Fig. 1: Primary solution of mixed-cation [Y_2−xGd_xC]²⁺·2e⁻ electrides.

a−d Layered crystal structures of mixed-cation [Y_2−xGd_xC]²⁺·2e⁻ (a) and rare-earth binary [Re₂C]²⁺·2e⁻ (Re = Y or Gd) electrides (b). Edge-sharing CY_6−xGd_x octahedral units are highlighted in gray color. IAE (O) and IAE (T) are the interstitial electrons confined in the octahedral (c) and tetrahedral (d) cavities, respectively. Red and blue arrows indicate spin-up and spin-down states of IAEs, respectively. IAE (O) has a majority spin-up state (c), whereas IAE (T) can have both minority spin-up and minority spin-down states (d). The IAEs exhibit the spin-alignments of ferrimagnetic nature in [Y_2−xGd_xC]²⁺·2e⁻, super-PM in [Y₂C]²⁺·2e⁻ and FM in [Gd₂C]²⁺·2e⁻, respectively. e Lattice parameters of [Y_2−xGd_xC]²⁺·2e⁻ obtained by the Rietveld refinements of the XRD data (Supplementary Fig. 1 and Table 1). Details of structural parameters are provided in Supplementary Fig. 2. f Actual Gd contents versus nominal Gd contents. Actual Gd contents are obtained from the ICP–MS (Supplementary Table 2) and Rietveld analysis. g, h XRD patterns of 2θ (g) and ϕ (h) scans of the cleaved single crystal [YGdC]²⁺·2e⁻, respectively. XRD patterns of [Re₂C]²⁺·2e⁻ also provided in g as references. Inset figures represent the picture of the cleaved surface (g) and STEM images (h) of single crystal sample. For STEM images, both the annular bright-field (ABF) and the high-angle annular dark-filed (HAADF) images of (010) plane are displayed.