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Materials Data on Tm(FeGe)2 by Materials Project

Tm(FeGe)2 crystallizes in the tetragonal I4/mmm space group. The structure is three-dimensional. Tm is bonded in a 8-coordinate geometry to eight equivalent Fe and eight equivalent Ge atoms. All Tm–Fe bond lengths are 3.22 Å. All Tm–Ge bond lengths are 3.07 Å. Fe is bonded to four equivalent Tm and four equivalent Ge atoms to form a mixture of distorted face, edge, and corner-sharing FeTm4Ge4 tetrahedra. All Fe–Ge bond lengths are 2.35 Å. Ge is bonded in a 9-coordinate geometry to four equivalent Tm, four equivalent Fe, and one Ge atom. The Ge–Ge bond length is 2.56 Å.

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Materials Data on Li(FeGe)6 by Materials Project

Li(FeGe)6 crystallizes in the hexagonal P6/mmm space group. The structure is three-dimensional. there are two inequivalent Li sites. In the first Li site, Li is bonded to twelve equivalent Fe and eight Ge atoms to form distorted corner-sharing LiFe12Ge8 hexagonal bipyramids. All Li–Fe bond lengths are 3.22 Å. There are two shorter (2.70 Å) and six longer (2.86 Å) Li–Ge bond lengths. In the second Li site, Li is bonded to twelve Fe and eight Ge atoms to form a mixture of distorted corner and face-sharing LiFe12Ge8 hexagonal bipyramids. There are six shorter (3.20 Å) and six longer (3.22 Å) Li–Fe bond lengths. There are two shorter (2.69 Å) and six longer (2.88 Å) Li–Ge bond lengths. There are two inequivalent Fe sites. In the first Fe site, Fe is bonded in a 12-coordinate geometry to two Li, four Fe, and six Ge atoms. All Fe–Fe bond lengths are 2.51 Å. There are four shorter (2.47 Å) and two longer (2.61 Å) Fe–Ge bond lengths. In the second Fe site, Fe is bonded in a 12-coordinate geometry to two equivalent Li, four equivalent Fe, and six Ge atoms. There are a spread of Fe–Ge bond distances ranging from 2.46–2.60 Å. There are four inequivalent Ge sites. In the first Ge site, Ge is bonded in a 8-coordinate geometry to one Li, six Fe, and one Ge atom. The Ge–Ge bond length is 2.61 Å. In the second Ge site, Ge is bonded in a 7-coordinate geometry to one Li and six Fe atoms. In the third Ge site, Ge is bonded in a 8-coordinate geometry to two equivalent Li and six Fe atoms. In the fourth Ge site, Ge is bonded in a 8-coordinate geometry to one Li, six equivalent Fe, and one Ge atom. The Ge–Ge bond length is 2.59 Å.

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Materials Data on Np(FeGe)2 by Materials Project

Np(FeGe)2 crystallizes in the tetragonal I4/mmm space group. The structure is three-dimensional. Np is bonded in a 8-coordinate geometry to eight equivalent Fe and eight equivalent Ge atoms. All Np–Fe bond lengths are 3.13 Å. All Np–Ge bond lengths are 3.09 Å. Fe is bonded to four equivalent Np and four equivalent Ge atoms to form a mixture of distorted corner, edge, and face-sharing FeNp4Ge4 tetrahedra. All Fe–Ge bond lengths are 2.32 Å. Ge is bonded in a 9-coordinate geometry to four equivalent Np, four equivalent Fe, and one Ge atom. The Ge–Ge bond length is 2.49 Å.

