Candidate quantum spin liquid due to dimensional reduction of a two-dimensional honeycomb lattice.

As with quantum spin liquids based on two-dimensional triangular and kagome lattices, the two-dimensional honeycomb lattice with either a strong spin-orbital coupling or a frustrating second-nearest-neighbor coupling is expected to be a source of candidate quantum spin liquids. An ammonium salt [(C3H7)3NH]2[Cu2(C2O4)3](H2O)2.2 containing hexagonal layers of Cu(2+) was obtained from solution. No structural transition or long-range magnetic ordering was observed from 290 K to 2 K from single crystal X-ray diffraction, specific heat and susceptibility measurements. The anionic layers are separated by sheets of ammonium and H2O with distance of 3.5 Å and no significant interaction between anionic layers. The two-dimensional honeycomb lattice is constructed from Jahn-Teller distorted Cu(2+) and oxalate anions, showing a strong antiferromagnetic interaction between S = 1/2 metal atoms with θ = -120 (1) K. Orbital analysis of the Cu(2+) interactions through the oxalate-bridges suggests a stripe mode pattern of coupling with weak ferromagnetic interaction along the b axis, and strong antiferromagnetic interaction along the a axis. Analysis of the magnetic susceptibility shows that it is dominated by a quasi-one-dimensional contribution with spin chains that are at least as well isolated as those of well-known quasi-one-dimensional spin liquids.

Magnetic systems exhibit, most commonly, classical long-range order at low temperature. To avoid magnetic ordering the interactions between magnetic atoms can be frustrated by the topology of the underlying lattice and/or compete with one another, the dimensionality of the lattice can be reduced by weakening the interactions between planes or chains, or the spin of magnetic units can be reduced to S = 1/2 to promote quantum fluctuation12345. Examples of geometric frustration include antiferromagnetic materials based on a triangular lattice or a Kagome lattice on which triangles share their corners rather than edges. For a perfect system, this frustration would result in the ground state being inherently highly degenerate, even a spin liquid state345. For real systems, the degree of frustration is described by the parameter f = θ, the Curie-Weiss temperature θ showing how strong the magnetic interactions are and the n class="Chemical">Néel temperature T defining the onset of magnetic order. An unfrustrated system has f = 1, a spin frustrated system has f ≥ 10 and in an ideal spin frustrated system f tends to infinity23.

Quantum spin liquids have attracted particular attention since Anderson proposed their possible connection to the superconductivity of n class="Chemical">cuprates67. But most compounds with triangular-lattices or Kagome lattices showed long-range magnetic order due to structural distortion or crystal defects89101112131415. So far, quantum spin liquid states were observed in four triangular lattice compounds, namely κ-(BEDT-TTF)2Cu2(CN)3 (BEDT-TTF = bis(theylenedithio)tetrathiafulvalene), (C2H5)(CH3)3Sb[Pd(dmit)2]2 (dmit = 1,3-dithiole-2-thione-4,5-dithiolate), H3(Cat-EDT-TTF)2 and LiZn2Mo3O816171819. In kagome lattices, a stronger spin frustration is expected than for triangular lattices and quantum spin liquid states were observed in the two compounds ZnCu3(OH)6Cl2 and [NH4]2[C7H14N][V7O6F18]20212223. In one dimensional system including KCuF3 and copper pyrazine dinitrate the spinon continuum associated with the spin liquid state has been observed directly and it has also been confirmed for the two-dimensional kagome system ZnCu3(OH)6Cl2222425.

Quantum spin liquids with two-dimensional lattices should not only be limited to triangular lattices and Kagome lattices226. The S = 1/2 honeycomb lattice (Figure 1) with strong spin –orbital coupling described by the exactly-solvable Kitaev n class="Species">honeycomb model has been proposed as a candidate quantum spin liquid and may exhibit Majorana Fermions that could enable future schemes for quantum computation2728293031. This is an idealization of real systems where Heisenberg-like and next-nearest-neighbor J coupling lead to an even richer assortment of phases, including other spin-liquids. However, the best-known model honeycomb compound Na2IrO3 shows long-range magnetic ordering at 13.3 K and other higher spin systems such as Bi3Mn4O12(NO3), Na2Co2TeO6, Na3Co2SbO6, RNi3Al9, Cu3Ni2SbO6, Cu2Co2SbO6, and Ba3Co2O6(CO3)0.2 – all order magnetically323334353637. The quest for S = 1/2 honeycomb systems that exhibit strong magnetic frustration therefore continues to excite the physics community, and at the same time challenge the chemistry community.

