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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), $2\times2\times2$ 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 $2\times2$ CDW in the $ab$ plane persists as a long-range order demonstrated by strong electronic modulation in the d$I$/d$V$ 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., Comment: 22 pages, 6 figures. Comments on the manuscript are welcome

At ambient conditions SrAl4 adopts the BaAl4 structure type with space group I4/mmm. It undergoes a charge-density-wave (CDW) transition at TCDW = 243 K, followed by a structural transition at TS = 87 K. Temperature-dependent single-crystal X-ray diffraction (SXRD) leads to the observation of incommensurate superlattice reflections at q = \sigma c* with \sigma = 0.1116 at 200 K. The CDW has orthorhombic symmetry with the acentric superspace group F222(00sigma)00s, where F222 is a subgroup of Fmmm as well as of I4/mmm. Atomic displacements mainly represent a transverse wave, with displacements that are 90 deg out of phase between the two diagonal directions of the I-centered unit cell, resulting in a helical wave. Small longitudinal displacements are provided by the second harmonic modulation. The orthorhombic phase realized in SrAl4 is similar to that found in EuAl4. Electronic structure calculations and phonon calculations by density functional theory (DFT) have failed to reveal the mechanism of CDW formation. However, DFT reveals that Al atoms dominate the density of states near the Fermi level, thus, corroborating the SXRD measurements. SrAl4 remains incommensurately modulated at the structural transition, where the symmetry lowers from orthorhombic to b-unique monoclinic. We have identified a simple criterion, that correlates the presence of a phase transition with the interatomic distances. Only those compounds XAl4-xGax(X = Ba, Eu, Sr, Ca; 0 < x <4) undergo phase transitions, for which the ratio c/a falls within the narrow range 2.51 < c/a < 2.54.

Charge density wave (CDW) in kagome materials with the geometric frustration is able to carry unconventional characteristics. Recently, a CDW has been observed below the antiferromagnetic order in kagome FeGe, in which magnetism and CDW are intertwined to form an emergent quantum ground state. However, the CDW is only short-ranged and the structural modulation originating from it has yet to be determined experimentally. Here we realize a long-range CDW order by post-annealing process, and resolve the structure model through single crystal x-ray diffraction. Occupational disorder of Ge resulting from short-range CDW correlations above $T_\mathrm{CDW}$ is identified from structure refinements. The partial dimerization of Ge along the $c$ axis is unveiled to be the dominant distortion for the CDW. Occupational disorder of Ge is also proved to exist in the CDW phase due to the random selection of partially dimerized Ge sites. Our work provides useful insights for understanding the unconventional nature of the CDW in FeGe., Comment: 4 figures and 1 table in the main text. Supplementary materials included. To be published in SCIENCE CHINA Physics, Mechanics & Astronomy (SCPMA)

Anisotropic transport, Shubnikov-de Haas (SdH), and de Haas-van Alphen (dHvA) quantum oscillations studies are reported on a high-quality CoSi single crystal grown by the Czochralski method. Temperature-dependent resistivities indicate the dominating electron-electron scattering. Magnetoresistance (MR) at 2 K reaches 610% for I||[111] and B||[01-1], whereas it is 500% for I||[01-1] and B||[111]. A negative slope in field-dependent Hall resistivity suggests electrons are the majority carriers. The carrier concentration extracted from Hall conductivity indicates no electron-hole compensation. In 3D CoSi, the electron transport lifetime is found to be approximately in the same order as quantum lifetime, whereas in 2D electron gas the long-range scattering drives the transport life much larger than the quantum lifetime. From linear and Hall SdH oscillations the effective masses and Dingle temperatures have been calculated. The dHvA oscillation reveals three frequencies at 18 ($\gamma$), 558 ($\alpha$) and 663 T ($\beta$)), whereas, SdH oscillation results in only two frequencies $\alpha$ and $\beta$. The $\gamma$ frequency observed in dHvA oscillation is a tiny hole pocket at the $\Gamma$ point.

Single crystals of ${\rm Ce_2Re_3Si_5}$ and ${\rm Pr_2Re_3Si_5}$ have been grown by Czochralski method in a tetra-arc furnace. Powder x-ray diffraction confirmed that these compounds crystallize in the ${\rm U_2Mn_3Si_5}$-type tetragonal crystal structure with space group $P4/mnc$ (No. 128). The anisotropic physical properties have been studied comprehensively by measuring the magnetic susceptibility, isothermal magnetization, electrical transport and specific heat. The low value of magnetic susceptibility together with no magnetic transition down to $2$~K gives evidence that the Ce-ions are in the intermediate valence state in ${\rm Ce_2Re_3Si_5}$. On the other hand ${\rm Pr_2Re_3Si_5}$ revealed a magnetic ordering at $9$~K. The sharp drop in the magnetic susceptibility and a spin flip like metamagnetic transition, for $H~\parallel~[001]$ in the magnetization plot of ${\rm Pr_2Re_3Si_5}$ suggest an Ising-type antiferromagnetic ordering. Based on magnetic susceptibility and isothermal magnetization data, a detailed crystal electric field (CEF) analysis shows that degenerate ${J} = 4$ Hund's rule derived ground state of ${\rm Pr^{3+}}$ ion splits into nine singlets with an overall splitting of $1179$~K. The magnetic ordering in ${\rm Pr_2Re_3Si_5}$ is due to the exchange-generated admixture of the lowest lying CEF energy levels. Heat capacity data reveal a sharp peak at $9$~K, that confirms the bulk nature of the magnetic ordering in ${\rm Pr_2Re_3Si_5}$., Comment: Article was already published