<?xml-model href='http://www.tei-c.org/release/xml/tei/custom/schema/relaxng/tei_all.rng' schematypens='http://relaxng.org/ns/structure/1.0'?><TEI xmlns="http://www.tei-c.org/ns/1.0">
	<teiHeader>
		<fileDesc>
			<titleStmt><title level='a'>Crystal Growth and Magnetism of Transition Metal Pyrochlore Fluorides</title></titleStmt>
			<publicationStmt>
				<publisher>American Chemical Society</publisher>
				<date>08/28/2023</date>
			</publicationStmt>
			<sourceDesc>
				<bibl> 
					<idno type="par_id">10511937</idno>
					<idno type="doi">10.1021/acs.inorgchem.3c01491</idno>
					<title level='j'>Inorganic Chemistry</title>
<idno>0020-1669</idno>
<biblScope unit="volume">62</biblScope>
<biblScope unit="issue">34</biblScope>					

					<author>Lakshani W Masachchi</author><author>Navindra Keerthisinghe</author><author>Gregory Morrison</author><author>Anna A Berseneva</author><author>Mark D Smith</author><author>Hans-Conrad zur_Loye</author>
				</bibl>
			</sourceDesc>
		</fileDesc>
		<profileDesc>
			<abstract><ab><![CDATA[Geometric magnetic frustration arises when the geometry of a structure prevents the simultaneous fulfillment of nearest-neighbor antiferromagnetic interactions and is commonly observed in lattices that exhibit a triangular topology, such as those found in the pyrochlore structure. Via a mild hydrothermal route, we have synthesized seven quaternary β-pyrochlore related fluorides AxM2+xM3+(2–x)F6, (A = Cs and Rb; M2+ = Co2+, Ni2+ and Zn2+; and M3+ = V3+ and Fe3+). Crystal structures and compositions were determined using a combination of single-crystal X-ray diffraction and energy-dispersive spectroscopy. After adjusting the reaction conditions, phase pure products of AxM2+xM3+(2–x)F6 were obtained. The magnetic susceptibility and isothermal magnetization data for all seven compounds were collected to interpret the magnetic behavior, which ranged from paramagnetic to antiferromagnetic with and without a ferromagnetic component. We found that the magnetic behavior of the AxM2+xV3+(2–x)F6 pyrochlore structures strongly depends on the presence or absence of unpaired electrons on the M2+ position. The titled pyrochlore compounds, with the exception of the Zn-analog, can be considered frustrated materials, with frustration indices in the range of 6 –13.]]></ab></abstract>
		</profileDesc>
	</teiHeader>
	<text><body xmlns="http://www.tei-c.org/ns/1.0" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:xlink="http://www.w3.org/1999/xlink">
<div xmlns="http://www.tei-c.org/ns/1.0"><head>Introduction</head><p>The phenomenon of magnetic frustration has captured significant attention in recent years, encompassing a spectrum of exotic and degenerate magnetic ground states, such as spin glass, spin ice, and spin liquid. <ref type="bibr">1</ref> The defining characteristic of magnetic frustration is the lack of magnetic order despite appreciable magnetic exchange coupling, which in the ideal case, can persist down to absolute zero temperature. This frustration primarily arises from the geometric configuration of the lattice, often featuring triangular or tetrahedral structure units with antiferromagnetic interactions that cannot all be satisfied simultaneously. <ref type="bibr">[2]</ref><ref type="bibr">[3]</ref><ref type="bibr">[4]</ref> The ideal pyrochlore structure is denoted as A2M2X6Y, where A and M are metal cations and X and Y are anions. A and M cations form two interpenetrating networks of corner-sharing tetrahedra, representing a quintessential framework for geometrically frustrated materials with magnetic ions occupying either the A or M sites. <ref type="bibr">[1]</ref><ref type="bibr">[2]</ref><ref type="bibr">[3]</ref><ref type="bibr">[4]</ref> Over the past few decades, a plethora of oxide pyrochlore materials have been reported and extensively investigated for their magnetic properties. <ref type="bibr">2,</ref><ref type="bibr">3,</ref><ref type="bibr">5</ref> Magnetic ions contained in oxide pyrochlores are mostly limited