Classification of magnons in Rotated Ferromagnetic Heisenberg model and their competing responses in transverse fields

Abstract

Competing orders is a general concept to describe various quantum phases and transitions in various materials. One efficient way to investigate competing orders is to first classify different class of excitations in a given quantum phase, then study their competing responses under various external probes. This strategy may not only lead to deep understanding of the quantum phase itself, but also its deep connections to various other quantum phases nearby. We implement this approach by studying the Rotated Ferromagnetic Heisenberg model (RFHM) in two different transverse fields $h_x$ and $h_z$ which can be intuitively visualized as studying spin-orbit couplings (SOC) effects in 2d Ising or anisotropic XY model in a transverse field. At a special SOC class, it was known that the RFHM at a zero field owns an exact ground state called Y-x state. It supports non only the commensurate C-C${}_0$ and C-C${}_{\pi }$ magnons, but also the in-commensurate C-IC magnons. These magnons are non-relativistic, not contained in the exact ground state, so need to be thermally excited. Their dramatic response under the longitudinal $h_y$ field was recently worked out by the authors. Here we find they respond very differently under the two transverse fields. Any $h_x$ ($h_z$) changes the collinear Y-x state to a canted co-planar YX-x (YZ-x) state which suffers quantum fluctuations. The C-C${}_0$, C-C${}_{\pi }$ and C-IC magnons sneak into the quantum ground state, become relativistic and play leading roles even at $T=0$. We map out the boundaries among the C-C${}_0$, C-C${}_{\pi }$ and C-IC magnons, especially the detailed evolution of the C-IC magnons inside the canted phases. As $h_x$ ($h_z$) increases further, the C-C${}_0$ magnons always win the competition and emerge as the seeds to drive a transition from the YX-x (YZ-x) to the X-FM ( Z-FM ) which is shown to be in the 3d Ising universality class.

15 Pages, REVTEX4-1, 10 Color figures

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Cited by in corpus (7)

• Hubbard model with Rashba or Dresselhaus spin-orbit coupling and Rotated Anti-ferromagnetic Heisenberg Model
• Magnon Condensation in Dimerized Antiferromagnets with Spin-Orbit Coupling
• Topological depletions and sub-leading scalings across topological phase transitions
• High Chern number topological superfluids and new class of topological phase transitions of Rashba spin-orbit coupled fermions on a lattice
• Response of a strongly interacting spin-orbit coupling system to a Zeeman field
• Spin-Orbit Coupling-Driven Chirality Switching of Spin Waves in Altermagnets
• Quantum spin liquids in a square lattice subject to an Abelian flux