Superconducting YAu3Si and Antiferromagnetic GdAu3Si with an Interpenetrating Framework Structure Built from 16-Atom Polyhedra

Investigations of reaction mixtures REx(Au0.79Si0.21)100–x (RE = Y and Gd) yielded the compounds REAu3Si which adopt a new structure type, referred to as GdAu3Si structure (tP80, P42/mnm, Z = 16, a = 12.8244(6)/12.7702(2) Å, and c = 9.0883(8)/9.0456(2) Å for GdAu3Si/YAu3Si, respectively). REAu3Si was afforded as millimeter-sized faceted crystal specimens from solution growth employing melts with composition RE18(Au0.79Si0.21)82. In the GdAu3Si structure, the Au and Si atoms are strictly ordered and form a framework built of corner-connected, Si-centered, trigonal prismatic units SiAu6. RE atoms distribute on 3 crystallographically different sites and each attain a 16-atom coordination by 12 Au and 4 Si atoms. These 16-atom polyhedra commonly fill the space of the unit cell. The physical properties of REAu3Si were investigated by heat capacity, electrical resistivity, and magnetometry techniques and are discussed in the light of theoretical predictions. YAu3Si exhibits superconductivity around 1 K, whereas GdAu3Si shows a complex magnetic ordering, likely related to frustrated antiferromagnets exhibiting chiral spin textures. GdAu3Si-type phases with interesting magnetic and transport properties may exist in an extended range of ternary RE–Au–Si systems, similar to the compositionally adjacent cubic 1/1 approximants RE(Au,Si)∼6.


INTRODUCTION
Polar intermetallic compounds of gold with electropositive and post-transition metals/semimetals from groups 12−14 display peculiarities in their structural chemistry and physical properties, which has been attributed to the extraordinarily high electronegativity of gold (which is the highest among metallic elements) and associated relativistic effects in chemical bonding. 1 The family of gold polar intermetallics is rather diverse and also includes icosahedral quasicrystals (iQCs), such as i-Na−Au−Ga, i-Ca−Au−Al(Ga)(In), i-RE−Au−Al (RE = Yb and Tm), i-RE−Au−Sn (RE = Ca and Yb), and a larger range of 1/1 cubic approximant crystal (AC) phases. 2− 11 The majority of gold-based iQCs are of Tsai-type 12 and also contain rare-earth (RE) elements. These iQCs have attracted considerable attention because of expectations about unique physical properties associated to the quasiperiodic structure. 13, 14 Tsai-type iQCs are distinguished by their atomic cluster building unit ("Tsai-cluster") consisting of four concentric shells and centered by a tetrahedral moiety. 15 The radial dimension of a Tsai-cluster in gold-based iQCs is 15−16 Å. Their related 1/1 ACs are also built from Tsai-clusters and have similar chemical composition but are conventional (3D periodic) crystals. 16 In both Tsai-type QCs and 1/1 ACs, RE atoms are arranged into icosahedra which represent one of the shells of a Tsai-cluster. AC phases play a pivotal role by providing local structural information (from standard crystallographic techniques) needed to determine the structures of iQCs and by providing references for physical properties of 3D periodic systems. Since the stability of Tsai-type QCs is linked to a very narrow valence electron per atom ratio, 1/1 ACs are found much more frequently than QCs. 17 There are many phase diagrams (i.e., RE−Au−Si and RE−Au−Ge) for which hitherto only the 1/1 AC phase is known.
We recently reported that for Tsai-type 1/1 ACs in RE− Au−Si systems (RE; e.g., Gd, Tb, and Ho) the central tetrahedron of the Tsai clusters can be systematically replaced by a single RE atom, giving rise to a distinctly different variant of 1/1 AC phase with a composition RE ∼15.4 (Au,Si) ∼84. 6 instead of RE ∼13.6 (Au,Si) ∼86. 4 . 18 The regular ((Au,Si) tetrahedron centered) and RE-centered phase were termed AC(IT) and AC(CC), respectively. During the course of this study we discovered an even more RE-rich phase, which formed from the peritectic decomposition of AC(CC) at temperatures above 900°C. In this paper, we report on the strictly Au,Si ordered structure and the physical properties of REAu 3 Si (RE = Y and Gd). With an RE content of 20 at. % the structure of REAu 3 Si significantly deviates from the Tsai-type cluster based and Au,Si disordered 1/1 AC structure, yet locally similarities are maintained (i.e., a 16-atom coordination environment for RE and icosahedral arrangement of RE atoms).

