2 Triangles

Article pubs.acs.org/cm

Polar Materials with Isolated V4+ S = 1/2 Triangles: NaSr2V3O3(Ge4O13)Cl and KSr2V3O3(Ge4O13)Cl Liurukara D. Sanjeewa,† Michael A. McGuire,‡ Colin D. McMillen,† Vasile O. Garlea,§ and Joseph W. Kolis*,† †

Department of Chemistry and Center for Optical Materials Science and Engineering Technologies (COMSET), Clemson University, Clemson, South Carolina 29634-0973, United States ‡ Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, United States § Quantum Condensed Matter Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, United States S Supporting Information *

ABSTRACT: Crystals of ASr2V3O3(Ge4O13)Cl, A = Na, K, were synthesized from high-temperature hydrothermal brines, and their structure and magnetic properties were investigated. These materials present a unique combination of a salt inclusion lattice, a polar crystal structure, and isolated V4+ (S = 1/2) trimer magnetic clusters. The structures consist of a trimeric V3O13 unit based on V4+ (S = 1/2), having rigorous 3fold symmetry with a short V−V separation of 3.325(3) Å. The trinuclear V4+ units are formed by three edge shared VO6 octahedra sharing a central μ3-oxygen atom, which also imparts a polar sense on the structure. The V3O13 units are isolated from one another by tetranuclear Ge4O13 units, which are similarly arranged in a polar fashion, providing a unique opportunity to study the magnetic behavior of this triangular d1 system as a discrete unit. Magnetization measurements indicate spin-1/2 per V atom at high temperature, and spin-1/2 per V3 trimer at low temperature, where two V moments in each triangle are antiferromagnetically aligned and the third remains paramagnetic. The crossover between these two behaviors occurs between 20 and 100 K and is well-described by a model incorporating strong antiferromagnetic intra-trimer interactions and weak but nonzero inter-trimer interactions. More broadly, the study highlights the ability to obtain new materials with interesting structure−property relationships via chemistry involving unconventional solvents and reaction conditions.

1. INTRODUCTION Recently we have been investigating new transition metal compounds with low-dimensional structural features that can lead to interesting magnetic properties.1,2 In particular, emptyshell tetrahedral building blocks are interesting units since they can serve as spacers and linkers both to direct the structural chemistry and also to achieve magnetic and electronic insulation of open-shell transition metal oxide frameworks.3 Importantly, the 3-fold rotational symmetry of the tetrahedra are amenable to long-range 3-fold space symmetry, which can in turn enable spin frustration of transition metals, leading to complex magnetic effects.4−6 Vanadium is especially interesting for such studies given its stability in a variety of oxidation states and coordination environments.7,8 It is unique in that it can perform the dual role of being the tetrahedral building block in the V5+ state (as the (VO4)3− oxyanion), as well as serve as the magnetic metal center in the V3+ or V4+ states. We recently found that it can perform both roles in the same compound.2 The hydrothermal method provides a number of advantages as a synthetic technique for the vanadates.9,10 Although we employ reaction temperatures that are considered high for hydrothermal reactions (600−700 °C), they remain relatively low compared to typical solid-state reactions and crystal growth © 2017 American Chemical Society

methods. These comparatively modest synthesis temperatures allow access to a large number of new phases, while still inducing reactivity among some otherwise sluggish reagents (i.e., refractory metal oxides).11 The use of an aqueous solvent also allows for the manipulation of the typical synthetic variables that chemists exploit to generate new compounds (stoichiometry, pH, oxidation potential, and counterions etc.) and can often lead to the growth of sizable crystals (2−3 mm) of high quality. This enables the study of a number of physical properties that are a function of bulk structure. For magnetic materials this is especially useful for single crystal neutron diffraction and inelastic neutron scattering measurements. The high-temperature hydrothermal fluids have somewhat of a reducing nature, as we have observed several instances of final products containing Mn2+, Eu2+, and V4+ from starting materials based on Mn3+, Eu3+, and V5+, respectively. With this in mind we began to use V2O5 as a reagent in the reaction mixture to target reduced vanadium species having low-value spin states from V4+ (S = 1/2) or V3+ (S = 1). Low-dimensional spin Received: December 15, 2016 Revised: January 3, 2017 Published: January 3, 2017 1404

DOI: 10.1021/acs.chemmater.6b05320 Chem. Mater. 2017, 29, 1404−1412

Article

Chemistry of Materials systems with S = 1 and 1/2 are most commonly based on d9 copper and d8 nickel containing compounds,12,13 but the investigation of d1 or d2 metal ions is also of interest to provide counterpoint low-dimensional magnetic systems. Since hydrothermal reactions are well-suited to amphoteric oxides,14,15 the hydrothermal chemistry of germanates as building blocks in combination with open-shell transition metals and rare earth elements appears promising.16−19 Germanates provide an interesting distinction from the related silicates. Unlike the silicates, which exist exclusively in tetrahedral sites, germanates can adopt a variety of four-, five-, and six-coordinate environments.20,21 They also have a tendency to form large multinuclear units with complex structures. Despite these interesting structural properties, they are relatively unexplored relative to the silicates, except as potential new open-framework analogues to zeolites.22,23 Interestingly, vanadium germanates also form a series of unusual compounds whereby the vanadium and germanium ions can act as both building block and coordinated metal ion.24−26 Previously, structures were reported of V3+ (S = 1) containing 1-D structures where GeO4 serves as an oxy-anion building block in the structure.16,17,27 These formed as highquality single crystals using a high-temperature hydrothermal method, which encourages extension of the descriptive chemistry and phase space exploration. While high-temperature hydrothermal reactions typically employ hydroxide as the mineralizer in the growth process, hydrothermal brines, especially fluids with high concentrations of chloride ions, are also powerful mineralizers and provide a less-explored pathway to completely different chemistry. This led us to isolate the new compounds ASr2V3O3(Ge4O13)Cl (A = Na, K) as large highquality single crystals. The compounds have a complicated structure with several unique aspects. Several important features are displayed, including a polygermanate building block that acts as both a structural spacer and an electronic and magnetic insulator for discrete, geometrically spin frustrated, V3O13 trimers based on V4+ (S = 1/2). Also, despite the intricacy of the framework, it possesses a clear polar structure. This is important because the ability to introduce a low-dimensional magnetic structure as well as a possible ferroelectric transition raises the possibility of generating a new class of multiferroics.28−31 Additionally, non-centrosymmetric structures having helical magnetism can also host skyrmion ground states.32,33 Finally, the strontium and alkali cations form infinite chains with the halides, and this serves an additional insulating building block in the lattice that can also direct structure. The structure and unusual magnetic features of this novel series of structures is discussed herein.

