# Incommensurate and commensurate antiferromagnetic orders in the kagome compound UV 6 Sn 6

Midori Amano Patino, Stéphane Raymond, Georg Knebel, Pierre Le Berre, Stanislav Savvin, E. Pachoud, Eric Ressouche, James Fettinger, Olivier Leynaud, Jacques Pecaut, et al.

► To cite this version:

Midori Amano Patino, Stéphane Raymond, Georg Knebel, Pierre Le Berre, Stanislav Savvin, et al. "Incommensurate and commensurate antiferromagnetic orders in the kagome compound UV 6 Sn 6." Physical Review B, 2025, 111 (17), pp.174432. 10.1103/PhysRevB.111.174432. hal-05222770

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Incommensurate and commensurate antiferromagnetic orders in the kagome
compound UV₆Sn₆

Midori Amano Patino,<sup>1,2</sup> Stephane Raymond,<sup>3</sup> Georg Knebel,<sup>2</sup> Pierre Le Berre,<sup>2</sup> Stanislav Savvin,<sup>4</sup>

Elise Pachoud,<sup>1</sup> Eric Ressouche,<sup>3</sup> James C. Fettinger,<sup>5</sup> Olivier Leynaud,<sup>1</sup> Jacques Pecaut,<sup>6</sup> Peter

Klavins,<sup>7</sup> Klaus Hasselbach,<sup>1</sup> Jean-Pascal Brison,<sup>2</sup> Gerard Lapertot,<sup>2</sup> and Valentin Taufour<sup>7,*</sup>

<sup>1</sup>Univ. Grenoble Alpes, CNRS, Grenoble-INP, Institut Néel, 38000 Grenoble, France

<sup>2</sup>Univ. Grenoble Alpes, CEA, Grenoble-INP, IRIG, Pheliqs, 38000 Grenoble, France

<sup>3</sup>Univ. Grenoble Alpes, CEA, IRIG, MEM, MDN, 38000 Grenoble, France

<sup>4</sup>Institut Laue Langevin, Grenoble, France

<sup>5</sup>Department of Chemistry, University of California, Davis, California 95616, USA

<sup>6</sup>Univ. Grenoble Alpes, CEA, IRIG-SyMMES, 38000 Grenoble, France

<sup>7</sup>Department of Physics and Astronomy, University of California, Davis, California 95616, USA

We report on the synthesis of single crystals of the kagome compound, UV₆Sn₆, and present the results of magnetization, electrical resistivity, heat capacity, x-ray, and neutron diffraction experiments to characterize the structure and magnetic properties. UV₆Sn₆ crystallizes in a large supercell of the HfFe₆Ge₆ parent structure with an hexagonal symmetry in which some of the U atoms are shifted by c/2 in an ordered fashion. Below T<sub>N1</sub> ≈ 29 K, an incommensurate magnetic structure with a temperature-dependent wave vector (0, 0, k<sub>z</sub>) is observed. Below T<sub>N2</sub> = 23.5 K, the wave vector locks in to (0, 0, 0.5), forming an antiferromagnetic ground state. The U moments align along the c axis retaining a large magnetic anisotropy. These findings highlight the role of the 5f orbitals from uranium in this structural family in driving both magnetic ordering and structural modulation and distinguish UV₆Sn₆ from its lanthanide-based analogs.

# I. Introduction

Materials containing kagome networks have attracted a lot of attention for the study of topologically nontrivial phases, and intertwined orders [1–3]. Among them, the 166 family of compounds, characterized by the general formula RT₆X₆, represents a fertile platform for investigating the rich interplay of topology, electron correlations, and magnetism. The R element can be a rare-earth element or Li, Mg, Ca, Ti, Zr, Hf, T is a transition metal element, and X is typically a tetrel element such as Sn or Ge. In these materials, the kagome lattice, a two-dimensional network of corner-sharing triangles, facilitates the emergence of exotic phenomena, including charge density waves (CDWs) [4–6], phonon softening [7–9], gapped Dirac fermions and surface states [10–12], a nodal ring [13], anomalous and topological Hall effects [14–16], anomalous Nernst effect [17, 18], and an extraordinary structural diversity [19–26].

This combination of structural and electronic features has made the 166 family an important class of materials for studying the interplay of magnetic order, topology, and electron correlations. In this paper, we report on the synthesis and characterization of a recent member of the 166 family, UV₆Sn₆. The introduction of uranium in the lattice structure may give rise to rich magnetic and electronic properties due to the strong spin-orbit coupling and the duality between localized and itinerant character of the uranium 5f electrons. We find evidence for a superstructure in the *ab* plane in UV₆Sn₆, where addi-

tional Bragg peaks are observed both in x-ray and neutron diffraction experiments. Below T<sub>N1</sub> ≈ 29 K, the U moments order antiferromagnetically in an incommensurate magnetic structure, as detected by neutron scattering. A commensurate antiferromagnetic ground state is observed below 23 K. From resistivity and heat capacity data, we show that UV₆Sn₆ is a weakly correlated metal.

# II. Methods

Single crystals of UV₆Sn₆ were grown using a self-flux method similar to that reported for YV₆Sn₆ [11]. Natural uranium ingots (99.27% <sup>238</sup>U, 0.72% <sup>235</sup>U, trace <sup>234</sup>U, from an internal stock at CEA Grenoble) were cut in ~0.5 g pieces and cleaned by electrolytic etching to remove the oxides on the surface [27]. Some crystals were grown at UC Davis following the same procedure with natural uranium from the NBL Program office (99.24% <sup>238</sup>U, 0.72% <sup>235</sup>U, trace <sup>234</sup>U). Vanadium pieces (99.9%, Aldrich) and tin shots (99.999%, Thermo Fisher Scientific) were cleaned with 30 vol.% HCl (Sigma-Aldrich). The clean metals were introduced in a Canfield crucible set [28, 29] in the 1:6:20 molar ratio, and sealed in a silica ampoule with 1/3 atm argon gas. The ampoule was heated to 1150 °C in 7 h, held there for 36 h, slowly cooled to 1050 °C in 287 h. At 1050 °C, the formed crystals were decanted by removing the ampoule from the furnace, inverting it, and immediately spinning it in a centrifuge [30]. Only crystals of UV₆Sn₆ were obtained with this temperature profile. The experiments with cooling to 780 °C resulted in additional single crystals of USn₃. The as-synthesized UV₆Sn₆ single crystals exhibit a metallic gray color and hexagonal pyra-

<footnote>* vtaufour@ucdavis.edu</footnote>
midal morphology with edge lengths of 0.3–0.8 mm (volume ~0.02–0.33 mm³, Fig. 1d). Laue x-ray diffraction confirms that the *c* axis is oriented perpendicular to the hexagonal base, while the *a* and *b* axes extend toward the in-plane hexagonal vertices.

