From Complex Magnetic Ground States to Magnetocaloric Effects: A Review of Rare Earth R$_2$In Intermetallic Compounds

TL;DR

The review addresses why $R_2$In intermetallics exhibit complex magnetic ground states and large magnetocaloric effects at cryogenic temperatures, integrating crystallography, magnetism, MCE, and theory. It combines experimental insights with DFT and mean-field models to connect electronic structure—particularly $f$-electron valence fluctuations and $f$–$d$–$p$ hybridization—with phase stability and transition order, introducing charge-induced strain as a predictive descriptor for structural tendencies. A key finding is that light rare-earth members (e.g., Eu$_2$In, Pr$_2$In, Nd$_2$In) can show nonhysteretic first-order transitions accompanied by giant MCE, with Eu$_2$In exemplifying a prototypical GMCE material driven by a topological Fermi-surface reconstruction; heavier rare-earth members typically display second-order transitions with more moderate caloric responses. Collectively, the work provides design principles for tunable, low-hysteresis cryogenic magnetocaloric materials and outlines future directions, including pseudobinary mixing, strain engineering, and enhancing ambient stability, to advance practical cryogenic cooling technologies.

Abstract

R2In (R = rare earth) intermetallics exhibit unusual magnetic and magnetocaloric properties, driven by subtle electronic effects, lattice distortions, and spin-lattice coupling. Most of these binary compounds adopt the hexagonal Ni2In-type structure at room temperature, with Eu2In and Yb2In stabilizing in the orthorhombic Co2Si-type lattice. Lighter lanthanide compounds Eu2In, Nd2In, and Pr2In undergo first-order magnetic transitions with negligible hysteresis and minimal lattice volume change and exhibit giant cryogenic magnetocaloric effects, while heavy lanthanide R2In compounds including Gd2In show second-order transitions with moderate magnetocaloric effect. No lanthanide-based R2In compound exhibits symmetry-breaking structural transition, while Y2In transforms from hexagonal to orthorhombic structure near 250 K. Secondary low-temperature transitions, including spin reorientation or antiferromagnetic ordering, further enrich the magnetic phase landscape in these compounds. Integrating theoretical descriptors such as charge-induced strain and electronic structure provides predictive insight into phase stability and magnetocaloric performance, guiding the design of rare-earth intermetallics with tunable magnetic properties for cryogenic applications

Figures (9)

• Figure 1: Crystal structure (top-right half, color-coded) and nature of the magnetic phase transition (bottom-left half, color-coded) of R$_2$In compounds for different rare-earth elements. The numbers in the top-right corners indicate the valence state of the rare-earth ions in the corresponding compounds.
• Figure 2: (a) and (b) Room-temperature X-ray diffraction patterns for Gd$_2$In and Yb$_2$In, collected using Mo K$_\alpha$ and Cu K$_\alpha$ radiation, respectively: representative of Ni$_2$In-type hexagonal and Co$_2$Si-type orthorhombic structures adopted by R$_2$In. Figures (a, b) are reprinted with permission from Singh2025, Copyright (2025) by the American Physical Society. (c, d) Corresponding Ni$_2$In hexagonal and Co$_2$Si orthorhombic unit cells (red = R, blue = In), with rare-earth atoms on two inequivalent sites. (e) Experimental unit-cell volume versus atomic number $Z$ for the lanthanide series: unit-cell volume of hexagonal compounds (blue) decreases monotonically from La to Lu, while the volume of orthorhombic Eu$_2$In and Yb$_2$In cells (red; normalized cell volume shown, i.e., half the full cell) is much higher but follows the same contracting trend. The lattice volume values are taken from Table \ref{['tab:structure']}.
• Figure 3: Formation energies ($E_{\mathrm{form}}$) per atom for R$_2$In across the lanthanide series (La $\rightarrow$ Lu). Blue circles mark calculated $E_{\mathrm{form}}$ (eV$\cdot$atom$^{-1}$) for compounds relaxed in the hexagonal ($P6_3/mmc$) motif, while the two red squares at $f = 6$ and $f = 13$ indicate much less negative enthalpies and a ground-state switch to an orthorhombic ($Pnma$) structure (shaded columns). The abrupt energy increase at these two $f$-counts ($\approx 0.15$–0.18 eV/atom relative to neighbors) signals $f$-electron/valence-driven changes in bonding (e.g., divalent character or $f$-localization) and coincides with the annotated $P6_3/mmc$$\rightarrow$$Pnma$ structural change. Figure is reprinted with permission from Singh2025, Copyright (2025) by the American Physical Society.
• Figure 4: (a) Variation of the $T_{\mathrm{C}}$ of R$_2$In compounds (blue dots) and the de Gennes factor (dG) of the corresponding rare-earth elements (red dots) with atomic number ($Z$). For Eu$_2$In ($Z = 63$) and Yb$_2$In ($Z = 70$), dG is calculated assuming the divalent state of rare-earth elements, whereas for all other compounds, the tri-valency of rare-earths is considered. (b) $T_{\mathrm{C}}$ versus de Gennes factor for the hexagonal R$_2$In compounds. Here transition temperatures of R$_2$In compounds are taken from Refs. Guillou2018Biswas2020Forker2005Bhattacharyya2009Ravot1993Singh2012Bhattacharyya2009bBiswas2022bMcAlister1984bChen1989.
• Figure 5: The first-order transition with negligible thermomagnetic hysteresis in Pr$_{2-x}$Nd$_x$In ($x = 0,\,1,\,2$) is evidenced by a sharp transition in the $M$ vs. $T$ plots shown in (a) Biswas2020Biswas2022aBiswas2022bBiswas2023. Open and closed circles represent $M(T)$ data taken during heating and cooling cycles, respectively. (b) The temperature dependence of the specific heat for Eu$_2$In exhibits a pronounced $\delta$-like peak at the transition, indicating a large latent heat. Inset: $C_p(T)$ near the transition during heating and cooling cycles Guillou2018. Figure (b) is reproduced from Ref. Guillou2018 under Creative Commons Attribution 4.0 International license.