Figure 1. Optical micrographs of hydrothermally grown (a) NaSr2V3O3(Ge4O13)Cl and (b) KSr2V3O3(Ge4O13)Cl crystals. The average size of the crystals is ∼1 mm. using SrCO3, V2O5, and GeO2 with 3 M NaCl and 3 M KCl as the mineralizers, respectively. Here, a total of 0.4 g of reactants (0.1374 g of SrCO3, 0.0678 g of V2O5 and 0.1948 g of GeO2) were used in the molar ratio of 5:2:10. 2.2. X-ray Diffraction. A Rigaku AFC8 diffractometer equipped with Mo Kα radiation (λ = 0.71073 Å; graphite monochromated) and a Mercury CCD detector were used to collect single crystal X-ray diffraction data at room temperature. The data were processed, including the use of a multiscan absorption correction, using the CrystalClear software package.34 Crystals were identified as belonging to the hexagonal crystal system, and a space group determination of P63mc was made based on the systematic absences evaluated using the XPREP module of SHELX.35 The structures were solved by direct methods (SHELXS) and subsequently refined using full-matrix leastsquares techniques (SHELXL). All atoms were refined anisotropically. The atom O(5) was found to be half-occupied at a general position based on its anisotropic displacement parameters (ADPs) and in order to establish a tetrahedral environment about the germanium atoms. Upon initial refinements, the Sr site (a 6c site) was also observed to have somewhat larger ADPs. Based on the elemental composition determined by energy dispersive X-ray analysis (Supporting Information Table S1), this site was determined to be a substitutional disorder of 2/3 Sr and 1/3 Na/K. These atoms were constrained to this occupancy, and their coordinates and ADPs were likewise constrained to be identical, resulting in significantly improved ADPs and refinement statistics. Furthermore, this ratio established the charge-balanced formula of ASr2V3O3(Ge4O13)Cl (A = Na, K), where the vanadium atoms are tetravalent (confirmed by the magnetic study below). The vanadium valence was further verified based on a bond valence analysis (Supporting Information Table S2).36,37 The proper absolute configuration of the non-centrosymmetric structure was established on the basis of the Flack parameter.38 Crystallographic data from the structure refinements are given in Table 1. Selected interatomic distances and angles are provided in Table 2. Powder X-ray diffraction (PXRD) measurements were performed using a Rigaku Ultima IV diffractometer equipped with Cu Kα radiation (λ = 1.5406 Å). Data were collected in 0.02° increments over the 2θ range of 5−65° at a rate of 0.1° min−1. Figure 2 compares the observed PXRD patterns for well-ground single crystals of ASr2V3O3(Ge4O13)Cl (A = Na, K) with the calculated PXRD pattern b a s e d o n t he s in gle c r ys t a l s t r u c t u r e r e fi n e m e nt o f NaSr2V3O3(Ge4O13)Cl. 2.3. Magnetic Property Characterization. Magnetization measurements were carried out using a magnetic property measurement system (Quantum Design) using collections of small crystals of NaSr2V3O3(Ge4O13)Cl and KSr2V3O3(Ge4O13)Cl with total masses of 3.4 and 2.8 mg, respectively. The crystals were attached to a fused silica rod using GE varnish. Temperature dependent data were collected upon cooling in a magnetic field of 10 kOe. Isothermal magnetization versus applied field curves were collected at 300 and 2 K.

2. EXPERIMENTAL METHODS 2.1. Synthesis of ASr2V3O3(Ge4O13)Cl, A = Na and K. The chemicals used in this study were SrCO3 (Alfa Aesar, 99%), V2O5 (Alfa Aesar, 99.6%), GeO2 (HEFA Rare Earth, 99.999%), NaCl (Alfa Aesar, 99.9%), and KCl (Alfa Aesar, 99.9%) and were used as-received. A typical reaction consisted of 0.4 g of reactants with 0.8 mL of appropriate mineralizer. The reactants and the mineralizers were loaded into 2.5 in. long silver ampules with an outer diameter of 3/8 in. The welded silver ampules were placed in a Tuttle cold seal autoclave filled with water to provide suitable counter pressure. The autoclave was heated to 600 °C for 6−7 days with a typical pressure of 175 MPa. After the reaction period, dark green crystals (Figure 1) of ASr2V3O3(Ge4O13)Cl, A = Na and K, were recovered. Both NaSr2V3O3(Ge4O13)Cl and KSr2V3O3(Ge4O13)Cl were synthesized

3. RESULTS AND DISCUSSION 3.1. Synthesis and Structure of ASr2V3O3(Ge4O13)Cl, A = Na and K. The title compounds were synthesized using 3 M 1405


Article

Chemistry of Materials Table 1. Crystallographic Data for ASr2V3(Ge3O13)O3Cl (A = Na, K) empirical formula FW cryst syst cryst dimens, mm space group, Z T, K a, Å c, Å V, Å3 D(calc), g/cm3 F(000) Tmax, Tmin 2θ range no. of unique reflcns no. of params final R [I > 2σ(I)]: R1, Rw2 final R (all data): R1, Rw2 GoF largest diff. peak/hole, e/Å3 μ(Mo Kα), mm−1 extinction coeff Flack param

NaSr2V3(Ge4O13)O3Cl 932.86 hexagonal 0.28 × 0.10 × 0.08 P63mc (No. 186), 2 298 10.4084(3) 7.2791(2) 682.93(2) 4.536 858 1.000, 0.5653 2.26−26.44 545 59 0.0365/0.1042 0.0365/0.1042 1.092 0.959/−1.352 18.694 0.0081(16) 0.029(8)

KSr2V3(Ge4O13)O3Cl 948.97 hexagonal 0.22 × 0.16 × 0.12 P63mc (No. 186), 2 298 10.4679(7) 7.2427(5) 687.31(10) 4.585 874 1.000, 0.6047 3.60−26.06 513 59 0.0380/0.0846 0.0379/0.0846 1.057 0.688/−0.919 18.847 0.0020(6) −0.07(2)

Table 2. Selected Interatomic Distances (Å) and Angles (deg) NaSr2V3(Ge4O13)O3Cl

KSr2V3(Ge4O13)O3Cl

3.169(19) 2.665(13) 2.928(18) 2.626(17) 2.54(3) 3.136(8) 2.916(8)