Single-crystal x-ray diffraction data were collected at 100–150 K using the four-circle Kappa geometry diffractometers: Rigaku XCallibur (Rigaku CrysAlis CCD software), and Bruker D8 Venture (APEX software). In both instruments, a Mo *K*α radiation source was used (0.71073 Å). The structural refinement was carried out using the crystallography software package GSAS-II [31].

Magnetization measurements were performed using an MPMS3 SQUID magnetometer (Quantum Design) in VSM scan mode. The crystallographic axes of the sample were determined using Laue diffraction followed by polishing to obtain a flat surface perpendicular to the *c* axis.

Resistivity measurements were performed in a physical property measurement system (PPMS, Quantum Design) using a four point lock-in technique; 15 µm Au wires were spot welded to the sample for electrical contacts. Due to the irregular shape of the sample and the unperfect alignment of the electrical contacts, absolute values of the resistivity were not determined. The specific heat was measured using the PPMS with the heat pulse relaxation method; heat pulses of 0.5, 1, and 2% of the actual temperature gave similar results. The samples for specific heat had masses of 1.45 and 0.9 mg, thus the specific heat of the sample was small compared to the addenda contribution.

Neutron diffraction experiments were carried out at Institut Laue Langevin, Grenoble on the two-axis diffractometer D23 and the large solid angle detector diffractometer XtremeD. A single-crystal sample with a mass of 1.48 mg was pre-aligned using x-ray diffraction (Laue method) with the *b* axis oriented vertically, so the horizontal scattering plane was (*a**, *c**) in a hexagonal setting. D23 is equipped with a lifting detector reaching 30° and neutrons of wavelength 1.28 Å and 2.36 Å were used with a copper monochromator and a pyrolitic graphite (PG) monochromator, respectively. In this latter case, a PG filter was inserted in the incoming beam to remove higher order contamination. On XtremeD, the wavelength of 2.45 Å provided by a PG monochromator was used, the angular coverage of the detector was of 130° in the horizontal plane and 24° in the vertical plane. A PG filter was also installed. An oscillating radial collimator was placed in front of the detector bank to suppress the sample environment contribution to the collected data and reduce background. For both experiments, the sample was inserted in an helium flow cryostat. The MAG2POL software was used to refine the nuclear and magnetic structures [32].

### III. Results and discussion

#### A. Crystal structure

The structure of UV₆Sn₆ can be described as a 7 × 7 modulation of a HfFe₆Ge₆-type cell on the *ab* plane. In the latter *parent* cell (hexagonal symmetry, space group P6/mmm), the V atoms form a kagome network and the U atoms form a triangular lattice which stack in layers along the *c* crystallographic axis (Fig. 1a-c). Ignoring the superstructure first, a model of this HfFe₆Ge₆-type parent cell can be refined against single-crystal x-ray diffraction data with full occupancy for all sites, as summarized in Table I of Appendix A.

Although the goodness-of-fit value of 1.76 (GOF, Table I in Appendix A) suggests reasonable agreement between the measured and calculated average intensities, the high value of the weighted profile factor, *wR*2 = 20.76%, reveals a significant discrepancy between the observed and calculated structure factors.

Careful examination of both the x-ray and neutron diffraction data revealed that the discrepancies with the HfFe₆Ge₆-type model arise from very weak intensity at some families of Bragg reflections and the presence of additional satellite reflections around them. Notably, it was at the instrument XtremeD at ILL that we first observed these satellite reflections (see Appendix B), motivating further x-ray diffraction experiments. The satellite reflections are particularly evident in the reconstruction of reciprocal space (calculated precession images) centered on planes *hkl*, with *l* = 3 and *h* = 2, from x-ray diffraction data (Fig. 2b,e). On the *hk*3 plane (Fig. 2b), we clearly observe groups of satellite reflections around the expected Bragg reflections (e.g. 003, 103, and 013 marked in blue in Fig. 2a), as well as along the *h* and *k* directions, forming a triangular grid. Meanwhile, on the *2kl* plane (Fig. 2e), the apparent discrepancy in the expected peak intensity and the presence of satellite reflections are evident for all odd values of *l* (i.e., *l* = 1, 3, 5, etc.).

We note that due to the anomalous intensity and satellite reflections occurring at *l* = odd planes, a refinement using a structural model with a lattice parameter of *c*/2 relative to the HfFe₆Ge₆-type cell yields an improved *wR*2 of 10.05% (details in the Appendix C). This structural model corresponds to a YCo₆Ge₆-type cell, which is related to the HfFe₆Ge₆-type structure by a *c*/2 translation, a halving of the unit cell along *c* and a resulting 50% occupancy at the U and Sn atomic positions along the *c* axis (positions 1*a* and 2*c* in Table III of Appendix C, Fig. 10). This cell type is therefore often referred to as a disordered Y₀.₅Co₃Ge₃-type structure. During this study, a monoclinic distortion of the YCo₆Ge₆-type cell with an incommensurate structural wave vector was independently reported for UV₆Sn₆ with even better *wR*2 [33]. The halving of the unit cell along *c* means that the *l* = odd planes are no longer integers, so Bragg reflections are not expected there, requiring an
<figure><img src="image_2.png" /><figcaption>FIG. 1. The HfFe₆Ge₆-type parent structure of UV₆Sn₆, where the V atoms (red) form a kagome network (a), and the U atoms (blue) form a triangular lattice (b). The V kagome and U triangular lattices arrange in layers to form the structure depicted in (c), where the V and Sn atoms around U form a hexagonal cavity represented as a polyhedron. A picture of a representative single-crystal sample on a millimeter grid is shown in (d). The ordering of the cavities can lead to patterns such as the one shown in (e). These patterns extend the structures of RT₆X₆ compounds into supercells, like the one depicted in (f). The structure of UV₆Sn₆ can be described as a supercell where a periodic modulation of the HfFe₆Ge₆-type parent cell—marked in black in (f), yields a 7 × 7 superstructure on the ab plane. The hexagonal cavities occupied by a U shift along the c axis by c/2 yielding the pattern shown in (e). This pattern is identical along the b crystallographic axis (a = b).</figcaption></figure>