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Materials Data on Er9(FeGe)10 by Materials Project

Er9(FeGe)10 crystallizes in the orthorhombic Immm space group. The structure is three-dimensional. there are four inequivalent Er sites. In the first Er site, Er is bonded in a 7-coordinate geometry to four equivalent Fe and seven Ge atoms. There are two shorter (3.09 Å) and two longer (3.25 Å) Er–Fe bond lengths. There are a spread of Er–Ge bond distances ranging from 2.92–3.08 Å. In the second Er site, Er is bonded in a 7-coordinate geometry to five Fe and six Ge atoms. There are one shorter (2.95 Å) and four longer (3.13 Å) Er–Fe bond lengths. There are a spread of Er–Ge bond distances ranging from 2.82–3.09 Å. In the third Er site, Er is bonded in a 6-coordinate geometry to four equivalent Fe and six Ge atoms. All Er–Fe bond lengths are 3.15 Å. There are a spread of Er–Ge bond distances ranging from 2.89–3.21 Å. In the fourth Er site, Er is bonded in a 6-coordinate geometry to twelve Fe and two equivalent Ge atoms. There are four shorter (2.98 Å) and eight longer (3.20 Å) Er–Fe bond lengths. Both Er–Ge bond lengths are 2.93 Å. There are two inequivalent Fe sites. In the first Fe site, Fe is bonded in a 12-coordinate geometry to five Er, three Fe, and four Ge atoms. There are a spread of Fe–Fe bond distances ranging from 2.48–2.73 Å. There are a spread of Fe–Ge bond distances ranging from 2.47–2.56 Å. In the second Fe site, Fe is bonded in a 12-coordinate geometry to three Er, five Fe, and two equivalent Ge atoms. The Fe–Fe bond length is 2.61 Å. Both Fe–Ge bond lengths are 2.64 Å. There are four inequivalent Ge sites. In the first Ge site, Ge is bonded in a 10-coordinate geometry to eight Er and two equivalent Ge atoms. There are one shorter (2.67 Å) and one longer (2.68 Å) Ge–Ge bond lengths. In the second Ge site, Ge is bonded in a 9-coordinate geometry to five Er and four equivalent Fe atoms. In the third Ge site, Ge is bonded in a 9-coordinate geometry to five Er and four equivalent Fe atoms. In the fourth Ge site, Ge is bonded in a 10-coordinate geometry to four Er and six Fe atoms.

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Materials Data on Ho3(FeGe)4 by Materials Project

Ho3(FeGe)4 crystallizes in the orthorhombic Immm space group. The structure is three-dimensional. there are two inequivalent Ho sites. In the first Ho site, Ho is bonded in a 12-coordinate geometry to six equivalent Fe and six Ge atoms. There are two shorter (2.92 Å) and four longer (3.06 Å) Ho–Fe bond lengths. There are two shorter (2.92 Å) and four longer (3.03 Å) Ho–Ge bond lengths. In the second Ho site, Ho is bonded to six Ge atoms to form distorted edge-sharing HoGe6 octahedra. There are four shorter (2.93 Å) and two longer (2.98 Å) Ho–Ge bond lengths. Fe is bonded in a 4-coordinate geometry to three equivalent Ho, one Fe, and four Ge atoms. The Fe–Fe bond length is 2.43 Å. There are a spread of Fe–Ge bond distances ranging from 2.50–2.57 Å. There are two inequivalent Ge sites. In the first Ge site, Ge is bonded in a 9-coordinate geometry to three Ho and six equivalent Fe atoms. In the second Ge site, Ge is bonded in a 9-coordinate geometry to six Ho, two equivalent Fe, and one Ge atom. The Ge–Ge bond length is 2.63 Å.

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Materials Data on Tm(FeGe)6 by Materials Project

