Multiple polarization phases and strong magnetoelectric coupling in the layered transition metal phosphorus chalcogenides $TM{\mathrm{P}}_2{X}_6\left(T=\mathrm{Cu},\mathrm{Ag};M=\mathrm{Cr},\mathrm{V};X=\mathrm{S},\mathrm{Se}\right)$ by controlling the interlayer interaction and dimension

Magnetoelectric multiferroic materials are the potential candidates for the high-density nonvolatile data storage devices. However, up to now, multiferroic materials with strong magnetoelectric coupling are still rare. Here, based on the first-principles calculations and theoretical model, we predict a different class of single phase multiferroic materials, transition metal phosphorus chalcogenides $TM{\mathrm{P}}_2{X}_6\left(T=\mathrm{Cu},\mathrm{Ag};M=\mathrm{Cr},\mathrm{V};X=\mathrm{S},\mathrm{Se}\right)$ with multiple polarization phases and strong magnetoelectric coupling. The ferroelectric polarization originates from the movement of Cu/Ag atoms breaking the symmetry of spatial inversion and the magnetism arises from partially filled $d$ orbitals of the V/Cr atoms. It is predicted that the different ferroelectric phases of $TM{\mathrm{P}}_2{X}_6$ bulk have different band gaps, providing a way to control electronic and transport properties by the external electric field. Most prominently, for $\mathrm{CuV}{\mathrm{P}}_2{\mathrm{S}}_6$ bilayer and few layers, one of the ferroelectric phases has ferromagnetic ground state and the other has antiferromagnetic states, realizing the electric-field control of magnetism. We reveal that the physical mechanism of the strong magnetoelectric coupling is from the reduced dimension and symmetry by constructing a theoretical model including the crystal field splitting, electric polarization effect, and exchange interaction. This work not only predicts a different class of magnetoelectric multiferroic materials, but also proposes a strategy to design them by controlling the interlayer interaction in van der Waals layered materials.

Figure 1

Side views of three different polarization phases of the $TM{\mathrm{P}}_2{X}_6$ bulks. Two FE phases are labeled as the $\mathrm{F}{\mathrm{E}}_{\mathrm{in}}$ (a) and $\mathrm{F}{\mathrm{E}}_{\mathrm{out}}$ (b). PE phase is also shown in (c). (d) Four magnetic configurations including one FM and three AFM states. The blue ball represents the V/Cr atoms. Red and green arrows represent the direction of spins.

Figure 2

Band structure of the $TM{\mathrm{P}}_2{X}_6$ bulks. Red and blue colors represent spin-majority and spin-minority levels, respectively. Square, circle, and rhombus represent V/Cr, Cu, and S/Se, respectively. The Fermi level is set to zero.

Figure 3

Side views of the $TM{\mathrm{P}}_2{X}_6$ bilayer (a)–(c), three layers (g)–(i), and four layers (k)–(m). The different magnetic configurations are shown for bilayer (f), three layers (j), and four layers (n). Variation of total energy of the (d) $\mathrm{F}{\mathrm{E}}_{\mathrm{out}}$ and (e) $\mathrm{F}{\mathrm{E}}_{\mathrm{in}}$ phase with the lattice constant are shown for bilayer $\mathrm{CuV}{\mathrm{P}}_2{\mathrm{S}}_6$.

Figure 4

Layer-projected band structures for $\mathrm{CuV}{\mathrm{P}}_2{\mathrm{S}}_6$ bilayer, three-layer, and four-layer films. Here, Γ (0, 0, 0), $X$ (0.5, 0, 0), $Y$ (0, 0.5, 0), and $S$ (0.5, 0.5, 0) are high symmetric points of 2D Brillouin zone. The Fermi level is set to zero.

Figure 5

(a)–(c) Schematic diagrams of orbital analysis and (d)–(f) projected density of states analysis of $\mathrm{CuV}{\mathrm{P}}_2{\mathrm{S}}_6$ bilayer. In (a)–(c) the red and green bars represent spin-majority and spin-minority levels, respectively.

Figure 6

Minimum energy pathway and corresponding energy barrier between the $\mathrm{F}{\mathrm{E}}_{\mathrm{in}}, \mathrm{F}{\mathrm{E}}_{\mathrm{out}}$, and PE phases for (a) $\mathrm{CuV}{\mathrm{P}}_2{\mathrm{S}}_6$ bulk and (b) $\mathrm{CuV}{\mathrm{P}}_2{\mathrm{S}}_6$ bilayer. (c) Minimum energy pathway between the $\mathrm{F}{\mathrm{E}}_{\mathrm{in}}$ and AFE phases in $\mathrm{CuV}{\mathrm{P}}_2{\mathrm{S}}_6$ bilayer. (d) Schematic illustration of a magnetoelectric switching/memory device.