Large out-of-plane piezoelectric response of ferromagnetic monolayer MoXF (X=S, Se): First principles predictions

Two-dimensional ferromagnetic semiconductors of rare-earth monolayer GdX2 (X = Cl, Br, I) with large perpendicular magnetic anisotropy and high Curie temperature

For two-dimensional (2D) materials, piezoelectric ferromagnetism with large out-of-plane piezoresponse is highly desirable for multifunctional ultrathin piezoelectric device application. Here, we predict that Janus monolayer CrSCl is an out-of-plane ferromagnetic semiconductor with large vertical piezoelectric response and high Curie temperature. The predicted out-of-plane piezoelectric strain coefficient d31 is −1.58 pm/V, which is higher than that of most 2D materials (compare absolute values of d31). The large out-of-plane piezoelectricity is robust against electronic correlation and biaxial strain, confirming reliability of large d31. The calculated results show that tensile strain is conducive to high Curie temperature, large magnetic anisotropy energy, and large d31. Finally, by comparing d31 of CrYX (Y = S; X = Cl, Br, I) and CrYX (Y = O; X = F, Cl, Br), we conclude that the size of d31 is positively related to electronegativity difference of X and Y atoms. Such findings can provide valuable guidelines for designing 2D piezoelectric materials with large vertical piezoelectric response.

Magnetic units with large magnetic anisotropy energy (MAE) and high Curie temperature (Tc) are crucial for spintronic and quantum computing devices, which are a persisting demand for miniaturization of magnetic units. Using first-principles calculations and Monte Carlo simulation, it is found that monolayer 1T-CrTe2 exhibits strong perpendicular magnetic anisotropy with a MAE of approximately 5.29 meV and high Tc of ∼136 K. Interestingly, we find that the MAE and Tc of monolayer 1T-CrTe2 are tunable through electron/hole doping, strain, and heterostructure engineering. The magnetic easy-axis can be adjusted from out of plane to in plane, which is mainly attributed to the coupling between Te atomic orbitals (px, py). Second-order perturbation theory reveals that the spin–orbit coupling interaction between the occupied px and unoccupied py orbitals in opposite spin channel near Fermi level gives rise to negative contribution of MAE. Moreover, Tc can be enhanced to ∼230 K through super–superexchange mechanism of heterostructure due to the electron hopping between t2g/eg orbitals of Cr4+ ions and e1/a1 orbitals of Fe2+ ions. Importantly, we find that Tc can be boosted above room temperature by applying moderate strain (6%), ascribing to significant enhancement of MAE and exchange coupling constant. The present work indicates that monolayer 1T-CrTe2-based two-dimensional materials are very promising for room temperature application in magnetic storage and information processing.

In the past few years, two-dimensional (2D) high-temperature ferromagnetic semiconductor (FMS) materials with novelty and excellent properties have attracted much attention due to their potential in spintronics applications. In this work, using first-principles calculations, we predict that the H-MnN2 monolayer with the H-MoS2-type structure is a stable intrinsic FMS with an indirect band gap of 0.79 eV and a high Curie temperature (Tc) of 380 K. The monolayer also has a considerable in-plane magnetic anisotropy energy (IMAE) of 1005.70 μeV/atom, including a magnetic shape anisotropy energy induced by the dipole-dipole interaction (shape-MAE) of 168.37 μeV/atom and a magnetic crystalline anisotropy energy resulting from spin-orbit coupling (SOC-MAE) of 837.33 μeV/atom. Further, based on the second-order perturbation theory, its in-plane SOC-MAE of 837.33 μeV/atom is revealed to mainly derive from the couplings of Mn-dxz,dyz and Mn-dx2-y2,dxy orbitals through Lz in the same spin channel. In addition, the biaxial strain and carrier doping can effectively tune the monolayer's magnetic and electronic properties. Such as, under the hole and few electrons doping, the transition from semiconductor to half-metal can be realized, and its Tc can go up to 520 and 620 K under 5% tensile strain and 0.3 hole doping, respectively. Therefore, our research will provide a new, promising 2D FMS for spintronics devices.

