1. Introduction
Magnetic materials adopting crystal structures based on the kagome lattice are of interest as model systems for the study of geometric magnetic frustration [
1,
2]. Particular interest has been focused on kagome lattice compounds containing
S = ½ ions [
3,
4,
5,
6]—for example, Cu
2+ and V
4+—since quantum fluctuations can often compete with the tendency towards long-range magnetic order, leading to unusual magnetic ground states such as quantum spin-liquids (QSLs) or valence-bond solids (VBS). A family of mixed metal fluorides of general composition A
2B′B
3F
12 (B = Cu
2+, B′ = a tetravalent cation) [
7] has recently received attention due to the observation of an exotic VBS ground state in Rb
2SnCu
3F
12 [
8]. The first members of this family to be reported were Cs
2ZrCu
3F
12 and Cs
2HfCu
3F
12, which were found to be structurally analogous to the aristotype Cs
2NaAl
3F
12 at room temperature [
9]. This structure type may be considered as a derivative of the pyrochlore structure, with 1:3 ordering of cations on the B-site leading to a layered structure with kagome layers of composition [B
3F
12] isolated from each other by the tetravalent cations. The aristotype structure has rhombohedral symmetry, space group
Rm, and exhibits a structurally “perfect” kagome lattice of co-planar, corner-shared equilateral triangles (
Figure 1).
Figure 1.
View along the ab-plane (a) and down the c-axis (b) of the aristotype structure of Cs2NaAl3F12.
Figure 1.
View along the ab-plane (a) and down the c-axis (b) of the aristotype structure of Cs2NaAl3F12.
The range of substitutions possible at the A and B′ sites of A
2B′Cu
3F
12 have so far been limited to A = Rb
+ or Cs
+ and B′ = Zr
4+, Hf
4+, Sn
4+ and Ce
4+. Earlier crystallographic studies [
10] have shown that, although Cs
2ZrCu
3F
12 adopts the aristotype structure at room temperature, a first-order structural phase transition occurs in cooling (~225 K), which may trigger the observed onset of a canted antiferromagnetic state at low temperatures (~24 K) rather than a QSL or other unconventional magnetic ground state. Magnetic studies have also shown long-range order rather than quantum-delocalised states for other members of the family, Cs
2HfCu
3F
12 and Cs
2SnCu
3F
12 [
11]. In the case of Cs
2ZrCu
3F
12, the structural phase transition, which breaks the perfection of the
S = ½ kagome lattice and leads to a monoclinic unit cell, is related to the increase in Zr
4+ coordination from six to seven.
Cs
2SnCu
3F
12 is also found to adopt the aristotype structure at room temperature but again the magnetic data suggest some form of structural transition below ambient temperature (~185 K). The nature of this transition was originally suggested, from single crystal X-ray diffraction (SCXD), to be a doubling of the unit cell
a and
b parameters [
11] (hexagonal setting of the rhombohedral cell) leading to a unit cell similar to that found for Rb
2SnCu
3F
12 (see below). However, a recent powder diffraction study has shown that although there is indeed a distortion of the kagome lattice, the adoption of a monoclinic unit cell occurs. This distortion is different from that found for Cs
2ZrCu
3F
12 and is unrelated to an increase in coordination number at the B′ site; Sn
4+ retains octahedral coordination, but an optimisation of bonding at the Sn
4+ site is suggested to be the driver [
12]. It should be noted that differences have been reported for structural transitions in powder and single crystal samples of Rb
2SnCu
3F
12 [
13] and so it is difficult to state whether the inconsistencies between the single crystal and powder studies on Cs
2SnCu
3F
12 are genuine; indeed, as will be seen, this is one of the interesting aspects of this family.
Rb
2SnCu
3F
12 has been previously found [
14] to display an imperfect kagome lattice at room temperature. In this case, the unit cell is rhombohedral, space group
R, but doubled in the
ab-plane when compared to that reported for Cs
2NaAl
3F
12. This distortion leads to four different Cu
2+–Cu
2+ distances being present and thus a loss in the perfectly frustrated triangular environment. The reasons behind this slightly different structure are most likely related to the smaller size of Rb
+ as compared to Cs
+. There is also a disorder relating to the positions some of the F
− ions, which is found to be independent of temperature [
13] Magnetically, Rb
2SnCu
3F
12 has generated the most interest as it shows a very unusual VBS ground state reminiscent of a “pinwheel” [
8]. Structurally, Rb
2SnCu
3F
12 shows particularly unusual behaviour; for powder samples at temperatures below ambient, a structurally re-entrant phase transition is observed, with the intermediate phase being a complex triclinic unit cell. This is not the case for single crystals, however, making the exact nature of the intermediate phase challenging to ascertain [
13].
The largest reported B′ cation is Ce
4+ [
15]. At room temperature, there is a major “corrugation” distortion of the kagome layer, caused by the coordination requirements of the larger Ce
4+, which in this case is eight-coordinated. This inherent distortion leads to a complex ferromagnetically-ordered structure that is far removed from the highly frustrated ground state of interest.