3.079(16) 2.710(11) 2.912(13) 2.645(14) 2.60(2) 3.155(8) 2.980(7)

2.256(18) 1.62(2) 1.955(15) 2.006(10)

2.258(15) 1.639(17) 1.955(13) 2.009(8)

1.77(3) 1.77(3)

1.77(3) 1.78(2)

1.735(14) 1.766(17) 1.85(3) 3.325(3) 95.0(10) 112.0(8)

1.736(11) 1.756(15) 1.80(2) 3.321(3) 94.7(8) 111.5(7)

[Sr/A(1)]O10 SrA(1)−O(2) SrA(1)−O(2) × 2 SrA(1)−O(3) × 2 SrA(1)−O(3) × 2 SrA(1)−O(5) SrA(1)−Cl(1) SrA(1)−Cl(1) V(1)O6 V(1)−O(1) V(1)−O(2) V(1)−O(3) × 2 V(1)−O(4) × 2 Ge(1)O4 Ge(1)−O(1) Ge(1)−O(5) × 3 Ge(2)O4 Ge(1)−O(3) × 2 Ge(1)−O(4) Ge(1)−O(5) V····V V(1)−O(1)−V(1) V(1)−O(4)−V(1)

of the ampule. Furthermore, no silver was observed in the elemental analysis of the crystals. The product obtained from the 3 M chloride mineralizers proved to be phase pure based on PXRD (Figure 2). The compounds crystallize in the polar hexagonal space group P63mc (No. 186), and possess a complex threedimensional framework constructed from interconnected [V3O13]−14 and [Ge4O13]−10 units, which encompass a salt lattice (Figure 3). The polyvanadate and polygermanate building blocks comprising the oxide framework are of particular interest because of their contributions to the polar nature of the structure and the magnetic properties. The V4+

aqueous NaCl and KCl solutions, which served as both the mineralizing fluid and the source of both the alkali and chloride ions. At 3 M concentrations, the aqueous chloride is sufficient to dissolve the metal oxide feedstocks and induce the growth of large crystals. The crystals were dark green in color, suggesting the presence of reduced vanadium in the product. When the chloride concentration is increased to 5 M the silver ampules are visibly corroded by the fluid, perhaps suggesting that increased reactivity of the silver facilitates vanadium reduction from the V2O5 starting material. As a general observation, however, we find the hydrothermal growth conditions themselves to be mildly reducing, even without visible reactivity 1406


Article

Chemistry of Materials

Figure 2. PXRD patterns of (a) calculated NaSr2V3O3(Ge4O13)Cl, and observed PXRD patterns of (b) NaSr2V3O3(Ge4O13)Cl and (c) KSr2V3O3(Ge4O13)Cl.

Figure 4. (a) [V3O13]−14 unit of ASr2V3O3Ge4O13Cl (A = Na, K) made from edge sharing VO6 octahedra. The dotted lines represent the contact pathways between V4+, which forms an equilateral triangle with a V····V distance of 3.325(3) Å with the μ3-oxygen atom, O(1), aligned with the center of the triangle. (b) Packing of discrete [V3O13]−14 units within the unit cell indicating a concerted alignment of vanadyl oxygen atoms, O(2), and trans-oxygen atoms, O(1) imparting a net polarity along the c-axis.

bridging V−O−V angles range from 95.0(9)° to 112.0(8)° and from 94.7(8)° to 111.6(7)° for NaSr2V3O3(Ge4O13)Cl and KSr2V3O3(Ge4O13)Cl, respectively. The individual VO6 octahedra are highly distorted with respect to their V−O bond lengths, which range from 1.62(2) to 2.256(18) Å and from 1.638(17) to 2.258(15) Å in NaSr2V3O3(Ge4O13)Cl and KSr2V3O3(Ge4O13)Cl, respectively. This has significance in establishing the polar nature of the crystal structure. The VO6 group takes on a 1 + 4 + 1 type distortion with the shortest V−O bond length within the range expected for a vanadyl bond and the longest V−O bond in a trans-arrangement to the vanadyl bond.42 The trans-bond is made to the μ3-oxygen atom of the V3O13 unit. In this way, all of the vanadyl bonds in the structure have the same general directionality along the c-axis, and likewise, all of the transbonds take on the opposite general directionality, Figure 4b. The equatorial V−O bonds average 1.981(15) Å for the two analogues. The infrared spectra of the title compounds exhibit a relatively strong band in the vicinity of 880−900 cm−1 (SI, Figure S1) that is likely attributed to the vanadyl stretching vibration of the VO6 units. There are two crystallographically distinct Ge4+ sites that form connected GeO4 tetrahedra. One Ge(1) atom (3m site symmetry) is corner sharing through the partially occupied O(5) atoms to three Ge(2) atoms (m symmetry) to form the discrete Ge4O13 unit. The O(5) disorder creates two possible arrangements for oxygen corner sharing within the Ge4O13 unit (SI, Figure S2). Since O(5) does not maintain any connection to the V3O13 units, the disorder probably has minimal influence

Figure 3. Structure of NaSr2V3O3(Ge4O13)Cl projected along the caxis, showing the 6-fold symmetry around the one-dimensional channels where mixed Sr/Na and Cl ions reside.

ions form the vertices of an equilateral triangle in the form of the trimeric V3O13 unit built of three edge-sharing VO6 octahedra (Figure 4a). The unit shares a common μ3-oxygen atom, O(1), containing the 3-fold symmetry element (3m site symmetry). These are discrete units, isolated from one another by the germanate building blocks (see below). The V3O13 arrangement is a common subunit in polyoxovanadate species, but less common as a discrete solid-state building block.39 In general the [V3O13]14‑ unit is considered to have too high of a charge density to exist as a stand-alone unit. Efforts have been made to stabilize the unit by capping with organic species and similar units.40 In this case the discrete cluster is stabilized in the lattice by the presence of the germanate framework and alkali halide chains. However, its magnetic behavior as a discrete unit is very interesting since the rigorous 3-fold symmetry of the V3O13 unit presents a potentially spinfrustrated system containing three symmetry equivalent V4+ (S = 1/2) metal centers. In NaSr2V3O3(Ge4O13)Cl, the V····V separation distance is 3.325(3) Å, which is shorter than a V4+ Kagome type inorganic−organic hybrid material previously reported by Clark et al. (3.60−3.75 Å).41 The short V····V distances should enable a strong, direct exchange pathway. The 1407