to rare earth metals and some transition metals with higher oxidation states. <ref type="bibr">3</ref> Increasingly, fluoride pyrochlores are drawing attention due to their ability to accommodate transition metals with low oxidation states, a feature that is not attainable with oxide pyrochlores. <ref type="bibr">4</ref> Despite having different oxidation states, with fluoride being -1 and oxygen being -2, fluoride and oxide anions share similarities in their ionic radii (r(O 2-) =1.4 &#197;, r(F -) = 1.33 &#197;) and electronegativities (3.44 for O and 3.98 for F). Upon substituting divalent oxide (O 2-) with monovalent fluoride (F -), the elemental composition must adjust to accommodate the lower anion charge, which can result in the formation of new materials that retain the pyrochlore structure. <ref type="bibr">4</ref> Furthermore, the strong coupling of transition metals containing unpaired electrons favors the formation of magnetic interactions at accessible temperatures; this happens more so for transition metals rather than for rare earth metals. <ref type="bibr">6</ref> The initial report of polycrystalline products of fluoride pyrochlores dates back to 1970. <ref type="bibr">4</ref> However, magnetic studies of these pyrochlores were conducted only recently, when the Cava group obtained large single crystals of AA'M2F7 type pyrochlores using the floating zone method. <ref type="bibr">6- 8</ref> Here, A denotes alkali elements and A' represents alkaline earth elements that are fully disordered, and M are transition metals. The result of these studies have shown that NaA'M2F7 materials (A' = Ca or Sr and M = Ni, Co, or Fe) display strong antiferromagnetic interactions with frustration indices ranging from 19-58, <ref type="bibr">[6]</ref><ref type="bibr">[7]</ref><ref type="bibr">[8]</ref><ref type="bibr">[9]</ref> where the frustration index &#119891; = &#120579; !" &#8725; &#119879; ! , denotes the strength of magnetic frustration based on the ratio of the Weiss temperature, &#120579; !" , to the transition temperature, &#119879; ! . <ref type="bibr">6</ref> The level of frustration in a material can be estimated by the &#119891; value where, typically, when the frustration index &#119891; exceeds 10, the material is classified as being in a state of frustration. <ref type="bibr">10</ref> Geometrically frustrated magnetism can be observed in both ideal (A2M2X6Y) and &#946;pyrochlore (&#9633;M 2 X 6 A) materials. In &#946;-pyrochlores, the A cations occupy the Y sites of the ideal pyrochlore (A 2 M 2 X 6 Y) leaving vacancies at the original A crystallographic sites. <ref type="bibr">11,</ref><ref type="bibr">12,</ref><ref type="bibr">13</ref> The displacement of the non-magnetic A cation does not affect the M cation network in &#946;-pyrochlores.</p><p>For fluoride pyrochlores, the ideal pyrochlore formula can be denoted as A 2 M 2 F 6 F', while the &#946;pyrochlores formula is &#9633;M 2 F 6 A. In &#946;-pyrochlores, mixed valent transition metals can occupy the M site and denoted as &#9633;M 2+ M 3+ F 6 A, or AM 2+ M 3+ F6 as used in this manuscript. Typically, the cubic &#946;-pyrochlores are disordered, where both M 2+ and M 3+ cations occupy the same site. <ref type="bibr">14</ref> However, ordered orthorhombic structures have been reported with crystallographically ordered M 2+ and M 3+ cations. <ref type="bibr">15,</ref><ref type="bibr">16</ref> Previous studies have shown that orthorhombic pyrochlores, such as CsFeFeF6 (&#119891; = 19), RbFeFeF6 (&#119891; = 17), and CsMnMnF6 (&#119891; = 4), exhibit lower magnetic frustration compared to their cubic counterparts, including CsNiFeF6 (&#119891; = 37), CsCoFeF6 (&#119891; = 54), and CsMnFeF6 (&#119891; = 11). <ref type="bibr">14,</ref><ref type="bibr">15,</ref><ref type="bibr">[17]</ref><ref type="bibr">[18]</ref><ref type="bibr">[19]</ref><ref type="bibr">[20]</ref><ref type="bibr">[21]</ref><ref type="bibr">[22]</ref> Therefore, we are interested in studying &#946;-pyrochlores