additional incommensurate structural wave vector. The YCo₆Ge₆-type structure has also been reported for the compound UFe₆Ge₆ [34], and was originally reported for DyFe₆Sn₆ and HoFe₆Sn₆ [35]. However, similar to the latter cases, we found that this YCo₆Ge₆-type model does not accurately represent our UV₆Sn₆ structure.

We discovered that the satellite reflections observed in the diffraction patterns of UV₆Sn₆ can be accounted for by a supercell arising from a modulation of the HfFe₆Ge₆-type parent cell. The modulation corresponds to a periodic expansion of the parent unit cell by a factor of 7 along the *a* and *b* axes (Fig. 1d-e), yielding a 7 × 7 superstructure in the *ab* plane. There is no evidence of cell expansion along *c*. The crystal symmetry remains hexagonal, P6/mmm, and the supercell lattice parameters are *a* = *b* = 38.548(2) Å; *c* = 9.154(1) Å, with α = β = 90°; γ = 120°. As detailed in the Appendix D, this modulation arises from the ordering of hexagonal cavities occupied by uranium in UV₆Sn₆ (Fig. 1c,e,f; these cavities are also referred to as voids in the literature). This type of ordering is observed in other RT₆X₆ compounds,

compounds, leading to patterns that extend the structures into supercells with modulations ranging from 2 to 68 parent unit cells [21, 22]. These atomic arrangements are explained by electrostatic and steric (size-related) effects, which impose preferences regarding the simultaneous occupation of neighboring cavities along *c* [22]. We note that in contrast to other modulated structures such as RFe₆Sn₆ with *R* = Er, Y, Tb [22], the modulation in our UV₆Sn₆ superstructure retains the hexagonal symmetry. An orthorhombic or monoclinic cell with a single *q* modulation such as the one proposed in Ref. [33] only accounts for a pair of satellite reflections rather than the six we observe in the *hk*3 plane in Fig. 2b. It is possible that our observations result from triply twinned crystals with the monoclinic structure proposed by Thomas *et al* [33]. From diffraction data collected from various single crystals of different sizes—including some of dimensions comparable to those reported for x-ray diffraction in Ref. [33], we consistently observe satellite reflections that retain the global hexagonal symmetry within the *ab* plane. This is also observed in the neutron diffraction
<figure><img src="image_3.png" /></figure>

FIG. 2. Comparison of the calculated and observed reconstructions of the reciprocal space centered on planes *hk3* and *2kl* for UV₆Sn₆. The calculated diffraction patterns in (a) and (d) show the expected Bragg spots (reflections, marked in blue) for a HfFe₆Ge₆-type cell on planes *hk3* and *2kl*, respectively. The observed *hk3* pattern in (b) shows undetectable intensity at the expected Bragg spots and the presence of six satellite reflections around them. Additional satellite reflections are observed along *h* and *k* directions. The observed *2kl* pattern in (e), indexed in the HfFe₆Ge₆-type cell, shows discrepancies in the intensity of the expected Bragg reflections, as well as satellite peaks on either side of the Bragg spots along *k*ᵢ. These unexpected features are true for every *l* = odd value (i.e., *l* = 1, 3, 5, etc.). Our simulated diffraction patterns for an expanded 7 × 7 cell (Fig. 1e-f) replicate the observed precession images for the *hk3* and *2kl* planes (14*kl* in the expanded cell), as shown in (c) and (f), respectively. The inset in (f) provides a magnified view at *l* = 3, where the satellites along *k*ᵢ are observed.

data shown in Fig. 9 of Appendix B. It is thus likely that we have crystallized a high-temperature structure with a hexagonal symmetry, different from the monoclinic structure reported in Ref. [33]. This is possible considering the different temperature profile compared to that in Ref. [33]. A sensitivity to the thermal treatment for the stabilization of different crystal structures has been reported for other RT₆X₆ phases [36, 37], and may be critical for understanding the tunability of the magnetic and charge ordered phases of RMn₆Sn₆, RFe₆Ge₆ and LnNb₆Sn₆ (Ln = lanthanide), respectively [3, 26, 38].

In our proposed extended cell of UV₆Sn₆, the uranium-occupied hexagonal cavities shift along the *c* axis by *c*/2 from their original position in the HfFe₆Ge₆-type parent structure, as illustrated in Fig. 1e. Labelling the shifts

of the hexagonal cavities as *z* = 0 for the original position and *z* = ½ for the *c*/2 shifted (in orange and blue, respectively, in Fig. 1e), the resulting pattern along the *a* and *b* crystallographic axes is 0, 0, ½, ½, ½, ½, 0. There is nearly an equal number of *z* = 0 and *z* = ½ sites in the supercell (25 and 24). This further explains why a refinement against the YCo₆Ge₆-type cell, with 50% occupancy at the U sites, yields a reasonable fit. Refinement of this supercell is challenging due to the large number of parameters and data points. However, the simulated diffraction patterns for our proposed UV₆Sn₆ expanded cell accurately replicate the diffracted spots observed in the reconstructed precession images, as demonstrated in Figs. 2c,f.