METHODS
2.1. Synthesis. The starting materials were granules of the elements Gd and Au (Chempur 99.99%), Y (Chempur 99.9%), and Si (Highways International 99.999%). Prior the synthesis reactions, Au and Si were arc-melted in a ratio 79:21 (at. %) corresponding to the eutectic composition in the Au−Si phase diagram. The arc-melting procedure was repeated five-times to get homogeneous ingot. Actual reaction mixtures then constituted compositions Gd x (Au 0.79 Si 0.21 ) 100−x with x in the range of 15−18. Reaction mixtures were investigated with differential scanning calorimetry (DSC) prior to solution-growth synthesis to extract liquid temperatures. Synthesis reactions targeting REAu 3 Si were carried out in alumina (Al 2 O 3 ) crucibles from LSP Industrial Ceramics (USA), in the form of "Canfield Crucible Sets (CCS)". The CCS consists of two flat-bottomed cylindrical crucibles and an alumina frit-disc with holes of ∼0.7−1 mm in diameter designed to separate solid grains from the liquid melt during centrifugation. 19 A total mass of about 3 g was weighed inside a glovebox (Ar-atmosphere, <0.1 ppm O 2 ) and loaded into the CCS, which was then encapsulated inside a stainless-steel ampule. Ampules were heated in a commercial multistep programmable muffle furnace to 1050°C over a period of 10 h and dwelled for 3 h to ensure a homogeneous melt. Subsequently, the temperature was lowered to 920°C using a cooling rate of 1°C/h, and reactions were terminated by isothermally centrifuging off excess melt at the target temperatures.
2.2. Phase and Structure Analysis. The samples were studied with powder X-ray diffraction (PXRD), single-crystal X-ray diffraction (SCXRD), DSC, scanning electron microscopy (SEM) coupled with energy-dispersive X-ray spectroscopy (EDX), and magnetic property measurements. A Bruker D8 powder diffractometer with θ−2θ diffraction geometry and a Cu Kα radiation (Kα 1 = 1.540598 Å and Kα 2 = 1.544390 Å) was used for collecting PXRD intensities at room temperature. PXRD data were analyzed with the HighScore Plus 3.0 software from PANalytical 20 and the Fullprof Suite. 21 Powdered samples were applied to a zero-diffraction plate, and diffraction patterns were measured in a 2θ range of 7−90°. A Bruker D8 VENTURE single-crystal X-ray diffractometer with Mo Kα radiation (Kα = 0.71073 Å) with Incoatec microfocus source (IμS 3.0) and Photon II CCD area detector was utilized to collect SCXRD intensities at room temperature. Diffraction data covering a half (full) sphere in reciprocal space were collected with 100% completeness. SCXRD data reduction and numerical absorption corrections were carried out using the APEX III software from Bruker. 22 The crystal structure was solved and refined using the software SHELXT 23 and JANA2006, 24 respectively. The structures were visualized using Diamond 3.2K4. 25 Electron densities were visualized using the software VESTA. 26 DSC measurements were carried out with a NETZSCH STA 449 F1 Jupiter instrument. Sample specimens (typically faceted grains, REAu 3 Si) with total mass of ∼50 mg were placed in polycrystalline sapphire crucibles (OD = 5 mm, ID = 4 mm) and a heating/cooling cycle to 1150°C was carried out at a rate of 10°C /minute under an Ar flow of ∼40 mL/min. An empty crucible served as reference. The crucibles used for the actual DSC measurement were first carried through identical heating/cooling protocol to the sample and the data were used as background. Scanning electron microscopy (SEM) investigations employed a Zeiss−Merlin instrument equipped with energy-dispersive X-ray (EDX) spectroscopy for elemental analysis with X-Max 80 mm 2 Silicon Drift Detector with high sensitivity and high count rates. Prior to the SEM/EDX experiments samples were cross section polished gently for 20 h using Ar + -ion beam in a Cross-Section Polisher SM-09011 instrument from JEOL. EDX data was collected with an acceleration voltage of 20 kV over larger areas (∼100 × 100 μm 2 ) on at least 20 points.
