Hidden Magnon Berry Curvature drives Vertical Magnon Transport

TL;DR

This paper predicts a hidden magnon Berry curvature that causes a novel form of vertical magnon transport in 2D magnets, with potential for experimental detection in layered van der Waals materials.

Contribution

It introduces the concept of hidden magnon Berry curvature and demonstrates its role in vertical magnon transport, including both linear and nonlinear effects, in realistic magnetic models.

Findings

Hidden magnon Berry curvature causes vertical magnon transport.

Linear and nonlinear VMT depend on hidden magnon BC and its dipoles.

VMT signatures are observable in 2D magnetic materials like CrX3.

Abstract

We predict an in-plane, or hidden, Berry curvature (BC) for magnons in electrically insulating quasi-2D magnets and demonstrate that the hidden magnon Berry curvature (HMBC) gives rise to a previously unrecognized form of vertical, out-of-plane, magnon transport. Combining a semiclassical framework with Boltzmann transport theory, we show that the vertical magnon transport (VMT) currents respond both linearly and nonlinearly to the in-plane gradients of magnetic field and temperature. The linear transport coefficients are tied to the total hidden magnon BC, while the nonlinear (second-order) coefficients for the magnetic field and temperature gradients are determined by the hidden magnon BC dipole and the hidden extended magnon BC dipole, respectively. Using linear spin-wave theory, we find that the hidden magnon BC over the Brillouin zone is given by the expectation value of a pseudo-${{\cal Z}}$ operator, representing vertical displacements, evaluated in the space of paraunitary matrices that diagonalize the magnon Hamiltonian. We estimate VMT in spin models of realistic magnets with ferro- and antiferromagnetic order, including the buckled honeycomb (BHC) lattice and bilayer Chromium trihalide (CrX$_3$; X = Cl, Br, I) systems. In BHC, both linear and nonlinear VMT arise when time-reversal symmetry is broken by Dzyaloshinskii-Moriya interactions. In CrX$_3$ systems, the nonlinear coefficients dominate, while the linear responses vanish due to time-reversal symmetry. Both systems exhibit distinctive features across a broad range of temperatures and parameters. Therefore, our prediction of VMT and its characteristic signatures is directly testable in present-day magnonic experiments, especially in atomically thin, few-layered van der Waals magnets.