having cubic symmetry in order to test their magnetic frustration. The cubic pyrochlore compositions reported in the literature were obtained using the flux method, and some of the orthorhombic charge-ordered pyrochlores were synthesized using both flux and mild hydrothermal methods. <ref type="bibr">20,</ref><ref type="bibr">23</ref> Although cubic AM 2+ M 3+ F6 pyrochlores (A = Cs and Rb; M 2+ =Co 2+ , Ni 2+ , and Mn 2+ ; and M 3+ = Fe 3+ and Cr 3+ ) have been studied</p><p>for their magnetism, those with M 3+ = V 3+ remain unexplored. Even though some &#946;-pyrochlores, such as CsCoVF6, CsNiVF6, CsZnVF6, and CsZnFeF6, have been reported previously, magnetic analyses for these materials are yet to be performed. <ref type="bibr">[24]</ref><ref type="bibr">[25]</ref><ref type="bibr">[26]</ref> In order to identify the contribution of individual M 2+ and M 3+ cations toward frustration, it is necessary to synthesize additional compounds belonging to this family.</p><p>Herein we report the mild hydrothermal synthesis of seven &#946;-pyrochlore related compounds. Compounds 1-6, Cs0.86Co0.86V1.14F6, Cs0.9 Ni0.9V1.1F6, Cs0.9 Zn0.9V1.1F6, CsZnFeF6, Rb0.93Co0.93V1.07F6, and Rb0.97Ni0.97V1.03F6, respectively, are disordered cubic while compound 7, Rb(Zn0.2V0.8)(Zn0.8V0.2)F6, is a partially charged ordered orthorhombic phase. Their synthesis, crystal structures, and magnetic behaviors are discussed.</p></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head>Experimental</head></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head>Synthesis</head><p>Materials: RbCl (99.8%, Alfa Aesar), CsCl (99%, Alfa Aesar), CsF (99%, Alfa Aesar), V2O3 (95%, Alfa Aesar), Fe(C5H7O2)3 (99%, Stem), Mn(CH3COO)2&#8226;4H2O (98%, Alfa Aesar),</p><p>Co(CH3COO)2&#8226;4H2O (98%, Alfa Aesar), and HF (49% aqueous, VWR &#174; ) were used as received.</p><p>Caution! Hydrofluoric acid is highly corrosive and acutely toxic and must be handled with proper safety precautions in a well-ventilated space. In case of exposure, proper treatment with immediate medical attention is essential.</p><p>Using the mild hydrothermal synthesis, <ref type="bibr">15,</ref><ref type="bibr">16</ref> seven mixed metal &#946;-pyrochlore related fluorides with compositions AM 2+ VF6 (A = Cs and Rb; and M 2+ = Ni 2+ , Co 2+ , and Zn 2+ ) and</p><p>CsZnFeF6 were successfully synthesized. The starting materials (Table <ref type="table">1</ref>) were added to a 23 mL PTFE liner along with 1 mL of deionized water and 1 mL of 49% aqueous HF and sealed in a steel autoclave. The autoclave was heated to 200 &#176;C at 10 &#176;C/min in a programmable convection oven, allowed to dwell for 12 hours, and cooled to room temperature by shutting off the oven. The polycrystalline powders were isolated via vacuum filtration and washed with methanol and acetone. Following this, the isolated products were sonicated for 30 minutes in methanol, and the final products were collected by vacuum filtration. Single-Crystal X-ray Diffraction (SXRD) X-ray intensity data were collected at 298(2) or 301(2) K using a Bruker D8 QUEST diffractometer equipped with a PHOTON-II area detector and an Incoatec microfocus source (Mo K&#945; radiation, &#955; = 0.71073 &#197;). The crystals were mounted on a microloop using immersion oil. The raw area detector data frames were reduced and corrected for absorption effects using the SAINT+ and SADABS programs. <ref type="bibr">27,</ref><ref type="bibr">28</ref> Final unit cell parameters were determined by least-squares refinement. Initial structural models were obtained with SHELXT. <ref type="bibr">29</ref> Subsequent difference Fourier calculations and full-matrix least-squares refinement against F 2 were performed with SHELXL-2018 using Olex2. The crystallographic data and results of the diffraction experiments are summarized in Table <ref type="table">2</ref>.