2.3. Physical Property Measurements. (Polycrystalline) samples for physical property measurements were prepared from pieces of crushed specimens obtained from the solution-growth synthesis experiments. Direct current (dc) magnetization measurements (on ∼10 mg sample specimens) were carried out using an MPMS XL SQUID magnetometer equipped with a superconducting magnet (up to ±50 kOe) and a Physical Property Measurement System (PPMS) with a superconducting magnet (up to ±90 kOe), both from Quantum Design, Inc. Heat capacity measurements were carried out using a Bluefors dilution refrigerator equipped with a superconducting magnet (up to ±120 kOe). The heat capacity data was collected down to 100−200 mK on tiny sample fragments (with a volume of approximately 1 × 10 5 μm 3 ) using a differential membranebased nanocalorimeter. 27 We calibrated the specific-heat values in molar unit by multiplying the heat capacity data by a constant to match the model curve of γT + C D at high temperatures, where γ is the electronic specific heat coefficient (we determined γ = 1 mJ/K 2 mol for GdAu 3 Si and YAu 3 Si) and C D is the specific heat of the Debye model (we determined the Debye temperature θ D = 170 K for GdAu 3 Si and θ D = 193 K for YAu 3 Si); see also ref 28. The electrical resistivity (for sample specimens with dimension ∼0.2 × 0.25 × 1 mm 3 ) was measured using the conventional four-probe method with the dilution refrigerator and the PPMS.
2.4. Theoretical Calculations. The ground state of GdAu 3 Si was studied theoretically using a first-principles density functional theory (DFT) approach within the projector-augmented wave (PAW) method 29 as implemented in Vienna Ab Initio Simulation Package (VASP). 30−32 The generalized gradient approximation in its Perdew-Burke-Erzernhof flavor for exchange and correlation potential and energy was used. 33 All simulations of magnetic properties were done using the Molecular Dynamics Monte Carlo (MDMC) method. 34 Standard approach at 0 K is to compare known magnetic orderings (for example, FM and simple AFM) and choose the state with the lowest total energy. In the case of complex magnetism, like different ferrimagnetic states, such an approach easily misleads to a wrong ground-state magnetic structure. The MDMC method 34 solves this issue. It finds the proper magnetic ordering in the course of standard first-principles calculations. At 0 K, the method is based on a Monte Carlo (MC) technique and efficiently explores the whole phase space of magnetic structures. At higher temperatures, the method takes care of coupling between spins and atomic vibrations via AIMD, and in particular can treat non-Heisenberg systems. Only collinear 0 K MDMC simulations were carried out in this work. Further, the obtained magnetic structures were tested by the noncollinear version of VASP and found to be collinear. All calculations referred to the 80 atom unit cell of magnetic GdAu 3 Si. The structures were relaxed to p = 0 GPa with the accuracy of few kbar. A 2 × 2 × 2 k-point Monkhorst−Pack grid 35 was used for all integrations over the Brillouin zone. LDA+U approximation in Dudarev's formulation 36 with U = 6 eV was applied on the f-electron states of Gd. 37 All the calculations were done at temperature T = 0 K. The energy cutoff for plane waves was set to 400 eV. were terminated by centrifuging off isothermally excess liquid. High-melt crystallization typically affords ultrapure, singlecrystalline products. 38 For x up to 10−11 they corresponded to regular 1/1 AC phase with an orientationally disordered (Au,Si) 4 tetrahedron at the Tsai-cluster center ((AC(IT)) cf. inset in Figure 1). For higher x (12−13), a variant of the 1/1 AC phase with a single RE atom at the cluster center was found (AC(CC)). 