We present a theoretical mapping to show that a ferromagnet with gain (loss) is equivalent to an antiferromagnet with an equal amount of loss (gain). Our findings indicate a novel first-order ferromagnet-antiferromagnet phase transition by tuning the gain-loss parameter. As an appealing application, we demonstrate the realization as well as the manipulation of the antiferromagnetic Skyrmion, a stable topological quasiparticle not yet observed experimentally, in a chiral ferromagnetic thin film with gain. We also consider ferromagnetic bilayers with balanced gain and loss and show that the antiferromagnetic Skyrmion can be found only in cases with a broken parity-time symmetry phase. Our results pave the way for investigating the emerging antiferromagnetic spintronics and parity-time symmetric magnonics in ferromagnets.

Disorder effects on three-dimensional second-order topological insulators (3DSOTIs) are investigated numerically and analytically. The study is based on a tight-binding Hamiltonian for noninteracting electrons on a cubic lattice with a reflection symmetry that supports a 3DSOTI in the absence of disorder. Interestingly, unlike the disorder effects on a topological trivial system that can only be either a diffusive metal (DM) or an Anderson insulator (AI), disorders can sequentially induce four phases of 3DSOTIs, three-dimensional first-order topological insulators (3DFOTIs), DMs, and AIs. At a weak disorder when the on-site random potential of strength $W$ is below a low critical value $W_{c1}$ at which the gap of surface states closes while the bulk sates are still gapped, the system is a disordered 3DSOTI characterized by a constant density of states and a quantized integer conductance of $e^2/h$ through its chiral hinge states. The gap of the bulk states closes at a higher critical disorder $W_{c2}$, and the system is a disordered 3DFOTI in a lower intermediate disorder between $W_{c1}$ and $W_{c2}$ in which electron conduction is through the topological surface states. The system becomes a DM in a higher intermediate disorder between $W_{c2}$ and $W_{c3}$ above which the states at the Fermi level are localized. It undergoes a normal three-dimensional metal-to-insulator transition at $W_{c3}$ and becomes the conventional AI for $W>W_{c3}$. The self-consistent Born approximation allows one to see how the density of bulk states and the Dirac mass are modified by the on-site disorders.

The Anderson localization problem for a noninteracting two-dimensional electron gas subject to a strong magnetic field, disordered potential, and spin-orbit coupling is studied numerically on a square lattice. The nature of the corresponding localization-delocalization transition and the properties of the pertinent extended states depend on whether the spin-orbit coupling is uniform or fully random. For uniform spin-orbit coupling (such as Rashba coupling due to a uniform electric field), there is a band of metallic extended states in the center of a Landau band as in a “standard” Anderson metal-insulator transition. However, for fully random spin-orbit coupling, the familiar pattern of Landau bands disappears. Instead, there is a central band of critical states with definite fractal structure separated at two critical energies from two side bands of localized states. Moreover, finite size scaling analysis suggests that for this novel transition, on the localized side of a critical energy $E_c$, the localization length diverges as $\xi (E)\propto \exp (\alpha /\sqrt{|E-E_c|})$, a behavior which, together with the emergence of a band of critical states, is reminiscent of a Berezinskii-Kosterlitz-Thouless transition.

Absence of quasiparticle-level anticrossing in random non-Hermitian systems is demonstrated. As a result, the general Wigner-Dyson distributions of energy-level spacing of diffusive metals in the usual Hermitian systems is replaced by the Poisson distribution for quasiparticle-level (the real parts of complex eigenenergies) spacing of non-Hermitian disordered metals in the thermodynamic limit of infinite system size. This is a very surprising result because Poisson statistics is universally true for the Anderson insulators where energy eigenstates do not overlap with each other, so energy levels are independent from each other. For disordered metals where different eigenstates overlap with each other, one should expect different levels trying to stay away from each other, so the Poisson distribution should not apply there. Our results show that the larger non-Hermitian energy (dissipation) can invalidate the quasiparticle-level anticrossing that holds dearly in Hermitian metals. Thus, our theory provides a unified picture for recently discovered “level attraction” in various systems, as well as a theoretical basis for manipulating quasiparticle energy levels.

We study the collective dynamics of a two-dimensional honeycomb lattice of magnetic skyrmions. By performing large-scale micromagnetic simulations, we find multiple chiral and nonchiral edge modes of skyrmion oscillations in the lattice. The nonchiral edge states are due to the Tamm-Shockley mechanism, while the chiral ones are topologically protected against structure defects and hold different handedness depending on the mode frequency. To interpret the emerging multiband nature of the chiral edge states, we generalize the massless Thiele's equation by including a second-order inertial term of skyrmion mass as well as a third-order non-Newtonian gyroscopic term, which allows us to model the band structure of skyrmion oscillations. Theoretical results compare well with numerical simulations. Our findings uncover the importance of high-order effects in strongly coupled skyrmions and are helpful for designing novel skyrmionic topological devices.

Magnetic skyrmions are believed to be the promising candidate of information carriers in spintronics. However, the skyrmion Hall effect, due to the nontrivial topology of skyrmions, can induce a skyrmion accumulation or even annihilation at the edge of the devices, which hinders the real-world applications of skyrmions. In this work, we theoretically investigate the current-driven skyrmion motion on magnetic nanotubes which can be regarded as ‘edgeless’ in the tangential direction. By performing micromagnetic simulations, we find that the skyrmion motion exhibits a helical trajectory on the nanotube, with its axial propagation velocity proportional to the current density. Interestingly, the skyrmion’s angular speed increases with the increase of the thickness of the nanotube. A simple explanation is presented. Since the tube is edgeless for the tangential skyrmion motion, a stable skyrmion propagation can survive in the presence of a very large current density without any annihilation or accumulation. Our results provide a new route to overcome the edge effect in planar geometries.