Anisotropy, elastic exchange

As a framework for the discussion of the magnetization, magnetic anisotropy and magnetostriction we consider a hamiltonian which comprises the following isotropic exchange, effective single-ion anisotropy, elastic, magnetoelastic and Zeeman terms ... 

Up to now the best agreement between experimental ground state properties like cohesive energy, lattice constants, and bulk modulus and the corresponding DFT results were obtained with the PBE functional. However, in a recent survey it has been shown that the anisotropy of the bonding in Zn, as reflected by the elastic constants, is not described in a well-balanced manner even with this functional. Indeed, the elastic constants related to distortions in the a-Z)-plane are reproduced better with hybrid functionals with Hartree-Fock and DFT exchange mixed. The drawback of these latter functionals is a worse description of the interlayer interaction, leading with even to a shift of the e value by 0.79A or... 

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