18,28 In this case, centrifugation temperatures above 800°C had to be employed, and it is not (yet) clear whether the AC(CC)-phases are thermodynamically stable at low temperatures or represent high-temperature phases. The RE content in the AC(CC) phases is significantly increased (which has profound consequences to their magnetic properties 18 ). However, the Au/Si composition of the AC(IT) and A C ( C C ) p h a s e s , R E 1 3 . 6 ( A u ∼ 0 . 8 2 S i ∼ 0 . 1 8 ) 8 6 . 4 a n d RE 15.4 (Au ∼0.81 Si ∼19 ) 84.6 , respectively, are very close to nominally employed Au 0.79 Si 0.21 which justifies the pseudobinary approach. AC(CC) phases undergo peritectic decomposition at around 900°C into melt and a phase even more rich in RE. 18,28 This observation stimulated the extension of solution-growth experiments to the more RE-rich side for which melts with x ≈ 18 and centrifugation temperatures around 920°C were employed. For this study, RE = Y and Gd were chosen. As typical of this method, large (millmeter-sized) and facetted crystal specimens could be isolated (inset in Figure 2). EDX analyses of the synthesis products resulted in Gd 21.1(2) Au 60.9(2) Si 18.0(1) and Y 19.7(1) Au 62.5(1) Si 17.8(1) ; see Figure  S1. This pointed strongly to a stoichiometric composition REAu 3 Si and indicates that with increasing RE content (x > 17−18) the phase diagram cannot be considered anymore as pseudobinary RE x (Au 0.79 Si 0.21 ) 100−x . Figure 2 shows the PXRD patterns for GdAu 3 Si and YAu 3 Si. These are very similar and can be indexed to a primitive tetragonal lattice with a ≈ 12.8 Å and c ≈ 9.05 Å. The whole diffraction profile fitting of the patterns, using the structure model obtained from SCXRD refinement, is shown in Figure S2. Figure 3 shows the DSC traces for GdAu 3 Si and YAu 3 Si upon a heating and cooling cycle. The small event at 870/850°C (heating/cooling) for GdAu 3 Si is attributed to melting/ crystallization of a small amount of residual flux with the composition Au ∼0.9 Si ∼0.1 on the surface of the employed crystal specimen. The event at 1045/1040°C indicates the liquid/ solid temperature for the composition Gd 20 Au 60 Si 20 and most likely corresponds to congruent melting/solidification of GdAu 3 Si, since the sample specimen after the DSC cycle appeared spherical and the PXRD pattern was virtually unchanged. In contrast, the heating trace of YAu 3 Si shows several smaller but distinguished endothermic events before the pronounced event indicating formation of liquid phase (at around 1000°C). An annealing experiment at 875°C (after the first endothermic event) produced a mixture of YAu 3 Si and AC(CC) phase (see Figures S3). Thus, the thermal behavior of YAu 3 Si remains unclear. It may be suspected that this compound represents a (metastable) high-temperature phase     Table 1 and independent atomic positions and displacement parameters are listed in Table 2. The primitive tetragonal unit cell (space group P4 2 /mnm (#136)) contains 80 atoms which are distributed over 9 crystallographically independent sites: 5 Au, 3 Gd, and 1 Si. There is no detectable chemical (Au/Si) disorder, which is characteristic for the 1/1 AC systems. However, unlike in the GdAu 3 Si compound, an 8i Au position was found positionally disordered in YAu 3 Si (see Figure S4).
Hence, the position was modeled as a mutually exclusive Au3/ Au3′ split position with ∼0.93/0.07 occupancies, respectively. Furthermore, the atomic displacement parameters for YAu 3 Si are about twice that for GdAu 3 Si. This and the positional disorder may also be indicating a room temperature metastable nature of YAu 3 Si. The following description of the structure will be based on the parameters for GdAu 3 Si. Table 3 lists relevant interatomic distances (an extended distance table is given in Table S1).