</p><p>Powder X-ray Diffraction (PXRD)</p><p>Powder X-ray diffraction data were collected on a Bruker D2 Phaser powder X-ray diffractometer using Cu K&#945; radiation to confirm the phase purity of polycrystalline samples obtained by grinding single crystals (Figure <ref type="figure">S1</ref> and<ref type="figure">S2</ref>). The data were collected between the angular range 5-65 &#8226; 2&#952; in step of 0.04 &#8226; over 60 minutes.</p></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head>Energy-Dispersive Spectroscopy (EDS)</head><p>EDS was performed on single crystals using a TESCAN Vega-3 SBU scanning electron microscope (SEM) with a Thermo EDS attachment operated in low-vacuum mode (Table <ref type="table">S1</ref>). The crystals were mounted on an SEM stub with carbon tape and analyzed using 20 kV accelerating voltage and an accumulation time of 20 seconds.</p></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head>Magnetic Measurements</head><p>Susceptibility and magnetization measurements were performed on ground single crystals using a Quantum Design MPMS3 SQUID magnetometer. Susceptibility measurements were collected under zero-field cooled (ZFC) and field-cooled (FC) conditions in the temperature range of 2-300 K at an applied field of 0.1 T. Magnetization as a function of the field was measured at 2 K in an applied field ranging from -5 to +5 T. The raw data were corrected for radial offset and shape effects. <ref type="bibr">30</ref> AC measurements were performed on Cs0.86Co0.86V1.14F6 at applied field 0.025</p><p>Oe with a frequency of 100, 200, 500, and 1000 Hz (Figure <ref type="figure">S12</ref>) to further study the magnetic transition.</p><p>Inductively coupled plasma optical emission spectroscopy (ICP-OES)</p><p>ICP-OES was performed using a Perkin Elmer Avio 200 spectrometer on digested samples of Cs0.9Zn0.9V1.1F6 and Rb(Zn0.2V0.8)(Zn0.8V0.2)F6. The digestion was performed in PerkinElmer's Titan MPS Microwave Sample Preparation System. The crystalline sample (&#8776; 2.0 mg) was loaded into a Teflon liner with 8 mL of aqua regia (HNO3, HCl, and deionized water were mixed in a 4:8:3 volume ratio). The Teflon liner was placed into a programmable microwave oven. The oven was ramped to 175 &#176;C and 30 bars in 30 min. The sample was held at that temperature and pressure for 10 minutes and cooled down to 50 &#176;C in 125 min. Once at room temperature, the digested sample was diluted to the appropriate concentrations using 5 wt % HNO3. The calibration curves were measured for Zn and V by axial detector (Table <ref type="table">S4</ref>).</p></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head>Electron paramagnetic resonance (EPR) measurements</head><p>EPR measurements were carried out on a Bruker EMX plus equipped with a Bruker Xband microwave bridgehead and Xenon software (v 1.2). Solid samples were loaded into quartz tubes. All spectra were recorded at room temperature and a microwave frequency of 9.705 GHz.</p></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head>Results and Discussion</head></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head>Synthesis</head><p>The mild hydrothermal synthesis method is convenient for preparing many fluoride materials, which motivated us to use this approach to target the synthesis of new compositions of &#946;-pyrochlore fluorides. <ref type="bibr">15,</ref><ref type="bibr">[31]</ref><ref type="bibr">[32]</ref><ref type="bibr">[33]</ref> Single crystals along with polycrystalline powders of AM 2+ M 3+ F 6 (A = Cs and Rb; M 2+ = Co 2+ , Ni 2+ , and Zn 2+ ; and M 3+ = V 3+ and Fe 3+ ) were successfully obtained hydrothermally using HF as a fluorinating agent and as a solvent at the relatively low temperature of 200&#176;C. The conditions were adjusted after several trial syntheses to obtain phase-pure singlecrystal products. The desired target products were obtained by varying starting reagents and their ratios and concentrations, HF and water volume ratio, and temperature profiles. The initial reagent ratios were selected according to the stoichiometry of the desired product (Table <ref type="table">1</ref>) with 1 mmol of M 2+ and 1 mmol of M 3+ being used. However, for Rb(Zn0.2V0.8)(Zn0.8V0.2)F6, a phase pure product was obtained only when the starting reagent atomic ratio of M 2+ :M 3+ was 2:1. Using FeCl3&#8226;6H2O and CsCl as starting reagents for CsZnFeF6 resulted in a mixed-valent iron phase CsFe 2+ Fe 3+ F6. The Fe 2+ component results from the in-situ reduction of Fe 3+ , which is facilitated by the oxidation of Cl -. <ref type="bibr">15</ref> Therefore, CsF and Fe(C5H7O2)3 were used to grow CsZnFeF6 crystals.