Field-tunable toroidal moment in a chiral-lattice magnet
Lei Ding, Xianghan Xu, Harald O. Jeschke, Xiaojian Bai, Erxi Feng, Admasu Solomon Alemayehu, Jaewook Kim, Feiting Huang, Qiang Zhang, Xiaxin Ding, Neil Harrison… 展开作者
Lei Ding, Xianghan Xu, Harald O. Jeschke, Xiaojian Bai, Erxi Feng, Admasu Solomon Alemayehu, Jaewook Kim, Feiting Huang, Qiang Zhang, Xiaxin Ding, Neil Harrison, Vivien Zapf, Daniel Khomskii, Igor I. Mazin, Sang-Wook Cheong, Huibo Cao
A toroidal dipole moment appears independent of the electric and magnetic dipole moment in the multipole expansion of electrodynamics. It arises naturally from vortex-like arrangements of spins. Observing and controlling spontaneous long-range orders of toroidal moments are highly promising for spintronics but remain challenging. Here we demonstrate that a vortex-like spin configuration with a staggered arrangement of toroidal moments, a ferritoroidal state, is realized in a chiral triangular-lattice magnet BaCoSiO4. Upon applying a magnetic field, we observe multi-stair toroidal transitions correlating directly with metamagnetic transitions. We establish a first-principles microscopic Hamiltonian that explains both the formation of toroidal states and the metamagnetic toroidal transition as a combined effect of the magnetic frustration and the Dzyaloshinskii-Moriya interactions allowed by the crystallographic chirality in BaCoSiO4.
Combining magnetism with band topology provides various novel phases that are otherwise impossible. Among several cases, noncollinear metallic antiferromagnets can reveal particularly rich topological physics due to their diverse magnetic ground states. However, there are only a few experimental studies due to the lack of suitable materials, especially with triangular lattice antiferromagnets. Here, we report that metallic triangular antiferromagnet Co1/3TaS2 exhibits a substantial anomalous Hall effect (AHE) related to its noncollinear magnetic order. Our first-principles calculations found t…
We present a general formalism of multipole descriptions under the space-time inversion group. We elucidate that two types of atomic toroidal multipoles, i.e., electric and magnetic, are fundamental pieces to express electronic order parameters in addition to ordinary electric and magnetic multipoles. By deriving quantum-mechanical operators for both toroidal multipoles, we show that electric (magnetic) toroidal multipole higher than dipole (monopole) can become a primary order parameter in a hybridized-orbital system. We also demonstrate emergent cross-correlated couplings between electric, m…
We investigate a dynamical magnetoelectric effect due to a magnetic resonance in helical spin structures through the coupling between magnetization and electric polarization via a spin current mechanism. We show that the magnon has both the dynamical magnetic moment $ΔM^ω$ and the electric moment $ΔP^ω$ ($\perp ΔM^ω$), i.e., a dynamical toroidal moment, under external magnetic fields, and thus it is named the {\em toroidalmagnon}. The toroidalmagnon exists in most conical spin structures owing to the generality of the spin current mechanism. In the absorption of electromagnetic waves, the toro…
The microscopic conditions for the emergence of nonreciprocal magnon excitations in noncentrosymmetric magnets are theoretically investigated. We show that asymmetric magnon excitations appear when a bond magnetic toroidal dipole becomes active, which is defined as a parallel component between the Dzyaloshinskii-Moriya vector and the averaged spin moments at the ends of the bonds. Depending on magnetic structures accompanying the bond magnetic toroidal dipoles, the higher-rank magnetic toroidal multipoles can also be activated in a magnetic cluster, which describes various angle dependences of…
Molecular magnetic toroidal moments are molecule-based structures of quantum spins that are expected to boost magnetic storage technology and quantum computing. We study selected fictitious but typical examples of single-molecule toroidal magnet behavior, discuss the essence of the concept and clarify inappropriate or even wrong assignments of physical properties. We provide an outlook that discusses necessary ingredients to the concept of toroidicity.
