Enrique
Burzurí
*abc,
María José
Martínez-Pérez
d,
Carlos
Martí-Gastaldo
e,
Marco
Evangelisti
d,
Samuel
Mañas-Valero
e,
Eugenio
Coronado
e,
Jesús I.
Martínez
d,
Jose Ramon
Galan-Mascaros
fg and
Fernando
Luis
*d
aDepartamento de Física de la Materia Condensada, Universidad Autónoma de Madrid, E-28049 Madrid, Spain. E-mail: enrique.burzuri@uam.es
bCondensed Matter Physics Center (IFIMAC) and Instituto Universitario de Ciencia de Materiales “Nicolás Cabrera” (INC), Universidad Autónoma de Madrid, E-28049 Madrid, Spain
cIMDEA Nanociencia, C\Faraday 9, Ciudad Universitaria de Cantoblanco, Madrid, Spain
dInstituto de Nanociencia y Materiales de Aragón (INMA), CSIC-Universidad de Zaragoza, Zaragoza 50009, Spain. E-mail: fluis@unizar.es
eInstituto de Ciencia Molecular (ICMol), Universidad de Valencia, Calle Catedrático José Beltrán 2, Paterna, 46980, Spain
fInstitute of Chemical Research of Catalonia (ICIQ), The Barcelona Institute of Science and Technology (BIST), Av. Paisos Catalans 16, Tarragona 43007, Spain
gICREA, Passeig Lluís Companys 23, Barcelona 08010, Spain
First published on 22nd March 2023
A quantum spin liquid (QSL) is an elusive state of matter characterized by the absence of long-range magnetic order, even at zero temperature, and by the presence of exotic quasiparticle excitations. In spite of their relevance for quantum communication, topological quantum computation and the understanding of strongly correlated systems, like high-temperature superconductors, the unequivocal experimental identification of materials behaving as QSLs remains challenging. Here, we present a novel 2D heterometallic oxalate complex formed by high-spin Co(II) ions alternating with diamagnetic Rh(III) in a honeycomb lattice. This complex meets the key requirements to become a QSL: a spin ½ ground state for Co(II), determined by spin–orbit coupling and crystal field, a magnetically-frustrated triangular lattice due to the presence of antiferromagnetic correlations, strongly suppressed direct exchange interactions and the presence of equivalent interfering superexchange paths between Co centres. A combination of electronic paramagnetic resonance, specific heat and ac magnetic susceptibility measurements in a wide range of frequencies and temperatures shows the presence of strong antiferromagnetic correlations concomitant with no signs of magnetic ordering down to 15 mK. These results show that bimetallic oxalates are appealing QSL candidates as well as versatile systems to chemically fine tune key aspects of a QSL, like magnetic frustration and superexchange path geometries.
Quantum spin liquids were first theorized by Anderson for spin networks with magnetic frustration.13 In this framework, two-dimensional (2D) triangular and kagomé lattices showing strong antiferromagnetic interactions are natural physical systems to host frustration and strong quantum fluctuations that may lead to a QSL (see Fig. 1a). In a QSL, any two antiparallel spins in the lattice pair up into a spin singlet. The resulting wave function is a liquid-like quantum superposition of all possible configurations of singlets that can be accessed via quantum fluctuations. This quantum superposition gives rise to the so-called spinons.14
The lack of a defined magnetic order parameter and the presence of spin frustration hindered the development of a theoretical framework describing QSLs. For the same reason, identifying materials that provide physical realizations of this state also remains challenging. Some examples of QSL candidates in magnetically frustrated systems are: 1-TaS2,15 κ-(BEDT-TTF)2Cu2 (CN)3 (triangular),16 ZnxCu4−x(OH)6Cl2 (Kagome),17 and the recent NdTa7O19 (triangular),18 among others.1,19
In 2006, the search for QSLs took a big leap forward when Kitaev proposed an exact solution for a S = 1/2 honeycomb lattice6 that can be extended to any tri-coordinated spin lattice.20,21 In this model, magnetic frustration is replaced as ingredient by directional spin–spin exchange interactions through the bonds connecting the spins, i.e.: the bond-dependent Kitaev interaction. Kitaev's solution expands QSLs beyond frustrated magnetic lattices and thus the availability of experimental candidates grows. In real materials, such anisotropic Kitaev interaction can arise in transition metals showing strong spin–orbit coupling (SOC) with a J = 1/2 ground state resulting from the entanglement of spin and orbital moments.20–22 Inequivalent bond-dependent Kitaev interactions appear through otherwise equivalent tridentate ligands. Some recent examples include inorganic materials like α-RuCl38,23,24 and iridates25,26 in which direct evidence of dominant bond–directional interactions has been obtained.27
However, the main obstacle for inorganic materials to be good Kitaev QSLs is the presence of strong direct exchange interactions that may compete with Kitaev interactions and even lead, in many of them, to a classical long-range antiferromagnetic order.8,26 A possible alternative may be found in coordination materials, where the metal centres carrying the spin are spaced by non-magnetic organic ligands.20,21 Direct exchange interactions can be largely suppressed leaving only the weak through-bond superexchange interactions. Interestingly, Jackeli and Khaliullin showed theoretically that Kitaev interactions can be dominant in these compounds for specific geometries.22 Two main requirements need to be met by the transition metal centre: (i) a spin–orbit entangled, low effective spin ground state (J = 1/2) and (ii) an octahedral coordination site with oxygens (see Fig. 1b) leading to multiple superexchange paths (see Fig. 1c). In this geometry, two equivalent parallel paths can interfere destructively exactly suppressing isotropic superexchange22 whereas any remnant direct exchange contribution is suppressed exponentially with distance.