</p><p>Exploring the use of different volume ratios of HF to H2O resulted in many different ternary and quaternary phases, some known and some new, which will be described in a separate paper. Only  have been previously reported as stoichiometric phases. <ref type="bibr">[24]</ref><ref type="bibr">[25]</ref><ref type="bibr">[26]</ref> However, they differ from our single crystal structure determinations of 1-3, Cs0.86Co0.86V1.14F6, Cs0.9 Ni0.9V1.1F6, and Cs0.9 Zn0.9V1.1F6, that do not refine to full site occupancies, although the structures are otherwise the same.</p><p>The three-dimensional framework of the &#946;-pyrochlore structure consists primarily of  <ref type="table">S2</ref>).  </p></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head>Magnetic Properties</head><p>The M 2+ F6 and M 3+ F6 polyhedra in the cubic and orthorhombic pyrochlore structures are arranged into a corner-sharing tetrahedral arrangement shown in Figure <ref type="figure">3a</ref>. As a result, each M 2+ /M 3+ site is associated with three Kagome layers. The three Kagome layers in the cubic pyrochlore structure are identical and consist of equilateral triangles (Figure <ref type="figure">3b</ref>); on the other hand, the Kagome layers of the orthorhombic pyrochlore structure are different in that two of them consist of isosceles triangles (Figure <ref type="figure">3c</ref>) and one is comprised of scalene triangles (Figure <ref type="figure">3d</ref>).</p><p>When these M 2+ /M 3+ sites are occupied with magnetic cations, it leads to geometrically frustrated magnetism. <ref type="bibr">4,</ref><ref type="bibr">14,</ref><ref type="bibr">15</ref> To investigate the magnetic behavior of the title compounds, we collected zero field-cooled and field-cooled DC magnetic susceptibility vs. temperature and magnetization vs.</p><p>field data, the results of which are summarized in Table <ref type="table">3</ref>.  Magnetic susceptibility and inverse susceptibility as a function of temperature plots are shown in Figure <ref type="figure">4</ref>. The high-temperature regions (150 to 300 K) of the plots were fit to the Curie-</p><p>, where &#120594; is the magnetic susceptibility, C is the Curie constant, &#932; is temperature, and &#120579; !" is the Weiss temperature. <ref type="bibr">15,</ref><ref type="bibr">33</ref> Both cobalt-containing compounds (Cs0.86Co0.86V1.14F6 and Rb0.93Co0.93V1.07F6) have an experimental magnetic moment that is larger than the spin-only moment, presumably due to spin-orbital coupling of Co 2+ . <ref type="bibr">33</ref> For Cs0.9Zn0.9V1.1F6, and Rb(Zn0.2V0.8)(Zn0.8V0.2)F6, notably reduced experimental magnetic moments are observed when compared to the calculated moments (Table <ref type="table">3</ref>). In previous literature reports, this discrepancy is reported for V 3+ -compounds and is explained by the contribution of spin-spin coupling or spin-orbital coupling to the overall magnetic moment. <ref type="bibr">34,</ref><ref type="bibr">35</ref> To confirm the reduced moment of V 3+ in these samples, a second sample of each was prepared and it's magnetic properties measured. Furthermore, we performed inductively coupled plasma optical emission spectroscopy (ICP-OES) for both of these samples and confirmed the formula derived from SXRD (see SI for more information, Table <ref type="table">S4</ref>). Finally, to address the oxidation state of vanadium in Cs0.9Zn0.9V1.1F6 and Rb(Zn0.2V0.8)(Zn0.8V0.2)F6 