Article


Finally, the vanadium germanate framework is penetrated by a salt lattice, where the mixed Sr/Na or Sr/K sites and Cl atoms are located in channels that propagate along the c-axis (refer to Figure 3). The salt lattice consists of 10-coordinate alkali/Sr sites having interactions with eight oxygen atoms and two chloride ions. The chloride ions each coordinate six alkali/Sr atoms to form salt chains that propagate along the c-axis (Figure 7). The salt chains are slightly larger for the potassium

on the properties arising from those units, and the disorder does not affect the c-axis polarity. The bridging Ge(2)−O(5) bonds within the Ge4O13 unit are slightly elongated, but the average Ge−O bond lengths are within the expected range. The Ge4O13 formula is somewhat rare itself and has been observed as a finite chain in Na4Sc2(Ge4O13),43 and as an isolated island in Cu2Fe2(Ge4O13)44 and Cu2Sc2(Ge4O13).45 Similar structural variety is known among the more common silicate-based materials,46 and we recently encountered a class of silicates, NaBa3Ln3Si6O20 (Ln = Y, Nd, Sm, Eu, Gd), that feature Si4O13 islands and also crystallize in a polar space group.47,48 Interestingly, in the present structures the apex of the Ge(1) tetrahedron along the 3-fold rotation axis occurs as O(1), which is the μ3-oxygen atom of the V3O13 trimer (the trans-oxygen atom of the VO6 units), so each of the Ge4O13 tetramers also exhibits a defined polarity via alignment of these apexes along the c-axis. The Ge4O13 tetramers serve to fully isolate the V3O13 trimers from one another, as each trimer is surrounded by five Ge4O13 tetramers and vice versa (Figure 5). Thus, the trimers

Figure 7. (a) Sr/Na−Cl salt lattice of NaSr2V3O3(Ge4O13)Cl. (b) Partial view of the infinite (Sr/Na)6Cl salt chains that propagate along the c-axis.

analogue compared to the sodium analogue (Na/Sr−Cl = 2.916(8) and 3.136(8) Å; K/Sr−Cl = 2.980(7) and 3.155(8) Å), and this is accommodated by a modest expansion of the vanadium germanate channels evident by an increase in the alattice parameter. Such a halide structural unit is reminiscent of the salt inclusion structures, which typically occur when the materials are synthesized in molten salts.49−51 3.2. Magnetic Properties of ASr2V3O3(Ge4O13)Cl, A = Na and K. Results of the magnetization measurements are summarized in Figure 8. No sharp anomalies indicative of magnetic ordering transitions are observed in the temperature dependence of the magnetic susceptibility (χ). However, inspection of 1/χ versus temperature, shown in the insets of Figure 8, reveals an evolution from one linear, Curie−Weisslike behavior at high temperature to another, different, linear behavior at low temperature. The Curie−Weiss model can be used as a simplified way to understand the data shown in Figure 8. Fits to the data using χ(T) = χ 0 + C/(T − θ) were performed using data collected above 100 K and separately using data collected below 20 K for both materials. The effective moments (μeff), determined from the Curie constants (C), from each fit are listed in Figures 8 and 9. Note that the effective moment is given per V at high temperature and per V3-trimer at low temperature. Also listed are the Weiss temperatures (θ), which indicate the strength and nature of the magnetic interactions. The fitted values of χ0 were typically near −4 × 10−4 cm3/(mol·FU) At high temperature (100−300 K), the effective moment of each compound is close to the value expected (1.73 μB) for a spin 1/2 moment on each V4+ ion, and the Weiss temperature is relatively large and negative, indicating strong antiferromagnetic interactions (Figure 8). Since the structures contain isolated triangular V3O13 units (V3 triangles), the magnetic

Figure 5. Connectivity of five V3O13 trimers to a central Ge4O13 tetramer. The Ge4O13 tetramer is shown as a single yellow polyhedron, which exhibits the polar character of this unit. Blue polyhedra representing the V3O13 units are constructed from only the vanadyl and trans-oxygen (the μ3-oxygen) atoms, again to highlight this unit’s polarity.

and tetramers stack in an alternating arrangement along the caxis of the structure (Figure 6). Oxygen corner sharing between GeO4 and VO6 units form the Ge−O−V connections that comprise the three-dimensional oxide framework.

Figure 6. Alternating stacking of Ge4O13 tetramers (yellow atoms and tetrameric polyhedra) with V3O13 trimers (blue atoms and triangular polyhedra). Oxygen atoms provide connectivity between neighboring Ge4O13 and V3O13 units to create the three-dimensional vanadium germanate framework, but are omitted for clarity. 1408


Article


Figure 9. Results of fitting the magnetic susceptibilities of (a) NaSr2V3(Ge4O13)O3Cl and (b) KSr2V3(Ge4O13)O3Cl over the full temperature range (2−300 K) using the model described by eq 1. The data and fitted curves are presented in the form χT.

both compounds. The network of trimers is three-dimensional and can be described as edge-sharing chains of edge-sharing triangles (SI, Figure S3). Assuming similar strength antiferromagnetic coupling between trimers separated by 7.0 and 7.3 Å, this is a geometrically frustrated lattice; however, the weak interactions do not allow any related effects to be manifest in the temperature range studied. The low-temperature spin 1/2 trimer state is further supported by the field dependence of the magnetic moment measured at 2 K, as shown in Figure 8c for both materials. The data is plotted in units of Bohr magnetons per formula unit (per V3 triangle). The behavior is essentially identical for both compounds. Also shown on the plot is the theoretical curve describing a simple paramagnet with one spin 1/2 per V3 triangle. This is given by the m(H) = μBgSBS(x), where g = 2 is the electron g-factor, S = 1/2 is the spin, and BJ(x) is the Brillouin function with argument x = gμBS H/(kBT), kB being the Boltzmann constant. Note that Figure 8c shows not a fit to the data but rather a comparison with a theoretical model that has no adjustable parameters. The excellent agreement is good evidence that a single effective spin 1/2 moment per V3 trimer with little inter-trimer interaction is the correct description of the low-temperature magnetic state. This crossover upon cooling from individual S = 1/2 ions with strong intra-trimer interactions to trimer states with S = 1/ 2 and weak inter-trimer interactions has been observed in several other materials. These are mostly complexes of divalent copper,52−57 but trivalent titanium58 and tetravalent vanadium59 have also been examined. Simple magnetic clusters such as the triangles found in these materials provide useful model systems for comparing measured magnetic excitation spectra to simple models.56 The hydrogen-free inorganic compounds studied here are particularly well-suited for such studies using inelastic neutron scattering. The temperature dependence of the magnetic susceptibility for equilateral triangles of spin 1/2 moments with no intertrimer interactions can be calculated by assuming an effective