Effective modulating the electronic and magnetic properties of VI3 monolayer: A first-principles calculation

Two-dimensional (2D) intrinsic ferromagnetic materials with large magnetic anisotropy (MA) and high Curie temperature (TC) are desirable for low-dimensional spintronic applications. In this work, a highly stable Janus NbXY (X, Y = S, Se and Te, X ≠ Y) monolayers with intrinsic ferromagnetism is investigated by using first-principles calculations. The results demonstrate that the MAE values of the NbSSe, NbSTe and NbSeTe MLs are as high as −2.185 meV, −4.013 meV and −4.495 meV per unit cell, respectively, which is higher than the previously reported 2D intrinsic ferromagnetic materials such as FeBrI, NiI2, and VSSe MLs etc. And they are still large enough for practical applications. The Curie temperature (Tc) is estimated to be 160 K for NbSSe monolayer, 260 K for NbSTe monolayer, and 200 K for NbSeTe monolayer based on Monte Carlo simulation. The MAE and Tc could be effectively controlled and enhanced by the biaxial strains. The MAE of NbSSe, NbSTe and NbSeTe MLs can be increased by 8.7%, 24.9% and 14.1%, and reach up to −2.375, −5.015 and −5.131 meV at 5% compressive strain, respectively. Remarkably, at 5% tensile strain, the room temperature Tc of 300 K can be reached for NbSTe monolayer, which is rather promising for its practical application. The large magnetic anisotropy energy and controllable Curie temperature make the NbXY monolayers a promising candidate for applications in spintronic devices at the nanoscale and in high-density data storage.

Materials with large intrinsic valley splitting and high Curie temperature are a huge advantage for studying valleytronics and practical applications. In this work, using first-principles calculations, a new Janus TaNF monolayer is predicted to exhibit excellent piezoelectric properties and intrinsic valley splitting, resulting from the spontaneous spin polarization, the spatial inversion symmetry breaking and strong spin-orbit coupling (SOC). TaNF is also a potential two-dimensional (2D) magnetic material due to its high Curie temperature and large magnetic anisotropy energy. The effective control of the band gap of TaNF can be achieved by biaxial strain, which can transform TaNF monolayer from semiconductor to semi-metal. The magnitude of valley splitting at the CBM can be effectively tuned by biaxial strain due to the changes of orbital composition at the valleys. The magnetic anisotropy energy (MAE) can be manipulated by changing the energy and occupation (unoccupation) states of d orbital compositions through biaxial strain. In addition, Curie temperature reaches 373 K under only −3% biaxial strain, indicating that Janus TaNF monolayer can be used at high temperatures for spintronic and valleytronic devices.

Coexistence of ferromagnetism, piezoelectricity and valley in two-dimensional (2D) materials is crucial to advance multifunctional electronic technologies. Here, Janus ScXY (X≠Y = Cl, Br and I) monolayers are predicted to be piezoelectric ferromagnetic semiconductors with dynamical, mechanical and thermal stabilities. They all show an in-plane easy axis of magnetization by calculating magnetic anisotropy energy (MAE) including magnetocrystalline anisotropy energy and magnetic shape anisotropy energy. The MAE results show that they intrinsically have no spontaneous valley polarization. The predicted piezoelectric strain coefficients d 11 and d 31 (absolute values) are higher than ones of most 2D materials. Moreover, the d 31 (absolute value) of ScClI reaches up to 1.14 pm V−1, which is highly desirable for ultrathin piezoelectric device application. To obtain spontaneous valley polarization, charge doping are explored to tune the direction of magnetization of ScXY. By appropriate hole doping, their easy magnetization axis can change from in-plane to out-of-plane, resulting in spontaneous valley polarization. Taking ScBrI with 0.20 holes per f.u. as an example, under the action of an in-plane electric field, the hole carriers of K valley turn towards one edge of the sample, which will produce anomalous valley Hall effect, and the hole carriers of Γ valley move in a straight line. These findings could pave the way for designing piezoelectric and valleytronic devices.