compounds, we conducted electron paramagnetic resonance (EPR) measurements. For both samples, we observed an EPR single in the X-band, which was well-refined (R 2 &gt; 0.995) with only one Lorentz derivative profile, and multicomponent fitting did not improve fitting characteristics (Figures <ref type="figure">S10</ref> and<ref type="figure">S11</ref>). Therefore, SXRD, ICP-OES, and EPR support the formulas of Cs0.9Zn0.9V 3+ 1.1F6 and Rb(Zn0.2V 3+ 0.8)(Zn0.8V 3+ 0.2)F6</p><p>and that the reduced magnetic moments in these compounds are a feature of V 3+ . Both Cs0.9Zn0.9V1.1F6 and Rb(Zn0.2V0.8)(Zn0.8V0.2)F6 exhibit only paramagnetic behavior and do not exhibit a magnetic transition down to 2 K (Figures <ref type="figure">4a</ref> and<ref type="figure">4b</ref>). However, a magnetic transition is evident in all the other vanadium compounds, (Cs0.86Co0.86V1.14F6, Cs0.9Ni0.9V1.1F6, Rb0.97Ni0.97V1.03F6, and Rb0.93Co0.93V1.07F6), in the very low-temperature region as illustrated in Figures <ref type="figure">4c-4f</ref>, respectively. This highlights that in order for the V 3+ -containing &#946;-pyrochlores to exhibit magnetic order it is necessary to have cations with unpaired electrons on the M 2+ site.  <ref type="table">3</ref>). <ref type="bibr">36</ref> It is worth pointing out that CsZnFeF6 is an outlier when compared to the vanadium compounds. As shown in Figure <ref type="figure">5</ref>, no long-range magnetic transition is evident down to 2K. Nonetheless, a large negative Curie-Weiss temperature (-217 K) is observed for CsZnFeF6, indicative of stronger antiferromagnetic interactions when compared to the vanadium analogs. The reported Weiss temperatures (&#120579; !" ) for the known &#946;-pyrochlores, such as CsNiFeF6, CsCoFeF6, CsMnFeF6, CsNiCrF6, CsCoCrF6, CsMnCrF6, and CsFeCrF6, are -210 K, -240 K , -300 K, -70 K, -76 K, -68 K, and -98 K, respectively (Table <ref type="table">4</ref>). <ref type="bibr">[17]</ref><ref type="bibr">[18]</ref><ref type="bibr">[19]</ref><ref type="bibr">22</ref> According to Goodenough, the Weiss temperature in &#946;-pyrochlores represents the sum of the nearest-neighbor interactions between the magnetic ions, as per his superexchange rules. <ref type="bibr">18,</ref><ref type="bibr">37</ref> Due to the random distribution of magnetic ions on the M 2+ /M 3+ site, there will be interactions involving the cations pairs (M 2+ -M 3+ ), (M 2+ -M 2+ ), and (M 3+ -M 3+ ). <ref type="bibr">18,</ref><ref type="bibr">22</ref> According to the Berkooz et.al, <ref type="bibr">18</ref> a moderate ferromagnetic contribution for the interaction (M 2+ -F-M 3+ ), a weak antiferromagnetic contribution for the interaction (M 3+ -F-M 3+ ), and a strong antiferromagnetic contribution (M 2+ -F-M 2+ ), were suggested for the &#946;-pyrochlore compounds that contain ion pairs (Fe 2+ , V 3+ ), (Mn 2+ , Cr 3+ ) and (Fe 2+ , Cr 3+ ). Also, all nearest neighbor interactions within CsM 2+ Fe 3+ F6 (M 2+ = Ni 2+ and Mn 2+ ) compounds are predicted to be strongly antiferromagnetic. <ref type="bibr">18</ref> Thus, for the Cr 3+ and V 3+</p><p>compounds, (M 2+ -F-M 3+ ) interactions should be moderately ferromagnetic, thus reducing the negative value of &#120579; !" compared to the CsM 2+ Fe 3+ F6 compounds where all the magnetic interactions are antiferromagnetic. <ref type="bibr">18</ref> Moreover, the known inverse weberite compounds also exhibited higher Weiss temperatures for M 2+ Fe 3+ F5(H2O)2 compared to M 2+ Cr 3+ F5(H2O)2, and</p><p>, where M 2+ is Ni 2+ /Co 2+ : e.g., CoFeF5(H2O)2, CoCrF5(H2O)2, NiCrF5(H2O)2, and NiVF5(H2O)2, &#120579; !" is equal to -175 K, -46 K, -56 K, and -56 K, respectively (Table <ref type="table">4</ref>). <ref type="bibr">33</ref> We therefore suggest that, based on the type of interaction present between (M 2+ -F-M 3+ ), the magnitude of the Weiss temperature can be estimated. If M 2+ -F-M 3+ exhibits a ferromagnetic component, the negative value of the Weiss temperature will be reduced, and if the interaction between M 2+ -F-M 3+ is antiferromagnetic, the negative value of the Weiss temperature will be further increased. According to the Kanamori-Goodenough rules, the 180&#176; superexchange interactions between the same kind of cations in octahedral sites generally exhibit antiferromagnetic interaction (180&#176; cation-anion-cation superexchange rule also applies to the ~139&#176; interactions, Table <ref type="table">S3</ref>).   