As noted above, the superstructure of UV₆Sn₆ is sig-
nificantly different from other $RT_6X_6$ compounds. While the atomic sizes and lattice parameters in UV$_6$Sn$_6$ are similar to those of other $RV_6Sn_6$ compounds (where R = Y, Sm, Gd, Dy-Lu), most of these compounds typically adopt either the undistorted, non modulated $HfFe_6Ge_6$-type structure or the partially disordered $SmMn_6Ge_6$-type structure (with the $YCo_6Ge_6$-type at the fully disordered extreme) [26, 37]. We observe that, generally, larger radii at R seem to lead to modulated structures, which could be explained from the expansion of the hexagonal cages (Fig. 1c), which imposes additional steric constraints. The superstructure in UV$_6$Sn$_6$ might also be driven by the spatially extended nature of the U 5f orbitals.

As will be discussed below, we do not find evidence of a CDW state in UV$_6$Sn$_6$. This contrasts with the closely related compound $ScV_6Sn_6$ [4, 6]. The radius of Sc, ~ 0.89 Å, is considerably smaller than that of U, ~ 1.14 Å, (VIII-coordinate Shannon radius [39] as compared in Ref. [26]). An additional consequence of the expansion of the hexagonal cavities when occupied by atoms with increasing radii is the reduction of Sn–Sn distances. This bond shortening limits the displacement of Sn along the *c* axis, thus suppressing the “rattling” R-Sn-Sn-*R* bond modulation, identified as a potential CDW instability in $ScV_6Sn_6$ [6, 26, 40].

## B. Magnetization

The magnetization data collected from a single crystal of UV$_6$Sn$_6$, with a field of 1 T applied parallel and perpendicular to the crystallographic *c* axis, is presented in Fig. 3. The magnetization as a function of temperature reveals a strong magnetic anisotropy, with the *c* axis being the easy magnetization axis (Fig. 3a). Along the *ab*-plane, the magnetization remains low and nearly constant across the entire temperature range. Notably, the magnetization parallel to the *c* axis exhibits a clear maximum at $T_{N1}$ ≈ 29 K. A second transition occurring at approximately 23 K is also revealed as a kink in the magnetization curve (inset Fig. 3a and Fig. 12 in Appendix E). The effective magnetic moment, derived from the Curie-Weiss fit which holds down to about 70 K (Fig. 3b) along the *c* axis, is found to be 3.89(1) µ$_B$/U. This value is slightly higher than the effective moment of the U$^{3+}$ or U$^{4+}$ configurations. The polycrystalline averaged susceptibility ($\chi_{avg} = \frac{1}{3}\chi_c + \frac{2}{3}\chi_{ab}$) does not follow the Curie-Weiss behavior over a large temperature range, indicating the importance of the crystal electric field (CEF). A detailed CEF analysis was recently reported [33]. The results indicate that the first excited CEF level is between 18 to 25 meV, consistent with an isolated ground state of easy-axis moments [33].

The magnetization isotherms $M(H)$ collected at 2 K are shown in Fig. 3c. When the magnetic field is applied parallel to the *c* axis, a clear hysteresis effect is observed, along with two notable changes in the magnetization.

There is a sharp change in slope at approximately 3 T, followed by a tendency towards saturation starting around 4 T. The magnetization at 6 T is roughly 1 $\mu_B$, which is lower than the ordered moment of the free U ion. However, as discussed below, the magnetization at 6 T does not correspond to the fully polarized moment.

<figure><img src="image_4.png" /><figcaption>FIG. 3. (a) Temperature dependence of the magnetization under an applied magnetic field of 1 T parallel and perpendicular to the *c* axis. Inset: Enlarged view at low temperatures. The arrows indicate the anomalies at the two transitions. (b) Temperature dependence of the inverse susceptibility at 1 T along the *c*-axis and for a polycrystalline average: $\chi_{avg} = \frac{1}{3}\chi_c + \frac{2}{3}\chi_{ab}$. The dashed line is a fit to the Curie-Weiss law. (c) Magnetic field dependence of the magnetization at 2 K for the field parallel and perpendicular to the *c* axis.</figcaption></figure>
### C. Resistivity

The temperature dependence of the normalized electric resistivity at magnetic fields of 0 and 9 T applied along the *c* axis is presented in Fig. 4. The resistivity ratio $RRR = R(300\text{K})/R(1.8\text{K}) \approx 3$ is rather low. A similar value was reported recently [33]. On cooling the resistivity first increases slightly and shows a maximum around 180 K. At high temperatures, no magnetoresistance occurs and down to 90 K the temperature dependence at 9 T is similar to that at zero magnetic field. On further cooling, the resistivity shows a marked kink at the onset of the magnetic order near $T_{N1} \approx 29$ K (see Fig. 4b). At 6 T, the magnetic transition is still visible by a clear kink, while it disappears at 9 T.

Figure 4c presents the derivative of the normalized resistivity as a function of temperature. It shows a mean-field-like anomaly at the transition, as expected from the Fisher-Langer behavior $d\rho/dT \propto C_p$, often observed in metallic systems [41, 42]. In particular, we do not observe an increase of resistivity upon lowering the temperature through the magnetic transition, unlike other incommensurate antiferromagnets due to the opening of a superzone gap in the electronic band structure [43–48]. This may be due to the electrical current direction being perpendicular to the magnetic wave vector (see neutron scattering and the magnetic structure discussion below).

In the temperature derivative of the resistivity we observe a second anomaly at $T_{N2} \approx 23$ K. This indicates a change of the magnetic structure, as discussed below in section III E.

