In this review, we consider state-of-the-art density functional theory (DFT) investigations of strongly correlated systems performed with the meta-generalized gradient approximation (meta-GGA) strongly constrained and appropriately normed (SCAN) functional during the last five years. The study of such systems in the framework of the DFT is complicated because the well-known exchange–correlation functionals of the local density approximation (LDA) and generalized gradient approximation (GGA) families are not designed for strong correlations. The influence of the exchange–correlation effects beyond classical LDA and GGA are considered in view of the prediction of the ground state structural, magnetic, and electronic properties of the magnetic materials, including pure metals, binary compounds, and multicomponent Heusler alloys. The advantages of SCAN and points to be enhanced are discussed in this review with the aim of reflecting the modern state of computational materials science.

The stability of the nonmodulated martensitic phase, the austenitic Fermi surface, and the phonon dispersion relations for ferromagnetic ${\mathrm{Ni}}_2\mathrm{MnGa}$ are studied using density functional theory. Exchange-correlation effects are considered with various degrees of precision, starting from the simplest local spin density approximation (LSDA), then adding corrections within the generalized gradient approximation (GGA), and finally, including the meta-GGA corrections within the strongly constrained and appropriately normed (SCAN) functional. We discuss a simple procedure to reduce a possible overestimation of magnetization and underestimation of nesting vector in SCAN by parametrically decreasing self-interaction corrections.

We have performed a combined experimental and theoretical investigation of the vibrational properties of ${\mathrm{Ni}}_2\mathrm{Mn}\mathrm{Sn}$ Heusler alloys. Sn-partial vibrational density of states (VDOS) of ${}^{119}\mathrm{Sn}$ was measured by nuclear resonant inelastic x-ray scattering at temperatures of 15 and 300 K, while magnetism and local environment of Sn was resolved by ${}^{119}\mathrm{Sn}$ Mössbauer spectroscopy. Using density functional theory, we associate the peaks in the VDOS with particular features in the element-resolved phonon dispersion of $\mathrm{L}{2}_1$ ordered ${\mathrm{Ni}}_2\mathrm{Mn}\mathrm{Sn}$. The good agreement between theory and experiment in the low-energy region provides the evidence that the inversion of optical modes at $\mathrm{\Gamma }$ involving the displacement of Ni and the heavier main group element atoms, which was predicted previously for other Ni-Mn-based Heusler compounds, is also a characteristic property of ${\mathrm{Ni}}_2\mathrm{Mn}\mathrm{Sn}$. Introducing different types of magnetic and antisite disorder in our calculations results in a distinctive redistribution and broadening of the Sn-VDOS, suggesting that considering partial disorder further improves the agreement with the experiment in particular at the highest phonon energies.

Magnetic frustration in ferromagnetic metallic systems is unusual due to the long-range and symmetric nature of the exchange interactions. In this work we prove that it is possible to obtain a highly frustrated ferromagnetic phase in a multisublattices cubic structure through a fine-tuning of the magnetic interactions. This peculiar state is achieved in Ni-Mn-(In, Sn) Heusler alloys and results in the effective decoupling of their two intertwined ferromagnetic sublattices. One sublattice is ferromagnetic long-range ordered below the macroscopic Curie temperature ($T_C$) whereas the second one remains disordered until a crossover to a polarized state occurs at $T\ll T_C$. This result points out that a fine engineering of the magnetic interactions in metallic systems can lead to interesting novel and emergent phenomena.

Chemical ordering in NiMn-based Heusler alloys with magnetostructural phase transition is crucial for understanding the physics of the phase transition. In the new field of all-d-metal Ni(Co)MnTi Heusler alloys, the experimental determination of chemical order is challenging due to the low difference in scattering power of the different elements. Here, we report a combined approach of neutron and x-ray diffraction for an analysis of chemical order in Ni(Co)MnTi alloys and show that no Heusler-typical $L{2}_1$ order between Ti and Mn is present. Furthermore, Co and Ni atoms do not exhibit order among them; however, the phase transition of Co containing samples can be shifted significantly by changing the degree of $B2$ order with proper heat treatment. Using first-principles calculations, we reveal how the structural and magnetic sub-systems depend on the degree of $B2$ disorder.