Towards Magnetic Cluster Expansion Monte Carlo Simulations of Battery Electrodes

Non-invasive characterization techniques such as magnetometry, nuclear magnetic resonance (NMR), and electron paramagnetic resonance (EPR) spectroscopies are invaluable for interrogating the working principles and failure mechanisms of Li-ion battery cathodes. Interpreting these magnetic changes demands a physics-driven understanding of the spin dynamics underlying the low-energy magnetic configurations in these cathodes. Such comprehensive simulations can equip us with a robust toolkit to analyze experimental data acquired both <i>ex situ </i>and <i>operando</i>.<br/>In this work, we utilize first principles computational and statistical mechanical methods such as cluster expansions and Monte Carlo, implemented <i>via</i> the CASM software package, to model magnetic interactions in the high-voltage LiNi_0.5Mn_1.5O₄ (LNMO) spinel battery material. Density functional theory (DFT) calculations of several Ni-Mn orderings, including the ordered ground state (space group P4₃32), reveal a preference for an antiferrimagnetic arrangement of the Ni and Mn sublattices due to strong antiferromagnetic superexchange interactions between Mn⁴⁺ and Ni²⁺ ions. Magnetic cluster expansions of these structures further verify these results, with strong antiferromagnetic Ni-Mn magnetic exchange coupling constants and ferromagnetic Mn-Mn and Ni-Ni exchange interactions among adjacent transition metals. We also study how the magnetic properties are tuned by Li composition.<br/>Further simulations of the LNMO magnetic system were conducted using Metropolis Monte Carlo to investigate finite temperature magnetic properties, through various magnetic models. While these simulations effectively replicate experimental magnetic states at both high and low temperatures, the Ising model fell short in accurately predicting the experimental transition temperature between ordered and disordered magnetic states. In this work, we demonstrate that the Heisenberg model, which aligns better with actual spin behavior, addresses this discrepancy, and very accurately predicts experimental transition temperatures observed in magnetometry measurements. Additionally, we implement a “Semi-Quantum-Semi-Classical” Monte Carlo sampling method, which better represents spins at low temperatures by incorporating quantum behavior. Our results provide invaluable insights into the complex magnetic interactions underpinning these cathode materials, with applications that extend to the broader materials science community.