It has long been speculated that electronic flatband systems can be a fertile ground for hosting novel emergent phenomena including unconventional magnetism and superconductivity 1-14 . Here we use scanning tunnelling microscopy to elucidate the atomically resolved electronic states and their magnetic response in the kagome magnet 15-20 Co3Sn2S2. We observe a pronounced peak at the Fermi level, which is identified to arise from the kinetically frustrated kagome flatband. Increasing magnetic field up to ±8T, this state exhibits an anomalous magnetization-polarized Zeeman shift, dominated by an orbital moment in opposite to the field direction. Such negative magnetism can be understood as spin-orbit coupling induced quantum phase effects 21-25 tied to non-trivial flatband systems. We image the flatband peak, resolve the associated negative magnetism, and provide its connection to the Berry curvature field, showing that Co3Sn2S2 is a rare example of kagome magnet where the low energy physics can be dominated by the spinorbit coupled flatband. Our methodology of probing band-resolved ordering phenomena such as spin-orbit magnetism can also be applied in future experiments to elucidate other exotic phenomena including flatband superconductivity and anomalous quantum transport.

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Magnetic topological phases of quantum matter are an emerging frontier in physics and material science [1][2][3][4]. Along these lines, several kagome magnets [5][6][7][8][9] have appeared as the most promising platforms. However, the magnetic nature of these materials in the presence of topological state remains an unsolved issue [5][6][7][8][9]. Here, we explore magnetic correlations in the kagome magnet Co 3 Sn 2 S 2 . Using muon spin-rotation, we present evidence for competing magnetic orders in the kagome lattice of this compound. Our results show that while the sample exhibits an outof-plane ferromagnetic ground state, an in-plane antiferromagnetic state appears at temperatures above 90 K, eventually attaining a volume fraction of 80% around 170 K, before reaching a nonmagnetic state. Strikingly, the reduction of the anomalous Hall conductivity above 90 K linearly follows the disappearance of the volume fraction of the ferromagnetic state. We further show that the competition of these magnetic phases is tunable through applying either an external magnetic field or hydrostatic pressure. Our results taken together suggest the thermal and quantum tuning of Berry curvature field via external tuning of magnetic order. Our study shows that Co 3 Sn 2 S 2 is a rare example where the magnetic competition drives the thermodynamic evolution * Electronic address: zurab.guguchia@psi.ch of the Berry curvature field, thus tuning its topological state.The kagome lattice is a two-dimensional pattern of corner-sharing triangles. With this unusual symmetry and the associated geometrical frustration, the kagome lattice can host peculiar states including flat bands [8], Dirac fermions [5,6] and spin liquid phases [7,10]. In particular, magnetic kagome materials offer a fertile ground to study emergent behaviors resulting from the interplay between unconventional magnetism and band topology. Recently, transition-metal based kagome magnets [5][6][7][8][9][10][11][12][13] are emerging as outstanding candidates for such studies, as they feature both large Berry curvature fields and unusual magnetic tunability. In this family, the kagome magnet Co 3 Sn 2 S 2 is found to exhibit both a large anomalous Hall effect and anomalous Hall angle, and is identified as a promising Weyl semimetal candidate [9,11,14,15]. However, despite knowing the magnetic ground state is ferromagnetic below T C = 177 K [16] with spins aligned along the c-axis [9, 11, 17] (see Figs. 1 a and b) there is no report of its magnetic tunability or phase diagram, and its interplay with the topological band structure. Here we use high-resolution µSR to systematically characterize the phase diagram, uncovering another intriguing in-plane antiferromagnetic phase. The magnetic competition between these two phases is further found to be highly tunable via applying either pressure [18][19][20][21] or magnetic field. Combined with first principles calculations, we discover that the tunable magnetic correlation plays a key role in determining the giant anomalous Hall transp...

Charge density wave (CDW) is a startling quantum phenomenon, distorting a metallic lattice into an insulating state with a periodically modulated charge distribution. Astonishingly, such modulations appear in various patterns even within the same family of materials. Moreover, this phenomenon features a puzzling diversity in its dimensional evolution. Here, we propose a general framework, unifying distinct trends of CDW ordering in an isoelectronic group of materials, 2H-MX 2 (M = Nb, Ta and X = S, Se). We show that while NbSe 2 exhibits a strongly enhanced CDW order in two dimensions, TaSe 2 and TaS 2 behave oppositely, with CDW being absent in NbS 2 entirely. Such a disparity is demonstrated to arise from a competition of ionic charge transfer, electron-phonon coupling, and electron correlation. Despite its simplicity, our approach can, in principle, explain dimensional dependence of CDW in any material, thereby shedding new light on this intriguing quantum phenomenon and its underlying mechanisms.