In coordination chemistry, 2D honeycomb frameworks as well as 3D hyper-honeycomb ones, such as those provided by the metal-oxalate coordination polymers,28 seem to present an optimal geometry to host the Jackeli–Khaliullin mechanism (Fig. 1a). In these compounds, the metal coordination is octahedral with each oxalate being contained in orthogonal xy, yz and xz planes (see Fig. 1b). Moreover, the coupling between metal centres is mediated via two equivalent parallel paths (see Fig. 1c). Kitaev interactions are therefore expected to become dominant, as recently proposed theoretically.20,21 A first experimental result suggesting an oxalate-based QSL was reported for the homometallic Cu2+ oxalate hyper-honeycomb framework. Note, however, that the main QSL indication was the absence of magnetic order in susceptibility measurements limited to temperatures above 2 K,29,30 whereas similar homometallic31 and bimetallic32,33 oxalates have shown antiferromagnetic phases not far from that temperature region. These fingerprints could still be associated with a spin glass1,34 or with magnetic order below the experimentally accessible temperatures. Besides, Cu2+ does not present significant spin–orbit coupling, which is a necessary ingredient for the predominance of Kitaev interactions.
Here we report a novel bimetallic oxalate complex in which magnetic Co2+ centres are coordinated through oxalate bridges to non-magnetic Rh3+ centres, and vice versa, leading to a 2D honeycomb lattice, as shown in Fig. 1a. The resulting spin network is a triangular planar lattice in which exchange and superexchange interactions between Co2+ ions are further suppressed by very long –(ox)–Rh3+–(ox)– bridges (Fig. 1c), as compared with the links present in conventional homometallic counterparts. Besides, a double equivalent super-exchange path is maintained throughout the bridge (Fig. 1c). Exploiting a combination of different and complementary experimental techniques (magnetic resonance, heat capacity and micro-SQUID ac susceptometry), we characterize the effective magnetic properties of each Co2+ ion, determine the average energy scale associated with their mutual spin correlations in the 2D metal-oxalate lattice and explore the magnetic response down to very low temperatures to look for the existence (rather absence) of long range magnetic order in the vicinity of absolute zero. On basis of these results, we discuss the possibility that this molecular system provides a realization of a QSL.
In this compound, the [CoRh(ox)3]− layers are spaced and held together in the crystal by non-magnetic molecular cations PNP, as seen in Fig. 1d. The average distance between adjacent bimetallic layers is dz = 14.5 Å,35 thus larger than the average separation (d = 9 Å) between magnetic ions within these layers and considerably larger than in previously reported compounds (3.5 Å),29 due to the larger size of the cation. In addition, the layer packing is AB-hexagonal. Therefore, the Co2+ atoms are not aligned along the out-of-plane crystal axis (see Fig. 1d), thus reducing even further the magnetic interactions between different 2D layers.
