited by 246 publications

(243 citation statements)

References 28 publications

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“…Closely related to it kagomé ferromagnet system is currently under investigation 16 . Similar set-ups, in relation to thermal Hall effect, have been recently discussed in 17,18 . We subject kagomé antiferromagnet to a strong magnetic field B = Bẑ which exceeds the saturation field B sat above which the spins are fully polarized.…”

Section: Kagomé Antiferromagnet With Dzyaloshinskii-moriya Interamentioning

confidence: 97%

Equilibrium currents in chiral systems with nonzero Chern number

Mishchenko

Starykh

2014

Phys. Rev. B

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We describe simple quantum-mechanical approach to calculating equilibrium particle current along the edge of a system with non-trivial band spectrum topology. The approach does not require any a priori knowledge of the band topology and, as a matter of fact, treats topological and non-topological contributions to the edge currents on the same footing. We illustrate its usefulness by demonstrating the existence of 'topologically non-trivial' particle currents along the edges of three different physical systems: two-dimensional electron gas with spin-orbit coupling and Zeeman magnetic field, surface state of a topological insulator, and kagomé antiferromagnet with Dzyaloshinskii-Moriya interaction. We describe relation of our results to the notion of orbital magnetization.

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Section: Kagomé Antiferromagnet With Dzyaloshinskii-moriya Interamentioning

confidence: 97%

Equilibrium currents in chiral systems with nonzero Chern number

Mishchenko

Starykh

2014

Phys. Rev. B

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“…With a relativistic spin-orbit interaction, this leads to the intrinsic spin Hall effect 66 , the quantized version of which has led to the discovery of topological insulators, described in the next section. Another extension is to consider the Berry phase for neutral particles, such as photons 77,78 and magnons [79][80][81] .…”

Section: Berry Phase Engineeringmentioning

confidence: 99%

Emergent functions of quantum materials

2017

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Materials can harbour quantum many-body systems, most typically in the form of strongly correlated electrons in solids, that lead to novel and remarkable functions thanks to emergence-collective behaviours that arise from strong interactions among the elements. These include the Mott transition, high-temperature superconductivity, topological superconductivity, colossal magnetoresistance, giant magnetoelectric e ect, and topological insulators. These phenomena will probably be crucial for developing the next-generation quantum technologies that will meet the urgent technological demands for achieving a sustainable and safe society. Dissipationless electronics using topological currents and quantum spins, energy harvesting such as photovoltaics and thermoelectrics, and secure quantum computing and communication are the three major fields of applications working towards this goal. Here, we review the basic principles and the current status of the emergent phenomena and functions in materials from the viewpoint of strong correlation and topology.E mergence is a concept developed for many-body systems, indicating the properties, phenomena, and functions that never appear in the individual elements but are realized only when a huge number of elements get together 1 . Inside materials, emergent phenomena are often seen due to the interaction of electronic states; with recent developments on electronic states in solids schematically summarized in Fig. 1a. Electrons in solids have several degrees of freedom: charge, spin and orbital, and are characterized by the topological nature determined by the atomic potential on the crystal lattice structure, as schematically shown in Fig. 1b. These five attributes are coupled together and determine the overall responses to stimuli, which appear as materials' electrical, magnetic, optical, thermal, and mechanical properties.These collective electrons demonstrate various macroscopic quantum phenomena, the representative example of which is superconductivity. One of the big challenges in condensed matter physics is to increase the temperature (T c ) at which superconductivity can be observed to above room temperature. However, there are many other macroscopic quantum phenomena that are already observable above room temperature. One is magnetism (by the Bohr-van Leeuwen theorem), and the other is ferroelectricity 2,3 . Remarkably, there are common features of these three macroscopic quantum phenomena: the order parameter, which is of quantum origin, behaves as a classical quantity, and the quantum topology plays a crucial role.The topological nature of the electronic states is the key concept in the most recent developments in understanding quantum materials. The quantum Hall effect, topological insulators, and topological superconductors are all characterized by nontrivial topologies in Hilbert space. The Berry phase, which describes the connection and curvature of the subspace of Hilbert space, plays the central role in the unified principle to describe this topological nature 4 . ...

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“…Coupling of the energy density H i to the pseudogravitational potential ψ i is an effective way to derive the thermal response function. [6][7][8]17 In brief, the total Hamiltonian including the gravitational coupling H = …”

Section: Spin Linear Response Theorymentioning

confidence: 99%

“…14 Stimulated by their observations, we go beyond the existing magnon description of the thermal Hall effect [4][5][6][7][8][9][10] and formulate the phenomenon using the spin language entirely. It is then applied to discuss Hall effects of spin both in the paramgnetic as well as the ferromagnetic regime.…”

Section: Introductionmentioning

confidence: 99%

“…Magnons -quantized small fluctuations of an ordered magnet -can in principle exhibit similar Hall transport driven by thermal gradient, as first predicted theoretically by Katsura, Nagaosa, and Lee 4 and confirmed experimentally in an insulating pyrochlore magnet Lu 2 V 2 O 7 by the Tokura group 5 . Formulation of the magnon Hall effect was perfected by Murakami and collaborators in a series of papers [6][7][8] after correcting for the missing, magnetization current term in the original derivation of Ref. 4.…”

Section: Introductionmentioning

confidence: 99%

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Thermal Hall effect of spins in a paramagnet

2015

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Theory of Hall transport of spins in a correlated paramagnetic phase is developed. By identifying the thermal Hall current operator in the spin language, which turns out to equal the spin chirality in the pure Heisenberg model, various response functions can be derived straightforwardly. Subsequent reduction to the Schwinger boson representation of spins allows a convenient calculation of thermal and spin Hall coefficients in the paramagnetic regime using self-consistent mean-field theory. Comparison is made to results from the Holstein-Primakoff reduction of spin operators appropriate for ordered phases.

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Rotational motion of magnons and the thermal Hall effect

Cited by 246 publications

References 28 publications

Equilibrium currents in chiral systems with nonzero Chern number

Equilibrium currents in chiral systems with nonzero Chern number

Emergent functions of quantum materials

Thermal Hall effect of spins in a paramagnet

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