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Register a new userStabilization of magnetic skyrmions by RKKY interactions
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We study the stabilization of an isolated magnetic skyrmion in a magnetic monolayer on a nonmagnetic conducting substrate via the Ruderman-Kittel-Kasuya-Yosida (RKKY) exchange interaction. Two different types of the substrate are considered, usual normal metal and single-layer graphene. While the full stability analysis for skyrmions in the presence of the RKKY coupling requires a separate effort that is outside the scope of this work, we are able to study the radial stability (stability of a skyrmion against collapse) using variational energy estimates obtained within first-order perturbation theory, with the unperturbed Hamiltonian describing the isotropic Heisenberg magnet, and the two perturbations being the RKKY exchange and the easy-axis anisotropy. We show that a proper treatment of the long-range nature of the RKKY interaction leads to a qualitatively different stabilization scenario compared to previous studies, where solitons were stabilized by the frustrated exchange coupling (leading to terms with the fourth power of the magnetization gradients) or by the Dzyaloshinskii-Moriya interaction (described by terms linear in the magnetization gradients). In the case of a metallic substrate, the skyrmion stabilization is possible under restrictive conditions on the Fermi surface parameters, while in the case of a graphene substrate the stabilization is naturally achieved in several geometries with a lattice-matching of graphene and magnetic layer.
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Magnetic skyrmions in chiral-lattice ferromagnets are currently attracting enormous research interest because of their potential applications in spintronic devices. However, they emerge in bulk specimens only in a narrow window of temperature and magnetic field. This limited stability regime is recognized as an obstacle to technical applications. Recent experiments demonstrated that the thermodynamic stability of magnetic skyrmions is enhanced or suppressed by the application of a uniaxial strain depending on its axial direction in bulk chiral-lattice ferromagnets MnSi [Y. Nii et al., Nat. Commun. 6, 8539 (2015), A. Chacon et al., Phys. Rev. Lett. 115, 267202 (2015)] and Cu2OSeO3 [S. Seki et al., Phys. Rev. B 96, 220404(R) (2017)]. Motivated by these experimental discoveries, we theoretically investigated the effects of anisotropic Dzyaloshinskii--Moriya interactions on the stability of magnetic skyrmions caused by this uniaxial strain. We find that magnetic skyrmions are significantly stabilized (destabilized) in the presence of anisotropic DM interactions when an external magnetic field lies perpendicular (parallel) to the anisotropy axis, along which the DM coupling is strengthened. Our results account completely for the experimentally observed strain-induced stabilization and destabilization of magnetic skyrmions and provide a firm ground for possible strain engineering of skyrmion-based electronic devices.
Quantized transports of fermions are topological phenomena determined by the sum of the Chern numbers of all the energy bands below the Fermi energy. For bosonic excitations, e.g. phonons and magnons in a crystal, topological transport is dominated by the Chern number of the lowest energy band because the energy distribution of the bosons is limited below the thermal energy. Here, we demonstrate the existence of topological transport by bosonic magnons in a lattice of magnetic skyrmions - topological defects formed by a vortex-like texture of spins. We find a distinct thermal Hall signal when the ferromagnetic spins in an insulating polar magnet GaV4Se8 form magnetic skyrmions. Its origin is identified as the topological thermal Hall effect of magnons in which the trajectories of these magnons are bent by an emergent magnetic field produced by the magnetic skyrmions. Our theoretical simulations confirm that the thermal Hall effect is indeed governed by the Chern number of the lowest energy band of the magnons in a triangular lattice of magnetic skyrmions. Our findings lay a foundation for studying topological phenomena of other bosonic excitations.
We examine the RKKY interactions of CeB$_6$ between multipole moments based on the effective Wannier model obtained from the bandstructure calculation including 14 Ce-$f$ orbitals and 60 conduction orbitals of Ce-$d,s$ and B-$p,s$. By using the $f$-$c$ mixing matrix elements of the Wannier model together with the conduction band dispersion, the multipole couplings with the RKKY oscillation are obtained for the active moments in $Gamma_{8}$ subspace. Both of the $Gamma_{5g}$ quadrupole $O_{xy}$ and the $Gamma_{2u}$ octupole $T_{xyz}$ couplings are largely enhanced with $bm{q}=(pi,pi,pi)$ which naturally explains the antiferro-quadrupolar phase of the phase II, and are also enhanced with $bm{q}=(0,0,0)$ corresponding to the elastic softening of $C_{44}$. Also the couplings of the $Gamma_{5u}$ octupole $T_{z}^{beta}$ is quite large for $bm{q}=(0,0,pi)$ which is related to the antiferro-octupolar ordering of a possible candidate for the phase IV of Ce$_{x}$La$_{1-x}$B$_6$.
Recent experiments have reported on controlled nucleation of individual skyrmions in chiral magnets. Here we show that in magnetic ultra-thin films with interfacial Dzyaloshinskii-Moriya interaction, single skyrmions of different radii can be nucleated by creating a local distortion in the magnetic field. In our study, we have considered zero temperature quantum nucleation of a single skyrmion from a ferromagnetic phase. The physical scenario we model is one where a uniform field stabilizes the ferromagnet, and an opposing local magnetic field over a circular spot, generated by the tip of a local probe, drives the skyrmion nucleation. Using spin path integrals and a collective coordinate approximation, the tunneling rate from the ferromagnetic to the single skyrmion state is computed as a function of the tips magnetic field and the circular spot radius. Suitable parameters for the observation of the quantum nucleation of single skyrmions are identified.
The competition between the indirect exchange interaction (IEC) of magnetic impurities in metals and the Kondo effect gives rise to a rich quantum phase diagram, the Doniach Diagram. In disordered metals, both the Kondo temperature and the IEC are widely distributed due to the scattering of the conduction electrons from the impurity potential. Therefore, it is a question of fundamental importance, how this Doniach diagram is modified by the disorder, and if one can still identify separate phases. Recently, it has been investigated the effect of Ruderman-Kittel-Kasuya-Yosida (RKKY) correlations on the Kondo effect of two magnetic impurities, renormalizing the Kondo interaction based on the Bethe-Salpeter equation and performing the poor mens renormalization group (RG) analysis with the RKKY-renormalized Kondo coupling. In the present study, we extend this theoretical framework, allowing for different Kondo temperatures of two RKKY-coupled magnetic impurities due to different local exchange couplings and density of states. As a result, we find that the smaller one of the two Kondo temperatures is suppressed more strongly by the RKKY interaction, thereby enhancing their initial inequality. In order to find out if this relevance of inequalities between Kondo temperatures modifies the distribution of the Kondo temperature in a system of a finite density of randomly distributed magnetic impurities, we present an extension of the RKKY coupled Kondo RG equations. We discuss the implication of these results for the interplay between Kondo coupling and RKKY interaction in disordered electron systems and the Doniach diagram in disordered electron systems.
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