Effects of Edge on-Site Potential in a Honeycomb Topological Magnon Insulator

Pantaleón, Pierre A.; Xian, Yang

doi:10.7566/jpsj.87.064005

Cited by 24 publications

(31 citation statements)

References 59 publications

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“…Compared to previous studies [29][30][31]33], we here adopt a more general form for the solutions, suitable for bounded systems. These phase factors along the x-axis are intrinsic to the phase field matching theory [16][17][18][19][20][21].…”

Section: Field Theory Formulationmentioning

confidence: 99%

“…Real and imaginary solutions correspond to evanescent and bulk exchange spin wave modes respectively. Note that in our approach, the boundary conditions are solved simultaneously on both edges, unlike previous approaches[29][30][31]33] where the boundary conditions are solved separately on the edges, similar to the semi-infinite lattice case.For the imaginary solutions, it is convenient to substitute = ( is the wavevector component along the x-direction) in equations(12) and get the equivalent equations can be easily shown that none of equations(14) admit continuous solutions in for finite ̃ and . The wavevector along the nanoribbon bounded width 2 is hence discrete and the number of solutions depends on this width.…”

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confidence: 99%

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Discretized dynamics of exchange spin wave bulk and edge modes in honeycomb nanoribbons with armchair edge boundaries

Ghader

Khater

2019

J. Phys.: Condens. Matter

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We develop a field theory to study the dynamics of long wavelength exchange spin wave excitations on honeycomb nanoribbons characterized by armchair edge boundaries and the Néel antiferromagnetic ordering state. Appropriate boundary conditions are established by requiring that the bulk and edge spins precess with the same frequency for any given spin wave eigenmode in these systems. A set of characteristic boundary equations, common for bulk and edge spin wave modes, are hence derived. The equations of motion for the spin dynamics are then solved to determine the propagating and evanescent exchange spin wave modes. We prove in general that the bulk spin wave dynamics is discretized due to the finite width of the nanoribbon. For an isotropic magnetic nanoribbon, the Dirac cone is reduced to a single linear dispersion curve due to this discretization. The number and wavelengths of allowed bulk modes for isotropic and anisotropic nanoribbons are determined from the derived characteristic boundary equations. As witnessed by our numerical results for different examples it is shown that the characteristics of these modes depend on the width of the nanoribbon and its antiferromagnetic anisotropy. Further, anisotropic nanoribbons, even those with the slightest anisotropy, present evanescent modes with non-linear dispersion relations. The spatial variation of the amplitudes of the evanescent exchange spin waves across the finite widths of the nanoribbons, is found to be strongly dependent on the system magnetic anisotropy and its width. The developed theoretical approach is general and can be applied for nanoribbons with all types of boundary edges.

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Section: Field Theory Formulationmentioning

confidence: 99%

mentioning

confidence: 99%

Discretized dynamics of exchange spin wave bulk and edge modes in honeycomb nanoribbons with armchair edge boundaries

Ghader

Khater

2019

J. Phys.: Condens. Matter

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“…Nonreciprocal spin waves have received intensive theoretical and experimental attention in view of their importance for technological applications [20][21][22][23][24]. The important recent discovery of magnetic properties in Dirac materials attracted substantial interest in their magnetic excitations [25][26][27][28][29][30][31][32][33][34][35][36][37]. The novel characteristics for magnetic excitations in Dirac materials is believed to open important new opportunities in the field of magnonics.…”

Section: Introductionmentioning

confidence: 99%

“…Solving the bulk equations of motion consistently with the boundary conditions yields the edge and discretized bulk exchange spin waves for both types of nanoribbons in the long wavelength part of the Brillouin zone. Unlike previous theoretical studies [25,33,34,37] where the boundary conditions are derived and solved on one edge of the nanoribbon, in our approach the derived boundary equations are solved simultaneously on both edges. Edge spin waves are obtained for both types of nanoribbons, with and without magnetic anisotropy.…”

Section: Introductionmentioning

confidence: 99%

Asymmetric dynamics of edge exchange spin waves in honeycomb nanoribbons with zigzag and bearded edge boundaries