Tm(FeGe)6 crystallizes in the orthorhombic Immm space group. The structure is three-dimensional. there are two inequivalent Tm sites. In the first Tm site, Tm is bonded to twelve Fe and eight Ge atoms to form distorted TmFe12Ge8 hexagonal bipyramids that share corners with four equivalent TmFe12Ge8 hexagonal bipyramids, faces with eight equivalent FeTm2Fe4Ge6 cuboctahedra, and faces with four TmFe12Ge8 hexagonal bipyramids. There are a spread of Tm–Fe bond distances ranging from 3.24–3.28 Å. There are a spread of Tm–Ge bond distances ranging from 2.81–2.98 Å. In the second Tm site, Tm is bonded to twelve Fe and eight Ge atoms to form distorted face-sharing TmFe12Ge8 hexagonal bipyramids. There are eight shorter (3.26 Å) and four longer (3.27 Å) Tm–Fe bond lengths. There are a spread of Tm–Ge bond distances ranging from 2.80–2.98 Å. There are four inequivalent Fe sites. In the first Fe site, Fe is bonded in a 12-coordinate geometry to two equivalent Tm, four equivalent Fe, and six Ge atoms. All Fe–Fe bond lengths are 2.56 Å. There are four shorter (2.50 Å) and two longer (2.68 Å) Fe–Ge bond lengths. In the second Fe site, Fe is bonded to two equivalent Tm, four Fe, and six Ge atoms to form distorted FeTm2Fe4Ge6 cuboctahedra that share corners with four equivalent FeTm2Fe4Ge6 cuboctahedra, edges with two equivalent FeTm2Fe4Ge6 cuboctahedra, faces with four equivalent FeTm2Fe4Ge6 cuboctahedra, and faces with four equivalent TmFe12Ge8 hexagonal bipyramids. There are two shorter (2.56 Å) and two longer (2.57 Å) Fe–Fe bond lengths. There are a spread of Fe–Ge bond distances ranging from 2.50–2.68 Å. In the third Fe site, Fe is bonded in a 12-coordinate geometry to two equivalent Tm, four Fe, and six Ge atoms. Both Fe–Fe bond lengths are 2.55 Å. There are a spread of Fe–Ge bond distances ranging from 2.48–2.68 Å. In the fourth Fe site, Fe is bonded in a 12-coordinate geometry to two Tm, four Fe, and six Ge atoms. There are one shorter (2.56 Å) and one longer (2.57 Å) Fe–Fe bond lengths. There are a spread of Fe–Ge bond distances ranging from 2.51–2.67 Å. There are nine inequivalent Ge sites. In the first Ge site, Ge is bonded in a 12-coordinate geometry to three Tm and six Fe atoms. In the second Ge site, Ge is bonded in a 6-coordinate geometry to six Fe atoms. In the third Ge site, Ge is bonded in a 12-coordinate geometry to three Tm and six Fe atoms. In the fourth Ge site, Ge is bonded in a 6-coordinate geometry to six Fe atoms. In the fifth Ge site, Ge is bonded in a 8-coordinate geometry to two equivalent Tm and six Fe atoms. In the sixth Ge site, Ge is bonded in a 7-coordinate geometry to one Tm and six Fe atoms. In the seventh Ge site, Ge is bonded in a 8-coordinate geometry to one Tm, six Fe, and one Ge atom. The Ge–Tm bond length is 2.80 Å. All Ge–Fe bond lengths are 2.67 Å. The Ge–Ge bond length is 2.50 Å. In the eighth Ge site, Ge is bonded in a 8-coordinate geometry to one Tm, six Fe, and one Ge atom. Both Ge–Fe bond lengths are 2.68 Å. The Ge–Ge bond length is 2.50 Å. In the ninth Ge site, Ge is bonded in a 8-coordinate geometry to one Tm, six Fe, and one Ge atom. The Ge–Ge bond length is 2.49 Å.

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Materials Data on Er3(FeGe)4 by Materials Project

