Zero modes in magnetic systems: general theory and an efficient computational scheme

Abstract

The presence of topological defects in magnetic media often leads to normal modes with zero frequency (zero modes). Such modes are crucial for long-time behavior, describing, for example, the motion of a domain wall as a whole. Conventional numerical methods to calculate the spin-wave spectrum in magnetic media are either inefficient or they fail for systems with zero modes. We present a new efficient computational scheme that reduces the magnetic normal-mode problem to a generalized Hermitian eigenvalue problem also in the presence of zero modes. We apply our scheme to several examples, including two-dimensional domain walls and Skyrmions, and show how the effective masses that determine the dynamics can be calculated directly. These systems highlight the fundamental distinction between the two types of zero modes that can occur in spin systems, which we call special and inertial zero modes. Our method is suitable for both conservative and dissipative systems. For the latter case, we present a perturbative scheme to take into account damping, which can also be used to calculate dynamical susceptibilities.

64 pages, 15 figures

References in corpus (7)

• Microscopic approach to current-driven domain wall dynamics
• Spin-Wave Modes and Their Intense Excitation Effects in Skyrmion Crystals
• Rotating skyrmion lattices by spin torques and field or temperature gradients
• Inertia and chiral edge modes of a skyrmion magnetic bubble
• Graphene as a Prototype Crystalline Membrane
• Subatomic movements of a domain wall in the Peierls potential
• Domain wall propagation through spin wave emission

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• Chirality-dependent transmission of spin waves through domain walls
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• Theoretical formalism for collective spin-wave edge excitations in arrays of dipolarly interacting magnetic nanodots
• Motion of domain walls and the dynamics of kinks in the magnetic Peierls potential
• Stability of a skyrmion and interaction of magnons
• How a skyrmion can appear both massive and massless
• Symplectic eigenvalues of positive-semidefinite matrices and the trace minimization theorem
• Atomic-Scale Spin-Wave Polarizer Based on a Sharp Antiferromagnetic Domain Wall
• Two-dimensional dispersion of magnetostatic volume spin waves