### D. Heat capacity

The temperature dependence of the specific heat divided by temperature ($C_p/T$) below 40 K is displayed in Fig. 5. $C_p/T$ shows two anomalies which correspond to the magnetic transitions. While the anomaly at $T_{N1} \approx 29$ K is well defined and looks mean-field-like, the anomaly at $T_{N2} \approx 23$ K is tiny and rather broad. This indicates that the entropy change at $T_{N2}$ is rather small and is due to a change in the magnetic structure. The inset in Fig. 5 shows $C_p/T$ as a function of $T^2$. From the linear fit, we extract the Sommerfeld coefficient $\gamma = 15 \text{ mJ mol}^{-1} \text{K}^{-2}$ and the coefficient of the cubic term $\beta = 2.95 \text{ mJ mol}^{-1} \text{K}^{-4}$. This shows that UV₆Sn₆ is a weakly correlated U compound and magnetism is mainly due to localized 5f electrons. Although a larger $\gamma$ was obtained, a similar conclusion was reached in a recent study [33]. This is also in agreement with the susceptibility measurements, where the large effective moment is observed almost down to $T_{N1}$ (see Fig. 3b). It is also in accordance with the large U-U spacing in the unit cell, which is far above the Hill limit [49].

A combined plot of $dM/dT$, $C_p/T$, and $d\rho/dT$ as a function of $T$ is presented in Fig. 12 in Appendix E. $T_{N1}$ and $T_{N2}$ are confirmed from the three data sets.

<figure><img src="image_5.png" /><figcaption>FIG. 4. (a) Temperature dependence of the electrical resistivity at magnetic fields of 0 T and at 9 T applied along the *c* axis, normalized to the value at 300 K. (b) Zoom of the low temperature range for fields of 0, 6, and 9 T. The arrows indicate the magnetic ordering temperature $T_{N1}$. (c) Temperature derivative of the resistivity at zero field as a function of temperature. The arrows show the magnetic transition temperatures $T_{N1}$ and $T_{N2}$.</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>FIG. 5. Specific heat divided by temperature vs temperature of UV₆Sn₆ at zero magnetic field. The arrows indicate the position of $T_{N1} = 28.8$ K and $T_{N2} = 23$ K. The inset shows $C_p$ as a function of $T^2$. The dashed line is a linear fit to $C_p/T = \gamma + \beta T^2$ and we determine $\gamma = 15 \text{ mJ mol}^{-1} \text{K}^{-2}$ and $\beta = 2.95 \text{ mJ mol}^{-1} \text{K}^{-4}$.</figcaption></figure>

In Fig. 6a, we show the field dependence of the spe-
<figure><img src="image_7.png" /><figcaption>FIG. 6. (a) Specific heat divided by temperature at selected *T* values as a function of increasing magnetic fields. (b) Field dependence of the specific heat at 10 K in an enlarged view. (c) Magnetic phase diagram for field *H* || *c* from the field dependent specific heat measurements (increasing fields). (Lines are guides to the eyes.) An additional phase boundary within the AFM1 region was inferred from thermal expansion measurements [33].</figcaption></figure>

cific heat at various temperatures for increasing magnetic
fields. As shown explicitly in Fig. 6b for the curve at 10
K, a first increase of the specific heat is observed at 2.5 K
while a very marked anomaly occurs at 7.7 K. While the
low field anomaly for all temperatures is very small, the
high field anomaly appears as a very pronounced peak
with a first-order like behavior at 15 and 20 K. From these
anomalies, a magnetic phase diagram can be proposed as
illustrated in Fig. 6c. The low field anomaly is associated
with a change in the magnetic structure, as discussed be-
low.

E. Neutron scattering and magnetic structure

Mapping of the reciprocal space along the high-
symmetry lines of the Brillouin zone was carried out
on D23 with the copper monochromator to identify the
magnetic ordering wave vector at 1.41 K. The outcome
is the identification of a single wave vector that is de-
scribed below. Given the complexity of the UV₆Sn₆
crystal structure (Fig. 1), we approach the magnetic
structure characterization from the HfFe₆Ge₆-type par-
ent cell. Figure 7 shows scans around the momentum
transfer **Q** = (1, 0, 0.5) along the directions *Q*<sub>H</sub> (panel
a), *Q*<sub>K</sub> (panel b) and *Q*<sub>L</sub> (panel c) respectively, at 1.5 K
and 30 K. The coordinates of the momentum transfer **Q**
are given in reciprocal lattice units (r.l.u.). These data
clearly establish that the position of the magnetic peak
is **Q** = (1, 0, 0.5), which corresponds to the propagation
vector **k**=(0, 0, 0.5). The magnetic ground state is thus
antiferromagnetic (commensurate). The same magnetic
wave vector was recently reported from powder neutron
diffraction at 2 K [33]. The temperature dependence of
the intensity at the peak position **Q** = (1, 0, 0.5) is shown
in Fig. 8a. The signal vanishes at *T*<sub>N2</sub> = 23.5 K. To de-
termine the magnetic structure, a collection of magnetic
peaks was undertaken and is limited to eight peaks (7 in-
dependent ones) due to the weak signal associated with
the small sample for neutron diffraction experiment. The
scale factor and the extinction correction are obtained
from nuclear peaks (44 independent reflections). Among
the structural parameters given in Table I, the isotropic
thermal displacements (except for vanadium which has a
very small coherent neutron scattering cross section) and
the *z* position of Sn3 are refined yielding values consis-
tent with the x-ray refinement. The magnetic form factor
*f*(*Q*) is fixed to the one of U<sup>3+</sup> in the dipolar approxi-
mation *f*(*Q*)=j<sub>0</sub>(*Q*)+C<sub>2</sub>j<sub>2</sub>(*Q*) using the value C<sub>2</sub>=1.75,
where j<sub>0</sub>(*Q*) and j<sub>2</sub>(*Q*) are spherical Bessel functions [50].
All the magnetic reflections with **Q** parallel to the *c* axis,
namely, (0, 0, 0.5), (0, 0, 1.5) and (0, 0, 2.5), have zero in-
tensity, which, according to neutron scattering selection
rules point to the fact that the magnetic moment must
lie along the *c* axis. The magnitude of the moment is cal-
culated to be 1.43(3) µ<sub>B</sub>. The refined magnetic structure
is shown in Fig.8b.

