Goodenough–Kanamori rules applied to wurtzite crystals

Abstract

Goodenough-Kanamori (GK) criteria have provided a signi cant contribution to our understanding of the importance of the symmetry and the electron orbital characteristics in the development of the magnetic superexchange coupling [antiferromagnetic (AFM) or ferromagnetic (FM)] applied primarily to systems with bond angles of 180 • and 90 • . In the present work, we quantify and apply the GK criteria to wurtzite systems. Our approach is based on calculations of (i) the spin electron densities of the anions which are rst nearest neighbors (1nn) to the magnetic dopants and, (ii) the generalized exchange integrals which are derived by investigating the electronic properties of the systems under a magnetization density constraint. We demonstrate that the magnetization constraint can be used as a probe in investigating the magnetic properties of the materials under magnetization constraints. Our results indicate that the GK criteria applied to diluted magnetic semiconductors and transition metal oxides of wurtzite structures always lead to a FM coupling between two 1nn dopants of the same type. This is justi ed by ab initio calculations obtained for ZnO and GaN doped with 3d-transition metal dopants.

Magnetism versus band-gap relationship in diluted magnetic semiconductors: megatom impurity behavior of the magnetic dopant complexes

“…The energetics (eigenvalues) of the magnetic impurity megatom dictate the formation of the band gap states and, therefore, the band gap of the DMS. This supports previously reported conclusions [20,[28][29][30][31][32][33][34][35][36] suggesting that the defect induced magnetism in DMSs and TMOs has a strong contribution from the local intra dopant complex dynamics.…”

Estimation of sp–d exchange constants revisited

“…At the level of the GGA + U approximation we have shown that, the early 3d-TM dopants (V, Cr, Mn) form bond types, β type , of AFM type, while the late 3d-TM dopants (Fe, Co, Ni, Cu) form bonds of FM type with their first nearest neighboring (1nn) anion ligands in MoS 2 , GaN, GaP, CdS, ZnO and other hosts [18][19][20][21][22][23][24][25]. We assign β type = +1 (correspondingly, β type = −1) to an FM (correspondingly, AFM) bond type.…”

Codoping induced enhanced ferromagnetism in diluted magnetic semiconductors

“…At a qualitative level, Goodenough and Kanamori (GK) proposed a set of rules [101][102][103][104] which have been proven highly successful in rationalizing the magnetic properties of a wide range of materials. They are based on the symmetry relations and electron occupancy of the overlapping AOs (under the assumption that the localized Heitler-London, or the valence-bond model is more representative of the chemical bonding than is the delocalized or the Hund-Mulliken-Bloch, model).…”

“…Recently, we proposed a new computational method for specifying the GK-product [104,117,118]. It is based on the response properties of the doped system in the imposed boundary condition on magnetization density, M, of the system.…”

“…β GK can take the values +1 or −1 depending on whether the MC between the d-band of the dopant and the sp-band of the host anions is FM or AFM respectively. The bond type, β GK , plays a significant role in the GK rules (section 2.3.3) for predicting the inter-dopant coupling [101][102][103][104].…”