|Frustrated magnetic systems, whose behaviour is influenced by competing interactions between magnetic spins, have been an active area of research. There is a special class of materials called breathing pyrochlores, whose key difference from “regular” pyrochlores is the breaking of inversion symmetry. Copper-Aluminum-Chromium-Sulfide (CuAlCr₄S₈ ) is a
candidate for displaying a frustrated Heisenberg model on the breathing pyrochlore lattice.
There are two models used for CuAlCr₄S₈ , the Heisenberg model that goes up to third nearest neighbours (up-to-3rd-NN), and Heisenberg model that goes up to fifth-nearest neighbours (up-to-5th-NN). Both models have exchange couplings obtained from our collaborators using density-functional theory (DFT). Both Heisenberg models for CuAlCr₄S₈ have exchange couplings that are strongest between third-nearest neighbours, as opposed to more typical pyrochlores that possess stronger exchange couplings between first-nearest neighbours. The peculiarity of the Heisenberg models for CuAlCr₄S₈, combined with the emerging experimental data, makes it an ideal target for theoretical research. Individual’s methods for theoretical analysis are classical methods, which are mean-field-theory (MFT), large-N, and classical Monte Carlo (CMC) simulation. Collaborators’ methods for theoretical analysis are quantum methods, which are pseudo-fermion functional renormalization group (PFFRG) and pseudo-Majorana functional renormalization group (PMFRG). For the up-to-3rd-NN model, individual’s and collaborators’ results show peaks in the structure factor that are situated on the line 2π/a(±1, h, 0) up to permutation of the coordinates, for
some parameter h, and cubic supercell length a. MFT and large-N suggest peaks at h = 0, with a continuous decrease in the structure factor for h away from 0. Monte Carlo shows sharp Bragg peaks at h = 0 and h = ±1. Both of our collaborators’ quantum methods, PFFRG and PMFRG, give peaks at 0 < |h| < 1, for a seemingly incommensurate h, considering the available wavevector resolution. For the up-to-5th-NN model, individual’s classical methods all give Bragg peaks at h = 0 and h = ±1, while we are awaiting our collaborators’ quantum methods for this model. The magnetic peaks in the experimental data disagree with the expected results from all the classical methods that use the models provided by DFT. We test the possibility of the experimental peaks being the peaks seen in the quantum methods for the up-to-3rd-NN model and the peaks seen in classical methods when altering the exchange couplings provided by DFT. We explain possible causes for disagreements among individual’s classical methods, between individual’s methods and our collaborators’ quantum methods, and between theoretical methods and experimental data.