Er3(FeGe)4 crystallizes in the orthorhombic Immm space group. The structure is three-dimensional. there are two inequivalent Er sites. In the first Er site, Er is bonded to six Ge atoms to form distorted edge-sharing ErGe6 octahedra. There are four shorter (2.92 Å) and two longer (2.98 Å) Er–Ge bond lengths. In the second Er site, Er is bonded in a 12-coordinate geometry to six equivalent Fe and six Ge atoms. There are two shorter (2.92 Å) and four longer (3.06 Å) Er–Fe bond lengths. There are two shorter (2.91 Å) and four longer (3.02 Å) Er–Ge bond lengths. Fe is bonded in a 4-coordinate geometry to three equivalent Er, one Fe, and four Ge atoms. The Fe–Fe bond length is 2.43 Å. There are three shorter (2.50 Å) and one longer (2.57 Å) Fe–Ge bond lengths. There are two inequivalent Ge sites. In the first Ge site, Ge is bonded in a 9-coordinate geometry to three Er and six equivalent Fe atoms. In the second Ge site, Ge is bonded in a 9-coordinate geometry to six Er, two equivalent Fe, and one Ge atom. The Ge–Ge bond length is 2.63 Å.

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Materials Data on Tm3(FeGe)4 by Materials Project

Tm3(FeGe)4 crystallizes in the orthorhombic Immm space group. The structure is three-dimensional. there are two inequivalent Tm sites. In the first Tm site, Tm is bonded to six Ge atoms to form distorted edge-sharing TmGe6 octahedra. There are four shorter (2.91 Å) and two longer (2.97 Å) Tm–Ge bond lengths. In the second Tm site, Tm is bonded in a 12-coordinate geometry to six equivalent Fe and six Ge atoms. There are two shorter (2.91 Å) and four longer (3.06 Å) Tm–Fe bond lengths. There are two shorter (2.89 Å) and four longer (2.99 Å) Tm–Ge bond lengths. Fe is bonded in a 4-coordinate geometry to three equivalent Tm, one Fe, and four Ge atoms. The Fe–Fe bond length is 2.46 Å. There are a spread of Fe–Ge bond distances ranging from 2.48–2.55 Å. There are two inequivalent Ge sites. In the first Ge site, Ge is bonded in a 9-coordinate geometry to three Tm and six equivalent Fe atoms. In the second Ge site, Ge is bonded in a 9-coordinate geometry to six Tm, two equivalent Fe, and one Ge atom. The Ge–Ge bond length is 2.67 Å.

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Geometrically stabilized skyrmionic vortex in FeGe tetrahedral nanoparticles

The concept of topology has dramatically expanded the research landscape of magnetism, leading to the discovery of numerous magnetic textures with intriguing topological properties. A magnetic skyrmion is an emergent topological magnetic texture with a string-like structure in three dimensions and a disk-like structure in one and two dimensions. Skyrmions in zero dimensions have remained elusive due to challenges from many competing orders. Here, by combining electron holography and micromagnetic simulations, we uncover the real-space magnetic configurations of a skyrmionic vortex structure confined in a B20-type FeGe tetrahedral nanoparticle. An isolated skyrmionic vortex forms at the ground state and this texture shows excellent robustness against temperature without applying a magnetic field. Furthermore, our findings shed light on zero-dimensional geometrical confinement as a route to engineer and manipulate individual skyrmionic metastructures.

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Interacting spin and charge density waves in the kagome metal FeGe

Unveiling the interplay between spin density wave (SDW) and charge density wave (CDW) orders in correlated electron materials is important in obtaining a comprehensive understanding of their electronic, structural, and magnetic properties. Kagome lattice materials are interesting because their flat electronic bands, Dirac points, and Van Hove singularities can enable a variety of exotic electronic and magnetic phenomena. The kagome metal FeGe (the B35 phase), which exhibits a CDW order deep within an A-type antiferromagnetic (AFM) phase, was found to respond dramatically to postgrowth annealing—with the ability to tune the CDW repeatedly from long-range order to negligible order. Additionally, neutron scattering studies suggest that incommensurate magnetic peaks that onset at 𝑇 Canting = 𝑇 SDW ≈ 60 K in the system arise from a SDW order instead of the AFM double-cone structure. Here, in this study, we use inelastic neutron scattering to show that two distinct spin excitations exist below 𝑇 Canting corresponding to two coexisting magnetic orders in the system in both sets of annealed samples with and without CDW. While CDW order or negligible order can dramatically affect the onset temperature of 𝑇 Canting and elastic incommensurate magnetic scattering, its impact on low-energy spin fluctuations is more limited. In both samples, a pair of gapless incommensurate spin excitations arising from the SDW order wave vector coexist with gapped commensurate spin waves from the A-type AFM order across 𝑇 Canting . The low-energy spin excitations for both samples couple dynamically to the lattice through enhanced magnetic scattering intensity on cooling below 𝑇 CDW , regardless of the status of the static long-range CDW order. The incommensurate SDW order in the long-range CDW ordered sample also induces a tiny in-plane lattice distortion of the kagome lattice that is absent in the negligible CDW ordered sample, in a way that is different from the previously known SDW and CDW ordering materials.

