Electronic structure and magnetic properties of pyroxenes(Li,Na)TM(Si,Ge)2

Abstract

The results of the LSDA+U calculations for pyroxenes with diverse magnetic properties (Li,Na)TM(Si,Ge)2O6, where TM is the transition metal ion (Ti,V,Cr,Mn,Fe), are presented. We show that the anisotropic orbital ordering results in the spin-gap formation in NaTiSi2O6. The detailed analysis of different contributions to the intrachain exchange interactions for pyroxenes is performed both analytically using perturbation theory and basing on the results of the band structure calculations. The antiferromagnetic t2g − t2g exchange is found to decrease gradually in going from Ti to Fe. It turns out to be nearly compensated by ferromagnetic interaction between half-filled t2g and empty eg orbitals in Cr-based pyroxenes. The fine-tuning of the interaction parameters by the crystal structure results in the ferromagnetism for NaCrGe2O6. Further increase of the total number of electrons and occupation of eg sub-shell makes the t2g − eg contribution and total exchange interaction antiferromagnetic for Mn-and Fe-based pyroxenes. Strong oxygen polarization was found in Fe-based pyroxenes. It is shown that this effect leads to a considerable reduction of antiferromagnetic intrachain exchange. The obtained results may serve as a basis for the analysis of diverse magnetic properties of pyroxenes, including those with recently discovered multiferroic behavior.

Nature of the ferromagnetic ground state in the Mn4molecular magnet

“…In order to take into account strong electronic correlations on the Mn sites the GGA+U approximation (the generalized gradient approximation taking into account on-site U Hubbard correction) was applied [22] with the on-site Coulomb repulsion parameter U =4.5 eV and the intraatomic Hund's rule exchange J H =0.9 eV. [23] The spinorbit coupling was not taken into account in the present calculations, so that the effects related to this interaction (such as, e.g., the single-ion anisotropy) were not considered.…”

“…So that this electron transfer is highly unfavorable, because it costs 2U , where U ∼4.5-8 eV. [23,40] In contrast the second type of the electron transfer (from Mn 2+ to Mn 3+ back and forth) cost neither 2U nor even U , one only needs to spend the energy V . V is the energy of transfer (excitation) of an electron from Mn 2+ to Mn 3+ , determined by the local coordination of these ions and by the intersite Coulomb interaction.…”

“…7, while the another one will act via the second common oxygen). The e g /e g contribution in the shared edge geometry is expected to be small, since the electrons are supposed to hop via almost orthogonal ligand 2p orbitals, [23] and will not be considered here. In contrast the cross terms from the t 2g and e g orbitals are of the great importance.…”

Calculation of exchange constants of the Heisenberg model in plane-wave-based methods using the Green's function approach

“…• Mn-O-Mn geometry one might expect strong FM interaction between halffilled t 2g and empty e g orbitals of Mn 4+ ions [30,54,55]. We performed GGA and GGA+U calculations of the exchange parameters in Li 2 MnO 3 using Perdew-BurkeErnzerhof [38] exchange-correlation potential.…”

Crystal Structure and Magnetic Properties in Pyroxenes Li0.7Na0.3FeGe2O6

“…1) [9]. Magnetic interaction between the chains (Fe-O-Ge(Si)-O-Fe) is weakened due to the presence of non-magnetic Ge(Si)O 4 tetrahedra.…”