Quantum geometric origins of the orbital degrees of freedom of hybrid bosonic quasiparticles in magnetic systems

Abstract

The orbital degree of freedom has recently attracted significant attention due to the novel phenomena it enables in condensed matter systems. However, the interpretation of the orbital degree of freedom in bosonic quasiparticles remains conceptually ambiguous and the mechanisms governing the transfer of orbital angular moment (OAM) between distinct quasiparticles, such as magnons and phonons, are not yet fully understood. We investigate orbital dynamics in bosonic systems and identify two origins of OAM: (i) global rotational motion of the system, and (ii) the quantum geometry of wavefunctions. Focusing on the latter, we study strongly coupled magnon-phonon systems in two-dimensional antiferromagnets as a test case. We uncover finite OAM arising from quantum geometric effects via two mechanisms: (a) time-parity symmetry breaking, yielding intra band OAM, and (b) interband coupling, generating interband OAM. We propose that an electrical detection scheme based on the transverse voltage generated by hybrid magnon phonon modes can be used to experimentally probe the bosonic orbital degree of freedom. Our results establish a foundation for the emerging field of phonon orbitronics, providing both a conceptual bridge between phonon and magnon orbitronics and a tool for better understanding magnon-polarons. They also advance a unified framework for harnessing orbital degrees of freedom in bosonic systems and pave the way toward electrical control of magnetization and phononic transport.

Figures (3)

• Figure 1: (a) Schematic of magnon-polaron wavepacket dynamics in a two-dimensional honeycomb lattice. The wavepacket arises from the hybridization of an elastic wave and a spin wave. Inset (i) shows the elastic wave characterized by the displacement of atoms $\boldsymbol{u}$ around their equilibrium positions and an associated pseudospin due to in-plane circular motion. Inset (ii) shows the spin wave, which carries spin angular momentum originating from the precession of local magnetic moments. The inherent self-rotation of the hybridized wavepacket establishes the orbital degree of freedom, rooted in the quantum geometry of the magnon-polaron Bloch wavefunction. (b) Dispersion along the symmetry path $K-\Gamma-M$ of the phonon (red) and magnon (green) modes of a honeycomb AFM with Néel order. Hybridized magnon-polarons emerge at the energy degeneracy point as shown more clearly in the inset.
• Figure 2: Intra-band orbital angular moment-resolved band dispersions of magnon-polarons along the $K - \Gamma - M$ path in a 2D honeycomb antiferromagnet with Néel order: (a) without magnon–phonon coupling and (b) with finite magnon–phonon coupling, calculated under an externally applied magnetic field $B_{z}=0.1~\mathrm{T}$.
• Figure 3: (a) Schematic illustration of electric polarization and transverse voltage induced by magnon-polarons accumulating at the sample edges under a longitudinal temperature or strain gradient, which excites magnon-polarons in the system. The resulting transverse voltage along the $y$-direction, including contributions from Berry curvature ($V_{xy}^{S}$) and orbital moment ($V_{xy}^{O}$), is plotted as a function of: (b) the out-of-plane magnetic field $B_z$ at an average temperature of $T = 100$ K; (c) temperature $T$ at zero magnetic field; and (d) Relative magnon-phonon coupling strength ($\xi/\xi_{0}$ with $\xi_{0}=0.0292~meV$) at $T = 100$ K and $B_z = 0$.