ARTICLE pubs.acs.org/cm
Structural Phase Transition in the S = 1/2 Kagome System Cs2ZrCu3F12 and a Comparison to the Valence-Bond-Solid Phase in Rb2SnCu3F12 Sandra A. Reisinger,† Chiu C. Tang,‡ Stephen P. Thompson,‡ Finlay D. Morrison,† and Philip Lightfoot*,† † ‡
School of Chemistry and EaStChem, University of St. Andrews, St. Andrews, Fife, KY16 9ST, United Kingdom Diamond Light Source, Ltd., Harwell Science and Innovation Campus, Didcot, Oxfordshire, OX11 ODE, United Kingdom
bS Supporting Information ABSTRACT: The crystal structure of the S = 1/2 kagome system Cs2ZrCu3F12 has been determined at both 295 and 125 K via singlecrystal X-ray diffraction. A first-order structural phase transition is seen near 225 K, confirmed by variable-temperature synchrotron powder diffraction studies, in which the structure transforms from rhombohedral (R3m) to monoclinic (P21/m). A corresponding abrupt change in dielectric constant is observed near the same temperature. The phase transition is driven by a dramatic change in coordination around the Zr site, which changes from regular octahedral in the rhombohedral phase to a seven-coordinate environment in the monoclinic phase. This leads to a severe buckling of the copper fluoride kagome layers and significant changes in the geometry around the Cu sites, which correlates with both the observed dielectric anomaly and a previously observed anomaly in magnetic susceptibility. It is suggested that this structural phase transition ultimately permits long-range antiferromagnetic ordering in Cs2ZrCu3F12, contrasting markedly with the behavior of the analogue Rb2SnCu3F12, which exhibits a “pinwheel” valence-bond-solid ground state. KEYWORDS: kagome lattice, magnetic frustration, phase transition, copper fluoride
’ INTRODUCTION There is much current excitement in the condensed matter physics community concerning the fundamentals of frustrated magnetic systems. Particularly sought-after phenomena are exotic electronic ground states such as “valence-bond solids” (VBS) and “resonating valence bond” (RVB) states, the latter giving rise to the special case of a so-called “quantum spin-liquid” (QSL) state.1,2 The realization of each of these states requires a frustrated lattice of S = 1/2 magnetic centers, in which the spins “pair up” locally to produce a singlet state, in a similar sense as in a conventional chemical bond. The key difference between the VBS and RVB (or QSL) states is that, in the VBS state, the ground state has a specific pattern of localized, static spin pairs, which, in principle, breaks the lattice symmetry, whereas in the RVB state quantum fluctuations, even at zero temperature, are sufficient to disrupt this static, localized nature, leading to a state that can be considered as a superposition of many different valence-bond pairs (i.e., a “liquidlike” spin state). Perhaps the most widely studied materials that are likely and, to some extent, proven to exhibit these phenomena are based on the two-dimensional (2D) kagome lattice. Much of the recent work in the area of QSLs has focused on herbertsmithite (Cu3Zn(OH)6Cl2), which, despite very strong antiferromagnetic interactions, shows no long-range magnetic order down to 50 mK.3,4 Prior to the synthesis of herbertsmithite, another Cu2+based mineral, volborthite, acted as a model compound for kagome-lattice physics,5 and, very recently, the field has seen r 2011 American Chemical Society
