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Paper IPM / Physic / 14617  


Abstract:  
Using the modified spin wave method, we study the ##IMG## [http://ej.iop.org/images/09538984/28/40/406001/cmaa34e4ieqn003.gif] J_{1}−J_{2} Heisenberg model with first and second neighbor antiferromagnetic exchange interactions. For a symmetric S ï¿½??ï¿½??=ï¿½??ï¿½??1/2 model, with the same couplings for all the equivalent neighbors, we find three phases in terms of the frustration parameter ##IMG## [http://ej.iop.org/images/09538984/28/40/406001/cmaa34e4ieqn004.gif] ―α=J_{2}/J_{1} : (1) a commensurate collinear ordering with staggered magnetization (NÃ©el.I state) for ##IMG## [http://ej.iop.org/images/09538984/28/40/406001/cmaa34e4ieqn005.gif] 0\leqslant ―α <~0.207 , (2) a magnetically gapped disordered state for ##IMG## [http://ej.iop.org/images/09538984/28/40/406001/cmaa34e4ieqn006.gif] 0.207 <~―α <~0.369 , preserving all the symmetries of the Hamiltonian and lattice, which by definition is a quantum spin liquid (QSL) state and (3) a commensurate collinear ordering in which two out of the three nearest neighbor magnetizations are antiparallel and the remaining pair are parallel (NÃ©el.II state), for ##IMG## [http://ej.iop.org/images/09538984/28/40/406001/cmaa34e4ieqn007.gif] 0.396 <~―α\leqslant 1 . We also explore the phase diagram of a distorted ##IMG## [http://ej.iop.org/images/09538984/28/40/406001/cmaa34e4ieqn008.gif] J_{1}−J_{2} model with S ï¿½??ï¿½??=ï¿½??ï¿½??1/2. Distortion is introduced as an inequality of one nearest neighbor coupling with the other two. This yields a richer phase diagram by the appearance of a new gapped QSL, a gapless QSL and also a valence bond crystal phase in addition to the previous three phases found for the undistorted model.
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