Above $T_{N2}$, the search for the ordering wave vector was performed on XtremeD at ILL. A representative acquisition on the detector bank is shown in Fig.7d for a temperature of 24.9 K. It is obtained by rotating the single crystal sample with a step of 0.2° and an acquisition time of approximatively 10 minutes. A peak is observed at a position corresponding to the momentum transfer **Q** = (1, 0, 0.45). This incommensurate position is found to be temperature dependent and further measurements were performed on D23 to investigate this using the PG monochromator. The obtained temperature variation of the incommensurate position is shown in Fig.8c through the temperature dependence of the neutron intensity as a function of $Q_L$. Hence, the AFM1 phase is incom-
<figure><img src="image_8.png" /><figcaption>FIG. 7. Momentum transfer cuts obtained on D23 at 1.41 K (full blue circles) and 30 K (open red circles) along (a) **Q** = (Q<sub>H</sub>, 0, 0.5), (b) along **Q** = (1, Q<sub>K</sub>, 0.5), and (c) **Q** = (1, 0, Q<sub>H</sub>). Full lines are fits to Gaussian and dashed lines serve as guides to the eyes. (d) Neutron intensity obtained on the XtremeD detector bank at 24.9 K for the sample rotation angle achieving diffraction condition for the peak (1, 0, 0.45) (green spot).</figcaption></figure>

mensurate at zero magnetic field (the evolution of the propagation vector under magnetic field where additional phase boundaries are observed [33] is not addressed in the present paper). The temperature dependence of the Q_L-direction integrated intensity is shown in Fig. 8a. The intensity collapses at T_N1 ≈ 29 K. There is a temperature range near T_N2, where both antiferromagnetic and incommensurate phases coexist, in agreement with a transition of the first order. In addition, the mapping capabilities of XtremeD allow us to confirm that only the antiferromagnetic propagation vector **Q** = (1, 0, 0.5) is present at 1.5 K.

Among rare-earth based RV₆Sn₆ compounds, the magnetic structures were determined for *R* = Gd by resonant x-ray diffraction [51] and for *R* = Tb, Dy, Ho, Er by neutron diffraction [52]. In GdV₆Sn₆, two transitions are observed at 3.8 K and 5.2 K. In the high temperature phase, only an incommensurate propagation vector, **k**=(0, 0, *q*<sub>IC</sub>), is observed, with a small temperature dependence of *q*<sub>IC</sub> ranging between 0.46 and 0.47. Below the second transition, it coexists with a commensurate component **k**=(0, 0, 0.5) down to the lowest measured temperature of 2 K. A lock-in at lower temperatures is suggested. The magnetic moments lie presumably predominantly in the basal plane of the structure. TbV₆Sn₆, DyV₆Sn₆ and HoV₆Sn₆ are ferromagnetic materials with transition temperatures at 4.3 K, 3 K and 2.4 K respectively and moments along the *c* axis, except for *R* = Dy, where a 20° tilt toward the *a* axis is found. ErV₆Sn₆ is antiferromagnetic below 0.6 K with the propagation vector **k**=(0, 0, 0.5) and the magnetic moments along the *a* axis in the hexagonal plane. In these heavy rare-earth

<figure><img src="image_9.png" /><figcaption>FIG. 8. (a) Temperature dependence of the intensity at **Q** = (1, 0, 0.5) (left scale) and of the integrated intensity at **Q** = (1, 0, Q<sub>L</sub>) (right scale). (b) Sketch of the antiferromagnetic ground state structure (color of atoms as in Fig. 1). (c) Color-coded temperature dependence of the neutron intensity as a function of temperature and Q<sub>L</sub>.</figcaption></figure>

compounds, the magnetic moment lies in the range 6-9 µ<sub>B</sub> (while it is not determined for GdV<sub>6</sub>Sn<sub>6</sub>).

The magnetic structure of UV₆Sn₆ is distinct from each one reported for its rare-earth counterparts: it adopts the antiferromagnetic propagation vector common to Gd and Er compounds but the moment direction found in the Tb and Ho ones. One can also notice the highest transition temperature by almost one order of magnitude as compared to the rare-earth systems. The magnetic moment for 1.42(3) µ<sub>B</sub> is in the typical range of values found in uranium intermetallics. The ground-state antiferromagnetic phase is made of ferromagnetic planes, with presumably a strong exchange interaction given the positive Curie-Weiss temperature and with an antiferromagnetic stacking along the *c* axis involving likely a smaller interaction. The observed full lock-in transition from the incommensurate to the antiferromagnetic structure with decreasing temperature could be related to the highest transition temperature as compared to the Gd system, where the lock-in is partial. An interesting and open question concerns the arrangement of the spins in the supercell, of which determination goes beyond the present paper. One can mention the simplest structure
where all spins in the $z = 0$ and $z = 1/2$ layers (see notations above) of the supercell would be ferromagnetic. In this case, the global structure can be seen as composed of antiferromagnetic blocks made of the magnetic structure as described here in the $HfFe_6Ge_6$ cell with "sliding defects" in the structure at the boundary between $z = 0$ and $z = 1/2$ layers. Another related global description of the magnetic structure can be made in the $YCo_6Ge_6$ model, having a halving of the $c$ axis parameter and half occupancy of uranium sites (see above), where the magnetic arrangement is of type "+ - - -" with a propagation vector $k = (0, 0, 0.25)$.

tigation. Exploring pressure or chemical doping could help clarify the interplay between uranium's 5f-driven structural modulations and the vanadium kagome network in $UV_6Sn_6$. Applying pressure may suppress the $7 \times 7 \times 1$ supercell, providing insights into the relationship between steric and electronic contributions to the modulation, and shed some light on competing orders. Doping may tune the hybridization between the 5f and 3d orbitals in the kagome network. Such studies would advance our understanding of both the structural complexity of $UV_6Sn_6$ and the broader class of 166 kagome compounds.

## IV. Conclusion

Our study reveals that the $UV_6Sn_6$ structure deviates from the $HfFe_6Ge_6$-type structure commonly reported for $RT_6X_6$ systems. The structure is best described as a $7 \times 7 \times 1$ modulation of the $HfFe_6Ge_6$-type parent cell on the ab plane, driven by an ordering pattern of the uranium atoms. This model replicates the observed features in x-ray and neutron diffraction data.

