The Study Of Topological Magneton In Two-dimensional Ferromagnetic Kagome Lattice

With the rapid increase of the integration density of microelectronic devices,the huge Joule heat poses a challenge to the reliability and operating speed of the device,and at the same time,it also brings a huge waste of energy.Magnons,as a chargefree quasi-particle of spin wave,since it does not need charge carriers in the process of energy and information transmission,it has potential applications in non-dissipative information technology,which has attracted extensive attention of researchers.In recent years,in ferromagnetic materials,due to the Dzyaloshinskii-Moriya(DM)interaction which plays a role of vector potential similar to the Lorentz force,magnon Hall effect and topological magnon insulator were discovered one after another.In this work,using a well established nearest-neighbor Heisenberg ferromagnet model with DM interaction,here we uncover intriguing new aspects in flat magnon bands?topological phase transition and the chiral magnon edge transport in two-dimensional ferromagnetic kagome lattice.The main research contents are illustrated as follows.(1)In the ferromagnetic kagome lattice,it has been known that the top band is a flat band without DM interaction.We find that in a uniform ferromagnetic kagome lattice(two nearest neighbor spin exchanges of J are equal everywhere),with the change of DM interaction,the other two energy bands in the system can be flattened too.When the interaction strength of DM interaction is D = ±?3J/3 and D = ±?3J,the middle band and the bottom band of the kagome lattice are flat,respectively.With a general DM interaction the magnon bands become non-flat.However,there are flat line sketching a patten of David stars for all three magnon bands whose flatness is robust with changing exchange coupling or DM interaction.We show that each of the three flat bands is actually trivial topologically at the critical DM interaction.Furthermore we find that while the middle band keeps topologically trivial,for the other two bands D = 0 corresponds to a topologically phase transition where their Chern numbers exchange and when D = ±?3Jthe system undergos a phase transition to non-ferromagnetic state.(2)We know that at a critical DM interaction,topological phase transition occurs in ferromagnetic kagome lattice.With the change of the nonuniform exchange which break the inversion symmetry,we find that the system will undergo a series of topological phase transitions.In the kagome lattice with non-zero DM interaction,the inversion-symmetrybroken will eliminate the degeneracy of energy band at different corner of Brillouin zone.Through the magnon waveguide,we can observed the one valley magnon transport.With the change of DM interaction and non-uniform exchange,we systematically study the topological phase diagram,which provides a reference for topological magnon transport.(3)In non-uniform quasi one dimensional ferromagnetic kagome lattice,we study topological edge magnon transport with a definite chirality.Using the nonequilibrium Green's function theory,we characterize transport properties of magnons in equilibrium and nonequilibrium state by calculating the boundary local heat current and local density state of magnons.We find that for magnons with a certain frequency,when the direction of DM interaction exchanges,the magnon changes from one valley to the other in the wave vector space,and in the real space,the boundary of magnon transport does not change,but the chirality is opposite.If the DM interaction is fixed,we find that the chirality does not changed even though the valley and the boundary are reversed.The chirality of macroscopic boundary transport can be understood by the chiral local-heat current and local magnon density state in the unit cell.Generally speaking,in the two-dimensional ferromagnetic kagome lattice system,we predict a series of rich phenomena of magnon transport caused by DM interaction or non-uniform exchange.In a uniform system,we find each of the three magnon bands can be selectively flattened by changing DM interaction.In non-uniform exchange system,with the change of DM interaction,the system can emerge a series of multiple topological phase transitions.In the quasi-one-dimensional system,we predict that one-edge transport of topological valley magnons,which is caused by DM interaction and non-uniform exchange,where the distribution and chirality is dependent on both DM interaction and nonuniform exchange.These findings can help to enrich our microscopic understanding of spin excitations for future magnonics applications.