Two-dimensional bipolar ferromagnetic semiconductors from layered antiferromagnets

Bipolar magnetic semiconductors (BMSs) are a class of compounds possessing different valence band maximum (VBM) and conduction band minimum (CBM) in terms of electron spins, which are related to but distinct from half-metals. They allow one to switch one spin current to another by applying external gate voltage or chemical doping, which can meet the requirement of bipolar manipulation in spintronic devices. Designing and searching BMSs are still a challenge. Here we predict that monolayer ${\mathrm{CrPS}}_4$ and ${\mathrm{CrPSe}}_4$ are bipolar ferromagnetic semiconductors with Curie temperature 58 K and 82 K, respectively. We predicted that they can be exfoliated from their A-type antiferromagnetic bulk form. Electric-field gating could drive ${\mathrm{CrPS}}_4$ and ${\mathrm{CrPSe}}_4$ into half-metals with reversible spin-polarization directions, where the bipolar doping is relatively easier to access for ${\mathrm{CrPSe}}_4$ in experiment than ${\mathrm{CrPS}}_4$ for its suitable electron affinity and ionic potential. Furthermore, we highlight the role played by the different magnitude between spin exchange splitting and crystal field splitting in the formation of BMSs. The results presented here may provide new clues in designing or searching BMSs.

Figure 1

(a) Crystal structure of bulk ${\mathrm{CrP}X}_4$ ($X=\text{S}$, Se, Te), the red arrows represent the calculated alignment of spins. (b) Cleavage energy ($E_{\mathrm{cl}}$) as a function of separation distance ($d\text{−}{d}_0$) for ${\mathrm{CrP}X}_4$ ($X=\text{S}$, Se, Te), where $d$ is the separate distance and $d_0$ the distance between the layers at equilibrium state. (c–d) Crystal structure of monolayer ${\mathrm{CrP}X}_4$ ($X=\text{S}$, Se, Te) from side and top views, respectively. The blue dashed lines in (d) show the primitive cell of monolayer ${\mathrm{CrP}X}_4$ defined by vector ${\vec{a}}_p$ and ${\vec{b}}_p$, and the black dashed lines are the conventional cell defined by vector $\vec{a}$ and $\vec{b}$. ${\theta }_1$ and ${\theta }_2$ are Cr-$X$-Cr angles. (e) The first Brillouin zone of monolayer ${\mathrm{CrP}X}_4$. The black solid lines represent the folding of K points of the conventional lattice into the primitive cell. The VESTA [22] package was used to visualize the atomic structures.

Figure 2

Temperature-dependent (a) magnetic moment and (b) specific heat (${\mathrm{C}}_{\mathrm{v}}$) for monolayer ${\mathrm{CrP}X}_4$ ($X=\text{S}$, Se, Te) based on Monte Carlo simulations. The result for ${\mathrm{CrI}}_3$ is added for comparison, which agrees with the experimental value 45 K [7]. The dashed lines locate the $T_{\mathrm{c}}$. (c–e) Spin-resolved electronic structures of monolayer ${\mathrm{CrPS}}_4$, ${\mathrm{CrPSe}}_4$, and ${\mathrm{CrPTe}}_4$ with a PBE functional, respectively, where the Fermi level is set to be zero. The gray dashed lines show the band structures including spin-orbit coupling.

Figure 3

Spin-resolved partial density of states of monolayer (a) ${\mathrm{CrPS}}_4$, (b) ${\mathrm{CrPSe}}_4$, and (c) ${\mathrm{CrPTe}}_4$. (d) Schematic diagram of splitting and occupations of Cr-$d$ orbitals, where ${\mathrm{\Delta }}_{\mathrm{c}}$ is defined as the energy difference between VBM of spin-up channel and CBM of spin-up channel, and ${\mathrm{\Delta }}_{\mathrm{s}}$ the energy difference between the VBM of spin-up channel and CBM of spin-down channel. (e) Distorted ${\mathrm{CrX}}_6$ octahedron in monolayer ${\mathrm{CrP}X}_4$ ($X=\text{S}$, Se, Te). $l_1$, $l_2$, and $l_3$ label the bond lengths of Cr-$X$ summarized in Table S4 [24]. (f) Schematic diagram of superexchange interactions of Cr-$X$-Cr. (g) Angles of Cr-$X$-Cr labeled in Fig. 1.

Figure 4

(a, b) Energy differences between the FM and AFM1, AFM2, and AFM3 configurations as a function of doping carrier concentrations for ${\mathrm{CrPS}}_4$ and ${\mathrm{CrPSe}}_4$, respectively. The up and down arrows indicate that electrons across the Fermi level are spin-up and spin-down electrons, respectively, corresponding to red and green regions. The other region means that electrons of both spins occupy the Fermi level. (c) Manipulation of spin orientations by gate voltage. The middle picture shows the three energy band gaps of ${\mathrm{CrPSe}}_4$ calculated with an HSE06 functional. (d) Band alignment of ${\mathrm{CrP}X}_4$ ($X=\text{S}$, Se) calculated with an HSE06 functional together with other reported typical semiconductors shown for comparison; relevant data are taken from Ref. [42]. The green region indicates the bipolar doping windows.