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Magnetic materials are typically described in terms of the Heisenberg model,which provides an accurate account of thermodynamic properties when combinedwith first principles calculations. This approach is usually based on an energymapping between density functional theory and a classical Heisenberg model.However, for two-dimensional systems the eigenenergies of the Heisenberg modelmay differ significantly from the classical approximation, which leads tomodified expressions for exchange parameters. Here we demonstrate that densityfunctional theory yields local magnetic moments that are in accordance withstrongly correlated anti-ferromagnetic eigenstates of the HeisenbergHamiltonian. This implies that density functional theory provides a descriptionof these states that conforms with the quantum mechanical eigenstates of themodel. We then provide expressions for exchange parameters based on a propereigenstate mapping to the Heisenberg model and find that they are typicallyreduced by 10 % compared to a classical analysis. Finally, we calculate thecorrections to critical temperature for magnetic ordering for a previouslypredicted set of two-dimensional ferromagnetic insulators and find that theinclusion of quantum effects may reduce the predictions of criticaltemperatures by up to 7 %.

First Principles Heisenberg Models of 2D magnetic materials: The Importance of Quantum Corrections to the Exchange Coupling