another significant new impetus with the preparation of the first d1 (V4+)-based kagome system.6 In the case of the VBS state, a unique “pinwheel-like” arrangement of localized spin pairs has very recently been reported in the complex fluoride Rb2SnCu3F12.7,8 This compound is part of a wider family of structurally and compositionally related materials, A2BCu3F12 (where A+ = Rb, Cs and B4+ = Zr, Hf, Sn).9,10 However, despite their compositional similarities, the magnetic behaviors of these materials differ in very significant ways. In particular, Rb2SnCu3F12 is the only one of the family to exhibit VBS behavior, with no evidence of long-range magnetic order down to 1.3 K, and a low-lying singlet to triplet spin gap. The Cs analogues Cs2BCu3F12 (where B4+ = Zr, Hf, Sn), on the other hand, each exhibit long-range antiferromagnetic order with TN in the region of 2025 K.10,11 Moreover, their magnetic susceptibilities show anomalies at a much higher temperature (in the region of 200 K), which, again, is absent in Rb2SnCu3F12, which has been suggested to arise from a structural phase transition.10,11 The objective of this paper is to characterize the postulated structural phase transition in Cs2ZrCu3F12. This provides a simple structural chemistry basis for the dramatically differing magnetic behavior within this family, and it may also Received: June 21, 2011 Revised: August 2, 2011 Published: September 02, 2011 4234
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Table 1. Single-Crystal Data Collection and Refinement Details
Table 2. Selected Bond Distances and Bond Angles Bond Distances at 295 K
295 K
125 K
formula
Cs2Cu3ZrF12
Cs2Cu3ZrF12
crystal system space group
rhombohedral R3m
monoclinic P21/m
Bond Distances at 125 K
length (Å)
length (Å)
Cu1F1 (4)
1.892(2)
Cu1F2 (2)
Cu1F2 (2)
2.332(6)
Cu1F1 (2)
1.959(6)
Cu1F3
2.237(10)
Cu1F3
2.368(10)
unit-cell dimensions (Å)a Zr1F2 (6)
2.009(6)
1.930(6)
a
7.1560(19)
7.798(15)
b
b=a
7.212(14)
c
20.447(7)
10.351(19)
Cs1F1 (3)
3.151(6)
Cu2F1 (2)
1.906(6)
93.97(2)°
Cs1F2 (3)
3.432(6)
Cu2F5 (2)
2.018(5)
580.7(19)
Cs1F1 (3) Cs1F2 (6)
3.475(6) 3.604(2)
Cu2F6 (2) Cu3F7 (2)
2.191(7) 1.913(4)
Cu3F2 (2)
1.930(6)
Cu3F8 (2)
2.303(7)
β volume (Å3)
906.8(5)
Z wavelength (Å)
3
F(calc) (Mg/m3)
4.261
4.436
absorption coefficient (mm1)
12.11
12.60
2 0.71073
0.16 0.06 0.03
crystal size (mm)
Zr1F3
2.005(9)
Zr1F4
2.018(9)
theta range for data collection (°)
2.9925.17
1.9725.01
reflections collected
2675
5010
Zr1F8 (2)
2.043(7)
independent reflections
235
1114
completeness to θ = 25.17° (%) absorption correction
99.6 99.7 semiempirical from equivalents
Zr1F6 (2) Zr1F5
2.115(7) 2.294(9)
max. and min transmission
0.713/0.248
refinement method
Bond Angles at 295 K
1.000/0.707
full-matrix least-squares on F
data/restraints/parameters
235/0/22
1114/0/97
goodness-of-fit on F2
1.22
1.12
R indices [I > 2σ(I)], R1, wR2
0.0474, 0.0993
0.0489, 0.1022
R indices (all data), R1, wR2
0.0516, 0.1041
0.0620, 0.1087
largest diff. peak and hole (e Å3)
1.41, 1.16
1.98, 1.48
Cu1F1Cu1 (4)
142.1(3)
Cu1F1Cu2
137.5(3)
133.1(3)
Cu1F2Cu3
142.7(3)
The unit-cell parameters determined at 125 K from the single-crystal experiment are poorly determined, perhaps due to some microtwinning or mosaicity on passing through the phase transition; the observed diffraction maxima were noticeably less sharp than those at room temperature. For this reason, the unit-cell parameters derived from the powder diffraction study are deemed more reliable.