As this brief review of the A2B′Cu3F12 family shows, there is a large degree of substitutional flexibility in this structure type that leads to a number of significantly different structural (and magnetic) behaviours. Further variation of the constituent ions may lead to a material that retains its ideal kagome lattice down to the lowest temperatures, thus improving the chances of finding exotic magnetic ground states related to extreme frustration. When B′ increases in size (for Cs2 B′Cu3F12, B′ = Zr4+, Hf4+ and Ce4+), it is clear that the perfect kagome lattice is lost, due to the coordination demands of such large cations. When B′ is relatively large, but cannot support greater than six-coordinate environments (Cs2SnCu3F12), there appear to be other more subtle factors that encourage symmetry-breaking of the kagome lattice. On the contrary, if A is too small (Rb2SnCu3F12) there is also the presence of a distortion. This complex interplay of cation size matching, which apparently dictates structural distortion away from the ideal kagome geometry, with subsequent loss of magnetic frustration, has motivated us to expand the range of known members of this family. By decreasing the size of the B′ cation further, i.e., by incorporation of Ti4+, we have now produced the two novel materials Cs2TiCu3F12 and Rb2TiCu3F12. These represent the extremes of A/B′ cation size ratio and minimum A and B′ absolute cation size, respectively.
3. Experimental Section
Syntheses were performed in a number of ways depending on whether powder or single crystalline samples were required. For powder crystallographic studies, solid-state synthesis via reaction under flowing argon was performed. As TiF
4 is volatile below the reaction temperature, the precursor A
2TiF
6 (A = Cs, Rb) was first synthesised, by a route similar to that described in [
25]. CsCl (2 mM, Sigma Aldrich, 99%, Dorset, UK) or RbCl (2 mM, Sigma Aldrich, 99.8%) and TiO
2 (1 mM, ~99%) were mixed with deionised water (4 mL) in a 40 mL Teflon lined autoclave. Ethylene glycol (5 mL, Fisher Scientific, >99%) and HF
(aq) (1 mL, 48%–51%, Alfa Aesar, Heysham, UK) were then added to the autoclave, which was then sealed and heated under autogenous pressure at 433 K overnight. The resulting crystalline powders were then isolated by filtration, washing with water:ethylene glycol (1:1) and then dried overnight at ~330 K in air. The resulting A
2TiF
6 powders were then dried at 390 K and ~10
−4 mbar for 24 h.
The A2TiF6 powders were then mixed with CuF2 (Sigma Aldrich, 98%) in stoichiometric amounts (1:3) in an argon filled glove box. This mixture was ground and sealed in a gold tube by crimping the ends. The gold tube was then heated under flowing argon in the following manner: 20 K·min−1 373–873 K, 12 h at 873 K, 20 K·min−1 873–373 K. The resulting grey coloured powder was typically found to be 94% pure in the case of Cs2TiCu3F12 and 88% pure for Rb2TiCu3F12. Notable impurities (all <5% by powder XRD) were found to be A2TiF6, CuO and, for A = Rb, evidence of the further phases RbCuF3 and Cu2O was found.
A similar process could be adapted for the formation of single crystals; in this case the A2TiF6:CuF2ratio was adjusted to 1:2 and the heating rates in the furnace applied as follows: 20 K·min−1 373–1073 K, 12 h at 1073 K, ~3 K·min−1 1073–823 K and then 20 K·min−1 823–373 K. This method yielded colourless, platy crystals. Diffraction quality single crystals were only isolated for Cs2TiCu3F12; the crystals of Rb2TiCu3F12 seemed to suffer from a large degree of non-merohedral twinning that aggravated any meaningful single crystal X-ray diffraction study.
Samples that were synthesised for use in magnetic measurements underwent a slightly different synthesis process. CsF (or RbF), TiF4 and CuF2 were ground in stoichiometric amounts (2:1:3 molar ratio), pelletised inside an argon filled glove box and placed in a copper tube with a small crystal of XeF2, added to supply a fluorine rich atmosphere on decomposition. The tube was hermetically sealed by welding. For Cs2TiCu3F12 the tube was heated to 423 K for 24 h then 873 K for 72 h. The tube was then breached in an argon filled glove box, the contents reground, repelletised and sealed in a new copper tube with a small amount of XeF2. This new tube was then heated to 873 K for 48 h. A similar procedure was followed for Rb2TiCu3F12. For Cs2TiCu3F12 the only identifiable impurity was Cs2TiF6. For Rb2TiCu3F12 evidence of Rb2TiF6 was found and a small amount of RbCuF3 (<1%) was also identified.
Laboratory based powder X-ray diffraction (PXRD) for the purpose of phase identification was performed on a PANalytical Empyrean X-ray diffractometer (PANalytical Ltd., Cambridge, UK) using Cu Kα1 radiation and operating in either Bragg-Brentano geometry or transmission mode at the University of St Andrews and a Stoe Stadi-P diffractometer using Cu Kα1 radiation and operating in transmission mode at Moscow State University.