Magnetic characterization from magnetization and neutron diffraction measurements demonstrate two successive magnetic transitions at $T_{N1} \approx 29$ K and $T_{N2} = 23.5$ K. The first transition corresponds to an incommensurate antiferromagnetic ordering that locks to a commensurate antiferromagnetic ground state at $T_{N2}$. This behavior suggests competing exchange interactions. The slightly large effective moment (3.89(1) $\mu_B$/U) and strong uniaxial anisotropy along the $c$ axis point to significant spin-orbit coupling, a hallmark of uranium-based systems.

Our paper opens several future research avenues. The superstructure of $UV_6Sn_6$ emphasizes the unique role of uranium's 5f orbitals. The complexity of the crystallographic and magnetic structures invites further inves-

### A. Acknowledgements

We thank E. Bauer, P. Rosa, S. Thomas for letting us know about Ref. [33] as well as for sharing additional x-ray diffraction data. M.A.P. thanks F. Denis Romero for fruitful discussions about crystallography. M.A.P. and V.T. acknowledge funding from the Laboratoire d'excellence LANEF in Grenoble (ANR-10-LABX-51-01) and the support from the US National Science Foundation (NSF) Grant No. 2201516 under the Accelerated program of the Office of International Science and Engineering (OISE). P.L.B. was supported by QuantEdu-France (ANR-22-CMAS-0001). We further acknowledge financial support from the French National Agency for Research ANR within Project FRESCO (ANR-20-CE30-0020) and SCATE (ANR-22-CE30-0040).

### B. Data availability

The data that support the findings of this article are openly available [53, 54]. The rest of the data are available upon reasonable request from the authors.

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## A. Appendix A: Details of structural refinement of UV$_6$Sn$_6$ using a HfFe$_6$Ge$_6$-type model

The structural parameters and anisotropic parameters assuming a HfFe$_6$Ge$_6$-type structure are presented in tables I and II.

<table><caption>TABLE I. Structural parameters for UV$_6$Sn$_6$ refined against single-crystal x-ray diffraction data (Bruker D8 Venture, Mo K$_{\alpha}$ radiation, collected at 100 K). The isotropic displacement parameters ($U_{iso}$) are given in Å$^2 \times 10^3$. The anisotropic parameters are provided in Table. II.</caption><thead><tr><th>Atom</th><th>Site</th><th>x</th><th>y</th><th>z</th><th>Occ.</th><th>U<sub>iso</sub></th></tr></thead><tbody><tr><td>U</td><td>1a</td><td>0</td><td>0</td><td>0</td><td>0.991(5)</td><td>9.4(3)</td></tr><tr><td>Sn1</td><td>2d</td><td>1/3</td><td>2/3</td><td>1/2</td><td>0.990(9)</td><td>5.9(2)</td></tr><tr><td>Sn2</td><td>2c</td><td>1/3</td><td>2/3</td><td>0</td><td>0.981(9)</td><td>5.5(2)</td></tr><tr><td>Sn3</td><td>2e</td><td>0</td><td>0</td><td>0.3434(1)</td><td>1.000</td><td>6.2(1)</td></tr><tr><td>V</td><td>6i</td><td>1/2</td><td>0</td><td>0.2489(3)</td><td>1.000</td><td>6.9(4)</td></tr></tbody><tfoot><tr><td colspan="7">Space group P6/mmm (No. 191)</td></tr><tr><td colspan="7">a = b = 5.5082(1) Å; c = 9.1537(5) Å;</td></tr><tr><td colspan="7">α = β = 90°; γ = 120°</td></tr><tr><td colspan="7">GOF = 1.76, wR2 = 20.76%</td></tr></tfoot></table>

<table><caption>TABLE II. Anisotropic displacement parameters (Å$^2 \times 10^3$) for the UV$_6$Sn$_6$ structure summarized in Table I, refined using a HfFe$_6$Ge$_6$-type model against single-crystal x-ray diffraction data (Bruker D8 Venture, Mo K$_{\alpha}$ radiation, collected at 100 K).</caption><thead><tr><th>Atom</th><th>U<sub>11</sub></th><th>U<sub>22</sub></th><th>U<sub>33</sub></th><th>U<sub>12</sub></th><th>U<sub>13</sub></th><th>U<sub>23</sub></th></tr></thead><tbody><tr><td>U</td><td>6.4(4)</td><td>6.4(4)</td><td>15.3(5)</td><td>3.2(2)</td><td>0.00</td><td>0.00</td></tr><tr><td>Sn1</td><td>2.5(4)</td><td>2.5(4)</td><td>12.7(2)</td><td>1.3(1)</td><td>0.00</td><td>0.00</td></tr><tr><td>Sn2</td><td>2.4(3)</td><td>2.4(3)</td><td>11.8(2)</td><td>1.2(1)</td><td>0.00</td><td>0.00</td></tr><tr><td>Sn3</td><td>2.7(2)</td><td>2.7(2)</td><td>13.2(3)</td><td>1.4(1)</td><td>0.00</td><td>0.00</td></tr><tr><td>V</td><td>4.2(8)</td><td>3.9(7)</td><td>12.5(4)</td><td>2.0(5)</td><td>5.0(9)</td><td>0.00</td></tr></tbody></table>

## B. Appendix B: Evidence of superstructure in neutron diffraction

As mentioned in the main text, the superstructure peaks associated with the UV$_6$Sn$_6$ supercell were first observed using XtremD. Figure 9 shows representative data for the satellites associated with the (2, 0, -3) reflection (in the HfFe$_6$Ge$_6$-type cell) obtained from the XtremD detector bank at 27 K. These satellites were also observed
on D23 with the same positions at 24 K and 150 K, which rules out their link to the magnetic ordering below 29 K evidenced in this paper.

