Hole doping as an efficient route to increase the Curie temperature in monolayer CrI$_3$

TL;DR

This work tackles the low Curie temperature of semiconducting 2D magnets by examining carrier-doping as a control knob for magnetism in CrI3. It employs a multi-scale approach integrating DFT, Wannier-interpolated exchange pathways (TB2J), and Monte Carlo simulations to quantify how hole and electron doping modify isotropic exchanges, DMI, symmetric anisotropic exchange, and SIA. A key finding is a pronounced electron-hole asymmetry: hole doping markedly strengthens both isotropic exchanges and SOC-driven anisotropy, driving $T_c$ up to approximately $228$ K at $1$ hole/u.c., while electron doping yields smaller changes and can even reduce anisotropy; importantly, anisotropic exchange dominates MAE under hole doping, with DMI playing a secondary role. Overall, the cooperative enhancement of isotropic and anisotropic exchanges under strong hole doping establishes doping-induced anisotropy engineering as a viable route to high-temperature 2D ferromagnetism in vdW materials and likely generalizes to similar semiconducting 2D magnets.

Abstract

Two-dimensional van der Waals (vdW) magnets offer unprecedented opportunities to control magnetism at the atomic scale. Through charge carrier doping - realized by electrostatic gating, intercalation/adsorption, or interfacial charge transfer - one can efficiently tune exchange interactions and spin-orbit-induced effects in these systems. In this work, through a multi-scale theoretical framework combining density functional theory, spin Hamiltonian modeling, and Wannier-function analysis, we choose monolayer CrI$_3$ to unravel how carrier doping affects the isotropic as well as anisotropic exchange interactions in this prototypical vdW ferromagnet. The remarkable efficiency of hole doping in enhancing ferromagnetic exchange and magnetic anisotropy found in our study was explained through orbital-resolved analysis. Crucially, we demonstrated that unlike the undoped system - where isotropic exchange interactions govern magnetic long-range order - the hole-doped CrI$_3$ exhibits anisotropic terms comparable in magnitude to isotropic ones. Finally, we show that a high concentration of holes in a CrI$_3$ monolayer can increase its Curie temperature above 200 K. This work advances our understanding of doping-controlled magnetism in semiconducting 2D materials, demonstrating how anisotropy engineering can stabilize high-temperature magnetic order.

Figures (9)

• Figure 1: (a) Pairs of nearest-neighbors for which the exchange tensors are calculated in the depicted coordinate frame. (b) Doping dependency of isotropic exchanges between the first, second, and third nearest neighbors calculated by two different methodologies.
• Figure 2: (a) Reorientation of the local coordinate system in the unit cell to match the direction of Cr-I chemical bonds. (b) Decomposition of the Cr-Cr superexchange into distinct $d$ orbitals across the doping range from 1 holes/u.c. to 0.5 electrons/u.c. Non-negligible interaction pairs for the electron and hole doping are highlighted with colors.
• Figure 3: a) Schematic representation of competing FM and AFM interactions in undoped ${\rm CrI_3}$. b) Additional FM exchanges emerging from the interaction of occupied and partially empty $t_{2g}$ states under hole doping. c) Electron doping gives rise to new FM (AFM) exchange, represented through dotted arrows, arising from interaction of partially occupied $e_g$ with empty $e_g$ (occupied $t_{2g}$) states.
• Figure 4: (a-c) Illustrated superexchange pathways between a) $t_{2g}-t_{2g}$, b) $t_{2g}-e_{g}$ and c) $e_g-e_g$ orbitals. (d-f) Corresponding orbitally-resolved exchange interactions under doping conditions. (g,h) Projected density of states (PDOS) in the rotated coordinate system (see figure \ref{['fig:decomposition']}(a)) for g) Cr $d$ and h) I $p$ states.
• Figure 5: a) MAE and SIA show opposite signs in both electron and hole doping regions, suggesting different easy-axis orientations. Modeled MAE ($E^*_{\rm MAE}$) includes symmetric anisotropic exchange $E_{\rm K}$, solving the discrepancy in the entire doping range between the calculated MAE and SIA. b) Magnitude of the vector ${\bf D}$ at different doping concentrations; the inset indicates the interaction is prohibited among the first and third NN. c) Doping-dependent evolution of Curie temperatures computed using the Hamiltonians specified in the legend.