Magnetic exchange interactions in monolayer CrI$_3$ from many-body wavefunction calculations

TL;DR

This study combines advanced wavefunction calculations with model Hamiltonians to accurately determine magnetic interactions in monolayer CrI$_3$, providing detailed insights into its microscopic magnetic properties and benchmarking density functionals.

Contribution

It introduces a combined approach of multi-reference wavefunctions and model Hamiltonians to precisely quantify magnetic interactions in monolayer CrI$_3$, and evaluates density functionals against these results.

Findings

Ferromagnetic Heisenberg exchange J = -1.44 meV identified as dominant.

Single-ion anisotropy A = -0.10 meV causes out-of-plane easy axis.

Density functionals are benchmarked against accurate wavefunction results.

Abstract

The marked interplay between the crystalline, electronic, and magnetic structure of atomically thin magnets has been regarded as the key feature for designing next-generation magneto-optoelectronic devices. In this respect, a detailed understanding of the microscopic interactions underlying the magnetic responses of these crystals is of primary importance. Here, we combine model Hamiltonians with multi-reference configuration interaction wavefunctions to accurately determine the strength of the spin couplings in the prototypical single-layer magnet CrI$_3$. Our calculations identify the (ferromagnetic) Heisenberg exchange interaction $J = -1.44$ meV as the dominant term, being the inter-site magnetic anisotropies substantially {weaker}. We also find that single-layer CrI$_3$ features an out-of-plane easy axis ensuing from a single-ion anisotropy $A = -0.10$ meV, and predict $g$-tensor in-plane components $g_{xx} = g_{yy} = 1.90$ and out-of-plane component $g_{zz} = 1.92$. In addition, we assess the performance of a dozen widely used density functionals against our accurate correlated wavefunctions {calculations} and available experimental data, thereby establishing reference results for future first-principles investigations. Overall, our findings offer a firm theoretical ground to experimental observations.