The GdAu 3 Si structure may be described using the Gd coordination polyhedra which possess the local symmetries 4e (2mm), 4f (m2m), and 8i(m), as shown in Figure 4a. Each Gd atom is surrounded by 12 Au and 4 Si atoms, which provide a well-defined coordination shell with Gd−(Au,Si) distances in a range of 3.03−3.47 Å (cf. Table 3), clearly separated from next-nearest-neighbor distances starting off at 4.43 Å. The three kinds of polyhedra commonly provide space filling (Figure 4b). Their linkage can also be visualized as interpenetrating network (Figure 4c): Gd1 polyhedra are condensed into rows along the [001] direction via shared rectangular faces. These rows are linked by Gd2 polyhedra in the [110] direction to yield a primitive cubic arrangement with channels along (1/2, 0, z), which is the direction of the 4 2 axes. This network is interpenetrated by the framework formed by Gd3 polyhedra. Gd3 polyhedra are clustered into rows (via the 4 2 operations) along the c-direction and rows are connected via rectangular faces in the [110] direction. Si atoms are strictly coordinated by 6 Au atoms in a trigonal prismatic fashion (Si− Au distances are in a narrow range 2.45−2.59 Å, cf. Table 3), and the Au 3 Si partial structure corresponds to an array of corner connected SiAu 6/2 trigonal prisms (Figure 4d). Considering REAu 3 Si as polar intermetallics, the Au 3 Si substructure bears a polyanionic character. In this picture, bonding between Au−Au and Au−Si atoms is of a strong covalent nature, whereas interactions between RE (RE 3+ ) and Au/Si are essentially electrostatic. In the electronic density of states (DOS) of REAu 3 Si states near the Fermi level originate from Au−d states with minor contributions from Si and Gd orbitals (cf. Figure S5). This resembles strongly to other goldrich polar intermetallics, such as RE 3 Au 7 Sn 3 , for which a pronounced polar intermetallic character has been proven from detailed bonding analyses. 39 Yet a different view of the GdAu 3 Si structure is provided when analyzing the Gd partial structure and identifying Gd2 atoms at the center of icosahedra formed by 4 Gd1 and 8 Gd3 atoms (Figure 5a). Gd2−Gd distances are in a range of 4.73− 5.42 Å, and the edge lengths are between 3.94 and 5.42 Å (cf. Table 3). These icosahedral clusters in turn are arranged in a bcc-like (8 + 6) fashion (Figure 5b), where the nearestneighbor centers (8) are 7.9 Å apart and the distance to the next-nearest-neighbor centers is on average 9.1 Å (Figure 5c). The icosahedral arrangement of Gd reminds of to the 1/1 AC structure, albeit icosahedra in the tetragonal GdAu 3 Si structure are more distorted and in addition appear more compressed (the center to corner distances of 1/1 AC icosahedra are in a range of 5.2−5.71 Å). 18 Similar to the cubic 1/1 AC structure, the tetragonal GdAu 3 Si structure may represent a robust structure type that is realized for a larger number of REAu 3 Si and REAu 3 Ge compounds and thus could provide a playground for studying various physical properties and property changes when varying RE. In the following, we show superconductivity for YAu 3 Si and a peculiar magnetic behavior for GdAu 3 Si. Due to structural (positional) disorder in YAu 3 Si, the data collection strategy was extended to cover a full-sphere in reciprocal space with narrow step widths and longer exposure times; more parameters were refined. b The relatively higher GOF values come partly from using the program Jana2006.
Inorganic Chemistry pubs.acs.org/IC Article 3.3. Superconducting YAu 3 Si. Figure 6a shows the temperature dependence of the electrical resistivity for YAu 3 Si. We observe a superconducting behavior at T c = 0.94 K. The double-step behavior is attributed to a minor impurity of AC(CC) phase included in the YAu 3 Si grain which was used for this measurement. The Y−Au−Si AC(CC) phase has a slightly higher T c . 28 The presence of tiny amounts of an AC(CC) impurity phase was also found for GdAu 3 Si, and the reason for this is not clear since solution grown sample specimens are typically single phase. The impurity phase cannot be detected in PXRD and SEM analyses or specific heat measurements. It expresses only in the resistivity and low-field magnetization data. Figure 6b shows the normalized electronic specific heat divided by temperature (C el /γ n T) as a function of normalized temperature (T/T c ), where C el indicates the electronic contribution to the specific heat, and γ n = 1.1 mJ/K 2 mol is the electronic specific heat coefficient in the normal state. Note that we subtracted the phonon contribution (estimated from the C/T vs T 2 plot) from the specific heat to estimate C el . This confirms the bulk nature of the superconductivity. The overall behavior is similar to the weak-coupling Bardeen−Cooper− Schrieffer (BCS) model, suggesting that the superconductivity of YAu 3 Si is of a conventional BCS type. We plot the upper critical field (H c2 ) versus temperature in the inset of Figure 6b. From the lowest temperature value of H c2 , we estimate H c2 (0) ≈ 3.9 kOe. From the data near T c , we obtain dH c2 /dT = −4.86 kOe/K (cf. the solid line in the inset of Figure 6b), which allows us to estimate the orbital critical field at zero temperature using the Werthamer−Helfand−Hohenberg formula (in the dirty limit): 40 H c2 orb (0) = −0.693T c (dH c2 /dT) ≈ 3.15 kOe. The H c2 orb (0) value is close to H c2 (0); thus, the orbital effect mainly contributes to H c2 (rather than the spin paramagnetic effect). 