The emerging class of two-dimensional piezoelectric ferromagnetic (PFM) systems, combining intrinsic ferromagnetism and piezoelectricity, has attracted significant attention for their potential in multifunctional spintronic devices. In this work, we systematically investigate the electronic structure, magnetic properties, and piezoelectric performance of Janus MoTeX (X = Cl, Br, I) monolayers using first-principles calculations and Monte Carlo simulations. Our results demonstrate that these MoTeX monolayers are stable intrinsic ferromagnetic semiconductors. The Janus-structured MoTeCl, MoTeBr, and MoTeI monolayers exhibit out-of-plane piezoelectric coefficients (d 31) of 1.42, 1.08, and 0.50 pm V−1, respectively, surpassing most reported 2D materials. This enhanced piezoelectricity originates from the broken inversion symmetry along the vertical direction. Notably, MoTeCl, MoTeBr, and MoTeI monolayers display high Curie temperatures (T c ), with values of 190, 219, and 249 K. Furthermore, Janus MoTeX monolayers exhibit excellent mechanical flexibility. The application of biaxial tensile strain engineering significantly improves the PFM performance of MoTeCl monolayers: a 2% strain elevates T c to room temperature and induces a transition of the easy magnetization axis from in-plane to out-of-plane, substantially enhancing their practical applicability. These findings highlight Janus MoTeX monolayers as promising candidates for developing next-generation multifunctional spintronic devices.

High piezoelectric d31 coefficient and high Tc in PMW-PNN-PZT ceramics sintered at low temperature

Two-dimensional (2D) ferromagnetic (FM) semiconductors with high Curie temperature (T c ) and large perpendicular magnetic anisotropy (PMA) are promising for developing next-generation magnetic storage devices. In this work, we investigated the structural, electronic, and magnetic properties of MoF3 and Janus Mo2F3 X 3 (X = Cl, Br, I) monolayers by first-principles methods. These materials are 2D FM semiconductors with large PMA and half-semiconducting character as both VBM and CBM belonging to the spin-up channel. Biaxial strain can modulate band gap, reverse easy magnetization axis, and induce magnetic phase transitions in MoF3 monolayer and its Janus structures. Compared to MoF3 monolayers, Janus Mo2F3 X 3 monolayers can preserve the structural ability and the FM ground state over a wider range of strain. The magnetic anisotropy energies (MAEs) of these 2D materials can be enhanced to greater than 1 meV/Mo by tensile strains. Intrinsic T c of MoF3 monolayer and its Janus structures are less than 110 K and are insensitive to strain. However, hole doping with a feasible concentration can achieve a room-temperature half-metallicity in these 2D materials. The required hole concentration is lower in Janus Mo2F3 X 3 monolayers than MoF3 monolayer. Our results indicate that MoF3 and Janus Mo2F3 X 3 (X = Cl, Br, I) monolayers are promising candidates for 2D spintronic applications and will stimulate experimental and theoretical broad studies.

Recently, predictions have been made about quantum anomalous Hall (QAH) insulators in Lithium-decorated iron-based superconductor monolayer materials (LiFeX (X = S, Se and Te)) with very high Curie temperatures (0.00,0.00,1.00PRL 125, 086401 (2020)), which combine topological and ferromagnetic orders. It is interesting and useful to achieve the coexistence of intrinsic piezoelectricity, ferromagnetism, and nontrivial band topology in single two-dimensional (2D) materials, namely 2D piezoelectric quantum anomalous Hall insulators (PQAHIs). In this work, 2D Janus monolayer Li2Fe2SSe is predicted to be a room-temperature PQAHI, which possesses dynamic, mechanical, and thermal stabilities. It is predicted to be a half Dirac semimetal without spin–orbit coupling (SOC). It is found that the inclusion of SOC opens up a large nontrivial gap, which means nontrivial bulk topology (QAH insulator), confirmed by the calculation of Berry curvature and the presence of two chiral edge states (Chern number C = 2). Calculated results show that the monolayer Li2Fe2SSe possesses robust QAH states against biaxial strain and electronic correlations. Compared to LiFeX, the glide mirror G z of Li2Fe2SSe disappears, which will only induce an out-of-plane piezoelectric response. The calculated out-of-plane d 31 of the monolayer Li2Fe2SSe is −0.238 pm V−1, comparable with those of other known 2D materials. Moreover, a very high Curie temperature (about 1000 K) is predicted by using Monte Carlo simulations, which means that the QAH effect can be achieved at room temperature in the Janus monolayer Li2Fe2SSe. Similar to the monolayer Li2Fe2SSe, the PQAHI can also be realized in the Janus monolayer Li2Fe2SeTe. Our work opens a new avenue in searching for PQAHIs with high temperatures and high Chern numbers, which provide a potential platform for multi-functional spintronic applications.

