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Temperature dependence of the Gaussian depolarization rates in ZF and TF. Inset: typical low temperature TF depolarization data for the UD detectors (filled circles) and the fit as described in the text (solid line).
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We have carried out muon spin relaxation and rotation measurements on the newly discovered kagome metal KV3Sb5, and find a local field dominated by weak magnetic disorder which we associate with the nuclear moments present, and a modest temperature dependence which tracks the bulk magnetic susceptibility. We find no evidence for the existence of V4...
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We have used μSR and 23Na-NMR spectroscopic methods in the NaOsO3 antiferromagnetic phase to determine the temperature evolution of the magnetic order parameter and the role of the magnetic fluctuations at the N ́eel temperature. Additionally, we performed muon spin relaxation measurements in the vicinity of TA=30 K, where the appearance of an anom...
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... The AV 3 Sb 5 (A = K, Rb, Cs) family of Kagome metals is a case in point [5]. While these compounds do not display any sign of local spin moments [5,6], they still constitute a model material system which hosts a wide variety of novel physics. In particular, their band structure features a rare combination of nontrivial band topology, Fermi surface nesting and van Hove singularity at the Fermi energy [7][8][9]. ...
The $A$V$_3$Sb$_5$ ($A=$ K, Rb, Cs) family of Kagome metals hosts unconventional charge density wave order whose nature is still an open puzzle. Accumulated evidences point to a time-reversal symmetry breaking orbital flux phase that carries loop currents. Such an order may support anomalous Hall effect. However, the polar Kerr effect measurements that probe the a.c. anomalous Hall conductivity seems to have yielded contradictory results. We first argue on symmetry grounds that some previously proposed orbital flux order, most notably the one with Star-of-David distortion, shall not give rise to anomalous Hall or polar Kerr effects. We further take the tri-hexagonal orbital flux phase as an exemplary Kagome flux order that does exhibit anomalous Hall response, and show that the Kerr rotation angle at two relevant experimental optical frequencies generally reaches microradians to sub-milliradians levels. A particularly sharp resonance enhancement is observed at around $\hbar \omega =1$ eV, suggesting exceedingly large Kerr rotation at the corresponding probing frequencies not yet accessed by previous experiments. Our study can help to interpret the Kerr measurements on $A$V$_3$Sb$_5$ and to eventually resolve the nature of their CDW order.
... Motivated by the absence of local magnetic moments in the AV 3 Sb 5 family [2,57], we set ⟨n i↑ ⟩ = ⟨n i↓ ⟩ = ⟨n i ⟩ (i = A, B, C). We allow the possibility of CDW formation described by two electron-poor (rich) sites and one electron-rich (poor) site within the unit cell following the triangle rule [see Figs. ...
We study the interplay of attractive electron interactions and topological states in strained kagome lattices with spin-orbit coupling via a Hubbard Hamiltonian in the mean-field approximation. In the unstrained lattice, there is a topological phase transition from a quantum spin Hall state to a charge density wave (CDW) with increasing interaction strength. Upon applying a uniform uniaxial strain to the lattice, we find a new phase with coexisting CDWs and topological states. For increasing interaction strength or strain, the system is driven into a pure CDW, signaling topological phase transitions. The directionality (nematicity) of the CDW is controlled by the direction of the applied strain. When $s$ wave electronic pairing is allowed, the system develops a superconducting order beyond a threshold attraction, which is totally suppressed by the onset of a CDW with increasing interaction. Most interestingly, moderate strain allows the coexistence of superconductivity and CDWs for a range of interaction values. This illustrates how electronic interactions and single-particle topological structures compete to create unusual correlated phases in kagome systems.
... In the case of MnGe films, magnetic-fieldinduced melting of the static chiral spin order leads to a large σ T yx at high magnetic fields, probably due to significant skew scattering. However, 16,17 and frustrated magnets (solid symbols) 4,[7][8][9][10][11][12][13][45][46][47][48][54][55][56] . For conventional ferromagnets, scaling behaviors of σ A xy ∼ σ α xx were observed in the hopping regime (α = 1.6, green dashed line) and in the ultraclean regime (α = 1, orange dashed line), except in the intermediate regime showing a nearly constant σ A xy due to the momentum-space Berry curvature effect. ...