Ghader¹,

Khater²

2019

Sci Rep

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We report on the theoretical prediction of asymmetric edge spin waves, propagating in opposite directions at the boundaries of antiferromagnetic honeycomb nanoribbons with zigzag and bearded edges. The simultaneous propagation of edge spin waves along the same direction on both edges of the nanoribbons is forbidden. These asymmetric exchange spin waves at the edge boundaries are analogous to the nonreciprocal surface spin waves reported in magnetic thin films. Their existence is related to the nontrivial symmetry underlying these nanoribbons types. The discretized bulk and the edge exchange spin waves are calculated for the long wavelength part of the nanoribbon Brillouin zone (BZ), using the classical field spin wave theory and notably appropriate boundary conditions. In the absence of an external magnetic field in our study, the asymmetric edge spin waves propagate with equal frequencies and along opposite directions. The edge spin waves are characterized by linear dispersion relations for magnetically isotropic nanoribbons. For magnetically anisotropic nanoribbons, our calculations show that the energy gap between the edge and bulk spin waves is enhanced for both types of zigzag and bearded nanoribbons. The large energy gap separates the edge modes from overlapping the bulk ones. Also, we explain why our results for anisotropic zigzag nanoribbons go beyond previous studies based on a quantum approach in the linear spin wave approximation.

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“…is the exchange constant and ≥ 1 is the anisotropy parameter along the z-axis. The parameter determines the strength of the DMI, whereas the orientation of ⃗ ⃗⃗ in the honeycomb lattice is determined in the conventional way from the local geometry for a nonzero output with reference to the ribbon spin vectors [40,48,58].…”

Section: Resultsmentioning

confidence: 99%

A new class of nonreciprocal spin waves on the edges of 2D antiferromagnetic honeycomb nanoribbons

Ghader

Khater

2019

Sci Rep

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Antiferromagnetic two-dimensional (2D) materials are currently under intensive theoretical and experimental investigations in view of their potential applications in antiferromagnetbased magnonic and spintronic devices. Recent experimental studies revealed the importance of magnetic anisotropy and of Dzyaloshinskii-Moriya interactions (DMI) on the ordered ground state and the magnetic excitations in these materials. In this work we present a robust classical field theory approach to study the effects of anisotropy and the DMI on the edge and bulk spin waves in 2D antiferromagnetic nanoribbons. We predict the existence of a new class of nonreciprocal edge spin waves, characterized by opposite polarizations in counter-propagation. These novel edge spin waves are induced by the DMI and are fundamentally different from conventional nonreciprocal spin waves for which the polarization is independent of the propagation direction. We further analyze the effects of the edge structures on the magnetic excitations for these systems. In particular, we show that anisotropic bearded edge nanoribbons act as topologically trivial magnetic insulators with potentially interesting applications in magnonics. Our results constitute an important finding for current efforts seeking to establish unconventional magnonic devices utilizing spin wave polarization.The polarization of a spin wave is determined by the precessing direction of the magnetization and constitutes an important additional intrinsic degree of freedom, beside the spin wave amplitude and phase. Spin wave theory in a collinear antiferromagnet, composed of two magnetic lattices with opposite magnetization, is known to yield two bulk modes. The precession frequencies of these modes are characterized by opposite contributions from the exchange interaction [1-3]. As a consequence, the sublattice magnetizations precess clockwise in one of the modes and anticlockwise in the other [3]. The spin wave modes in an antiferromagnet are hence characterized by opposite polarizations, conventionally termed as right-handed and left-handed spin waves.The important advantages for utilizing spin wave polarization to encode and process information in antiferromagnet-based magnonics has recently received significant attention [4][5][6][7][8]. The Dzyaloshinskii-Moriya interactions (DMI) [9,10] was highlighted as a key ingredient to realize polarization-based magnonic devices. In particular, antiferromagnetic domain walls with DMI have been proposed as spin wave polarizer, retarder and transistor [4,5].

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Effects of Edge on-Site Potential in a Honeycomb Topological Magnon Insulator

Cited by 24 publications

References 59 publications

Discretized dynamics of exchange spin wave bulk and edge modes in honeycomb nanoribbons with armchair edge boundaries

Discretized dynamics of exchange spin wave bulk and edge modes in honeycomb nanoribbons with armchair edge boundaries

Asymmetric dynamics of edge exchange spin waves in honeycomb nanoribbons with zigzag and bearded edge boundaries

A new class of nonreciprocal spin waves on the edges of 2D antiferromagnetic honeycomb nanoribbons

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