Multiferroic properties of oxygen-functionalized magnetic i-MXene

Two-dimensional multiferroics inherit prominent physical properties from both low-dimensional materials and magnetoelectric materials, and they surpass their three-dimensional counterparts for their unique structures. Here, based on density functional theory calculations, a MXene derivative, i.e., i-MXene $({\mathrm{Ta}}_{2/3}{\mathrm{Fe}}_{1/3}{)}_2{\mathrm{CO}}_2$, is predicted to be a type-I multiferroic material. Originating from the reliable $5d^0$ rule, its ferroelectricity is robust, with a moderate polarization up to $\sim 12.33\mu \mathrm{C}/{\mathrm{cm}}^2$ along the $a$-axis, which can be easily switched and may persist above room temperature. Its magnetic ground state is layered antiferromagnetism. Although it is a type-I multiferroic material, its Néel temperature can be significantly tuned by the paraelectric-ferroelectric transition, manifesting a kind of intrinsic magnetoelectric coupling. Such a magnetoelectric effect originates from the conventional magnetostriction, but it is unexpectedly magnified by the exchange frustration. Our work not only reveals a nontrivial magnetoelectric mechanism, but it also provides a strategy to search for more multiferroics in the two-dimensional limit.

Figure 1

(a) The structure of the i-MAX phase of (${\mathrm{Ta}}_{2/3}{\mathrm{Fe}}_{1/3}{)}_2\mathrm{C}$. Both the top view (left) and side view (right) are shown. (b) Two types of oxygen adsorption on the (${\mathrm{Ta}}_{2/3}{\mathrm{Fe}}_{1/3}{)}_2\mathrm{C}$ surface. (c) The evolution of energy difference per O between the types A and B, as a function of $U_{\mathrm{eff}}$. The type A is always the lower-energy one. (d) The band gap of (${\mathrm{Ta}}_{2/3}{\mathrm{Fe}}_{1/3}{)}_2{\mathrm{CO}}_2$ (the type A oxygen adsorption and ferromagnetic state) as a function of $U_{\mathrm{eff}}$.

Figure 2

(a) The four typical AFM configurations for the bilayer triangular Fe sublattice in (${\mathrm{Ta}}_{2/3}{\mathrm{Fe}}_{1/3}{)}_2{\mathrm{CO}}_2$. The upper and lower layers are distinguished by colors, while the spin directions are denoted by signs + and −, respectively. The neighboring exchanges ${\mathit{J}}_1$/${\mathit{J}}_2$/${\mathit{J}}_3$ are also indicated. (b) The energy comparison of these AFM magnetic states as a function of $U_{\mathrm{eff}}$. The energy of the ferromagnetic state is taken as the reference. (c) The total DOS and element-projected PDOS of (${\mathrm{Ta}}_{2/3}{\mathrm{Fe}}_{1/3}{)}_2{\mathrm{CO}}_2$, which indicate the strong $d\text{−}p$ hybridization around the Fermi level. In (b) and (c) the ferroelectric structure is adopted.

Figure 3

(a) The point charge model analysis of dipole contributions to ferroelectric polarization. Each dipole is estimated using the nominal charge of ion and its displacement from the corresponding position in the paraelectric state. The $a$-, $b$-, and $c$-components are distinguished by colors (black, red, and green, respectively). The net dipole moments ($d_a$, $d_b$, and $d_c$) of all ions indicate the dominant component along the $a$-axis. The tiny value of $d_b$, which is beyond the reliable precision, comes from the fluctuation during the structure relaxation without symmetry restriction. (b) The energy barrier of ferroelectric switching. Inset: schematic of structures.

Figure 4

(a) The energy fluctuations during the AIMD simulations and the final structures of (${\mathrm{Ta}}_{2/3}{\mathrm{Fe}}_{1/3}{)}_2{\mathrm{CO}}_2$ at 300 and 700 K after 6 ps. (b) The averaged polarization estimated using the point charge model as a function of AIDM temperature. The estimated ferroelectric $T_{\mathrm{C}}$ is about ∼450 K.

Figure 5

(a) Comparison of magnetic transition temperatures (indicated by the peaks of heat capacity) of the paraelectric and ferroelectric phases. (b),(c) MC snapshots of spin configurations for the paraelectric and ferroelectric phases at 20 K. Left: upper Fe layer; right: lower Fe layer. Only the in-plane components are shown.