LaFe${}_{13-x}$Si${}_x$ compounds exhibit a giant magnetocaloric effect and they are considered as a good magnetocaloric working substance for an environmentally friendly cooling technique. Nevertheless as the Curie temperature $T_C$ is around 200 K, it is necessary to tune $T_C$ near room temperature for magnetic refrigeration. In this work we present a review of the various methods of synthesis and shaping of the LaFe${}_{13-x}$Si${}_x$ type compounds as well as the influence of chemical substitution, light element insertion or combination of both on $T_C$, magnetic entropy and adiabatic temperature variation ($\Delta S_{\mathrm{M}}$ and $\Delta T_{\mathrm{ad}}$), and stability upon cycling. The advantages and drawbacks of each method of preparation and type of element substitution/insertion are discussed. The implementation of these NaZn${}_{13}$ type materials in active magnetic refrigerator is presented and their performances are compared to that of Gd in prototypes.

The weak itinerant magnetic properties of A ₂ Ni ₇ compounds with A = {Y, La} have been investigated using electronic band structure calculations in the relation with their polymorphic crystal structures. These compounds crystallizes in two structures resulting from the stacking of two and three blocks of [ A ₂ Ni ₄ + 2 A Ni ₅ ] units for hexagonal 2 H -La ₂ Ni ₇ (Ce ₂ Ni ₇ type) and rhombohedral 3 R -Y ₂ Ni ₇ (Gd ₂ Co ₇ type) respectively. Experimentally, 2 H -La ₂ Ni ₇ is a weak itinerant antiferromagnet whereas 3 R -Y ₂ Ni ₇ is a weak itinerant ferromagnet. From the present first principles calculation within non-spin polarized state, both compounds present an electronic density of state with a sharp and narrow peak centered at the Fermi level corresponding to flat bands from 3 d -Ni. This induces a magnetic instability and both compounds are more stable in a ferromagnetic (FM) order compared to a paramagnetic state (Δ E ≈ −35 meV/f.u.). The magnetic moment of each of the five Ni sites varies with their positions relative to the [ A ₂ Ni ₄ ] and [ A Ni ₅ ] units: they are minimum in the [ A ₂ Ni ₄ ] unit and maximum at the interface between two [ A Ni ₅ ] units. For 2 H -La ₂ Ni ₇ , an antiferromagnetic (AFM) structure has been proposed and found with an energy comparable to that of the FM state. This AFM structure is described by two FM unit blocks of opposite Ni spin sign separated by a non-magnetic layer at z = 0 and ½. The Ni (2 a ) atoms belonging to this intermediate layer are located in the [La ₂ Ni ₄ ] unit and are at a center of symmetry of the hexagonal cell ( P 6 ₃ / mmc ) where the resultant molecular field is cancelled. Further non-collinear spin calculations have been performed to determine the Ni moment orientations which are found preferentially parallel to the c axis for both FM and AFM structures.

The influence of the partial Er for Y substitution on the crystal structure and magnetic properties of $\mathrm{YF}{\mathrm{e}}_2{\mathrm{D}}_{4.2}$ has been investigated by high field magnetization and neutron diffraction experiments. ${\mathrm{Y}}_{0.7}\mathrm{E}{\mathrm{r}}_{0.3}\mathrm{F}{\mathrm{e}}_2{\mathrm{D}}_{4.2}$ compound crystallizes in the same monoclinic structure as $\mathrm{YF}{\mathrm{e}}_2{\mathrm{D}}_{4.2}$ described in $Pc\left(P_1{c}_1\right)$ space group with D atoms located in 18 different tetrahedral interstitial sites. A cell volume contraction of 0.6% is observed upon Er substitution, inducing large modification of the magnetic properties. Electronic effect of D insertion as well as lowering of crystal symmetry are important factors determining the magnetic properties of Fe sublattice, which evolves towards more delocalized behavior and modifying the Er-Fe exchange interactions. In the ground state, the Er and Fe moments are arranged ferrimagnetically within the plane perpendicular to the monoclinic $b$ axis and with average moments $m_{\mathrm{Er}}=6.4\left(3\right){\mu }_B{\mathrm{Er}}^{-1}$ and ${\mathrm{m}}_{\mathrm{Fe}}=2.0\left(1\right){\mu }_B{\mathrm{Fe}}^{-1}$ at 10 K. Upon heating, $m_{\mathrm{Er}}$ decreases progressively until $T_{\mathrm{Er}}=55\mathrm{K}$. Between 55 K and 75 K, the Fe sublattice undergoes a first-order ferromagnetic-antiferromagnetic (FM-AFM) transition with a cell volume contraction due to the itinerant metamagnetic behavior of one Fe site. In the AFM structure, $m_{\mathrm{Fe}}$ decreases until the Néel temperature $T_{\mathrm{N}}=125\mathrm{K}$. At high field, two different types of field induced transitions are observed. The Er moments become parallel to the Fe one and saturates to the $\mathrm{E}{\mathrm{r}}^{3+}$ free ion value, leading to an unusual field induced FM arrangement at a transition field $B_{\mathrm{Trans}}$ of only 78 kG below 30 K. Then above ${T_{\mathrm{M}}}_0=66\mathrm{K}$, an AFM-FM transition of the Fe sublattice, accompanied by a cell volume increase is observed. $B_{\mathrm{Trans}}$ increases linearly versus temperature and with a larger $d{B}_{\mathrm{Trans}}/dT$ slope than for $\mathrm{YF}{\mathrm{e}}_2{\mathrm{D}}_{4.2}$. This has been explained by the additional contribution of Er induced moments above $B_{\mathrm{Trans}}$.