Magnetic transition in B2 Al-Cr-Co alloys

TL;DR

This work investigates a chemistry-driven magnetic transition in B2 Al–Cr–Co alloys by combining density functional theory (DFT) calculations with Monte Carlo (MC) simulations. Using EMTO-CPA to obtain total energies and exchange interactions $J_{ij}$, the authors construct a Heisenberg model and estimate Curie temperatures via mean-field theory, while MC simulations reveal the evolution of magnetic states across Co concentrations. They find that AlCr is antiferromagnetic and Co doping drives a transition to ferromagnetism around $\sim$30 at.% Co, with Cr–Cr exchanges changing sign and $T_C$ decreasing with increasing Co; experimental data at similar compositions show partial agreement. However, MC predictions of a disordered spin-glass-like state at higher Co contrast the DFT results and some experiments, indicating limitations of the current exchange-parameter approach and motivating further experimental/theoretical work. Overall, the study provides quantitative insight into how chemistry shapes exchange interactions in Al–Cr–Co B2 alloys and informs design strategies for magnetocaloric B2 materials.

Abstract

Using Density Functional Theory (DFT) calculations and Monte-Carlo (MC) simulations, we investigate the recently reported magnetic transition in B2 Al-Cr-Co alloys. The Cr sublattice is alloyed with different amounts of Co in the antiferromagnetic (AFM) B2 AlCr binary alloy and the resulting exchange interactions are analyzed within the Heisenberg Hamiltonian framework. DFT results reveal that at low Co concentrations the system favors the AFM order, while at high Co contents a transition to the ferromagnetic (FM) state is observed. Within the FM stability field, the Curie temperature (TC), obtained within the mean-field approximation, is below ~160 K and decreases with Co concentration. The calculated exchange parameters evolve systematically with Co content, and the trends are consistent with the DFT total energies. The magnetic configurations obtained from MC simulations follow the DFT results at low Cr levels but predict a spin-glass behavior for alloys containing more than 40 at.% Co on Cr sublattice. These findings provide a fundamental understanding of how the chemistry-driven changes in exchange interactions affect magnetism in the B2 Al-Cr-Co alloys.

Figures (4)

• Figure 1: Calculated magnetic energy difference ($\Delta E$ = $E^{\mathrm{FM}}$ – $E^{\mathrm{AFM}}$) and Wigner-Seitz radii ($w$) for the FM and AFM states for B2 Al–Cr–Co alloys as a function of Co content. ROM stand for the Wigner-Seitz radii estimated from the linear rule of mixture.
• Figure 2: Theoretical magnetic transition temperatures for the FM state as a function of Co composition calculated using the MFA for the B2 Al–Cr–Co alloys. The red dot represents the experimental $T_{\text{C}}$ value for the arc-melted $\mathrm{Al_{50}Cr_{38}Co_{12}}$ alloy with the B2 phase containing about 28 at.% Co. Dastanpour2025b
• Figure 3: The calculated Cr–Cr exchange interaction $J_{\text{0j}}$ for B2 AlCr, $\mathrm{Al_{50}Cr_{40}Co_{10}}$, $\mathrm{Al_{50}Cr_{30}Co_{20}}$, $\mathrm{Al_{50}Cr_{20}Co_{30}}$, and $\mathrm{Al_{50}Cr_{10}Co_{40}}$. $\mathrm{R}_{\mathrm{0}j}$ represents the distance between atom $j$ and atom at the origin in units of B2 lattice parameter $a$. The insets show the Cr–Co and Co–Co exchange interactions.
• Figure 4: Illustration of the low-temperature (1 K) antiferromagnetic order found for $\mathrm{Al_{50}Cr_{40}Co_{10}}$ alloy (panels a1-a3), and the disordered magnetic state found for $\mathrm{Al_{50}Cr_{20}Co_{30}}$ (panels b1-b3) in B2 structure. All magnetic configurations are shown in $x$-$y$ plane, $x$-$z$ plane, and $y$-$z$ plane. For comparison, we also show the magnetic state found for the hypothetical $\mathrm{Al_{50}Cr_{50}}$ alloy using the magnetic exchange interactions calculated for $\mathrm{Al_{50}Cr_{20}Co_{30}}$ (panels c1-c3). Displayed are the randomly distributed Cr and Co magnetic moments in panels a1-b3 and only Cr moments in panels c1-c3.