Magnetic monopoles and toroidal order are compelling features that have long been theorized but remain elusive in real materials. Multiferroic hexagonal ferrites are an interesting realization of frustrated triangular lattice, where magnetic order is coupled to ferroelectricity and trimerization. Here we propose a mechanism, through which magnetic monopolar and toroidal orders emerge from the combination of 120$^\circ$ antiferromagnetism and trimerization, present in hexagonal manganites and ferrites. The experimentally observable signatures of magnetic monopolar and toroidal orders are identi…
We theoretically investigate an antiferromagnetic structure in a hexagonal zigzag-chain compound Ce$_3$TiBi$_5$, which shows a linear magnetoelectric effect in metals and an unfamiliar temperature dependence of magnetic susceptibility. We find a partial magnetic order as a coexistence of a nonmagnetic zigzag chain and staggered antiferromagnetic zigzag chains. The latter accompany in-plane magnetic toroidal dipole moments which are responsible for the observed behaviors. We show that magnetic frustration arising from competing exchange interactions plays an important role to realize such a par…
Magnetization measurements under direct electric currents were performed for toroidal magnetic ordered state of UNi$_4$B to test a recent theoretical prediction of current-induced magnetization in a metallic system lacking local inversion symmetry.We found that each of the electric currents parallel to [$2\bar{1}\bar{1}0$] and [$0001$] in the hexagonal 4-index notation induces uniform magnetization in the direction of [$01\bar{1}0$].The observed behavior of the induced magnetization is essentially consistent with the theoretical prediction; however it also shows an inconsistency suggesting tha…
We report our theoretical results on spin conductivity in antiferromagnets by focusing on the role of the magnetic toroidal quadrupole (MTQ) in electron systems. The MTQ is characterized as a time-reversal-odd rank-2 polar tensor degree of freedom in electrons, which is distinct from conventional rank-1 magnetic and magnetic toroidal dipoles. Based on a microscopic $sd$ model analysis for a tetragonal system under both collinear and noncollinear antiferromagnetic orderings, we clarify that the MTQ becomes a source of an extrinsic spin conductivity even with neither a uniform magnetization nor …
Toroidal order, given by a composite of electric and magnetic orders, manifests itself not only in the peculiar magnetism but also in anomalous transport and magnetoelectric effect. We report our theoretical results on the influence and stability of a toroidal order in metals on the basis of a microscopic model. We consider an effective single-band Hubbard-type model with a site-dependent antisymmetric spin-orbit coupling, which is derived from a four-band tight-binding model including the atomic spin-orbit coupling, off-site hybridizations between orbitals with different parities, and odd-par…
A connection between creation of toroidal moments and breaking of the relativistic crystalline group associated to a given crystal, is presented in this paper. Indeed, if magnetoelectric effects exist, the interaction between electrons and elementary magnetic cells appears in such a way that the resulting local polarization and magnetization break the local relativistic crystalline symmetry. Therefore, Goldstone bosons, also associated to toroidal moments, are created and, as a consequence, corresponding toroidal phases in crystals. The list of the Shubnikov groups compatible with this kind of…
We report our theoretical study on nucleation of a magnetic vortex around a nonmagnetic impurity doped into ferromagnets. The mechanism lies in the asymmetric Dzyaloshinskii-Moriya interaction arising from the breaking of spatial inversion symmetry by the impurity. By using the spin-wave analysis and Monte Carlo simulations, we show that the asymmetric interaction induces a magnetic vortex with nonzero vorticity $l=+1$. The vortex is stabilized even for less frustration in exchange interactions and in the absence of an external magnetic field. We also find that the magnetic vortex is character…
A magnetic toroidal moment is a fundamental electronic degree of freedom in the absence of both spatial inversion and time-reversal symmetries and gives rise to novel multiferroic and transport properties. We elucidate essential model parameters of the nonlinear transport in the space-time ($\mathcal{PT}$) symmetric collinear antiferromagnetic metals accompanying a magnetic toroidal moment. By analyzing the longitudinal and transverse components of the second-order nonlinear conductivity on a two-dimensionally stacked zigzag chain based on the nonlinear Kubo formula, we show that an effective …
Atomic-scale visualization of the toroidal order in a trimeric Dy(III) single-molecule toroic
University of Tennessee（田纳西大学）；Oak Ridge National Laboratory（橡树岭国家实验室）；University of South Carolina（南卡罗来纳大学）；Indian Institute of Technology Bombay（印度理工学院孟买分校）；Kennesaw State University（肯尼索州立大学）
Effects of spontaneous toroidal ordering on magnetic excitation are theoretically investigated for a localized spin model that includes a staggered Dzyaloshinsky-Moriya interaction and anisotropic exchange interactions, which arise from the antisymmetric spin-orbit coupling and the multi-orbital correlation effect. We show that the model exhibits a Neel-type antiferromagnetic order, which simultaneously accompanies a ferroic toroidal order. We find that the occurrence of toroidal order modulates the magnon dispersion in an asymmetric way with respect to the wave number: a toroidal dipole order…
The optical Hall response is theoretically studied for spin-orbit coupled metals with ferroic orders of cluster-type magnetic multipoles. We find that different magnetic multipoles give rise to distinct spectra in the optical Hall conductivity. In the cases of monopole and quadrupole orders, the optical Hall response appears predominantly in high- and low-energy regions, which correspond to the energy scales of electron correlation and kinetic energy, respectively, while the response is dispersed and rather weak in the case of toroidal order. By decomposing the spectra into different interband…
A partial disorder on a layered triangular lattice is theoretically investigated from a viewpoint of toroidal ordering and magnetoelectric effects. We consider an extended periodic Anderson model including a site-dependent antisymmetric spin-orbit coupling between conduction and localized electrons. We show that, by the mean-field approximation, the model exhibits a coplanar vortex-lattice-type magnetic order as observed in a hexagonal uranium compound UNi4B, in the parameter region with intermediate hybridization and electron correlation. This peculiar state accommodates a toroidal order, whi…