... Such a narrow temperature window below~T N has been similarly observed in other frustrated magnets (Fig. 4c). For a Kagome metal KV 3 Sb 5 , the absence of signature of strong localized V spin moments 56 and the presence of the charge density wave phase in the temperature regime of a large Hall response below~50 K 57 have raised questions on the validity of spin-cluster skew scattering model, without ruling out the possibility of the conventional multiband effect. In the triangular-lattice magnetic semiconductor EuAs 55 , an unconventional AHE is observed up to~6T N , which has been attributed to spin cluster scattering by noncoplanar Eu 2+ spins on the triangular lattice. ...
Magnetic frustration, realized in the special geometrical arrangement of localized spins, often promotes topologically nontrivial spin textures in the real space and induces significantly large unconventional Hall responses. This spin Berry curvature effect in itinerant frustrated magnets mainly works with a static spin order, limiting the effective temperature range below the magnetic transition temperature and yielding the typical anomalous Hall conductivity below ~ 10³ Ω⁻¹cm⁻¹. Here we show that an ultraclean triangular-lattice antiferromagnet PdCrO2 exhibits a large anomalous Hall conductivity up to ~ 10⁶ Ω⁻¹cm⁻¹ in the paramagnetic state, which is maintained far above the Neel temperature (TN) up to ~ 4TN. The reported enhancement of anomalous Hall response above TN is attributed to the skew scattering of highly mobile Pd electrons to fluctuating but locally-correlated Cr spins with a finite spin chirality. Our findings point at an alternative route to realizing high-temperature giant anomalous Hall responses, exploiting magnetic frustration in the ultraclean regime.
... The magnetic moment of Fe shows a slight increase when it enters the CDW state, indicating a strong coupling between AFM and CDW orders. Its sizable magnetic moment (mFe 1.7 B) for AFM [36,37] in FeGe puts it in a category of strongly correlated electron systems while AV3Sb5 are non-magnetic with weak electron correlations [38]. CDW might be susceptible to and even suppressed by a ferromagnetic order as observed in colossal-magnetoresistance manganites [39] and Sm(Nd)NiC2 [40,41]. ...
Strongly correlated electron systems with a kagome lattice can host abundant exotic quantum states such as superconductivity and spin/charge density waves (CDW) due to the complicated interactions between different degrees of freedoms in the framework of a unique two-dimensional geometrically frustrated lattice structure. Recently, successive orders of A-type antiferromagnetism (AFM), 2 x 2 x 2 CDW and canted double-cone AFM have been manifested upon cooling in magnetic kagome FeGe. However, the mechanism of the CDW order and its interaction with magnetism are presently enigmatic at best. Here we investigate the evolution of CDW order with temperature across the spin canting transition in FeGe by single-crystal x-ray diffraction. Refinements of its modulated structure are presented using the superspace approach. Interestingly, the superlattice reflections originating from CDW-induced long-range structural modulation become extremely weak after the system enters the canted AFM while a 2 x 2 CDW in the ab plane persists as a long-range order demonstrated by strong electronic modulation in the dI/dV map of scanning tunneling spectroscopy. We discovered a novel CDW order without long-range structural modulation in FeGe probably because of the competition between CDW and canted AFM in determining the underlying crystal structure. In addition, occupational modulations of Ge1 atoms located in the kagome plane and displacive modulations of all the atoms were extracted from the refinements, confirming the existence of Ge atom dimerization along the c axis as the major distortion and indicating a dynamic transformation between different CDW domains.
... This prototypical band structure can be intertwined with a rich array of exotic electronic instabilities, which have been theoretically explored and experimentally realized in several families of kagome metals thus far. For example, Fe- [6][7][8][9][10][11][12][13][14][15] , Mn- [16][17][18][19][20][21] and Co- [22][23][24][25] based kagome magnets yielded the realization of topological flat bands 11,23,26 , Dirac and Weyl fermions 6,9,12,22,24,27 and Fermi arcs 22,24 ; a non-magnetic Vbased AV 3 Sb 5 (A = Cs, K, Rb) kagome metal family [28][29][30] on the other hand attracted a large interest [31][32][33][34][35][36][37][38][39][40][41] due to the emergence of superconductivity and various symmetry-breaking states including charge density waves potentially in connection to loop current orders 42 . ...