40 The estimated values of superconducting parameters are listed in Table 4. From the specific heat, we estimate the thermodynamic critical field H c by calculating the condensation energy. The Ginzburg−Landau (GL) parameter κ at T = 0 is then estimated from the relation H H 2 c2 c κ = . 41,42 Since 1/ 2 κ ≫ , the superconductivity must be of type-II. See the caption of Table 4 for the other parameters. The overall superconducting behavior is similar to the Y−Au−Si   Figures S8 and S9). 3.4. Antiferromagnetic GdAu 3 Si. The GdAu 3 Si structure type provides a new type of magnetic sublattice forming a network of distorted icosahedron-like polyhedra (cf. Figure 5). We observe a Curie−Weiss behavior of the magnetic susceptibility M/H above ∼50 K with an effective magnetic moment of p eff = 7.99 μ B /Gd (see Figure S10), which is in good agreement with the theoretical value for a free Gd 3+ ion (7.94 μ B /Gd). The estimated Curie−Weiss temperature is θ p ≈ −10 K, indicating that antiferromagnetic interactions are dominant. Figure 7a shows the temperature dependence of the magnetization (plotted as M/H) under the magnetic field of H = 5 and 50 kOe. We observe anomalies (denoted by T A , T B , and T m *) in the M−T curve. Figure 7b shows the M−H curves. We observe a slight meta-magnetic-like jump at H m * ∼ 10 kOe and a linear behavior above H m ** ∼ 50 kOe, indicating possible changes in the configuration of magnetic order, yet the overall feature is of antiferromagnetic-type. See Figures S11−S15 for more detailed magnetization data. Figures 7c,d shows the temperature and magnetic field dependence of the electrical    Figure 8a depicts the temperature dependence of the specific heat (plotted as C/T) under various magnetic fields at low temperatures. We observe two notable peaks corresponding to T A and T B , suggesting two-step magnetic transitions. The peak at T A is sharp for H ≤ 10 kOe, becomes broad in the range of 15 ≲ H ≲ 40 kOe, again becomes very sharp in 50 ≲ H≲ 80 kOe, and becomes broad above H ≳ 90 kOe (up to H = 120 kOe) with peak shifts toward lower temperatures as H increases. However, the peak at T B shifts toward lower temperatures as H increases and turns into an inflection for H ≳ 80 kOe. The specific heat at H = 90 kOe exhibits an additional peak corresponding to T*. The zero-field specific heat also exhibits a small anomaly at T** and two inflections at T B (denoted as T B ′ = 4.94 K and T B ′′ = 4.79 K) as shown in the insets of Figure 8a. Figure 8b depicts the magnetic field dependence of C/T at several temperatures around T A . We observed anomalies corresponding to H A , H B , and H C in the resistivity measurements. We estimated the magnetic contribution to the specific heat (C mag ) by estimating the lattice (phonon) contribution from the specific heat of YAu 3 Si (Figure 8c) and calculated the magnetic entropy (ΔS mag ) above 0.2 K (Figure 8d). See the Supporting Information (and Figure S16 therein) for details. The magnetic entropy ΔS mag (T) seems to saturate near R ln 8 (where R is the gas constant) above the magnetic transition temperature T A , indicating that Gd 3+ (J = 7/2) magnetic moments become free with almost full (2J + 1)-fold degeneracy (under crystal electric fields) above T A , which is in line with typical Gd compounds. 43 Note that the deviation from the value of R ln8 may be attributed to the missing contribution from below the base temperature (0.2 K) and/or shortcomings in the estimated phonon contribution. Figure 9 shows the characteristic temperatures (T A , T B , T*, T**, and T m *) and magnetic fields (H A , H B , H C , H m *, and H m **) obtained from the specific heat, magnetization, and electrical resistivity. It seems there are three different magnetic states below T A , depending on the external magnetic field (as highlighted with green, red, and blue hatchings). Each state is further separated at T B . We observe a hysteresis behavior crossing the H A line for 70 ≲ H ≲ 90 kOe, suggesting that the H A line for 70 ≲ H ≲ 90 kOe (probably terminated near a specific point denoted by T*) is first-orderlike.