Figure 8. Magnetic behavior of NaSr 2 V 3 (Ge 4 O 13 )O 3 Cl and KSr2V3(Ge4O13)O3Cl. The magnetic susceptibilities measured in a field of 10 kOe are shown in panels a and b, with solid curves generated by separate Curie−Weiss fits to data below 20 K and above 100 K (insets). The field dependence of the magnetic moment per formula unit measured at 2 K is shown in panel c, along with a theoretical curve for spin 1/2 per formula unit with g = 2. See text for details.

interactions reflected in this θ value are expected to be from the intra-trimer interactions. Antiferromagnetic interactions within triangular units are strongly frustrated; if one pair orders antiferromagnetically, the third member will not be able to satisfy its antiferromagnetic interactions with both members of the ordered pair simultaneously. Upon cooling through the intermediate temperature range of 100−20 K, the magnetic behavior clearly changes. Curie−Weiss fits to the data from 2−20 K give smaller values of C and nearzero values for θ. In fact, the low-temperature effective moments correspond not to one spin 1/2 per V, but to one spin 1/2 per V3 triangle. The small and negative Weiss temperatures indicate weak antiferromagnetic interactions in this temperature range. This shows that upon cooling the independent V4+ magnetic moments observed at high temperature condense into trimer states with effective spin of 1/2 per V3 unit, and with weak inter-trimer interactions. The strength of these interactions is not sufficient to produce any long-range order above T = 2 K among the well-separated S = 1/2 trimers, which are separated from neighboring trimers by 7.0−7.3 Å in 1409


Article

Chemistry of Materials Hamiltonian H = J(S1S2 + S2S3 + S1S3) + gμBH(S1 + S2 + S3), where J is the exchange constant representing the strength of the intra-trimer magnetic interaction. This results in two degenerate S = 1/2 ground states separated by an energy gap of 3J/2 from the S = 3/2 excited state. Calculation of the susceptibility per mole of trimer units gives χ (T ) = χ0 +

NAμB2 g 2 ⎡ 1 + 5e3J /2kBT ⎤ ⎢ ⎥ 4kBT ⎣ 1 + e3J /2kBT ⎦

ASr2V3O3(Ge3O13)Cl, but with an average valence of +3.67 for each Mo atom and quite short Mo−Mo intracluster distances (2.6 Å). As a result of the Mo−Mo bonding, there is only one unpaired spin per trimer, giving S = 1/2 per Mo3 unit.61 The intercluster distance is also shorter in LiZn2Mo3O8 (3.2 Å), and intercluster interactions within the triangular lattice of trimers result in an unusual form of order described as valence-bond condensation. This produces a crossover from S = 1/2 for every individual trimer to S = 1/2 for every three trimers. The associated magnetic susceptibility61 is quite similar to that shown in Figure 8 for ASr2V3O3(Ge3O13)Cl, but the behaviors arise from different mechanisms. For LiZn2Mo3O8 the crossover results from inter-trimer interactions, while for ASr2V3O3(Ge3O13)Cl the crossover is a consequence of intratrimer magnetic coupling. Inelastic neutron scattering was used to demonstrate collective magnetic excitations originating from the frustrated, antiferromagnetic, inter-trimer interactions in LiZn2Mo3O8.62 The relatively weak coupling between the isolated V3 units in ASr2V3O3(Ge3O13)Cl would allow similar neutron scattering techniques access to magnetic excitations associated with intra-trimer interactions.

(1)

where NA is Avogadro’s number and g is the g-factor relating the magnetic moment (μ) to the spin via μ = gS.54 Fits of this type are shown for both materials in Figure 9. For this purpose, the data are plotted as χT, which serves to best illustrate the fit over the entire temperature range. To account for the weak but nonvanishing inter-trimer interaction, T in eq 1 was replaced by T− Θ for the fits, where Θ plays a role similar to that of θ in the Curie−Weiss model.54 As demonstrated by Figure 9, this model fits the observed behavior quite well for both compounds and confirms the interpretation derived from the simple Curie−Weiss analysis presented above. It is interesting to compare the results of the two analyses. The temperature independent contribution χ0, which accounts for core diamagnetism and sample holder contributions, is, as expected, small and negative in both fits. The strength of the inter-trimer interactions is measured by the low-temperature value of θ from the Curie−Weiss fits and the value of Θ in eq 1. Similar values of these parameters are observed from the two fits for both materials. The size of the individual magnetic moment gS are determined by the effective moments in Figure 8 (which assumes g = 2) and by the value of g in Figure 9 (which assumes S = 1/2). Both are consistent with S = 1/2 with g close to 2. The fitted values of g found here are close to those reported for triangles of divalent Cu (g = 2.03−2.20)52,54 and V4+ triangles (g = 1.95) determined using a similar analysis.59 The strength of the intra-trimer interactions are indicated by the high-temperature value of θ in the Curie−Weiss (Figure 8) fits and by J/kB in the fit to eq 1 (Figure 9). In the mean field model, the relationship between the Weiss temperature and the exchange interaction strength is θ = (2/3)zS(S + 1)J/kB, where z is the number of nearest neighbors.60 For S = 1/2 and z = 2 in the triangular V3 units, this gives θ = J/kB. This is consistent with the similar values of the high-temperature θ and the value of J/kB, especially true for KSr2V3(Ge4O13)O3Cl. The values of J found here, 96 K for NaSr2V3(Ge4O13)O3Cl and 79 K for KSr2V3(Ge4O13)O3Cl, are similar to those reported for the shorter legs of isosceles V triangles studied by Luban et al. (J/kB = 65 K for dV−V = 3.22−3.25 Å).59 The V−V distances in NaSr2V3(Ge4O13)O3Cl and KSr2V3(Ge4O13)O3Cl are slightly longer, at 3.32 Å. The stronger exchange in the present compounds despite the longer distance is likely due to the more direct exchange pathway, through the bridging oxygen. For comparison, the intra-trimer exchange constants found for the Cu2+ complexes in the literature tend to be significantly higher, ranging from J/kB = 216−335 K.52,54,55,57 Note that Clerac et al.55 writes the intra-trimer interaction term in the Hamiltonian with a prefactor of 2J instead of J as in eq 1. That factor of 2 has been taken into account when making the comparison here. The spin-crossover behavior observed in compounds such as ASr2V3O3(Ge3O13)Cl and the similar Cu2+ complexes is reminiscent of that recently reported for LiZn2Mo3O8.61,62 The latter contains Mo3O13 units such as those found in