Charge density waves (CDWs) in kagome metals have been tied to many exotic phenomena. Here, using spectroscopic-imaging scanning tunneling microscopy and angle-resolved photoemission spectroscopy, we study the charge order in kagome metal ScV 6 Sn 6 . The similarity of electronic band structures of ScV 6 Sn 6 and TbV 6 Sn 6 (where charge ordering is absent) suggests that charge ordering in ScV 6 Sn 6 is unlikely to be primarily driven by Fermi surface nesting of the Van Hove singularities. In contrast to the CDW state of cousin kagome metals, we find no evidence supporting rotation symmetry breaking. Differential conductance d I /d V spectra show a partial gap Δ ¹ CO ≈ 20 meV at the Fermi level. Interestingly, d I /d V maps reveal that charge modulations exhibit an abrupt phase shift as a function of energy at energy much higher than Δ ¹ CO , which we attribute to another spectral gap. Our experiments reveal a distinctive nature of the charge order in ScV 6 Sn 6 with fundamental differences compared to other kagome metals.
... It has been demonstrated that there is no measurable local spin moments or magnetic correlations in AV 3 Sb 5 [11,35], so we perform a standard mean field procedures with the self-consistent conditions ⟨n iα↑ ⟩ = ⟨n iα↓ ⟩ = n α↑ = n α↓ = n α /2, without considering other order such as magnetism in this paper. The Hamiltonian (1) can be rewritten as the matrix form ...
Kagome lattice provides a distinctive platform to investigate various correlated electron orders. Recently, an unconventional charge density wave (CDW) with novel chirality is observed in the kagome metal AV3Sb5 (A = K, Rb, Cs), and the origin of which is still unclear. Here, using a tight-binding model and the mean-field method, we calculate the electron order in the quasi-2-dimensional kagome lattice with 1/3 electron filling, and show that the chiral CDW emerges under a set of parameters with C6 rotational symmetry but without mirror symmetry. Physically, the reason why we choose this set of parameters is based on the possible tangential distortion of the kagome lattice. Our results provide a fresh insight to understand the microscopic origin of the unconventional CDW in AV3Sb5.
... Whereas measurements like muon-spin depolarization in polycrystalline samples divulge negligible local moments [27], for single crystals, there is a striking enhancement of the internal field below T CO , implying the presence of a time-reversal symmetry breaking [28]. The most puzzling aspect of AV 3 Sb 5 is the presence of giant anomalous Hall effect (AHE) with anomalous Hall ratio being an order of magnitude higher than that of Fe [29,30]. ...
The V-based kagome systems AV3Sb5 (A=Cs, Rb, and K) are unique by virtue of the intricate interplay of nontrivial electronic structure, topology, and intriguing fermiology, rendering them to be a playground of many mutually dependent exotic phases like charge-order and superconductivity. Despite numerous recent studies, the interconnection of magnetism and other complex collective phenomena in these systems has yet not arrived at any conclusion. Using first-principles tools, we demonstrate that their electronic structures, complex fermiologies and phonon dispersions are strongly influenced by the interplay of dynamic electron correlations, nontrivial spin-polarization and spin-orbit coupling. An investigation of the first-principles-derived intersite magnetic exchanges with the complementary analysis of q dependence of the electronic response functions and the electron-phonon coupling indicate that the system conforms as a frustrated spin cluster, where the occurrence of the charge-order phase is intimately related to the mechanism of electron-phonon coupling, rather than the Fermi-surface nesting.
... Additionally, a charge density wave (CDW) is detected below ∼ 80 − 100 [26,[31][32][33][34][35], with scanning tunneling microscopy revealing 2 × 2 lattice distortions, emphasizing the important role of van-Hove singularities near point of the Brillouin zone. Intriguingly, these materials exhibit spontaneous time-reversal symmetry breaking (TRSB) after the CDW transition, evidenced through techniques such as muon spin relaxation and scanning tunneling microscope [11,32,36], alongside a large anomalous Hall effect [37] in the CDW phase without evidence of static magnetic order [27,31,38]. These observations indicate an unconventional CDW order in AV 3 Sb 5 . ...
