Topological magneto-optical effect from skyrmion lattice

Article https://doi.org/10.1038/s41467-023-41203-y Topological magneto-optical effect from skyrmion lattice Received: 5 April 2023 Accepted: 23 August 2023 1234567890():,; 1234567890():,; Check for updates Yoshihiro D. Kato Yoshinori Tokura 1 , Yoshihiro Okamura 1 , Max Hirschberger 1,2,3 & Youtarou Takahashi 1,2 1,2 , The magnetic skyrmion is a spin-swirling topological object characterized by its nontrivial winding number, holding potential for next-generation spintronic devices. While optical readout has become increasingly important towards the high integration and ultrafast operation of those devices, the optical response of skyrmions has remained elusive. Here, we show the magneto-optical Kerr effect (MOKE) induced by the skyrmion formation, i.e., topological MOKE, in Gd2PdSi3. The significantly enhanced optical rotation found in the skyrmion phase demonstrates the emergence of topological MOKE, exemplifying the light-skyrmion interaction arising from the emergent gauge field. This gauge field in momentum space causes a dramatic reconstruction of the electronic band structure, giving rise to magneto-optical activity ranging up to the sub-eV region. The present findings pave a way for photonic technology based on skyrmionics. Since its first discovery in a chiral magnet, the magnetic skyrmion, a nanometric quasiparticle composed of full-solid-angle oriented spin moments, has attracted much attention because of its potential for high density and low power consumption memory/logic devices1–8. The topological nature of each skyrmion, which is derived from the directions of constituent spins wrapping the unit sphere, gives rise to the robust stability and high electric-current controllability of the skyrmion particle, being useful as the information carrier3,9,10. This particular spin arrangement also hosts the quantized scalar spin chirality, generating a gauge field originating from the Berry phase. As a result, a fictitious magnetic field acts on the electronic system, often referred to as an emergent magnetic field, due to the skyrmion formation. For conduction electrons, this emergent magnetic field induces topological transport phenomena as exemplified by the topological Hall effect (THE) and topological Nernst effect9,11–14, which can be exploited for electrical readout of skyrmions. In recent years, much effort has been devoted to the exploration of new materials hosting small skyrmions15–18 and to the detailed elucidation of skyrmion dynamics such as the current-induced motion and creation/ annihilation processes19–21. These fundamental studies enable further advances towards the realization of higher density devices and their operation. On the other hand, these findings warrant the development of more sophisticated readout schemes, beyond simple transport experiments (THE), which are capable of sensitive, functional, and high-speed response. In this context, the magneto-optical effect, a light polarization rotation under breaking of time-reversal symmetry, is a promising candidate. It has been used as a local, fast, and contactless probe of magnetic domains22. The magnitude of the magneto-optical effect is usually proportional to the magnetization (M), and thus it is believed to be less sensitive to the emergence of skyrmions accompanying weak change in the net M23. Meanwhile, some recent theories predict the socalled topological magneto-optical effect induced by the formation of noncoplanar spin structures with finite scalar spin chirality24. This mechanism is essentially distinct from the conventional M-induced magneto-optical effect governed by the interplay between band exchange splitting and relativistic spin-orbit coupling25,26; the spinorbit coupling is not a prerequisite for the topological magneto-optical effect24,27. Thus, the emergent magnetic field arising from skyrmion formation potentially gives rise to the topological magneto-optical effect sensitive to the existence of skyrmion, analogous to the THE24,27, which can be exploited for the optical detection of skyrmions. 1 Department of Applied Physics and Quantum Phase Electronics Center, University of Tokyo, Tokyo 113-8656, Japan. 2RIKEN Center for Emergent e-mail: ; Matter Science (CEMS), Wako 351-0198, Japan. 3Tokyo College, University of Tokyo, Tokyo 113-8656, Japan. Nature Communications | (2023)14:5416 1 Article https://doi.org/10.1038/s41467-023-41203-y However, such an optical response driven by skyrmion formation has yet to be elucidated. Here, we report on the topological MOKE arising from the skyrmion lattice (SkL) in the centrosymmetric rare-earth intermetallic compound Gd2PdSi3. By using broadband magneto-optical spectroscopy, we observe a largely enhanced MOKE in the sub-eV region due to SkL formation, evidencing the existence of topological MOKE and a significant change in Bloch electron wavefunctions constituting band structure by the emergent magnetic field. Such a reconstruction of electronic bands is found to contribute to THE, providing a comprehensive understanding of emergent electrodynamics over an extended energy scale. Results The rare-earth intermetallic Gd2PdSi3 crystallizes in the AlB2-type structure; a triangular lattice of Gd atoms sandwiches a nonmagnetic honeycomb-lattice layer composed of Pd and Si atoms (Fig. 1a)28. Longrange magnetic order of the Gd 4f moments is stabilized below 20 K14,15,29. Because of frustrated magnetic interactions on the triangular network of Gd moments, this material shows a rich magnetic phase diagram including modulated spin structures with short magnetic periods (Fig. 1a, b). The SkL appears under moderate magnetic field parallel to the c axis, in between two incommensurate magnetic phases without net emergent magnetic field: spiral-like IC-1 and fan-like IC2 states (Supplementary Fig. 1)14,15,29. Each skyrmion is as small as a few nanometers in diameter, much smaller than the size of such textures in conventional chiral magnets. Since one skyrmion provides a single flux quantum, the high-density SkL generates exceedingly strong emergent magnetic fields, leading to enhanced topological transport a d e 3.0 c b a b phenomena; the Hall conductivity is steeply enhanced in the SkL phase due to the giant THE (Fig. 1c), while M shows a monotonic increase, with a step-like anomaly at each phase boundary14,15. To pursue the topological magneto-optical effect, we measured broadband MOKE spectra, i.e., the polarization rotation of reflected light from the sample surface, under magnetic fields parallel to the caxis. Figure 1d, e shows the magnetic field dependence of the Kerr rotation angle θK(ω) (0.04–0.08 eV and 0.1–0.8 eV) and Kerr ellipticity ηK(ω) (0.1–0.8 eV) at 8.4 K (see also Methods). The overall magnitude of magneto-optical responses tends to grow with increasing magnetic field, while a dramatic change of the MOKE spectra is observed upon entering the SkL phase. The IC-1 and IC-2 phases with no net emergent magnetic field show comm (...truncated)