Magnetic materials in which it is possible to control the topology of their magnetic order in real space or the topology of their magnetic excitations in reciprocal space are highly sought-after as platforms for alternative data storage and computing
architectures. Here we show that multiferroic insulators, owing to their magneto-electric coupling, offer a natural and advantageous way to address these two different topologies using laser fields. We demonstrate that via a delicate balance between the energy injection from a high-frequency laser and dissipation, single skyrmions---archetypical topological magnetic textures---can be set into motion with a velocity and propagation direction that can be tuned by the laser field amplitude and polarization, respectively. Moreover, we uncover an ultrafast Floquet magnonic topological phase transition in a laser-driven skyrmion crystal and we propose a new diagnostic tool to reveal it using the magnonic thermal Hall conductivity.
When the crystalline symmetries that protect a higher-order topological phase are not preserved at the boundaries of the sample, gapless hinge modes or in-gap corner states cannot be stabilized. Therefore, careful engineering of the sample terminatio
n is required. Similarly, magnetic textures, whose quantum fluctuations determine the supported magnonic excitations, tend to relax to new configurations that may also break crystalline symmetries when boundaries are introduced. Here we uncover that antiskyrmion crystals provide an experimentally accessible platform to realize a magnonic topological quadrupole insulator, whose hallmark signature are robust magnonic corner states. Furthermore, we show that tuning an applied magnetic field can trigger the self-assembly of antiskyrmions carrying a fractional topological charge along the sample edges. Crucially, these fractional antiskyrmions restore the symmetries needed to enforce the emergence of the magnonic corner states. Using the machinery of nested Wilson loops, adapted to magnonic systems supported by noncollinear magnetic textures, we demonstrate the quantization of the bulk quadrupole moment, edge dipole moments, and corner charges.
The use of spin waves (SWs) as data carriers in spintronic and magnonic logic devices offers operation at low power consumption, free of Joule heating. Nevertheless, the controlled emission and propagation of SWs in magnetic materials remains a signi
ficant challenge. Here, we propose that skyrmion-antiskyrmion bilayers form topological charge dipoles and act as efficient sub-100 nm SW emitters when excited by in-plane ac magnetic fields. The propagating SWs have a preferred radiation direction, with clear dipole signatures in their radiation pattern, suggesting that the bilayer forms a SW antenna. Bilayers with the same topological charge radiate SWs with spiral and antispiral spatial profiles, enlarging the class of SW patterns. We demonstrate that the characteristics of the emitted SWs are linked to the topology of the source, allowing for full control of the SW features, including their amplitude, preferred direction of propagation, and wavelength.
Disorder such as impurities and dislocations in Weyl semimetals (SMs) drives a quantum critical point (QCP) where the density of states at the Weyl point gains a non-zero value. Near the QCP, the asymptotic low energy singularities of physical quanti
ties are controlled by the critical exponents $ u$ and $z$. The nuclear spin-lattice relaxation rate, which originates from the hyperfine coupling between a nuclear spin and long-range orbital currents in Weyl fermion systems, shows intriguing critical behavior. Based on the self-consistent Born approximation for impurities, we study the nuclear spin-lattice relaxation rate $1/T_1$ due to the orbital currents in disordered Weyl SMs. We find that $(T_1T)^{-1}sim E^{2/z}$ at the QCP where $E$ is the maximum of temperature $T$ and chemical potential $mu(T)$ relative to the Weyl point. This scaling behavior of $(T_1T)^{-1}$ is also confirmed by the self-consistent $T$-matrix approximation, where a remarkable temperature dependence of $mu(T)$ could play an important role. We hope these results of $(T_1T)^{-1}$ will serve as an impetus for exploration of the disorder-driven quantum criticality in Weyl materials.
Achieving control over magnon spin currents in insulating magnets - where dissipation due to Joule heating is highly suppressed - is an active area of research that could lead to energy-efficient spintronics applications. However, magnon spin current
s supported by conventional systems with uniform magnetic order have proven hard to control. An alternative approach that relies on topologically protected magnonic edge states of spatially periodic magnetic textures has recently emerged. A prime example of such textures is the ferromagnetic skyrmion crystal which hosts chiral edge states providing a platform for magnon spin currents. Here, we show, for the first time, an external magnetic field can drive a topological phase transition in the spin wave spectrum of a ferromagnetic skyrmion crystal. The topological phase transition is signaled by the closing of a low-energy bulk magnon gap at a critical field. In the topological phase, below the critical field, two topologically protected chiral magnonic edge states lie within this gap, but they unravel in the trivial phase, above the critical field. Remarkably, the topological phase transition involves an inversion of two magnon bands that at the $Gamma$ point correspond to the breathing and anticlockwise modes of the skyrmions in the crystal. Our findings suggest that an external magnetic field could be used as a knob to switch on and off magnon spin currents carried by topologically protected chiral magnonic edge states.
We study the nuclear magnetic relaxation rate and Knight shift in the presence of the orbital and quadrupole interactions for three-dimensional Dirac electron systems (e.g., bismuth-antimony alloys). By using recent results of the dynamic magnetic su
sceptibility and permittivity, we obtain rigorous results of the relaxation rates $(1/T_1)_{rm orb}$ and $(1/T_1)_{rm Q}$, which are due to the orbital and quadrupole interactions, respectively, and show that $(1/T_1)_{rm Q}$ gives a negligible contribution compared with $(1/T_1)_{rm orb}$. It is found that $(1/T_1)_{rm orb}$ exhibits anomalous dependences on temperature $T$ and chemical potential $mu$. When $mu$ is inside the band gap, $(1/T_1)_{rm orb} sim T ^3 log (2 T/omega_0)$ for temperatures above the band gap, where $omega_0$ is the nuclear Larmor frequency. When $mu$ lies in the conduction or valence bands, $(1/T_1)_{rm orb} propto T k_{rm F}^2 log (2 |v_{rm F}| k_{rm F}/omega_0)$ for low temperatures, where $k_{rm F}$ and $v_{rm F}$ are the Fermi momentum and Fermi velocity, respectively. The Knight shift $K_{rm orb}$ due to the orbital interaction also shows anomalous dependences on $T$ and $mu$. It is shown that $K_{rm orb}$ is negative and its magnitude significantly increases with decreasing temperature when $mu$ is located in the band gap. Because the anomalous dependences in $K_{rm orb}$ is caused by the interband particle-hole excitations across the small band gap while $left( 1/T_1 right)_{rm orb}$ is governed by the intraband excitations, the Korringa relation does not hold in the Dirac electron systems.
