Spin-lattice coupling in frustrated antiferromagnets

We review the mechanism of spin-lattice coupling in relieving the geometrical frustration of pyrochlore antiferromagnets, in particular spinel oxides. The tetrahedral unit, which is the building block of the pyrochlore lattice, undergoes a spin-driven Jahn-Teller instability when lattice degrees of freedom are coupled to the antiferromagnetism. By restricting our considerations to distortions which preserve the translational symmetries of the lattice, we present a general theory of the collective spin-Jahn-Teller effect in the pyrochlore lattice. One of the predicted lattice distortions breaks the inversion symmetry and gives rise to a chiral pyrochlore lattice, in which frustrated bonds form helices with a definite handedness. The chirality is transferred to the spin system through spin-orbit coupling, resulting in a long-period spiral state, as observed in spinel CdCr2O4. We discuss explicit models of spin-lattice coupling using local phonon modes, and their applications in other frustrated magnets.Comment: 23 pages, 6 figures. Lecture notes for Trieste Summer School, August 2007. To appear as a chapter in "Highly Frustrated Magnetism", Eds. C. Lacroix, P. Mendels, F. Mil

Quantum Effects and Broken Symmetries in Frustrated Antiferromagnets

We investigate the interplay between frustration and zero-point quantum fluctuations in the ground state of the triangular and $J_1{-}J_2$ Heisenberg antiferromagnets, using finite-size spin-wave theory, exact diagonalization, and quantum Monte Carlo methods. In the triangular Heisenberg antiferromagnet, by performing a systematic size-scaling analysis, we have obtained strong evidences for a gapless spectrum and a finite value of the thermodynamic order parameter, thus confirming the existence of long-range N\'eel order.The good agreement between the finite-size spin-wave results and the exact and quantum Monte Carlo data also supports the reliability of the spin-wave expansion to describe both the ground state and the low-energy spin excitations of the triangular Heisenberg antiferromagnet. In the $J_1{-}J_2$ Heisenberg model, our results indicate the opening of a finite gap in the thermodynamic excitation spectrum at $J_2/J_1 \simeq 0.4$, marking the melting of the antiferromagnetic N\'eel order and the onset of a non-magnetic ground state. In order to characterize the nature of the latter quantum-disordered phase we have computed the susceptibilities for the most important crystal symmetry breaking operators. In the ordered phase the effectiveness of the spin-wave theory in reproducing the low-energy excitation spectrum suggests that the uniform spin susceptibility of the model is very close to the linear spin-wave prediction.Comment: Review article, 44 pages, 18 figures. See also PRL 87, 097201 (2001

Suppression of Dimer Correlations in the Two-Dimensional J1J_1-J2J_2 Heisenberg Model: an Exact Diagonalization Study

We present an exact diagonalization study of the ground state of the spin-half $J_1{-}J_2$ model. Dimer correlation functions and the susceptibility associated to the breaking of the translational invariance are calculated for the $4\times 4$ and the $6\times 6$ clusters. These results -- especially when compared to the one dimensional case, where the occurrence of a dimerized phase for large enough frustration is well established -- suggest either a homogeneous spin liquid or, possibly, a dimerized state with a rather small order parameter

Thermodynamics of the quantum easy-plane antiferromagnet on the triangular lattice

The classical XXZ triangular-lattice antiferromagnet (TAF) shows both an Ising and a BKT transition, related to the chirality and the in-plane spin components, respectively. In this paper the quantum effects on the thermodynamic quantities are evaluated by means of the pure-quantum self-consistent harmonic approximation (PQSCHA), that allows one to deal with any spin value through classical MC simulations. We report the internal energy, the specific heat, and the in-plane correlation length of the quantum XX0 TAF, for S=1/2, 1, 5/2. The quantum transition temperatures turn out to be smaller the smaller the spin, and agree with the few available theoretical and numerical estimates.Comment: 4 pages,3 postscript figure

Treatment responses to antiangiogenetic therapy and chemotherapy in nonsecreting paraganglioma (PGL4) of urinary bladder with SDHB mutation: a case report

Paraganglioma (PGL) is a rare neuroendocrine tumor. Currently, the malignancy is defined as the presence of metastatic spread at presentation or during follow-up. Several gene mutations are listed in the pathogenesis of PGL, among which succinate dehydrogenase (SDHX), particularly the SDHB isoform, is the main gene involved in malignancy. A 55-year-old male without evidence of catecholamine secretion had surgery for PGL of the urinary bladder. After 1 year, he showed a relapse of disease and demonstrated malignant PGL without evidence of catecholamine secretion with a germline heterozygous mutation of succinate dehydrogenase B (SDHB). After failure of a second surgery for relapse, he started medical treatment with sunitinib daily but discontinued due to serious side effects. Cyclophosphamide, vincristine, and dacarbazine (CVD) chemotherapeutic regimen stopped the disease progression for 7 months. Conclusion: Malignant PGL is a very rare tumor, and SDHB mutations must be always considered in molecular diagnosis because they represent a critical event in the progression of the oncological disease. Currently, there are few therapeutic protocols, and it is often difficult, as this case demonstrates, to decide on a treatment option according to a reasoned set of choices. Abbreviations: CVD = cyclophosphamide, vincristine and dacarbazine, HIF-1a = hypoxia inducible factor 1 alpha, PGL = paraganglioma, SDH = succinate dehydrogenase, VEGF = vasoendothelial growth factor

Absence of Translational Symmetry Breaking in Nonmagnetic Insulator Phase on Two-Dimensional Lattice with Geometrical Frustration

The ground-state properties of the two-dimensional Hubbard model with nearest-neighbor and next-nearest-neighbor hoppings at half filling are studied by the path-integral-renormalization-group method. The nonmagnetic-insulator phase sandwiched by the the paramagnetic-metal phase and the antiferromagnetic-insulator phase shows evidence against translational symmetry breaking of the dimerized state, plaquette singlet state, staggered flux state, and charge ordered state. These results support that the genuine Mott insulator which cannot be adiabatically continued to the band insulator is realized generically by Umklapp scattering through the effects of geometrical frustration and quantum fluctuation in the two-dimensional system.Comment: 4 pages and 7 figure

Spontaneous plaquette dimerization in the J1−J2J_1-J_2 Heisenberg model

We investigate the non magnetic phase of the spin-half frustrated Heisenberg antiferromagnet on the square lattice using exact diagonalization (up to 36 sites) and quantum Monte Carlo techniques (up to 144 sites). The spin gap and the susceptibilities for the most important crystal symmetry breaking operators are computed. A genuine and somehow unexpected `plaquette RVB', with spontaneously broken translation symmetry and no broken rotation symmetry, comes out from our numerical simulations as the most plausible ground state for $J_2/J_1 \simeq 0.5$.Comment: 4 pages, 5 postscript figure

Resonating Valence Bond Wave Functions for Strongly Frustrated Spin Systems

The Resonating Valence Bond (RVB) theory for two-dimensional quantum antiferromagnets is shown to be the correct paradigm for large enough ``quantum frustration''. This scenario, proposed long time ago but never confirmed by microscopic calculations, is very strongly supported by a new type of variational wave function, which is extremely close to the exact ground state of the $J_1{-}J_2$ Heisenberg model for $0.4 \lesssim J_2/J_1\lesssim 0.5$. This wave function is proposed to represent the generic spin-half RVB ground state in spin liquids.Comment: 4 Pages, 5 figures, accepted for publication in PR