To shed more light into the complex magnetic behavior of GdAu 3 Si, MDMC simulations were carried out. For these simulations, four initial distributions of magnetic moments, namely, ferromagnetic (FM), paramagnetic (PM), and two types of the ferrimagnetic one, were considered ( Figure 10). The paramagnetic distribution was created in a disordered local-moment (DLM) fashion 44 known to nicely mimic the true paramagnetic distribution while keeping magnetic moments collinear and the total magnetic moment equal to zero. The ferrimagnetic distribution of type 1 was created with magnetic moments at atoms on the Gd1 (4e) and Gd3 (8i) positions parallel to each other, while magnetic moments on the Gd2 (4f) position were aligned antiparallel to them. The ferrimagnetic distribution of type 2 was created with magnetic moments at atoms on the Gd2 and Gd3 positions in parallel, while the moments on the Gd1 position were antiparallel to them. Several initial distributions were tested in order to prove the convergence of all the starting configurations to the same magnetic state with the lowest energy. In addition, two values of the starting magnetic moment (3 and 7 μ B per atom) were tested which resulted always in a high-spin state with magnetic moments of Gd equal to 7.08−7.1 μ B . As already mentioned above, the resulting magnetic states were tested for a possible noncollinearity using the noncollinear version of VASP and appeared to be collinear.
As one can see from Figure 10, the initial FM distribution has the highest total energy, whereas the PM distribution has the lowest, which is rather close to the equilibrium magnetic The lower critical field H c1 (T = 0) is estimated from the following relation , which is valid for large κ values. 41 The coherence length ξ(T = 0) and penetration depth λ(T = 0) are estimated from the following relations: H c2 (0) = Φ 0 /2πξ(0) 2 and κ ≡ λ/ξ where Φ 0 is the magnetic flux quanta.
Inorganic Chemistry pubs.acs.org/IC Article state after the simulation. The energy differences between magnetic states are rather small. After approximately 160 MDMC steps, all considered initial distributions of magnetic moments converged to two configurations, which were very close in energy and remained unchanged through further MDMC runs. These two final states are antiferromagnetic (AFM), with 8 parallel and 8 antiparallel spins, and ferrimagnetic, with 9 parallel and 7 antiparallel spins (for the particular distributions, see Figure 11). Both states have collinear magnetism. As they are very close in energies (which should be considered as zero within the DFT accuracy), one might expect a frustrated magnetic behavior of the system. The collinear magnetic order suggests the presence of an easy-axis anisotropy.

DISCUSSION
The complex T−H phase diagram shown in Figure 9, which includes several regions of T−H in which the magnetic order is modulated, is reminiscent of centrosymmetric frustrated antiferromagnets (Gd-based intermetallic compounds) such as triangular lattice Gd 2 PdSi 3 45 and breathing-kagome-lattice Gd 3 Ru 4 Al 12 46 whose intriguing chiral (topological) spin textures called skyrmion lattices were recently reported. Similar to these Gd-based frustrated antiferromagnets, GdAu 3 Si has a centrosymmetric crystal structure (spatial inversion symmetry) with triangular magnetic units (which could cause geometrical frustration). Qualitatively one can assume the same exchangecoupling mechanism, i.e., Ruderman−Kittel−Kasuya−Yosida (RKKY)-type exchange interaction, which is also plausible from the DOS of GdAu 3 Si (cf. Figure S5b). However, GdAu 3 Si has a three-dimensional crystal structure (rather than a (quasi) two-dimensional), and the triangular units constituting the icosahedra are distorted (cf. Figure 5b). The quasi-degenerate feature (energetically close-lying magnetic states) found in our simulation and the complex magnetic behavior for H = 0, which is represented by additional anomalies in the specific heat (i.e., the anomaly at T** and the two-inflection behavior at T B ), may reflect magnetic frustration. The complex T−H phase diagram of GdAu 3 Si also bears some resemblance to those of noncentrosymmetric chiral-lattice magnets (with broken inversion symmetry) such as metallic MnSi 47 and insulating (multiferroic) Cu 2 OSeO 3 . 48 We note that the inversion symmetry with respect to magnetic Gd atoms is locally broken since the Gd2(Gd1,Gd3) 12 pseudo-icosahedron with the cluster-center Gd2 (see Figure 5b) does not have inversion symmetry, though the global inversion symmetry is conserved.