Based on the Cava group analysis, rearranging the Curie-Weiss law &#120594; = &#119862;/(&#119879; -&#120579; !" ) to</p><p>-1, can be used to create a normalized, dimensionless plot that is useful for comparing magnetic behavior of different compounds. <ref type="bibr">8,</ref><ref type="bibr">9</ref> In Figure <ref type="figure">6</ref>   include a ferromagnetic term for the nearest-neighbor interaction. <ref type="bibr">18</ref> Moreover, zero field cooled and field cooled splitting in the susceptibility plots of Cs0.86Co0.86V1.14F6, Cs0.9Ni0.9V1.1F6, Rb0.97Ni0.97V1.03F6, and Rb0.93Co0.93V1.07F6, imply the presence of a ferromagnetic component, such as canted antiferromagnetic behavior, in these materials (Figure <ref type="figure">4</ref>). <ref type="bibr">15</ref> This discrepancy is more pronounced for Cs0.86Co0.86V1.14F6 and Rb0.93Co0.93V1.07F6 (Figure <ref type="figure">4c</ref> and 4f, respectively), and hysteresis is observed in the M vs. H plots, shown in Figures <ref type="figure">S3</ref> and<ref type="figure">S7</ref>. Thus, it appears that the ferromagnetic interaction between Co 2+ and V 3+ is more prominent than between Ni 2+ and V 3+ . To test for the presence of spin glass behavior we performed AC measurements on Cs0.86Co0.86V1.14F6</p><p>and did not observe a shift in the peak as a function of frequency, suggesting that no spin glass behavior is present. (Figure <ref type="figure">S12</ref>). </p></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head>Magnetic Frustration</head><p>The frustration indices of the title compounds Cs0.86Co0.86V1.1F6, Cs0.9Ni0.9V1.1F6, Rb0.97Ni0.97V1.03F6, and Rb0.93Co0.93V1.07F6 fall into the range of 6-13 (Table <ref type="table">3</ref>). Typically, a frustration index larger than 10 implies a frustrated material. <ref type="bibr">7,</ref><ref type="bibr">8</ref> We cannot determine a frustration index for CsZnFeF6 as we could not observe a long range magnetic transition for CsZnFeF6 down to 2 K. Very low-temperature magnetic susceptibility studies can be conducted as a future investigation to reveal the magnetic ordering temperature of CsZnFeF6 and its magnetic behavior.</p><p>Using data from the literature, we also estimated the frustration indices for known &#946;-pyrochlores CsNiFeF6, CsCoFeF6, CsNiCrF6, and CsCoCrF6 |&#119891;| to be equal to 37, 54, 23, and 22, respectively (Table <ref type="table">4</ref>), <ref type="bibr">[17]</ref><ref type="bibr">[18]</ref><ref type="bibr">[19]</ref><ref type="bibr">22</ref> which highlight that the frustration indices for Cr 3+ and Fe 3+ containing cubic &#946;pyrochlores are higher compared to Cs0.9Ni0.9V1.1F6 and Cs0.9Co0.9V1.1F6 where the |&#119891;| is equal to 13 and 7, respectively (Table <ref type="table">3</ref>).</p><p>As mentioned earlier, the triangular topology may cause geometric frustration within the materials. In addition to pyrochlores, other structure types, such as weberite, and inverse weberite, exhibit a specific triangular topology, which results in magnetic frustration in these materials.