Figure 1

A schematic of four magnetic configuration of honeycomb lattice: (a) the ferromagnetic state, (b) the Néel antiferromagnetic state, (c) the stripy antiferromagnetic state, (d) the zigzag antiferromagnetic state, and (e) arrangement of anionic layer on the ab plane at 290 K.

Color code: Cu, blue; C, grey; O, red. White solid lines: Cu–O, C–C, C–O bond.

In 2011, spin fluctuation was observed in a charge-transfer salt (Bn class="Chemical">EDT-TTF)3[Cu2(C2O4)3](CH3OH)2 with S = 1/2 Cu2+ forming a distorted honeycomb lattice, the Weiss constant was −29.8(7) K and there was no long-range magnetic ordering observed above 2 K38. Two sets of spins exist in this compound: one coming from the donor molecules is similar to the S = 1/2 triangular lattice in κ-(BEDT-TTF)2Cu2(CN)3, the other coming from the anionic layer forming the S = 1/2 honeycomb lattice16. In order to focus on the properties of the S = 1/2 honeycomb lattice, an ammonium salt [(C3H7)3NH]2[Cu2(C2O4)3](H2O)2.2 (1) was synthesized and magnetic ordering was found to be strongly suppressed, setting a lower bound of 60 for the frustration parameter f.

Results

Temperature-dependent single crystal X-ray experiment

1 crystallizes in a monoclinic system with cell parameters: a = 9.3696(1) Å, b = 16.0340(2) Å, c = 22.7991(4) Å, β = 92.9561(5) °, V = 3420.60(8) Å3, Z = 4, at 290 K. Figure 2a shows the temperature dependent cell parameters from room-temperature to 100 K. When temperature decreased, the b and c axis contracted, the a axis and the β angle show a negative thermal expansion39. The negative thermal expansion coefficient as αa ≅ 1.9 × 10−5 K−1 above 140 K, 1.5 × 10−5 K−1 between 140 K and 100 K, and αβ ≅ 2.7 × 10−5 K−1 above 140 K. Below 140 K, the β value decreased while temperature decreased. The b axis, the c axis and the volume decreased when temperature decreased, and the space group remained P21/n in the X-ray diffraction experimental temperature range.

Figure 2

(a) Temperature-dependent cell parameters from 290 K to 100 K. (b) Specific heat data of 1 under 0 Oe (empty black square) and 80 kOe(red solid line). Inset, low-temperature range.

Crystal structure

At 290 K, there are two (C3H7)3NH+ in an asymmetric unit in 1. One of the propyl groups connects to N1, points in the direction perpendicular to the ab plane and intercalates into a cavity of the anionic honeycomb. The non-hydrogen-atoms on the ammonium of N2 are almost parallel to the ab plane, the hydrogen bond between N–H and O of oxalate anion was found to be N2–H2…O10 2.806 Å/166.96°. H2O molecules exist in five positions with populations of 0.50, 0.50, 0.50, 0.50 and 0.20, so there are 2.2 H2O in an asymmetric unit. There are hydrogen bonds between cation and H2O and between solvent and anionic layer. Two sheets of ammonium exist between the two anion layers and there is no weak interaction between ammoniums. This explains the nature of the crystal effectively, because it is always a thin plate crystal and cleaves easily (Figure S1).

In 1, Cu is coordinated by three bisbidentated oxalate anions, Cu1 and Cu2 are neighboring to each other, so a (6,3) honeycomb network is formed on the ab plane. The Cu-O distances are 1.969(2) ~ 2.310(2) Å for Cu1 and 1.966(2) ~ 2.340(2) for Cu2, and the Cu–O distances on the equatorial plane are shorter than those in the axial direction as a result of the Jahn-Teller distortion. The elongated bonds on the Jahn-Teller distorted octahedron around the Cu2+ are highlighted with black solid lines (Figure 1e). The cis-O–Cu–O angles are in the range 78.88 ~ 100.44(9)° for Cu1 and 77.99(9) ~ 98.29(9)° for Cu2, and the trans O–Cu–O angles are in the range 162.86(9) ~ 175.94(1)° for Cu1 and 162.27(8) ~ 174.88(10)° for Cu2. The oxalate-bridged Cu1…Cu2 distances are 5.5179(7) Å, 5.3593(6) Å and 5.3317(6) Å. The distance between the metal atoms separated by two oxalate anions inside a hexagonal ring vary from Cu1…Cu1 8.8801(7) Å and 9.3696(5) Å, Cu2…Cu2 9.7736(6) Å and 9.3696(5) Å. When temperature decreased, the Cu…Cu distance expanded along the a axis and contracted along the b axis. There are two enantiomers coexisting in the crystal: the Λ enantiomer (Cu1) and Δ enantiomer (Cu2) in one layer, and the Δ enantiomer (Cu1) and Λ enantiomer (Cu2) in another layer which are separated by cation and H2O. It is the same situation as found in the charge-transfer salts with honeycomb lattice [Cu2(C2O4)32−]n38. It is different from the coordination network isomerism of [Cu2(C2O4)32−]n in the (10,3) lattice, the configurations of Cu1 and Cu2 remain same as there are only the Δ enantiomer Cu1 and the Λ enantiomer Cu2 in a hyperhoneycomb lattice40.