Recent experiments on Kagome metals AV$_3$Sb$_5$ (A=Cs,Rb,K) indicated spontaneous time-reversal symmetry breaking in the charge density wave state in the absence of static magnetization. The loop current order (LCO) is proposed as its cause, but a microscopic model explaining the emergence of LCO through electronic correlations has not been firmly established. We show that the coupling between van-Hove singularities (vHS) with distinct mirror symmetries is a key ingredient to generate LCO ground state. By constructing an effective model, we find that when multiple vHS with opposite mirror eigenvalues are close in energy, the nearest-neighbor electron repulsion favors a ground state with coexisting LCO and charge bond order. It is then demonstrated that this mechanism applies to the Kagome metals AV$_3$Sb$_5$. Our findings provide an intriguing mechanism of LCO and pave the way for a deeper understanding of complex quantum phenomena in Kagome systems.
... A similar 2 × 2 × 2 CDW order (TCDW ≈ 100 K) was recently discovered [17] in B35-type FeGe with a kagome sublattice of Fe under the A-type antiferromagnetic (AFM) order (TN 410 K) [18][19][20] where electron correlations play an important role in stark contrast to the nonmagnetic AV3Sb5 [7,[20][21][22]. The magnetic moment of Fe is enhanced by around 0.05 μB in the CDW state, indicating a strong coupling between CDW and magnetism [17]. ...
Recently, charge density wave (CDW) has been observed well below the order of antiferromagnetism (AFM) in kagome FeGe in which magnetism and CDW are intertwined to form an emergent quantum ground state. The mechanism of CDW precipitating from an A-type AFM of Fe kagome sublattice is intensively debated. The structural distortion originating from the CDW has yet to be accurately determined in FeGe. Here we resolved the structure model of the CDW in annealed FeGe crystals through single crystal x-ray diffraction via a synchrotron radiation source. The annealed crystals exhibit strong CDW transition signals exemplified by sharp magnetic susceptibility drop and specific heat jump, as well as intense superlattice reflections from 2 × 2 × 2 CDW order. Occupational disorder of Ge atoms resulting from short-range CDW correlations above TCDW has also been identified from the structure refinements. The dimerization of Ge atoms along c axis has been demonstrated to be the dominant distortion for CDW. The Fe kagome and Ge honeycomb sublattices only undergo subtle distortions. Occupational disorder of Ge atoms is also proved to exist in the CDW phase due to the random selection of partial Ge sites to be dimerized to realize the structural distortion. Our work paves the way to understanding the unconventional nature of CDW in FeGe not only by solving the structural distortion below TCDW and identifying fluctuations above it but also by rationalizing the synthesis of high-quality crystals for in-depth investigations in the future.
... However, the measurements show that the muon spin relaxation has a clearly observable temperature dependence. The zero-field relaxation is decoupled by the application of a small external magnetic field applied longitudinal to the muon spin polarization, B LF = 50 G [66][67][68]98 . Therefore the observed relaxation is due to spontaneous fields which are static on the microsecond timescale. ...
Kagome lattices are intriguing and rich platforms for studying the intertwining of topology, electron correlation, and magnetism. These materials have been subject to tremendous experimental and theoretical studies not only due to their exciting physical properties but also as systems that may solve critical technological problems. We will review recent experimental progress on superconductivity and magnetic fingerprints of charge order in several kagome-lattice systems from the local-magnetic probe point of view by utilizing muon-spin rotation under extreme conditions, i.e., hydrostatic pressure, ultra low temperature and high magnetic field. The systems include: (1) The series of compounds A V 3 Sb 5 ( A = K, Rb, Cs) with V kagome lattice which form the first kagome-based family that exhibits a cascade of symmetry-broken electronic orders, including charge order and superconductivity. In these systems, we find a time-reversal symmetry-breaking charge ordered state and tunable unconventional time-reversal symmetry-breaking superconductivity. (2) The system LaRu 3 Si 2 with distorted kagome layers of Ru, in which our experiments and calculations taken together point to nodeless moderate coupling superconductivity. It was also found that the electron-phonon coupling alone can only explain a small fraction of T c from calculations, which suggests other factors enhancing T c such as the correlation effect from the kagome flat band, the van Hove point on the kagome lattice, and the high density of states from the narrow kagome bands. (3) CeRu 2 with a pristine Ru kagome lattice, which we classify as an exceedingly rare nodeless (with anisotropic s -wave gap symmetry) magnetic kagome superconductor.
