Electronic structure and magnetic properties of pyroxenes (Li,Na)TM(Si,Ge)2O6: novel low-dimensional magnets with 90 bonds

TL;DR

This study uses LSDA+U calculations to explore the electronic and magnetic properties of pyroxenes with various transition metals, revealing how orbital ordering and structural factors influence their magnetic interactions and potential multiferroic behavior.

Contribution

It provides a detailed theoretical analysis of magnetic exchange interactions in pyroxenes, highlighting the role of orbital ordering and crystal structure in their magnetic properties.

Findings

Orbital ordering induces spin-gap in NaTiSi2O6.

Exchange interactions vary systematically from Ti to Fe.

Oxygen polarization significantly affects magnetic exchange.

Abstract

The results of the LSDA+U calculations for pyroxenes with diverse magnetic properties (Li,Na)TM(Si,Ge)$_2$O$_6$, 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 NaTiSi$_2$O$_6$. 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 $t_{2g}-t_{2g}$ 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 $t_{2g}$ and empty $e_g$ orbitals in Cr-based pyroxenes. The fine-tuning of the interaction parameters by the crystal structure results in the ferromagnetism for NaCrGe$_2$O$_6$. Further increase of the total number of electrons and occupation of $e_g$ sub-shell makes the $t_{2g}-e_g$ 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.