Synchrotron X-ray powder diffraction (SXPD) was performed at beamline I11, Diamond Light Source Ltd., Harwell, UK [
26]. This utilised glass capillaries and operated in Debye-Scherrer mode typically with radiation of λ ≈ 0.82 Å (precisely predetermined using a known standard). For analysis of A
2TiCu
3F
12, a multi-analysing crystal based detector was used in order to collect the highest resolution data possible. Datasets were collected for 15 or 30 min at a range of temperatures; for A = Rb upon cooling from 300 to 100 K in 20 K steps followed by further cooling to 85 K before heating from 100 to 300 K in 20 K steps. For A = Cs, data were collected from 300 to 100 K in 20 K steps. On reaching the required temperature, a brief period (5–10 min) was employed in order ensure that the sample was equilibrated appropriately.
Neutron powder diffraction (NPD) was performed at beamline HRPD (High resolution powder diffraction), ISIS facility, Harwell, UK. Samples of ~2 g were mounted in 8 mm cylindrical vanadium cans before loading into the diffractometer in the standard manner. Patterns were collected at room temperature.
Rietveld refinement was performed using GSAS [
27] and the EXPGUI interface [
28]. This analysis sought to fit lattice parameters, phase fractions, peak profile shape (both Gaussian and Lorentzian and, in the case of A = Cs, anisotropic peak broadening), thermal parameters (grouped by atom type) and, in the case of A = Cs, atomic coordinates.
Single crystal X-ray diffraction (SCXD) was performed on a Rigaku SCXmini diffractometer using Mo K
α1 radiation. Indexing and data processing was performed with Rigaku CrystalClear 2.0 (Rigaku Americas, Woodlands, TX, USA) and the model was solved using Shelxs-97 [
29] and the WinGX [
30] add-on. Single crystal data collection was performed both at room temperature and 125 K.
At Edinburgh University, magnetometry used a Quantum Designs MPMS-XL SQUID. Single crystal magnetometry measurements were carried out with the aid of Kapton adhesive tape to support a number of small single crystals, which were then covered in another layer of Kapton tape. The resulting sample was then suspended securely in a plastic straw. The diamagnetic susceptibility of the kapton tape was measured separately and confirmed to be insignificant compared to the signal from the samples. In both cases multiple readings were taken at different temperatures (1.9–390 K) and different fields (±70,000 Oe). At Moscow State University, the magnetic measurements were taken using a Quantum Designs PPMS using a VSM add-on unit. Samples were mounted in plastic holders which were provided by the manufacturer for use. The specifics of measurements and analysis will be referred to in the following section.
4. Conclusions
In conclusion, we have prepared two new members of the A
2B′Cu
3F
12 family, with B′ = Ti
4+, A′ = Cs
+ or Rb
+. These compositions represent new extremes of both A/B′ cation size ratio and B′ absolute cation size within this family. By this size-directed crystal engineering, it was hoped that a perfect kagome lattice might be retained at low temperatures, thus prompting retention of a magnetically-frustrated ground state. However, it is found that Rb
2TiCu
3F
12 adopts a highly distorted, triclinic structural variant even at room temperature; detailed magnetic studies of this compound were thwarted by the presence of minor magnetic impurities. Cs
2TiCu
3F
12, on the other hand, does adopt the ideal kagome structure at ambient temperature, in common with the other Cs-containing members of this family. However, it undergoes a symmetry-lowering structural phase transition upon cooling. The nature of this phase transition differs for single crystal
versus polycrystalline samples: a phenomenon that has previously been observed in Rb
2SnCu
3F
12 and is also probable, though unconfirmed, in Cs
2SnCu
3F
12. Although the deviations from ideal kagome symmetry in both single crystal and powder cases are much smaller than those in either Rb
2SnCu
3F
12 or Cs
2ZrCu
3F
12, they are sufficient to break down the magnetic frustration, inhibiting the potential for realising a QSL or VBS ground state, and promoting long-range antiferromagnetic order. The possibilities for stabilising an ideal kagome geometry at low temperatures is this family therefore seem limited. The symmetry-lowering distortions of the kagome lattices in these materials seem to be driven by purely geometrical effects,
i.e., requirements to optimize bonding at the cation sites. Might it be possible to stabilise the ideal kagome geometry by introducing larger cations at the A-site? This will require the use of complex organo-cations such as protonated amines, and correspondingly different synthetic methods. The use of such templating cations is widespread in metal-organic frameworks and also in hybrid perovskites, for example. However, such materials usually do display symmetry-lowering structural phase transitions at lower temperatures, often mediated by hydrogen-bonding interactions [
31]. Hence, although this family does not appear promising for the realisation of a QSL ground state, it does display rich and varied structural chemistry and, in particular, the unusual phenomenon of differing behaviour between single crystal and powder samples within several members of this family is worthy of further study.
Further details of the crystal structures may be obtained from Fachinformationszentrum (FIZ) Karlsruhe, 76344 Eggenstein-Leopoldshafen, Germany (e-mail:
[email protected]) on quoting deposition numbers 429373, 429374, 429375.