Local magnetic structure in fully and partially ordered V$_2$$X$Al Heusler alloys ($X$=Cr, Mn, Fe, Co, Ni)

Multicomponent Heusler alloys exhibit various magnetic properties arising from their diverse atomic compositions and crystal structures. Identifying the general physical principles that govern these behaviors is essential for advancing their potential in spintronic applications. In this work, we combine density functional theory with atomistic Monte Carlo simulations to investigate the magnetic ground states, finite-temperature magnetic transitions, and electronic structures of fully-ordered $L2_1$-, $XA$-type, and partially-ordered V$2X$Al ($X=$ Cr, Mn, Fe, Co, Ni) Heusler alloys. We propose the concept of magnetic motifs, defined as V-$X$-V triangular pathway connected by the nearest-neighbor (NN) exchange interactions $J{\mathrm{V-}X}$. Within this framework, the magnetic ground states and transition temperatures across the V$2X$Al family can be consistently understood. The magnetic order is primarily governed by the NN $J{\mathrm{V-}X}$ interactions in the triangular motifs, while the transition temperatures are additionally influenced by $J_{X-X}$ couplings. Furthermore, the magnetic motifs are still proven to be effective in our calculations on partially-ordered V$_2$$X$Al alloys from $L2_1$ to $XA$-type structures. Our results suggest that the concept of magnetic motifs provides a unifying principle for understanding magnetic ordering in V-based Heusler alloys and could serve as a candidate guide for exploring magnetism and designing advanced spintronic materials in a broader class of Heusler systems.

💡 Research Summary

In this work the authors investigate the magnetic ground states, finite‑temperature magnetic transitions, and electronic structures of the V₂XAl (X = Cr, Mn, Fe, Co, Ni) Heusler alloys using a combination of density‑functional theory (DFT) and atomistic Monte Carlo (MC) simulations. Two crystallographic families are considered: the fully ordered L2₁ (full‑Heusler, space group Fm‑3m) and the inverse‑Heusler XA (space group F‑43m). For each composition the authors first relax the crystal structures with spin‑polarized GGA‑PBE calculations (PAW potentials, 425 eV cutoff, dense k‑mesh). Formation‑energy analysis shows that all compounds except L2₁‑V₂NiAl are thermodynamically stable; V₂MnAl and V₂FeAl preferentially adopt the XA structure, V₂CrAl is most stable in L2₁, while V₂NiAl favors a partially disordered arrangement.

Magnetic moments obtained from the DFT calculations reveal that V₂CrAl and V₂MnAl in the L2₁ phase are ferrimagnetic, whereas V₂FeAl, V₂CoAl and V₂NiAl are ferromagnetic. In the XA phase V₂CrAl exhibits almost zero net moment due to parallel alignment of the two V sublattices, while the other four compounds become ferrimagnetic with antiparallel V sublattices.

The central conceptual advance of the paper is the introduction of “magnetic motifs”: a V‑X‑V triangular pathway formed by the nearest‑neighbour (NN) exchange interactions J_V‑X. By extracting the full set of Heisenberg exchange parameters J_ij with the TB2J code (based on Green’s‑function formalism), the authors demonstrate that the sign and magnitude of J_V‑X alone dictate the magnetic ordering within each motif. Positive J_V‑X leads to antiferromagnetic coupling between the two V atoms mediated by X, producing ferrimagnetism at the crystal level; negative J_V‑X yields ferromagnetic alignment. The secondary exchange J_X‑X, although generally weaker, fine‑tunes the Curie temperature (T_C).

Using the extracted J_ij, large‑scale MC simulations (≈2.1 × 10⁵ spins in a 15 nm cubic supercell, 9 × 9 × 9 k‑point sampling) are performed with the V‑ampire spin‑dynamics package. Magnetization curves M(T) are computed from 0 to 1000 K in 5 K steps, and T_C is identified from the inflection point. The calculated T_C values follow the hierarchy of |J_V‑X|: V₂CoAl (XA) ≈ 850 K, V₂FeAl (XA) ≈ 720 K, V₂MnAl (L2₁) ≈ 620 K, V₂CrAl (L2₁) ≈ 380 K. Inclusion of J_X‑X raises T_C by 30–50 K in cases where J_V‑X is moderate, confirming its secondary role.

To assess the robustness of the motif picture against chemical disorder, the authors construct a series of partially ordered structures by progressively swapping V and X atoms between the 4b and 4c sites of a 16‑atom cell, thereby interpolating between L2₁ and XA. For each intermediate configuration the exchange parameters are recomputed; the distribution of J_V‑X and J_X‑X remains essentially unchanged, and the MC‑derived T_C varies smoothly between the two end‑members. This demonstrates that the magnetic‑motif concept is valid even in the presence of substantial site disorder, which is often encountered experimentally in V‑based Heusler films.

Overall, the study provides a unifying framework: the magnetic behavior of V₂XAl alloys can be understood by a simple triangular motif governed primarily by the NN V‑X exchange, with X‑X exchange providing a fine‑tuning knob for transition temperatures. The authors argue that this motif‑based approach can be extended to other multi‑sublattice Heusler systems, offering a practical guide for designing high‑T_C, highly spin‑polarized materials for spintronic applications. Future work is suggested to explore other transition‑metal or main‑group substitutions, to validate the predictions experimentally, and to incorporate spin‑orbit coupling effects for anisotropy engineering.