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The origin of ferromagnetic interactions in NaMnCl$_3$: how the response theory reconciles with Goodenough-Kanamori-Anderson rules
Strongly Correlated Electrons · Submitted 18 May 2022
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim The layered antiferromagnet NaMnCl$_3$ reveals quite a different story: while the Coulomb $U$ on the Mn sites controls the strength of antiferromagnetic superexchange interactions, an equally important parameter is the Stoner coupling ${\cal I}_{\rm Cl}$ on the ligand sites.
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The on-site Coulomb repulsion $U$ is the key ingredient for describing the magnetic properties of Mott insulators, leading to a popular believe that many limitations of the density-functional theory based methods can be cured by artificially incorporating such on-site interactions for localized electrons in the model form. The layered antiferromagnet NaMnCl$_3$ reveals quite a different story: while the Coulomb $U$ on the Mn sites controls the strength of antiferromagnetic superexchange interactions, an equally important parameter is the Stoner coupling ${\cal I}_{\rm Cl}$ on the ligand sites. The latter is responsible for large ferromagnetic contributions to the interatomic exchange interactions, which in NaMnCl$_3$ nearly cancel the effect of the superexchange interactions. Although such behavior is anticipated from the phenomenological Goodenough-Kamanori-Anderson rules, the quantitative description of the ligand-related contributions remains disputable. Considering NaMnCl$_3$ as an example, we discuss how they can be generally taken into account in the linear response theory to regain the dependence of the exchange interactions on ${\cal I}_{\rm Cl}$. The problem is complicated by the fact that, for the nearly filled Cl $3p$ shell, the parameters ${\cal I}_{\rm Cl}$ are sensitive to the model assumptions.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | The on-site Coulomb repulsion $U$ is the key ingredient for describing the magnetic properties of Mott insulators, leading to a popular believe that many limitations of the density-functional theory based methods can be cured by artificially incorporating such on-site interactions for localized electrons in the model form. | background 1.00 | 0.04 | 0.03 | asserted 0.99 |
| s1 | The layered antiferromagnet NaMnCl$_3$ reveals quite a different story: while the Coulomb $U$ on the Mn sites controls the strength of antiferromagnetic superexchange interactions, an equally important parameter is the Stoner coupling ${\cal I}_{\rm Cl}$ on the ligand sites. | result 0.93 | 0.61 | 0.51 | asserted 1.00 |
| s2 | The latter is responsible for large ferromagnetic contributions to the interatomic exchange interactions, which in NaMnCl$_3$ nearly cancel the effect of the superexchange interactions. | result 0.86 | 0.50 | 0.31 | asserted 1.00 |
| s3 | Although such behavior is anticipated from the phenomenological Goodenough-Kamanori-Anderson rules, the quantitative description of the ligand-related contributions remains disputable. | gap 0.87 | 0.06 | 0.06 | asserted 0.75 |
| s4 | Considering NaMnCl$_3$ as an example, we discuss how they can be generally taken into account in the linear response theory to regain the dependence of the exchange interactions on ${\cal I}_{\rm Cl}$. | contribution 0.80 | 0.70 | 0.17 | asserted 0.63 |
| s5 | The problem is complicated by the fact that, for the nearly filled Cl $3p$ shell, the parameters ${\cal I}_{\rm Cl}$ are sensitive to the model assumptions. | limitation 0.65 | 0.22 | 0.04 | asserted 1.00 |
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Original abstract
The on-site Coulomb repulsion $U$ is the key ingredient for describing the magnetic properties of Mott insulators, leading to a popular believe that many limitations of the density-functional theory based methods can be cured by artificially incorporating such on-site interactions for localized electrons in the model form. The layered antiferromagnet NaMnCl$_3$ reveals quite a different story: while the Coulomb $U$ on the Mn sites controls the strength of antiferromagnetic superexchange interactions, an equally important parameter is the Stoner coupling ${\cal I}_{\rm Cl}$ on the ligand sites. The latter is responsible for large ferromagnetic contributions to the interatomic exchange interactions, which in NaMnCl$_3$ nearly cancel the effect of the superexchange interactions. Although such behavior is anticipated from the phenomenological Goodenough-Kamanori-Anderson rules, the quantitative description of the ligand-related contributions remains disputable. Considering NaMnCl$_3$ as an example, we discuss how they can be generally taken into account in the linear response theory to regain the dependence of the exchange interactions on ${\cal I}_{\rm Cl}$. The problem is complicated by the fact that, for the nearly filled Cl $3p$ shell, the parameters ${\cal I}_{\rm Cl}$ are sensitive to the model assumptions.
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