4. CONCLUSION The synthesis of two unusual new compo unds ASr2V3(Ge4O13)O3Cl) (A = Na, K) is described. There are a number of unusual features to this chemistry. The first is the synthetic process itself. A high-temperature hydrothermal route was employed (T = 600 °C) that provided single crystals of relatively large size and high quality. This is well-known technology, but an unusual factor in the approach is the use of halide brines as a mineralizer in lieu of the more conventional alkali hydroxide. Not only is the evidence accruing that the alternative mineralizers lead to different chemistry and products, and the metal halides are becoming an integral part of the structure itself but also in this case the alkali and alkaline earth cations form chains with the chloride anions to form a significant part of the structure. This creates the possibility that an enormous range of new compounds can be synthesized via systematic variation of the alkali halide mineralizer composition. The structure of this class of compounds has several notable aspects. Its complexity and intricacy suggest that it is just the first in a large series. It contains a V4+ trimer building block with rigorous 3-fold symmetry. Although V4+ trimers are common subunits in larger polyoxometallates, isolated V4+ trimers are quite rare and considered somewhat unstable due to their high formal negative charge. In this case they are stabilized by germanate tetramers that isolate them within the complex oxide lattice. Isolated V4+ trimers are significant because they represent the electronic mirror image to the much more common Cu2+ trimers with d1 versus d9 S = 1/2 electronic configuration. As such they provide a direct comparison to the magnetic properties of the much more intensively studied cuprate trimers. The low-temperature magnetic susceptibilities reveal a paramagnetic ground state with S = 1/2 per trimer. Thermally induced magnetic excitations out of this ground state produce an effective S = 1/2 per V4+ ion at temperatures above about 100 K. The relatively simple magnetic clusters and lack of any hydrogen atoms makes these compounds ideally suited for fundamental studies of the evolution of these magnetic excitations using inelastic neutron scattering for comparison with theoretical models. Another important aspect of the structure is the polar nature of the solid. The polarity is created 1410


Article


(8) Zavalij, P. Y.; Whittingham, M. S. Structural Chemistry of Vanadium Oxides with Open Frameworks. Acta Crystallogr., Sect. B: Struct. Sci. 1999, 55, 627−663. (9) McMillen, C. D.; Kolis, J. W. Bulk Single Crystal Growth from Hydrothermal Solution. Philos. Mag. 2012, 92, 2686−2711. (10) McMillen, C. D.; Kolis. Hydrothermal Synthesis as a Route to Mineralogically-Inspired Structures. J. W. Dalton Trans. 2016, 45, 2772−2784. (11) McMillen, C. D.; Thompson, D.; Tritt, T.; Kolis, J. W. Hydrothermal Single Crystal Growth of Lu2O3 and Lanthanide Doped Lu2O3. Cryst. Growth Des. 2011, 11, 4386−4391. (12) Katsumata, K. Low Dimensional Magnetic Materials. Curr. Opin. Solid State Mater. Sci. 1997, 2, 226−230. (13) Dagotto, E.; Rice, T. M. Surprises on the Way from 1D to 2D Quantum Magnets: the Novel Ladder Materials. Science 1996, 271, 618−623. (14) Byrappa, K.; Yoshimura, M. Handbook of Hydrothermal Technology; Noyes: Park Ridge, NJ, USA, 2001. (15) Laudise, R. A. Hydrothermal Synthesis of Single Crystals. Prog. Inorg. Chem. 1962, 3, 1−47. (16) Emirdag-Eanes, M.; Kolis, J. W. Hydrothermal Synthesis Characterization and Magnetic Properties of NaVGe2O6 and LiVGe2O6. Mater. Res. Bull. 2004, 39, 1557−1567. (17) Emirdag-Eanes, M.; Kolis, J. W. Hydrothermal Synthesis and Characterization of a New Layered Compound Li2VGeO5. J. Alloys Compd. 2004, 370, 90−93. (18) Emirdag-Eanes, M.; Krawiec, M.; Kolis, J. W. Hydrothermal Synthesis and Structural Characterization of NaLnGeO4 (Ln= Ho, Er, Tb, Tm, Yb, Lu) family of lanthanide germanates. J. Chem. Crystallogr. 2001, 31, 281−285. (19) Emirdag-Eanes, M.; Pennington, W. T.; Kolis, J. W. Synthesis, Structural Characterization and Magnetic Properties of NaRE9(GeO4)6O2 (RE = Nd, Pr). J. Alloys Compd. 2004, 366, 76−80. (20) Demianets, L. N. Hydrothermal Synthesis of New Compounds. Prog. Cryst. Growth Charact. Mater. 1991, 21, 299−355. (21) Demianets, L. N.; Lobachev, A. N.; Emelchenko, G. E. Rare Earth Germanates, Crystals: Growth Properties and Applications; Springer: Berlin, Heidelberg, 1980; Vol. 4, pp 101−144. (22) Natarajan, S.; Mandal, S. Open Framework Structures of Transition Metal Compounds. Angew. Chem., Int. Ed. 2008, 47, 4798− 4828. (23) Bu, X.; Feng, P.; Stucky, G. D. Host-guest Symmetry and Charge Matching in Two Germanates with Intersecting Threedimensional Channels. Chem. Mater. 2000, 12, 1505−1507. (24) Whitfield, T.; Wang, X.; Zheng, L.-M.; Jacobson, A. J. Hydrothermal Synthesis of Germanium Vanadate Layered Compounds. J. Solid State Chem. 2003, 175, 13−19. (25) Whitfield, T.; Wang, X.; Jacobson, A. J. Vanadogermanate Cluster Anions. Inorg. Chem. 2003, 42, 3728−3733. (26) Zheng, Z.-T.; Zhang, J.; Yang, G.-Y. Hydrothermal Synthesis and Structure of a Novel Hybrid Germanium Vanadate:(2,2′bpy)2(VO2)2(H2GeO4)·6H2O. Inorg. Chem. Commun. 2004, 7, 861− 863. (27) Millet, P.; Satto, C. Synthesis and Structures of the Layered Vanadyl (IV) Silico-germanates Li2VO(Si1−xGex)O4 (x= 0, 0.5, 1). Mater. Res. Bull. 1998, 33, 1339−1345. (28) Cheong, S.-W.; Mostovoy, M. Multiferroics: A Magnetic Twist for Ferroelectricity. Nat. Mater. 2007, 6, 13−20. (29) Eerenstein, W.; Mathur, N. D.; Scott, J. F. Multiferroic and Magnetoelectric Materials. Nature 2006, 442, 759−765. (30) Ederer, C.; Spaldin, N. A. Recent Progress in First Principles Studies of Magnetoelectric Multiferroics. Curr. Opin. Solid State Mater. Sci. 2005, 9, 128−139. (31) Tokura, Y. Multiferroics - Toward Strong Coupling Between Magnetization and Polarization in a Solid. J. Magn. Magn. Mater. 2007, 310, 1145−1150. (32) Felser, C. Skyrmions. Angew. Chem., Int. Ed. 2013, 52, 1631− 1634.