</p><p>Weberite fluorides have the general formula of AM 2+ M 3+ F7 (A is an alkali metal, and M 2+ and M 3+ are 3d metal cations), which is similar to the formula of fluoride pyrochlore. However, both M 2+ and M 3+ cations in the weberite structure reside on distinct octahedral sites where each vertex of the M 2+ octahedron connects to another four M 2+ octahedra and two M 3+ octahedra, while only four vertices of M 3+ octahedra link to other M 2+ octahedra. <ref type="bibr">41</ref> This connectivity of magnetic ions creates two separate Kagome layers within the weberite structure. <ref type="bibr">33</ref> The inverse weberite (M 2+ M 3+ F5(H2O)2) has a structure similar to weberites, with the exception that the M 2+ and M 3+ octahedral sites are switched, that two F atoms are replaced by water molecules, and the absence of A cations. <ref type="bibr">33,</ref><ref type="bibr">39,</ref><ref type="bibr">40</ref> In general, the frustration indices of these compounds are less than 10 (Table <ref type="table">4</ref>), which indicates that pyrochlores are more magnetically frustrated compared to weberites and inverse weberites, as each magnetic cation belongs to three Kagome layers due to the corner-shared tetrahedral arrangement of magnetic ions in pyrochlores. By contrast, for weberite and inverse weberite, a magnetic cation is a part of only one or two Kagome layers. <ref type="bibr">15,</ref><ref type="bibr">33,</ref><ref type="bibr">39,</ref><ref type="bibr">40</ref>   <ref type="bibr">15,</ref><ref type="bibr">20,</ref><ref type="bibr">21</ref> Cubic to orthorhombic structure changes can influence the less homogenous exchange interactions between magnetic ions, which lead to a more ordered magnetic structure with fewer competing interactions and less frustration. This suggests that the frustration index is decreasing in going from the cubic pyrochlore to the orthorhombic pyrochlore to the inverse weberite and to the weberite structure.</p><p>This study shows the significance of having cations with unpaired electrons on the M 2+ site for the V 3+ -containing &#946;-pyrochlores to induce magnetic order and magnetic frustration within the materials. Nearest neighbor interactions between ions pairs also affect the Weiss temperature of the material; herein we suggest that the emergence of ferromagnetic interaction between (M 2+ -F-V 3+ ) can reduce the Weiss temperature of V 3+ -containing &#946;-pyrochlores compared to the Fe 3+based analogs. However, more compounds of this family need to be synthesized and studied to draw more definitive conclusions about the effect of the M 2+ and M 3+ cations on the overall frustration. V 3+ , which appear to be more pronounced than those between Ni 2+ and V 3+ . Paramagnetic behavior was observed for Cs0.9Zn0.9V1.1F6 and Rb(Zn0.2V0.8)(Zn0.8V0.2)F6 down to 2K, which highlights that the magnetic ordering of these compounds is disfavored when the M 2+ cation lacks unpaired electrons. In contrast, CsZnFeF6 exhibits a higher Weiss temperature compared to all vanadium analogs synthesized. Thus, we can suggest that all the nearest-neighbor magnetic interactions of CsZnFeF6 are antiferromagnetic, which is further supported by the strong antiferromagnetic deviation in the &#119862; (&#120594;|&#120579; !" |) = &#119879; |&#120579; !" | &#8260; &#8260; -1 plot. However, CsZnFeF6 does not order magnetically above 2K. To determine the actual magnetic behavior of CsZnFeF6 and to identify its magnetic structure will require a very low-temperature magnetic susceptibility study. Even though we can relate the effect of the M 2+ and M 3+ cations to the value of the Weiss temperature, there is still ambiguity surrounding how the magnetic ion's characteristics affect the frustration indices. Answering this question will require the synthesis and investigation of additional compounds of the pyrochlore family. However, we can infer that the frustration index is reduced in pyrochlores going from Fe 3+ to Cr 3+ to V 3+ , and also when progressing from cubic pyrochlore to orthorhombic pyrochlore, and then to inverse weberite and weberite.</p></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head>Conclusion</head></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head>Acknowledgment</head><p>Financial support for this work was provided by the National Science Foundation via award DMR-2221403 and is gratefully acknowledged. We thank Dr. Perry J. Pellechia for assistance in the EPR</p></div></body>
		</text>
</TEI>