Specific heat measurement

No λ-peak was observed from temperature dependent specific heat data from 200 K to 2 K under 0 Oe and 80 kOe (Figure 2b). So there is no evidence for a structural or magnetic transition from 200 K to 2 K. The crystal structure at 2 K is the same as the crystal structure at 290 K. The value of heat capacity at 2 K is 183 mJ K−1 mol−1.

Magnetic properties

On the χ-vs-T plot with the temperature decreasing, a broad maximum was observed at 52 K, and a turning point was observed at 14 K, then the χ value increased quickly and reached 0.0084 cm3mol−1 at 2 K. At 300 K, the χT value is 0.465 cm3 K mol−1, it is higher than 0.375 cm3Kmol−1 of an isolated Cu2+ with S = 1/2, and in the range of n class="Chemical">Cu2+ compounds with S = 1/241. The data above 80 K was fitted to the Curie-Weiss law with C = 0.650(2) cm3 mol−1 and θ = −120 (1) K. No bifurcation was observed from ZFC/FC/RM measurement above 2 K. This is consistent with the specific heat experiment showing no long-range magnetic ordering and indicates the absence of spin glass freezing20. The isothermal magnetization at 2 K increased in a smooth curve and reached 0.012 Nβ at 10 kOe, then the magnetization increased linearly and reached 0.044 Nβ at 65 kOe (Figure 3).

Figure 3

Magnetic characterization of 1: (a) χ-vs-T (black empty square) of 1 under an applied field of 1000 Oe, the red line is a fit to the Bonner-Fisher law plus an impurity term. (b) χT-vs-T plot (black empty circle) of 1 under an applied field of 1000 Oe, the red line is a fit to the Curie-Weiss law. (c) ZFCM (black empty square) and FCM (blue empty circle) under 100 Oe. (d) Isothermal magnetization at 2 K. The black line is experimental data, the red line is the contribution from impurity, the blue line is experimental data after subtraction of the impurity contribution.

Discussion

The distance between two anion layers which are separated by cation and H2O is longer than 3.5 Å, so there is no significant interaction between two-dimensional anion layers. The starting point for understanding the magnetic properties is therefore consideration of the independent two-dimensional n class="Species">honeycomb layers.

The magnetic configuration of the honeycomb lattice can be postulated from an orbital analysis424344. The unpaired electron exists in the magnetic orbital dx2-y2 on the equatorial plane. The orbital along the elongated octahedral n class="Chemical">Cu(II) is the dz2 orbital as highlighted by black solid lines in Figure 1e, and the dz2 orbital is perpendicular to the equatorial plane and the dx2-y2 orbital. The relationship between magnetic and structural properties of oxalate-bridged Cu2+ atoms was well established from one-dimensional Cu-oxalate compounds, for example, a ferromagnetic interaction was observed in [Cu(bpy)(C2O4)](H2O)2 when dx2-y2 orbitals on two oxalate-bridged Cu2+ atoms are parallel each other. Meanwhile, an antiferromagnetic interaction appeared when dx2-y2 orbitals on two oxalate-bridged Cu2+ atoms are perpendicular to each other4546. Ferromagnetic interaction along the b axis between oxalate-bridged Cu1 and Cu2 and antiferromagnetic interaction along the a axis between oxalate-bridged Cu1 and Cu2 were assumed. Because the antiferromagnetic interaction is stronger than the ferromagnetic interaction between oxalate-bridged Cu2+ atoms, antiferromagnetic behavior should be expected in 1 and the magnetic configuration of 1, if it orders, would be that of a system with a stripy antiferromagnetic ground state with a pair of spins up and a pair of spins down alternately on the honeycomb lattice (Figure 1c). This is distinct from the other possible magnetic configurations of honeycomb lattices (Figure 1a,b,d) and the stripy configuration is suggested by theoretical calculations to be the best candidate to lead to a quantum spin liquid474849.