We also analyzed the critical behavior of the specific heat at the magnetic transition at T A for H = 0, 5 and 60 kOe considering the minimal curve C = A ± |t| −α + B + Lt, 49 in which the first term describes a critical behavior, while the last two terms represent background contributions, where α, A ± , B, L are adjustable parameters and t ≡ (T − T N )/T N (with T N ≈ T A ); see the Supporting Information (and Figure S17 therein) for details. α is a critical exponent, and the subscript "+" and "−" indicates T > T N and T < T N , respectively. Our analysis suggests an approximate critical exponent of α = 0.2 ± 0.04 with A + /A − ∼ 0.66 for H = 0 and 5 kOe (the green region in the T−H diagram (see Figure 9), and α = 0.13 ± 0.03 with A + / A − ∼ 0.82 for H = 60 kOe (the blue region). The latter α value is close to those of the universality class of 3D-Ising (α = 0.11, A + /A − = 0.52). 49 This is in line with our computational result suggesting a uniaxial anisotropy. The low-field analysis (H = 0 and 5 kOe) yields parameters closer to those of the "chiral" Heisenberg type (α = 0.24 ± 0.08, A + /A − = 0.54 ± 0.2). 50 Interestingly, there is a qualitative similarity between the present GdAu 3 Si system and the quasi-two-dimensional triangular Heisenberg frustrated antiferromagnets referred to as VX 2 (X = Cl, Br, and I), which have been studied with respect to the "chiral" universality class. 50,51 This similarity between these completely different systems (having different structures and exchange-coupling mechanisms) may be due to the universality of the "chiral" Heisenberg class. 50 The VX 2 systems exhibit sharp peaks in their specific-heat curves at their magnetic transitions. According to refs 50 and 52, VCl 2 has a weak Ising-like anisotropy which causes two successive transitions in a very narrow temperature range, which is similar to the two-inflection structure at T B observed in the specific heat (H = 0) of GdAu 3 Si. We therefore conjecture that the uniaxial anisotropy (with the chiral Heisenberg behavior) plays an important role in GdAu 3 Si. Also, VI 2 exhibits two Inorganic Chemistry pubs.acs.org/IC Article distinct successive transitions (with respect to a transition to a 120°spin structure and to a collinear spin structure). 53 The latter exhibits a very sharp peak in its specific heat, which is similar to the very sharp peaks observed in the present system at T A in 50 ≲ H ≲ 80 kOe. From the similarity to VX 2 and the estimated critical exponents, it appears reasonable to suggest that GdAu 3 Si has a chiral−Heisenberg nature (with a uniaxial anisotropy) in the low-field region (the green region, H ≲ 50 kOe) and exhibits an Ising-like nature at the high-field region (the blue region, H ≲ 50 kOe).

CONCLUSIONS
The investigation of reaction mixtures RE x (Au 0.79 Si 0.21 ) 100−x (RE = Y and Gd) resulted in the compounds YAu 3 Si and GdAu 3 Si which crystallize in a new tetragonal structure type. The strictly (Au, Si) ordered structure features three crystallographically different RE atoms which are each   The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript.

Notes
The authors declare no competing financial interest.  . Distribution of magnetic moments in two neighboring icosahedral clusters Gd2(Gd1,Gd3) 12 for the two magnetic states corresponding to lowest total energies, as identified from MDMC simulations.