Fig. 2 EPR spectrum of a [PNP][CoRh(ox)3] powder sample, at 40 K. A broad asymmetric signal is observed centred at g ≈ 4.8. The inset shows the energy level diagram of a Co2+ in an octahedral crystal field and under spin–orbit coupling with strength λ. B4 is related to the strength of the crystal field. The ground state can be described with an effective angular momentum J = 1/2 and geff = 4.33. Distortion of the octahedral symmetry would cause some anisotropy of the actual g values around the effective one (see text and Fig. S3 in the ESI†), which is here averaged out by the effect of spin–spin interactions between Co(II) centres in the oxalate layer. |
No such broad peak anomaly is observed in specific heat data measured for B = 0. Instead, they show a monotonic increment of cp below T = 1.75 K that continues down to the lowest temperatures attained in these experiments (172 mK). Fig. 3b shows the zero-field magnetic specific heat cm after subtraction of the lattice component. Above roughly 0.5 K, this low temperature tail can be fitted to cm = αT−2 with α = 0.025 K2 (blue solid line). Note that in this temperature region we can safely discard the contribution of excited levels above the ground spin doublet of each Co2+ ion (see Fig. S5 in the ESI†). Hyperfine interactions are also too weak to give any sizeable contribution at these temperatures. Therefore, this dependence can be ascribed to growing correlations between spins.37 The fit of this T−2 “tail” to the high-temperature prediction for a J = 1/2 Heisenberg model allows estimating the spin–spin exchange interaction constant J ≃ 0.2 K.37 See ESI† for details. This analysis therefore shows the presence of relatively strong couplings between the spins located within each oxalate layer.
In spite of this, and quite remarkably, no indication of magnetic order is observed in the specific heat measured at lower temperatures. Even though no clear peaks, the fingerprints of Majorana fermions and a Kitaev QSL, may be observed in the experimental temperature range,39,40 the deviation from a T−2 dependence may be indicative of the saturation to a broad maximum that has been associated to quasiparticle excitations in QSLs.8 Interestingly, a better fit (red solid line) can be obtained over the whole temperature range by introducing an additional T−ξ contribution (green dotted line) that accounts for the contribution of the QSL state, such that cm = αT−2 + βT−ξ. The fit gives an exponent ξ = 0.65, which is consistent with values reported for other QSL candidates.41,42 As expected from the monotonic increase of cm with decreasing temperature, there remains a residual entropy for B = 0 T at the lowest temperature. This is shown in Fig. S6 and S7 in the ESI.† Although the observed behaviour is compatible with a QSL, it does not allow to completely discard a magnetic transition at temperatures lower than the experimental range.38
Fig. 4a shows the in-phase component χ′T measured in [PNP][CoRh(ox)3] at ω/2π = 1379 Hz down to T = 40 mK. [PNP][CoRh(ox)3] behaves as a paramagnet down to the lowest temperatures. The two consecutive drops observed in χ′T can be well reproduced by a susceptibility model45 that includes the contributions from the ground and an excited spin doublets and spin–spin antiferromagnetic interactions between neighbours (green curve). The mathematical description of this model and the fitting parameters are given in the ESI.† The high-temperature drop in χ′T marks the depopulation of the excited spin doublet, and allows determining the energy distance Δ = 366 K from the ground state. At T = 10 K, χ′T is close to 1.7 emu K mol−1, to which a system of non-interacting J = 1/2 spins with g = 4.3, close to those inferred from EPR and heat capacity measurements, would be expected to saturate (red dashed curve in Fig. 4a). However, the low-temperature drop shows a deviation from this picture, which can be associated with antiferromagnetic spin–spin interactions. This behaviour can be fitted by introducing an equivalent of the Weiss temperature T0 = −0.38 K (green solid line in Fig. 4a). The blue curve is the Curie–Weiss prediction for a J = 1/2, g = 4.3 system with Weiss constant θCW = −0.38 K. A plot of the reciprocal susceptibility (χ′)−1, shown in Fig. 4b, confirms this and shows below 10 K a close to linear behaviour compatible with a Curie–Weiss law with θCW = −0.39 K, similar to what has been found for other oxalates.33 These results show that, below ∼15 K, [PNP][CoRh(ox)3] can be safely described by a pure J = ½ system with quite sizeable short-range spin correlations between cobalt centres. This scenario is supported by the nearly negligible value of the high-order expansion parameters in the susceptibility model.45 See ESI† for additional details.