charge density waves↗

Discovery of Charge Order and Corresponding Edge State in Kagome Magnet FeGe

Kagome materials often host exotic quantum phases, including spin liquids, Chern gap, charge density wave, and superconductivity. Existing scanning microscopy studies of the kagome charge order have been limited to nonkagome surface layers. Here, we tunnel into the kagome lattice of FeGe to uncover features of the charge order. Our spectroscopic imaging identifies a 2×2 charge order in the magnetic kagome lattice, resembling that discovered in kagome superconductors. Spin mapping across steps of unit cell height demonstrates the existence of spin-polarized electrons with an antiferromagnetic stacking order. We further uncover the correlation between antiferromagnetism and charge order anisotropy, highlighting the unusual magnetic coupling of the charge order. Finally, we detect a pronounced edge state within the charge order energy gap, which is robust against the irregular shape fluctuations of the kagome lattice edges. Here, we discuss our results with the theoretically considered topological features of the kagome charge order including unconventional magnetism and bulk-boundary correspondence.

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Materials Data on Hf(FeGe)6 by Materials Project

HfFe6Ge6 crystallizes in the hexagonal P6/mmm space group. The structure is three-dimensional. Hf is bonded to twelve equivalent Fe and eight Ge atoms to form distorted face-sharing HfFe12Ge8 hexagonal bipyramids. All Hf–Fe bond lengths are 3.23 Å. There are two shorter (2.76 Å) and six longer (2.92 Å) Hf–Ge bond lengths. Fe is bonded in a 12-coordinate geometry to two equivalent Hf, four equivalent Fe, and six Ge atoms. All Fe–Fe bond lengths are 2.53 Å. There are a spread of Fe–Ge bond distances ranging from 2.48–2.64 Å. There are three inequivalent Ge sites. In the first Ge site, Ge is bonded in a 8-coordinate geometry to one Hf, six equivalent Fe, and one Ge atom. The Ge–Ge bond length is 2.55 Å. In the second Ge site, Ge is bonded in a 12-coordinate geometry to three equivalent Hf and six equivalent Fe atoms. In the third Ge site, Ge is bonded in a 6-coordinate geometry to six equivalent Fe atoms.

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Materials Data on Tb(FeGe)2 by Materials Project

TbFe2Ge2 crystallizes in the tetragonal I4/mmm space group. The structure is three-dimensional. Tb is bonded in a 8-coordinate geometry to eight equivalent Fe and eight equivalent Ge atoms. All Tb–Fe bond lengths are 3.33 Å. All Tb–Ge bond lengths are 3.07 Å. Fe is bonded to four equivalent Tb and four equivalent Ge atoms to form a mixture of distorted corner, edge, and face-sharing FeTb4Ge4 tetrahedra. All Fe–Ge bond lengths are 2.43 Å. Ge is bonded in a 9-coordinate geometry to four equivalent Tb, four equivalent Fe, and one Ge atom. The Ge–Ge bond length is 2.53 Å.

