Ferromagnetic instability of interlayer floating electrons in the quasi-two-dimensional electride ${\text{Y}}_2\text{C}$

Ab initio electronic structure calculations show that the recently identified quasi-two-dimensional electride ${\mathrm{Y}}_2\mathrm{C}$ is a weak itinerant ferromagnet or is at least close to a ferromagnetic instability. The ferromagnetism is induced by the electride electrons, which are loosely bound around interstitial sites and overlap with each other to form two-dimensional interlayer conduction bands. The semimetallicity and two-dimensionality of the band structure are the keys to understanding this ferromagnetic instability.

Figure 1

(a) Crystal structure (anti-${\mathrm{CdCl}}_2$ structure) of ${\mathrm{Y}}_2\mathrm{C}$. A supercell consisting of $3\times 3\times 1$ conventional (hexagonal) unit cells is shown. The large and small spheres represent Y and C atoms, respectively. A representative interstitial site is indicated by a red cross. A conventional unit cell (${\mathrm{Y}}_6{\mathrm{C}}_3$) is made of three primitive (rhombohedral) cells (${\mathrm{Y}}_2\mathrm{C}$). (b) Brillouin zone of ${\mathrm{Y}}_2\mathrm{C}$. $B_1$ is equivalent to $B$, and $X$ is equivalent to $Q$ by symmetry. (c) Band structure obtained by non-spin-polarized (black solid curves) and spin-polarized (blue dashed curves and red dashed-dotted curves) calculations using the PAW method. The zero energy is taken to be the Fermi level. (d) Fermi surfaces obtained from a non-spin-polarized calculation (paramagnetic state). (e) and (f) Fermi surfaces for the minority and majority spin channels, respectively, obtained from a spin-polarized calculation (ferromagnetic state). The electron (hole) pockets are colored in blue (yellow). The darker side of the surfaces corresponds to lower energy.

Figure 2

(a) Total DOS, (b) PDOS for Y, and (c) PDOS for the interstitial site calculated by non-spin-polarized calculations using the PAW method. Corresponding plots obtained from spin-polarized calculations are shown in (${\text{a}}^{\prime }$), (${\text{b}}^{\prime }$), and (${\text{c}}^{\prime }$), respectively. The positive and negative DOS for the spin-polarized case denote the majority and minority spin channels, respectively.

Figure 3

(a) Calculated magnetization density isosurface at $0.015{\mu }_{\text{B}}/{\AA }^3$. The blue (brown) spheres represent Y (C) atoms. (b) and (c) Magnetization densities in the (001) plane [indicated as H in (a)] and $a-c$ plane [indicated as V in (a)], respectively. (${\text{b}}^{\prime }$) and (${\text{c}}^{\prime }$) represent corresponding plots for valence charge density.

Figure 4

DOS of the lower conduction band (LCB) and upper conduction band (UCB) obtained by a non-spin-polarized FLAPW calculation (dashed curves). As a result of band overlapping, highlighted by a red circle, the total DOS (solid curve) is enhanced near $E_F$.