<figure><img src="image_10.png" /><figcaption>FIG. 9. Raw data as observed on the large solid angle XtremeD detector.</figcaption></figure>

### C. Appendix C: Refinement using a YCo₆Ge₆-type model

The YCo₆Ge₆-type structure is related to the HfFe₆Ge₆-type by a c/2 translation, and a halving of the unit cell along the c axis and of the occupancy at the U and Sn atomic positions, as illustrated in Fig. 10 (positions 1a and 2c in Table III). For this model, the HfFe₆Ge₆-type cell odd-l planes are no longer integers. This means that Bragg reflections are not expected at those values of l during refinement. Although refinement of this YCo₆Ge₆-type model against x-ray diffraction data leads to a reduced wR2 (Table III), it does not accurately describe the UV₆Sn₆ structure as discussed in the main text.

<table><caption>TABLE III. Structural parameters for UV₆Sn₆ refined using an YCo₆Ge₆-type model against single-crystal x-ray diffraction data (Rigaku XCallibur, Mo Kα radiation, collected at 150 K). The isotropic displacement parameters ($U_{iso}$) are given in Å² × 10³. The anisotropic parameters are provided in Table IV.</caption><thead><tr><th>Atom</th><th>Site</th><th>x</th><th>y</th><th>z</th><th>Occ.</th><th>U<sub>iso</sub></th></tr></thead><tbody><tr><td>U</td><td>1a</td><td>0</td><td>0</td><td>0</td><td>0.496(3)</td><td>8.6(8)</td></tr><tr><td>Sn1</td><td>2d</td><td>1/3</td><td>2/3</td><td>0</td><td>1.000</td><td>7.4(7)</td></tr><tr><td>Sn2</td><td>2c</td><td>0</td><td>0</td><td>0.322(1)</td><td>0.503(3)</td><td>7.7(9)</td></tr><tr><td>V</td><td>6i</td><td>1/2</td><td>0</td><td>1/2</td><td>1.000</td><td>7.0(9)</td></tr></tbody><tfoot><tr><td colspan="7">Space group P6/mmm (No. 191)<br/>a = b = 5.5124(2) Å; c = 4.5800(2) Å;<br/>α = β = 90°; γ = 120°</td></tr><tr><td colspan="7">GOF = 2.41, wR2 = 10.05%</td></tr></tfoot></table>

<figure><img src="image_11.png" /><figcaption>FIG. 10. The YCo₆Ge₆-type structure results from the superposition of the HfFe₆Ge₆-type cell depicted in (a) and its c/2 shifted version depicted in (b), sometimes referred to as the MgFe₆Ge₆-type structure. The resulting YCo₆Ge₆-type structure shown in (c), as two stacked cells along the c axis for clarity, exhibits statistical occupancy at the crystallographic sites along the c lattice parameter (details in Table III).</figcaption></figure>

<table><caption>TABLE IV. Anisotropic displacement parameters (Å² × 10³) refined for the YCo₆Ge₆-type structure of UV₆Sn₆ summarized in Table III.</caption><thead><tr><th>Atom</th><th>U<sub>11</sub></th><th>U<sub>22</sub></th><th>U<sub>33</sub></th><th>U<sub>12</sub></th><th>U<sub>13</sub></th><th>U<sub>23</sub></th></tr></thead><tbody><tr><td>U</td><td>6.6(8)</td><td>6.6(8)</td><td>12.6(8)</td><td>3.3(7)</td><td>0.00</td><td>0.00</td></tr><tr><td>Sn1</td><td>5.8(7)</td><td>5.8(7)</td><td>10.7(7)</td><td>2.9(3)</td><td>0.00</td><td>0.00</td></tr><tr><td>Sn2</td><td>5.1(9)</td><td>5.1(9)</td><td>13.1(9)</td><td>2.5(5)</td><td>0.00</td><td>0.00</td></tr><tr><td>V</td><td>5.1(8)</td><td>4.5(7)</td><td>11.4(9)</td><td>2.2(6)</td><td>0.2(9)</td><td>0.00</td></tr></tbody></table>

### D. Appendix D: RT₆X₆ supercells

To understand the origin of the satellite reflections observed in the diffraction patterns of UV₆Sn₆, the structure can be described as a variant of the stuffed CoSn-type cell depicted in Fig. 11. The CoSn-type structure comprises alternating layers of Sn honeycomb lattices and Sn-centered Co kagome networks (Fig. 11a-b). The HfFe₆Ge₆-type structure emerges when a rare-earth atom is introduced into the Sn honeycomb lattice, at the origin of the unit cell (as shown in Fig. 11a). The atomic environment for the rare-earth atom, and for U in the case of UV₆Sn₆, can be described as a cavity with hexagonal symmetry (Fig. 11c). The occupation of these hexagonal cavities in RT₆X₆ compounds leads to patterns that extend the structures into superstructures.
<figure><img src="image_12.png" /></figure>

FIG. 11. The CoSn-type structure is formed by alternating layers of (a) Sn honeycomb lattices and (b) Sn-centered Co kagome networks (Sn in gray and Co in green). The resulting structure depicted in (c)—note two unit cells are stacked along *c*-leads to the HfFe₆Ge₆-type structure when a rare-earth is introduced in (a), at the origin of the unit cell (marked in blue). The surrounding atoms at this position form a hexagonal cavity represented as a polyhedron in (c). Electrostatic and steric (size-related) effects impose preferences regarding the simultaneous occupation of neighboring cavities along *c* [22]. These preferences may lead to patterns that extend the unit cell into a supercell such as (d).

Figure 12, presents a comparison of the temperature dependence of the magnetization derivative, $dM/dT$–for a magnetic field applied along the *c* axis, the resistivity derivative, $dρ/dT$, and the specific heat divided by temperature, $C_p/T$. The arrows mark the magnetic transition temperatures $T_{N1}$ and $T_{N2}$. Rather good agreement is observed between the different measurements. The only slight discrepancy is that $T_{N2}$, as determined from the resistivity, appears slightly higher. This difference may arise from the use of a different single-crystal sample for that particular measurement.

E. Appendix E: Comparison of $T_N$

<figure><img src="image_13.png" /></figure>

FIG. 12. Determination of transition temperatures $T_{N1}$ and $T_{N2}$ by the temperature derivative of the magnetization for $H \parallel c$ (red) measured at 1 T, the resistivity (green, 0 T), and specific heat (blue, 0 T).