Quantum theory of spin waves in finite chiral spin chains

Roldán-Molina, A.; Santander, M.J.; Núñez, Álvaro S.; Fernández-Rossier, J.

doi:10.1103/physrevb.89.054403

Cited by 9 publications

(15 citation statements)

References 28 publications

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“…Now, we perform a HolsteinPrimakoff transformation [46,62,63], which will replace the spin operator by creation and annihilation spin-wave operators:…”

Section: Holstein-primakoff Transformationmentioning

confidence: 99%

Spin-resolved inelastic electron scattering by spin waves in noncollinear magnets

et al. 2018

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Topological noncollinear magnetic phases of matter are at the heart of many proposals for future information nanotechnology, with novel device concepts based on ultrathin films and nanowires. Their operation requires understanding and control of the underlying dynamics, including excitations such as spin waves. So far, no experimental technique has attempted to probe large wave-vector spin waves in noncollinear low-dimensional systems. In this paper, we explain how inelastic electron scattering, being suitable for investigations of surfaces and thin films, can detect the collective spin-excitation spectra of noncollinear magnets. To reveal the particularities of spin waves in such noncollinear samples, we propose the usage of spin-polarized electron-energy-loss spectroscopy augmented with a spin analyzer. With the spin analyzer detecting the polarization of the scattered electrons, four spin-dependent scattering channels are defined, which allow us to filter and select specific spin-wave modes. We take as examples a topological nontrivial skyrmion lattice, a spin-spiral phase, and the conventional ferromagnet. Then we demonstrate that, counterintuitively and in contrast to the ferromagnetic case, even non-spin-flip processes can generate spin waves in noncollinear substrates. The measured dispersion and lifetime of the excitation modes permit us to fingerprint the magnetic nature of the substrate.

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“…Now, we perform a HolsteinPrimakoff transformation [46,62,63], which will replace the spin operator by creation and annihilation spin-wave operators:…”

Section: Holstein-primakoff Transformationmentioning

confidence: 99%

Spin-resolved inelastic electron scattering by spin waves in noncollinear magnets

et al. 2018

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“…Here, i is an index that labels the spin-wave modes. After the Bogoliubov transformation, the Hamiltonian is in the above-mentioned harmonic approximation given by [42] …”

Section: Degeneracies and Fluctuationsmentioning

confidence: 99%

“…[42] and [43]. We quantize the spins and use a Holstein-Primakoff transformation to bosonic operatorsâ r andâ † r .…”

Section: Degeneracies and Fluctuationsmentioning

confidence: 99%

Degeneracies and fluctuations of Néel skyrmions in confined geometries

et al. 2015

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The recent discovery of tunable Dzyaloshinskii-Moriya interactions in layered magnetic materials with perpendicular magnetic anisotropy makes them promising candidates for stabilization and manipulation of skyrmions at elevated temperatures. In this article, we use Monte Carlo simulations to investigate the robustness of skyrmions in these materials against thermal fluctuations and finite-size effects. We find that in confined geometries and at finite temperatures skyrmions are present in a large part of the phase diagram. Moreover, we find that the confined geometry favors the skyrmion over the spiral phase when compared to infinitely large systems. Upon tuning the magnetic field through the skyrmion phase, the system undergoes a cascade of transitions in the magnetic structure through states of different number of skyrmions, elongated and half-skyrmions, and spiral states. We consider how quantum and thermal fluctuations lift the degeneracies that occur at these transitions, and find that states with more skyrmions are typically favored by fluctuations over states with less skyrmions. Finally, we comment on electrical detection of the various phases through the topological and anomalous Hall effects.

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“…After some algebra [30] the quadratic Hamiltonian can be reduced to a symmetric form in creation an annihilation operators written as:…”

Section: B Holstein-primakoff Representation and Spin-wave Hamiltonianmentioning

confidence: 99%

“…In consequence, the ground state |GS of the Hamiltonian is not the vacuum of the a bosons and, thereby, the ground-state energy at the spin-wave approximation level differs from the classical ground-state energy. The Hamiltonian H SW is solved by means of a paraunitary [30,31] transformation, analogously to the usual Bogoliubov u − v transformation for bosons [32], that leads to:…”

Section: B Holstein-primakoff Representation and Spin-wave Hamiltonianmentioning

confidence: 99%

Quantum fluctuations stabilize skyrmion textures

et al. 2015

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We study the quantum spin waves associated to skyrmion textures. We show that the zero-point energy associated to the quantum spin fluctuations of a noncollinear spin texture produce Casimir-like magnetic fields. We study the effect of these Casimir fields on the topologically protected noncollinear spin textures known as skyrmions. In a Heisenberg model with Dzyalonshinkii-Moriya interactions, chosen so the classical ground state displays skyrmion textures, we calculate the spin-wave spectrum, using the Holstein-Primakoff approximation, and the associated zero-point energy, to the lowest order in the spin-wave expansion. Our calculations are done both for the single-skyrmion case, for which we obtain a discrete set of skyrmion bound states, as well as for the skyrmion crystal, for which the resulting spectrum gives the spin-wave bands. In both cases, our calculations show that the Casimir magnetic field contributes up to 10% of the total Zeeman energy necessary to delete the skyrmion texture with an applied field.

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Quantum theory of spin waves in finite chiral spin chains

Cited by 9 publications

References 28 publications

Spin-resolved inelastic electron scattering by spin waves in noncollinear magnets

Spin-resolved inelastic electron scattering by spin waves in noncollinear magnets

Degeneracies and fluctuations of Néel skyrmions in confined geometries

Quantum fluctuations stabilize skyrmion textures

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