by polar stacking of the capped vanadate trimers as well as the similar orientation of the tetrageramanate building blocks. Polar lattices can potentially lead to ferroic structures, which when coupled with ferroic magnetic order, could lead to multiferroics. In these particular structures that is ultimately unlikely due to the weak coupling between the well-separated vanadate trimers. However, the new structures in this work do contain all the necessary building blocks for new ferroic materials, as well as potential skyrmion host lattices, and should be viewed as only the first in a large series, as the broad range of synthetic options creates the potential for the preparation of new classes of important materials.

■

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.chemmater.6b05320. Results of the single crystal structure refinements (CIF) Table of elemental analysis by EDX, table of bond valence sum analysis, infrared spectra, comparison of disordered Ge4O13 arrangements, and long-range interactions of V3O13 clusters (PDF)

■

AUTHOR INFORMATION

ORCID

Colin D. McMillen: 0000-0002-7773-8797 Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS We thank the National Science Foundation (Grant No. DMR1410727) for financial support. Work at Oak Ridge National Laboratory was supported by the U.S. Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division (magnetic measurements and analysis, M.A.M.).

■

REFERENCES

(1) Sanjeewa, L. D.; Garlea, V. O.; McGuire, M. A.; McMillen, C. D.; Cao, H. B.; Kolis, J. W. Structural and Magnetic Characterization of the One-dimensional S = 5/2 Antiferromagnetic Chain System SrMn(VO4) (OH). Phys. Rev. B: Condens. Matter Mater. Phys. 2016, 93, 224407. (2) Sanjeewa, L. D.; McGuire, M. A.; Garlea, V. O.; Hu, L.; Chumanov, G.; McMillen, C. D.; Kolis, J. W. Hydrothermal Synthesis and Characterization of Brackebuschite-type Transition Metal Vanadate: Ba2M(VO4)2(OH), M = V3+, Mn3+ and Fe3+. Inorg. Chem. 2015, 54, 7014−7020. (3) Sanjeewa, L. D.; McMillen, C. D.; Willett, D.; Chumanov, G.; Kolis, J. W. Hydrothermal Synthesis of Single Crystals of Transition Metal Vanadates in the Glaserite Phase. J. Solid State Chem. 2016, 236, 61−68. (4) Greedan, J. E. Geometrically Frustrated Magnetic Materials. J. Mater. Chem. 2001, 11, 37−53. (5) Ramirez, A. P. Strongly Geometrically Frustrated Magnetics. Annu. Rev. Mater. Sci. 1994, 24, 453−480. (6) Dai, D.; Whangbo, M.-H. Classical Spin and Quantum Mechanical Descriptions of Geometric Spin Frustration. J. Chem. Phys. 2004, 121, 672−680. (7) Chirayil, T.; Zavalij, P. Y.; Whittingham, M. S. Hydrothermal Synthesis of Vanadium Oxides. Chem. Mater. 1998, 10, 2629−2640. 1411


