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Home page > Frustrated magnetism versus spin liquids : towards a model kagomé compound

F. Bert, A. Olariu (doctorante), P. Mendels

Collaboration : F. Duc, J.-C. Trombe (CEMES), M.A. de Vries, A. Harrison (Edinburgh), ISIS, PSI

As early as in 1973, Anderson made the proposal that frustration in antiferromagnetic triangular lattices could generate novel magnetic states such as the "spin liquid" state where the spins do not order into Néel sublattices but fluctuate down to zero temperature. Such a state, named "resonating valence bond" state after Anderson, is built out of a superposition of resonating singlets. It has been at the heart of numerous theoretical studies for long, revived since the discovery of High Temperature Superconductivity which appears in cuprates in the vicinity of an antiferromagnetic insulating phase. In the latter context, Anderson proposed a modified version of his famous "RVB" state as a possible explanation of High Temperature Superconductivity.

Figure : Frozen magnetic fraction, as measured by µSR in samples exhibiting a magnetic transition (x< ou =0.5). In insert, the phase diagram obtained at 2 K for the Zn-paratacamite family.

In contrast with the huge theoretical developments in this field, only few experimental realizations were found to be good representatives of such a spin liquid state. Promising candidates are corner sharing antiferromagnetic networks such as kagomé or pyrochlore, preferentially with spins 1/2 which are expected to enhance the role of fluctuations. Whereas many compounds featured a fluctuating ground state at low temperature, the situation remained rather pending since a marginal transition, still poorly understood, set in at a finite temperature, preventing any susceptibility test of the proposed models for the kagomé or pyrochlore lattice. In this respect, the volborthite compound [1], appeared as one of the first examples of a quasi 2D network decorated with quantum 1/2 spins (Cu2+), though displaying non-equal antiferromagnetic interactions.

In 2005, one chemistry team in MIT was able to synthesize in laboratory a rare mineral, named Herbertsmithite and discovered in 2004, from the paratacamite family, ZnxCu4-x(OH)6Cl2 (x=1 for Herbertsmithite). In Herbertsmithite, Cu2+ ions (S=1/2) belong to perfect kagomé networks which are well decoupled through a Zn2+ plane sitting between Cu2+. The progressive substitution of Zn2+ by Cu2+ sets in a three dimensional connectivity. We have fostered a collaboration with two chemistry teams which produced high quality samples (CEMES, Toulouse and Edinburgh University). Our muon spin relaxation (muSR) detailed study [2] demonstrates the absence of freezing in the x=1 compound down to 50 mK, much smaller than the exchange constant which is of the order of 150 K. We can sketch the magnetic phase diagram of paratacamites. This is a strong evidence that this compound is the first ideal representative of the Heisenberg model on a kagomé lattice which should bring experimental answers to fundamental theory questions such as the singlet – triplet gap, the existence of original excitations, the effect of non magnetic impurities..., as many probes of the existence of a RVB ground state. The weak relaxation detected in our µSR investigation addresses the issue of defects and might indicate the absence of a singlet-triplet gap. The ultimate answer to this question is at the heart of on-going NMR studies (Olariu’s PhD work) and of sub-Kelvin experiments performed, in collaboration with SPEC (CEA Saclay, D. Lhote). As a second step, the microscopic understanding, through NMR, of the defects nature should enable us to get in touch with the perfect compound.

References :

[1] Ground State of the Kagome-Like S=1/2 Antiferromagnet Volborthite Cu3V2O7(OH)2. 2H2O F. Bert, D. Bono, P. Mendels, F. Ladieu, F. Duc, J.-C. Trombe et P. Millet, Phys. Rev. Lett. 95, 087203 (2005)

[2] Quantum magnetism in paratacamite family: Towards an ideal kagome lattice P. Mendels, F. Bert, M.A. de Vries, A. Olariu., A. Harrison, F. Duc, J.-C. Trombe, à paraître dans Phys. Rev. Lett. (2007).