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We predict staggered-field-stabilized collinear, spiral, cone, skrymion crystal (SkX), and square crystal (SC) of vortices and antivortices phases in antiferromagnets (see figure). In SkX and SC ph...
We predict staggered-field-stabilized collinear, spiral, cone, skrymion crystal (SkX), and square crystal (SC) of vortices and antivortices phases in antiferromagnets (see figure). In SkX and SC phases, magnons experience emergent gauge fields, which leads to magnon-mediated topological spin responses. The underlying physics can be qualitatively understood by considering magnon Landau levels induced by the fictitious magnetic flux. In the long wavelength limit, the unevenly spaced energy bands can be described by the relativistic Klein-Gordon equation. As we propose, these Landau levels can be also realized in antiferromagnetic magnonic topological insulator where the fictitious flux is induced by inhomogeneous DMI. A smoking gun experiment observing the Hofstadter's butterfly of magnons in AFM could establish the connection between emergent electromagnetism and topological properties of antiferromagnetic magnons.