Absence of collective effects in Heisenberg systems with localized magnetic moments

Abstract

Existence of collective effects in magnetic coupling in ionic solids is studied by mapping spin eigenstates of the Heisenberg and exact nonrelativistic Hamiltonians on cluster models representing KNiF 3 , K 2 NiF 4 , NiO, and La 2 CuO 4 . Ab initio techniques are used to estimate the Heisenberg constant J. For clusters with two magnetic centers, the values obtained are about the same for models having more magnetic centers. The absence of collective effects in J strongly suggests that magnetic interactions in this kind of ionic solids are genuinely local and entangle only the two magnetic centers involved. ͓S0163-1829͑97͒04634-1͔The proper and accurate description of magnetic interactions in systems with localized magnetic moments, i.e., ionic solids, is of importance not only from the point of view of basic knowledge but also to understand the electronic structure and magnetic behavior of superconductor parent compounds. 1 The experimental and theoretical study of the magnetic coupling in ionic solids is often based on the use of the Heisenberg Hamiltonian which may be written aswhere the ͗i, j͘ symbol means that the summation is restricted to nearest-neighbor i and j magnetic centers with total spin moment S. The question addressed in this work concerns whether J contains two-body interactions only or if it is better regarded as an effective two-body parameter containing collective effects from the whole solid. We must point out that existence of collective effects in J is claimed mainly from intuition and has not been theoretically or experimentally proven. Because ionic solids are extended systems, it is customary to investigate their electronic structure by using a solid-state approach, usually exploiting translational symmetry. Notice, that this approach cannot provide an answer to the above question because there is no way to separate the collective effects from the two-body interactions. From a purely ab initio, or first-principles, point of view of the theory of the electronic structure, these solid-state approaches are often based on modifications 2-6 of the local-density approach ͑LDA͒. Without these modifications the LDA fails to describe the antiferromagnetic order of many compounds such as NiO or La 2 CuO 4 . 7 More recently, the periodic HartreeFock, in its unrestricted or spin-polarized version, has been applied to a variety of antiferromagnetic systems with, on first sight, a rather good agreement with experiment. 8,9 An alternative approach, different albeit complimentary, is one based on the use of cluster models. [10][11][12][13][14][15][16][17][18] By construction, the cluster model permits one to investigate the importance of the collective effects. From a technical point of view, the main difference between periodic and local approaches lies in the way to estimate the instantaneous electron-electron interactions. Hence, while the former are constrained to the use of more or less approximate correlation ͑or exchangecorrelation͒ functionals, the latter permits the use of more accurate comput...

Local character of magnetic coupling in ionic solids

“…This is in agreement with the absence of cluster size effects reported in Ref. 20. The only physical effects that are included in the NOCI approach and not in the previous DDCI2 calculations arise from the instantaneous orbital relaxation for the physical situations where a charge transfer to a magnetic center occurs.…”

“…Recent work in many magnetic-center models does not show any noticeable dependence of the calculated J on the number of explicitly interacting magnetic centers. 20 The clue to the missing effects can be found in the nonorthogonal configuration interaction ͑NOCI͒ calculations of Van Oosten et al 21 for a series of cuprates. These authors were able to quantitatively reproduce the magnetic coupling constant using two magnetic centers only.…”

Ab initiostudy of magnetic interactions inKCuF3andK2Moreira1, Illas2 1999Phys. Rev. B32050View full textAdd to dashboardCite

“…Previous cluster model studies using sophisticated configuration interaction techniques [6][7][8][9][10][11][12][13][14][15][16][17][18] have shown that for wide gap ionic insulators, the magnetic coupling constant J is a local property that may be described correctly by means of a properly embedded finite model containing only two interacting magnetic centers. The Heisenberg Hamiltonian for such a cluster model reduces to…”

“…13,14,17 The fact that the experimentally determined magnetic coupling constant and the ab initio cluster model calculated value quantitatively agree is the fingerprint of the local two-body character of the magnetic coupling constant. 17,18 In this work we extend the ab initio cluster model approach [7][8][9][10][11][12][13][14][15][16][17][18] to the study of the electronic structure and magnetic coupling of KCuF 3 and K 2 CuF 4 low-dimensional systems in their various ordered polytype crystal forms. Earlier neutron diffraction studies on KCuF 3 ͑Ref.…”

Ab initioperiodic approach to electronic structure and magnetic exchange inA2CuO2X2Moreira1, Dovesi2 2003Phys. Rev. B10010View full textAdd to dashboardCite

“…The UHF approach can, in principle, account for the superexchange mechanism but provides too small antiferromagnetic coupling constants-usually 20-30 % of the experimental value. [62][63][64][65]100 This behavior can be rationalized by the changes in J arising from changes in the effective parameters of the Hubbard Hamiltonian or, more precisely, in the t/U ratio, i.e., the delocalization/repulsion ratio, in a variable extent depending on the particular approach to describe the electronic structure, which may be dramatically exaggerated ͑as in LDA or GGA's͒ or underestimated ͑as in UHF͒ or, in other words, as due to the too small amount of electronelectron correlation taken into account this approach ͑hence to a too large U value͒. Three different magnetic coupling constants have been calculated by means of the supercell approximation 54 -57 to generate several magnetic orderings or magnetic phases.…”