Spin-interactions in Mineral Libethenite Series: Evolution of   Low-dimensional Magnetism
  Interesting magnetic properties and spin-exchange interactions along various possible pathways in half-integral spin quantum magnetic tetramer system: A$_{2}$PO$_{4}$OH (A = Co, Cu) are investigated. Interplay of structural distortion and the magnetic properties with the evolution of localized band structure explain the gradual transition from a three-dimensional antiferromagnet to a low-dimensional frustrated magnetic system along the series. Detailed study of exchange mechanism in this system explores various possibilities of complex magnetic interaction. Electronic structure of this series, studied with the help of different appropriate density-functional approaches like N-th order Muffin-Tin orbital(NMTO) and Planewave Pseudopotential calculations incorporating onsite Coulomb repulsion(U), identifies the underlying magnetic exchange mechanism of this series. Thereafter a generalized minimal model spin-Hamiltonian is constructed for the low-dimensional system. Solution of this model Hamiltonian within first order perturbation theory results into the evaluation of spin-gap in the spin-tetramer system. In addition, the effects of size-confinement and volume reduction on the relevant exchange integrals and spin-gap of the low-dimensional system are also discussed. 
Debjani Karmakar and J. V. Yakhmi
cond-mat.mtrl-sci