On the χ-vs-T plot, a broad maximum at 52 K indicates short-range antiferromagnetic interactions in the low-dimensional system of metal atoms. The data above 2 K was fitted to several models: first the anisotropic n class="Species">honeycomb model of Curély et al, which showed good consistency with the orbital analysis above, giving an FM interchain interaction that is around 700 times weaker than the AF intrachain coupling50. The best fit to the data was however given by the 1D Bonner-Fisher model plus a small impurity term, indicating a highly 1D state. This strongly 1D state may be the result of weak interchain coupling plus a further frustration of the interchain coupling J′ by the second nearest neighbour interactions J″ (Figure 4)51. The parameters obtained from the fitting are: C = 0.4383(8) cm3mol−1, J = -43.82(7) K, nimpurity = 1.09(2)%, θimpurity = 1.27(3) K. From the value of J and the absence of magnetic ordering above 2 K we can provide an upper bound on the J′/J ratio of 2.2 × 10−2, around half that of the benchmark S = 1/2 Heisenberg antiferromagnetic chain system KCuF324.

Figure 4

Magnetic interactions in 1.

Strong AF interactions J along the vertical chains and weak ferromagnetic interactions J′ between the chains. An antiferromagnetic second nearest neighbour interchain coupling J″ leads to frustration of the already weak interchain coupling, leading to the highly 1D properties observed experimentally.

The specific heat data shows that neither magnetic ordering, nor a structural transition happened between 200 K and 2 K. The crystal structure at 2 K should be same as the crystal structure at 290 K, so the magnetic configuration remains in the stripy antiferromagnetic mode to 2 K. The value of the heat capacity at 2 K is 183 mJ K−1 mol−1, which is higher than the value in long-range magnetic ordered metal-n class="Chemical">oxalate-honeycomb compounds where the electron spins are frozen into an ordered array of magnetic dipoles. For example, it is 2.17 mJ K−1 mol−1 in Fe2+ (S = 2), and 43 mJ K−1 mol−1 in Co2+ (S = 3/2). Although there is a strong spin-orbital coupling in the Co2+ (S = 3/2) case, it is not a candidate spin liquid as it undergoes long range magnetic ordering at 21 K52. So the large heat capacity of 1 at 2 K suggests that the spins are in a quantum fluctuating spin liquid state53.

1 is different from reported low-dimensional octahedral coordinated Cu2+ compounds where the strong antiferromagnetic interaction and high f value were the result of interchain or interlayer interactions between n class="Chemical">Cu2+ atoms. For example in CuCl2(1,4-dioxane)(H2O)2, the hydrogen bonds through O–H…Cl between chains results in strong antiferromagnetic interaction with θ = -71.9 K, but spin frustration has not been observed54. 1 is an antiferromagnetic compound that our measurements suggest to be candidate for the 1D class of quantum spin liquids. In this case the combination of dimensional reduction and frustration turns a honeycomb system into one where the properties of well-isolated chains dominate the magnetic properties555657.

Methods

Sample preparation and X-ray diffraction experiments

Blue thin crystal plates of [(C3H7)3NH]2[Cu2(C2O4)3](H2O)2.2 (1) were obtained from n class="Chemical">methanol solution of Cu(NO3)2·3H2O, H2C2O4·2H2O and (C3H7)3N in a 1:3:5 ratio at room-temperature with yield of 31%. Element analysis: C24H48.4O14.2N2Cu2, F.W. = 719.345, calc. C 40.07, H 6.78, N 3.89; exp. C 40.45, H 6.82, N 3.91. A piece of single crystal was selected for single-crystal X-ray diffraction experiments at 290 K, 230 K, 180 K, 140 K and 100 K.

The specific heat experiments were carried out on a Quantum Design PPMS-9XL system from 200 K to 2 K under 0 Oe and 80 kOe. The polycrystal was fixed on the sample stage with N-grease. The contribution from sample stage and n class="Chemical">N-grease was subtracted from the raw data.

Magnetic measurement

The magnetization measurement was performed using a tightly packed 16.26 mg polycrystalline sample which was sealed by 5.62 mg parafilm in capsule on a Quantum Design MPMS-7XL SQUID system. Susceptibility data were corrected for diamagnetism of sample by Pascal constants (–190.4 × 10−6 cm3 mol−1 per Cu2+) and the background was determined by a measurement of the sample holder.