Non reciprocal spin waves have a chiral asymmetry so that their energy is different for two opposite wave vectors. They are found in atomically thin ferromagnetic overlayers with in plane magnetization and are linked to the anti-symmetric Dzyaloshinskii-Moriya surface exchange. We use an itinerant fermion theory based on first principles calculations to predict that non-reciprocal magnons can occur in Fe$_3$GeTe$_2$, the first stand alone metallic two dimensional crystal with off-plane magnetization. We find that both the energy and lifetime of magnons are non-reciprocal and we predict that acoustic magnons can have lifetimes up to hundreds of picoseconds, orders of magnitude larger than in other conducting magnets.
The Wigner-crystal phase of two-dimensional electrons interacting via the Coulomb repulsion and subject to a strong Rashba spin-orbit coupling is investigated. For low enough electronic densities the spin-orbit band splitting can be larger than the zero-point energy of the lattice vibrations. Then the degeneracy of the lower subband results in a spontaneous symmetry breaking of the vibrational ground state. The $60^{circ}-$rotational symmetry of the triangular (spin-orbit coupling free) structure is lost, and the unit cell of the new lattice contains two electrons. Breaking the rotational symmetry also leads to a (slight) squeezing of the underlying triangular lattice.
Using two cold-neutron triple-axis spectrometers we have succeeded in fully mapping out the field-dependent evolution of the non-reciprocal magnon dispersion relations in all magnetic phases of MnSi. The non-reciprocal nature of the dispersion manifests itself in a full asymmetry (non-reciprocity) of the dynamical structure factor $S(q, E, mu_0 H_{int})$ with respect to flipping either the direction of the applied magnetic field $mu_0 H_{int}$, the reduced momentum transfer $q$, or the energy transfer $E$.
We study the topological properties of magnon excitations in three-dimensional antiferromagnets, where the ground state configuration is invariant under time-reversal followed by space-inversion ($PT$-symmetry). We prove that Dirac points and nodal lines, the former being the limiting case of the latter, are the generic forms of symmetry-protected band crossings between magnon branches. As a concrete example, we study a Heisenberg spin model for a spin-web compound, Cu$_3$TeO$_6$, and show the presence of the magnon Dirac points assuming a collinear magnetic structure. Upon turning on symmetry-allowed Dzyaloshinsky-Moriya interactions, which introduce a small non-collinearity in the ground state configuration, we find that the Dirac points expand into nodal lines with nontrivial $Z_2$-topological charge, a new type of nodal lines unpredicted in any materials so far.
Recent articles have suggested that the quasi-two dimensional antiferromagnet MnPS$_3$ may have non-reciprocal magnons, whereby magnons in a Brillouin zone corner at +q have different energies than those at $-$q. The magnons along the Brillouin zone boundaries were measured using neutron three-axis spectrometry, paying careful attention to the resolution function, to determine whether such non-reciprocity was present. The data show that, within the resolution, there are no significant differences between the magnons in opposite Brillouin zone corners.
Spin waves in chiral magnetic materials are strongly influenced by the Dzyaloshinskii-Moriya interaction resulting in intriguing phenomena like non-reciprocal magnon propagation and magnetochiral dichroism. Here, we study the non-reciprocal magnon spectrum of the archetypical chiral magnet MnSi and its evolution as a function of magnetic field covering the field-polarized and conical helix phase. Using inelastic neutron scattering, the magnon energies and their spectral weights are determined quantitatively after deconvolution with the instrumental resolution. In the field-polarized phase the imaginary part of the dynamical susceptibility $chi(varepsilon, {bf q})$ is shown to be asymmetric with respect to wavevectors ${bf q}$ longitudinal to the applied magnetic field ${bf H}$, which is a hallmark of chiral magnetism. In the helimagnetic phase, $chi(varepsilon, {bf q})$ becomes increasingly symmetric with decreasing ${bf H}$ due to the formation of helimagnon bands and the activation of additional spinflip and non-spinflip scattering channels. The neutron spectra are in excellent quantitative agreement with the low-energy theory of cubic chiral magnets with a single fitting parameter being the damping rate of spin waves.
M. J. T. Costa
,J. Fernandez-Rossier
,N. M. R. Peres
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(2020)
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"Non-reciprocal magnons in a two dimensional crystal with off-plane magnetization"
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Antonio Costa
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