’ EXPERIMENTAL SECTION Synthesis. CsF, CuF2, and ZrF4 were weighed out in stoichiometric amounts and mixed under an inert atmosphere. The mixture was then transferred to a gold tube and crimped shut. The gold tube was dehydrated at 120 °C for 12 h and then heated to 750 °C for 12 h, to enable all starting materials to melt. It was then cooled to 500 °C over a period of 3 days. Single-Crystal X-ray Diffraction. Data were collected in air at 295 and 125 K, using a Rigaku Model SCXmini diffractometer. The same crystal was used for both measurements. The structures were solved by direct methods and refined using SHELXL-97.12 Powder X-ray Diffraction. Preliminary analysis of the sample quality was carried out in-house using a Stoe Model STADI/P diffractometer (CuKα1 radiation). Variable-temperature studies were performed at Beamline I11 at the Diamond Light Source synchrotron13 at a wavelength of 0.825558(2) Å, and at 19 temperatures between 125 K and 300 K, using an Oxford Cryostream Plus system. Samples were mounted in 0.5-mm-diameter glass capillaries. Rietveld refinements were carried out using the GSAS package.14
angle (°)
Cu1F2Zr1 (2)
a
provide insights into crystal-chemical mechanisms to design and control VBS and possibly RVB/QSL behavior in this series of compounds.
Bond Angles at 125 K
angle (°)
2
Cu2F5Cu2
126.7(5)
Cu3F7Cu3
140.9(5)
Cu1F3Zr1
127.4(4)
Cu1F4Zr1 Cu2F5Zr1 (2)
131.3(4) 109.9(2)
Cu2F6Zr1
110.2(3)
Cu3F8Zr1
140.3(3)
Electrical Measurements. Dielectric (capacitance and loss) measurements were carried out in the frequency range from 100 Hz to 10 MHz, using an Agilent Model 4294A impedance analyzer with an excitation voltage of 500 mV and in the temperature range between 50 and 340 K in a closed-cycle helium refrigerator with heating/cooling rates of 2 K min1. Electrodes were fabricated from silver paste applied to opposing faces of an agglomeration of single crystals. Because of the irregular geometry, it was not possible to determine the precise electrode area and separation; however, as a rough approximation, these were 1 mm2 on a sample of thickness of 1 mm.
’ RESULTS AND DISCUSSION Single-Crystal Structures. Details of the crystal structure analyses for the two polymorphs are given in Table 1, and selected bond distances and angles are given in Table 2. The crystal structure determined at 295 K is in excellent agreement with that previously reported by M€uller.9 Two-dimensional (2D) copperfluoride kagome sheets extend in the ab-plane (see Figure 1a), which are linked in the c-direction by regular ZrF6 octahedral units; Cs+ ions occupy the large open voids (Figure 2a). The kagome lattice itself is “perfect”, in the sense that the Cu2+ sublattice consists of a flat plane of corner-sharing equilateral triangles with a single Cu site (see Figure 3a). 4235
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Figure 1. (a) View of a single kagome sheet in the room-temperature polymorph (R3m) viewed down the c-axis (above) and perpendicular to this (below). (b) Corresponding views of the low-temperature polymorph (P21/m). Large spheres represent Cs+ ions. Zr4+ are not shown, for the sake of clarity.
Figure 2. (a) Polyhedral representation of the R3m polymorph perpendicular to the c-axis, showing regular ZrF6 octahedra linking neighboring kagome sheets. (b) Corresponding view of a portion of the P21/m polymorph showing the change to a ZrF7 polyhedron, and the resulting structural distortion.
However, the coordination around Cu2+ displays the expected JahnTeller distortion, with four short in-plane CuF bonds and two long out-of-plane CuF bonds. At 125 K, the single-crystal structure reveals dramatic distortions of the parent aristotype (see Figures 1b, 2b, and 3b). Although the underlying connectivity remains intact, the crystal symmetry is reduced to monoclinic (the matrix relating the rhombohedral and monoclinic cells is (1/3 2/3 1/3; 1 0 0; 2 4 1 /3 /3 /3), causing a significant buckling of the kagome layers and major changes in the coordination environment of each cation. The particularly striking feature is a change in the coordination around the Zr site, from regular octahedral to a distorted seven-coordinate arrangement (see Figure 4). In the R3m polymorph, Zr is coordinated by three F atoms from each of the two neighboring kagome sheets; these are the F(2) atoms, which form the longer, apical bonds of the CuF6 octahedra. Octahedral coordination is unusual in zirconium fluorides; recent
Figure 3. (a) “Perfect” 2D kagome lattice in the R3m polymorph, showing only the Cu2+ sites: all CuCu distances are equivalent. (b) Distorted kagome lattice in the P21/m polymorph. Note the three distinct Cu sites and corresponding “layered” arrangement of the different triangles. The lower plots represent projections along the kagome sheets, for comparison to Figure 1.