Fig. 4 (a) χ′T product as a function of temperature (from 40 mK to 100 K) measured at a fixed frequency 1379 Hz. The two drops observed in χ′T can be well reproduced by a susceptibility model43 that includes the ground and an excited spin doublets and spin–spin antiferromagnetic interactions between neighbour spins (green curve). The high-temperature drop in χ′T is mainly determined by the depopulation of an excited doublet separated Δ = 366 K from the ground state (green curve). The low-temperature drop can only be fitted by introducing antiferromagnetic spin–spin interactions with characteristic energy scales given by T0 = −0.38 K. Contrarily, by fixing T0 = 0 (red dashed curve) the theoretical prediction saturates to 1.7 emu K mol−1 corresponding to a system of non-interacting J = 1/2 spins with g = 4.3. The blue curve is the Curie–Weiss prediction for a J = 1/2, g = 4.3 system with a Weiss temperature θCW = −0.38 K. This result shows that, below ∼15 K, [PNP][CoRh(ox)3] can be safely described by a pure J = 1/2 system with antiferromagnetic interactions. (b) (χ′)−1 as a function of temperature. The Curie–Weiss fit and its extrapolation to (χ′)−1 = 0 (red solid line) provide a Curie–Weiss temperature θCW = −0.39 K. This negative value is a signature of significant antiferromagnetic interactions. (c) χ′ and (d) χ′′ measured in a wide range of frequencies from 15.85 mHz (dark red) to 158 kHz (dark purple) and down to T = 15 mK. The insets show the temperature dependence of the respective maxima. |
These findings agree with the results of specific heat measurements and, incidentally, also help understanding the EPR spectrum (Fig. 2). For a 2D exchange interaction with a Curie–Weiss temperature around 0.4 K (or 8 GHz) the resonance line broadens and the mean g factor shifts with respect to that expected for isolated Co2+ centres (see Fig. S3†).
Below T ≈ 70 mK, both χ′ and χ′′ develop a maximum that shifts to lower temperatures as frequency decreases, as shown in Fig. 4c and d. The frequency dependence signals a deviation of the spin response from equilibrium. Such slow magnetic relaxation has been observed in other compounds based on Co2+ in octahedral coordination.46–48 For isolated Co(II) centres, it has been explained in terms of temperature dependent direct spin–phonon processes.49 The maxima in χ′′ can be identified with the condition 1/ω = τ, where τ is the characteristic spin relaxation time. The inset in Fig. 4d shows that τ increases exponentially with decreasing temperature, with activation energy U ≈ 0.2 K, a behaviour that contrast sharply with the linear dependence expected for a direct process. Besides, the peaks in χ′ also approximately follow an Arrhenius dependence (see inset in Fig. 4c). This shows that the spin dynamics in this 2D oxalate layer slows down with decreasing temperature much more sharply than what would be expected for the isolated ions. Another characteristic trait is the low value of χ′′, that would be expected to reach a maximum of χ′′ = χ′/2 for a paramagnet with uncorrelated spins. This behaviour and the fact that U is close to the scale of spin–spin interactions point to an additional slowing down due to the growth of spin correlations.
The spin dynamics can be investigated more in depth by inspecting the frequency spectra of χ* at different temperatures, as shown in Fig. 5. Fig. 5b shows that χ′′ develops a low frequency tail that grows with decreasing temperature. This is a signature of the onset of multiple slow spin-relaxation mechanisms that, in turn, would explain the low intensity of the χ′′ peaks in Fig. 4d. The multiplicity of relaxation times in a spin system could again be originated by growing correlations between spins or by a certain degree of magnetic frustration in the triangular magnetic layers.
Fig. 5 Frequency spectra of (a) χ′ and (b) χ′′ measured at different temperatures from 18 mK (blue) up to 91 mK (dark red). The out-of-phase component develops a low-frequency tail indicting the emergence of multiple slow spin relaxation processes. These dynamics, together with the reduced χ′′ value in Fig. 4 has been typically associated to the growing presence of spin correlations or a certain degree of magnetic frustration. |
In spite of the onset of correlations and their effect on the spin dynamics, the magnetic susceptibility shows no signs of magnetic order nor of a spin glass-like transition down to 15 mK. This temperature is orders of magnitude lower than what has been found in some paradigmatic QSL candidates.8,29,50 Besides, it is also remarkably low when compared with θCW, setting a lower limit for the frustration factor of at least f > 45. Note also that the absence of magnetic order in this temperature range is significant when compared with the ferromagnetic transition at T = 13 K observed in analogous oxalates, like the [NBu4][CoMn], where both metallic species are magnetic.33
Bimetallic oxalate compounds containing magnetic centres (here Co2+) bridged by non-magnetic metal ions (such as Rh3+) are therefore promising candidates to realize QSLs. In addition, they provide versatile platforms to modulate key aspects of a QSL, like magnetic frustration, lattice dimensionality, superexchange paths geometry or even the relative influence of long-range dipolar interactions as compared to short range exchange couplings.51 Further measurements, as muon spin relaxation, will be performed to better characterize these QSL candidates in order to determine the spinon diffusion and critical parameters, allowing a more direct comparison with currently available theoretical models.
Footnote |
† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d2sc06407c |
This journal is © The Royal Society of Chemistry 2023 |