Article

Chemistry of Materials (33) Roessler, U. K.; Bogdanov, A. N.; Pfleiderer, C. Spontaneous Skyrmion Ground States in Magnetic Metals. Nature 2006, 442, 797− 801. (34) CrystalClear; Rigaku and Molecular Structure Corp.: The Woodlands, TX, USA, 2006. (35) Sheldrick, G. M. Crystal Structure Refinement with SHEXL. Acta Crystallogr., Sect. A: Found. Crystallogr. 2008, 64, 112−122. (36) Brese, N. E.; O’Keeffe, M. Bond-Valence Parameters for Solids. Acta Crystallogr., Sect. B: Struct. Sci. 1991, 47, 192−197. (37) Brown, I. D.; Altermatt, D. Bond Valence Parameters Obtained from a Systematic Analysis of the Inorganic Crystal Structure Database. Acta Crystallogr., Sect. B: Struct. Sci. 1985, 41, 244−247. (38) Parsons, S.; Flack, H. D.; Wagner, T. Use of Intensity Quotients and Differences In Absolute Structure Refinement. Acta Crystallogr., Sect. B: Struct. Sci., Cryst. Eng. Mater. 2013, 69, 249−259. (39) Mü l ler, A.; Peters, F.; Pope, M. T.; Gatteschi, D. Polyoxometalates: Very Large Clusters-Nanoscale Magnets. Chem. Rev. 1998, 98, 239−271. (40) Müller, A.; Meyer, J.; Bögge, H.; Stammler, A.; Botar. Trinuclear Frgaments as Nucleation Centers: New Polyoxoalkoxyvanadates by (Induced) Self-Assembly. Chem. - Eur. J. 1998, 4, 1388−1397. (41) Clark, L.; Aidoudi, F. H.; Black, C.; Arachchige, K. S. A.; Slawin, A. M. Z.; Morris, R. E.; Lightfoot, P. Extending the family of V4+ S = 1/2 Kagome Antiferromagnets. Angew. Chem., Int. Ed. 2015, 54, 15457−15461. (42) Schindler, M.; Hawthorne, F. C.; Baur, W. H. A CrystalChemical Approach to the Composition and Occurrence of Vanadium Minerals. Chem. Mater. 2000, 12, 1248−1259. (43) Gorbunov, Y. A.; Maximov, B. A.; Belov, N. V. Crystal Structure of Na,Sc-Germanate Na4Sc2Ge4O13. Dokl. Akad. Nauk SSSR 1973, 211, 591−594. (44) Masuda, T.; Chakoumakos, B. C.; Nygren, C. L.; Imai, S.; Uchinokura, K. A Novel Germanate Cu2Fe2Ge4O13, With a Four Tetrahedra Oligomer. J. Solid State Chem. 2003, 176, 175−179. (45) Redhammer, G. J.; Roth, G. Cu2Sc2Ge4O13, a Novel Germanate Isotypic with the Quasi-1D Compound Cu2Fe2Ge4O13 Between 100 and 298 K. J. Solid State Chem. 2004, 177, 2714−2725. (46) Wierzbicka-Wieczorek, M.; Kolitsch, U.; Tillmanns, E. Ba2Gd2(Si4O13): A Silicate with Finite Si4O13 Chains. Acta Crystallogr., Sect. C: Cryst. Struct. Commun. 2010, 66, i29−i32. (47) Sanjeewa, L. D.; Fulle, K.; McMillen, C. D.; Wang, F.; Liu, Y.; He, J.; Anker, J.; Kolis, J. W. Hydrothermal Synthesis, Structure, and Property Characterization of Rare Earth Silicate Compounds: NaBa3Ln3Si6O20 (Ln= Y, Nd, Sm, Eu, Gd). Solid State Sci. 2015, 48, 256−262. (48) Heyward, C. C.; McMillen, C. D.; Kolis, J. W. Hydrothermal Growth of Lanthanide Borosilicates. A Useful Approach to New Acentric Crystals Including a Derivative of Cappelenite. Inorg. Chem. 2015, 54, 905−913. (49) Huang, Q.; Ulutagay, M.; Michener, P. A.; Hwu, S.-J. Salt Templated Open Frameworks (CU-2): Novel Phosphates and Aresnates Containing M3(X2O7)22‑ (M = Mn,Cu, X = P, As) Micropores 5.3Å and 12.7Å in Diameter. J. Am. Chem. Soc. 1999, 121, 10323−10326. (50) Queen, W. L.; West, J. P.; Hwu, S.-J.; VanDerVeer, D. G.; Zarzyczny, M. C.; Pavlick, R. A. The Versatile Chemistry and Noncentrosymmetric Crystal Structures of Salt-Inclusion Vanadate Hybrids. Angew. Chem., Int. Ed. 2008, 47, 3791−3794. (51) Hwu, S.-J.; Ulutagay-Kartin, M.; Clayhold, J. A.; MacKay, R.; Wardojo, T. A.; O’Connor, C. J.; Krawiec, M. A New Class of Hybrid Materials via Salt Inclusion: Novel Copper Arsenates Na5ACu4(AsO4)4Cl2 (A = Rb, Cs) Composed of Alternating Covalent and Ionic Lattices. J. Am. Chem. Soc. 2002, 124, 12404−12405. (52) Emori, S.; Inoue, M.; Kishita, M.; Kubo, M.; Mizukami, S.; Kono, M. Synthesis and Magnetic Properties of N-[2-(2hydroxyethylthio)phenyl]arenesulfonatamidatocopper(II) Chelates. Inorg. Chem. 1968, 7, 2419−2422. (53) Sinn, E.; Harris, C. M. Schiff Base Metal Complexes as Ligands. Coord. Chem. Rev. 1969, 4, 391−422.

(54) Ferrer, S.; Haasnoot, J. G.; Reedijk, J.; Müller, E.; Biagini Cingi, M.; Lanfranchi, M.; Manotti Lanfredi, A. M.; Ribas, J. Trinuclear N,NBridged Copper(II) Complexes Involving a Cu3OH Core: [Cu3(μ3OH)L3A(H2O)2]A·(H2O)x {L = 3-Acetylamino-1,2,4-triazolate; A = CF3SO3 NO3,ClO4; x = 0, 2} Synthesis, X-ray Structures, Spectroscopy, and Magnetic Properties. Inorg. Chem. 2000, 39, 1859−1867. (55) Clérac, R.; Cotton, F. A.; Dunbar, K. R.; Hillard, E. A.; Petrukhina, M. A.; Smucker, B. W. Crystal Structure and Magnetic Behavior of Cu3(O2C16H23)6·1.2C6H12. An Unexpected Structure and an Example of Spin Frustration. C. R. Acad. Sci., Ser. IIc: Chim. 2001, 4, 315−319. (56) Stone, M. B.; Fernandez-Alonso, F.; Adroja, D. T.; Dalal, N. S.; Villagrán, D.; Cotton, F. A.; Nagler, S. E. Inelastic Neutron Scattering of a Quantum Spin Trimer. Phys. Rev. B: Condens. Matter Mater. Phys. 2007, 75, 214427. (57) Zhu, T.-T.; Sun, W.; Huang, Y.-X.; Sun, Z.-M.; Pan, Y.; Balents, L.; Mi, J.-X. Strong Spin Frustration from Isolated Triangular Cu(II) Trimers in SrCu(OH)3Cl with a Novel Cuprate Layer. J. Mater. Chem. C 2014, 2, 8170−8178. (58) Fieselmann, B. F.; Hendrickson, D. N.; Stucky, G. D. EPR and Magnetic Susceptibility Studies of the Trinuclear Complex Cyanuratotris[bis(.eta.5-methylcyclopentadienyl)titanium(III)], the Binuclear Complex uracilatobis[bis(.eta.5-methylcyclopentadienyl)titanium(III)], and Related Compounds. Inorg. Chem. 1978, 17, 1841−1848. (59) Luban, M.; Borsa, F.; Bud’ko, S.; Canfield, P.; Jun, S.; Jung, J. K.; Kögerler, P.; Mentrup, D.; Müller, A.; Modler, R.; Procissi, D.; Suh, B. J.; Torikachvili, M. Heisenberg Spin Triangles in [V6}-type Magnetic Molecules: Experiment and Theory. Phys. Rev. B: Condens. Matter Mater. Phys. 2002, 66, 054407. (60) Smart, J. S. Effective Field Theories of Magnetism; Saunders: Philadelphia, 1966. (61) Sheckelton, J. P.; Neilson, J. R.; Soltan, D. G.; McQueen, T. M. Possible Valence-bond Condensation in the Frustrated Cluster Magnet LiZn2Mo3O8. Nat. Mater. 2012, 11, 493−496. (62) Mourigal, M.; Fuhrman, W. T.; Sheckelton, J. P.; Wartelle, A.; Rodriguez-Rivera, J. A.; Abernathy, D. L.; McQueen, T. M.; Broholm, C. L. Molecular Quantum Magnetism in LiZn2Mo3O8. Phys. Rev. Lett. 2014, 112, 027202.

1412


2 Triangles

Recommend Documents