reviews15,16 demonstrate that the vast majority (>90%) of the 150 or more known zirconium fluorides feature Zr in 7- or 8-fold coordination. In the low-temperature polymorph, this preference of Zr for higher coordination numbers requires one of the F atoms, F(5), in the plane of the kagome sheet to become bonded, in addition to the six apical ones. This causes a severe distortion of the kagome sheet, as can be seen in the bond lengths and angles in Table 2. In particular, there are now three crystallographically distinct Cu sites, with a much wider range of CuF bond lengths and CuFCu bond angles. Notably, the JahnTeller distortion around the Cu(2) site is modified considerably to accommodate the additional bonding of F(5) to Zr. The Cs environment is also modified from a single 15-coordinated site to two sites with more varied geometries. In fact, 4236
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Figure 4. (a) Local coordination around the Zr site in the R3m polymorph. Note that the nearest Zr(1)F(2) contacts are at a distance of 3.99 Å. (b) Local Zr coordination in the P21/m polymorph. Note the additional bond from the F(5) site, leading to dramatic distortion of the overall structure.
bond-valence-sum analysis17,18 (see the Supporting Information for further details) suggests that the modification of the Cs environments may be a significant secondary factor directing the phase transiton: at 295 K, the bond-valence sums of Zr and Cs are 3.86 and 0.71, respectively, whereas at 125 K, the value for Zr is similar (3.72), whereas the two distinct Cs sites have values of 0.96 and 0.93, which is consistent with more optimal bonding. Variable-Temperature Powder Diffraction Study. The lack of a direct groupsubgroup relationship between the crystal structures at 295 and 125 K, and the discontinuous evolution of both magnetic susceptibility10,11 and dielectric constant (see below) at ∼225 K suggest a first-order phase transition. This was explored further by high-resolution powder X-ray diffraction. Upon cooling between 300 K and 230 K, the Cs2ZrCu3F12 structure refined well to the aristotype rhombohedral singlecrystal model. There was a significant amount of a second phase, identified as Cs2ZrF6, which was fit using the model of Bode19 (we note that this model is old and the true symmetry of this phase is likely to be lower than reported; however, this does not affect our conclusions). At 125 K, and all temperatures up to 180 K, the Cs2ZrCu3F12 phase refined well to the monoclinic singlecrystal model. In the range of 190225 K, a two-phase mixture of the monoclinic and rhombohedral phases was present, which confirms the first-order nature of the transition. All refinements proceeded smoothly, although there was significant preferred orientation present, which was modeled using a spherical harmonics function.20 Expanded Rietveld plots at 180, 220, and 230 K, emphasizing the dramatic differences between the two phases and the phase coexistence around the transition, are shown in Figure 5. Plots of the thermal evolution of the lattice parameters are given in Figure 6. Note that, for ease of comparison, the rhombohedral cell has been transformed to the corresponding monoclinic setting. Further details of the Rietveld analyses are given in the Supporting Information. Electrical Properties. Dielectric data (Figure 7) show a clear step in measured capacitance at temperatures corresponding to the structural phase transition observed in the crystallographic data. The change in capacitance was reversible upon heating and cooling, but with ca. 10 K hysteresis, which is consistent
Figure 5. Portion of the Rietveld refinement for Cs2ZrCu3F12 showing (a) aristotype R3m model at 230 K, (b) mixed phase R3m + P21/m at 220 K, and (c) single monoclinic P21/m phase at 180 K.
with the first-order nature of the transition. Capacitance data as a function of frequency (Supporting Information), show that, in the range measured, the capacitance is frequency-independent and, therefore, the change in magnitude does not arise from any dispersion between different relaxation processes. Capacitance data below 10 kHz became increasingly noisy and therefore were discarded. Similarly dielectric losses were typically below the sensitivity limit of the apparatus (