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Materials Data on Yb(FeGe)2 by Materials Project

YbFe2Ge2 crystallizes in the tetragonal I4/mmm space group. The structure is three-dimensional. Yb is bonded in a 8-coordinate geometry to eight equivalent Fe and eight equivalent Ge atoms. All Yb–Fe bond lengths are 3.31 Å. All Yb–Ge bond lengths are 3.05 Å. Fe is bonded to four equivalent Yb and four equivalent Ge atoms to form a mixture of edge, face, and corner-sharing FeYb4Ge4 tetrahedra. All Fe–Ge bond lengths are 2.38 Å. Ge is bonded in a 9-coordinate geometry to four equivalent Yb, four equivalent Fe, and one Ge atom. The Ge–Ge bond length is 2.61 Å.

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Materials Data on La(FeGe)2 by Materials Project

LaFe2Ge2 crystallizes in the tetragonal I4/mmm space group. The structure is three-dimensional. La is bonded in a 8-coordinate geometry to eight equivalent Fe and eight equivalent Ge atoms. All La–Fe bond lengths are 3.40 Å. All La–Ge bond lengths are 3.20 Å. Fe is bonded to four equivalent La and four equivalent Ge atoms to form a mixture of distorted corner, edge, and face-sharing FeLa4Ge4 tetrahedra. All Fe–Ge bond lengths are 2.45 Å. Ge is bonded in a 9-coordinate geometry to four equivalent La, four equivalent Fe, and one Ge atom. The Ge–Ge bond length is 2.73 Å.

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Materials Data on U(FeGe)2 by Materials Project

UFe2Ge2 crystallizes in the tetragonal I4/mmm space group. The structure is three-dimensional. U is bonded in a 8-coordinate geometry to eight equivalent Fe and eight equivalent Ge atoms. All U–Fe bond lengths are 3.12 Å. All U–Ge bond lengths are 3.11 Å. Fe is bonded in a 4-coordinate geometry to four equivalent U and four equivalent Ge atoms. All Fe–Ge bond lengths are 2.32 Å. Ge is bonded in a 9-coordinate geometry to four equivalent U, four equivalent Fe, and one Ge atom. The Ge–Ge bond length is 2.48 Å.

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Materials Data on Mg(FeGe)6 by Materials Project

MgFe6Ge6 crystallizes in the hexagonal P6/mmm space group. The structure is three-dimensional. Mg is bonded to twelve equivalent Fe and eight Ge atoms to form distorted face-sharing MgFe12Ge8 hexagonal bipyramids. All Mg–Fe bond lengths are 3.21 Å. There are two shorter (2.72 Å) and six longer (2.91 Å) Mg–Ge bond lengths. Fe is bonded in a 12-coordinate geometry to two equivalent Mg, four equivalent Fe, and six Ge atoms. All Fe–Fe bond lengths are 2.52 Å. There are four shorter (2.47 Å) and two longer (2.62 Å) Fe–Ge bond lengths. There are three inequivalent Ge sites. In the first Ge site, Ge is bonded in a 12-coordinate geometry to three equivalent Mg and six equivalent Fe atoms. In the second Ge site, Ge is bonded in a 6-coordinate geometry to six equivalent Fe atoms. In the third Ge site, Ge is bonded in a 8-coordinate geometry to one Mg, six equivalent Fe, and one Ge atom. The Ge–Ge bond length is 2.55 Å.

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Materials Data on Nd(FeGe)2 by Materials Project

NdFe2Ge2 crystallizes in the tetragonal I4/mmm space group. The structure is three-dimensional. Nd is bonded in a 8-coordinate geometry to eight equivalent Fe and eight equivalent Ge atoms. All Nd–Fe bond lengths are 3.36 Å. All Nd–Ge bond lengths are 3.14 Å. Fe is bonded to four equivalent Nd and four equivalent Ge atoms to form a mixture of distorted face, edge, and corner-sharing FeNd4Ge4 tetrahedra. All Fe–Ge bond lengths are 2.45 Å. Ge is bonded in a 9-coordinate geometry to four equivalent Nd, four equivalent Fe, and one Ge atom. The Ge–Ge bond length is 2.62 Å.

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