Two-dimensional (2D) ferromagnetic semiconductors are highly promising candidates for spintronics, but are rarely reported with direct band gaps, high Curie temperatures (Tc), and large magnetic anisotropy. Using first-principles calculations, we predict that two ferromagnetic monolayers, BiXO3 (X = Ru, Os), are such materials with a direct band gap of 2.64 and 1.69 eV, respectively. Monte Carlo simulations reveal that the monolayers show high Tc beyond 400 K. Interestingly, both BiXO3 monolayers exhibit out-of-plane magnetic anisotropy, with magnetic anisotropy energy (MAE) of 1.07 meV per Ru for BiRuO3 and 5.79 meV per Os for BiOsO3. The estimated MAE for the BiOsO3 sheet is one order of magnitude larger than that for the CrI3 monolayer (685 μeV per Cr). Based on the second-order perturbation theory, it is revealed that the large MAE of the monolayers BiRuO3 and BiOsO3 is mainly contributed by the matrix element differences between dxy and dx2-y2 and dyz and dz2 orbitals. Importantly, the ferromagnetism remains robust in 2D BiXO3 under compressive strain, while undergoing a ferromagnetic to antiferromagnetic transition under tensile strain. The intriguing electronic and magnetic properties make BiXO3 monolayers promising candidates for nanoscale electronics and spintronics.

Two-dimensional (2D) ferromagnetic (FM) materials with valley polarization are highly desirable for use in valleytronic devices. The 2D Janus materials have fascinating physical properties due to their asymmetrical structures. In this work, the electronic structure and magnetic properties of Janus RuXY (X, Y = Br, Cl, F, I, X ≠ Y) monolayers are systematically studied using first-principles calculations. RuBrCl, RuBrF, and RuClF monolayers are all FM semiconductors. The valley polarization is present in the band structure and this is determined by the spin orbit coupling (SOC). The valley splitting energy of the RuClF monolayer is as large as 204 meV, with a perpendicular magnetic anisotropy (PMA) energy of 1.918 mJ m-2 and a Curie temperature of 316 K. Therefore, spontaneous valley polarization at room temperature will be seen in the RuClF monolayer. The Curie temperature of the RuBrF monolayer is higher than that of the RuClF, but the magnetic anisotropy energy (MAE) is in-plane magnetic anisotropy (IMA). The valley splitting energy of the RuBrCl monolayer is higher and the PMA energy is lower than that of the RuClF monolayer. The Curie temperature was only 197 K. The valley polarization was modulated in the RuXY monolayers at different biaxial strains, during which the semiconductor properties are still maintained. The PMA of the RuClF and RuBrCl monolayers is enhanced by the biaxial compressive strains, which are mainly attributed to the variation of the (dyz, d2z) orbital matrix elements of the Ru atoms. The MAE of the RuBrF monolayer is tuned from IMA into PMA at a biaxial strain of -6%. These results show an example of a 2D Janus ferrovalley material.

The 2D materials with both ferromagnetism and semiconducting properties are desirable for spintronics applications. Here, inspired by the successful synthesis of single‐layer CoCl, it predicts that Janus single‐layer CoClBr is a 2D intrinsic ferromagnetic semiconductor with a direct bandgap of 3.71 eV by first‐principles calculations. Single‐layer CoClBr exhibits an in‐plane magnetic anisotropic energy (MAE) of 542.25 eV per Co atom and a Curie temperature (T) of 89.49 K. Biaxial strain can effectively modulate its bandgap, MAE, and T, but will not change the ferromagnetic ground state. Compressive strain can increase the Curie temperature and switch the spin moment from in‐plane direction to out‐of‐plane direction. Tensile strain can enlarge the bandgap and introduce a direct‐to‐indirect bandgap transition in CoClBr. The MAE of CoClBr reaches 391.73 eV per Co atom and 1560.49 eV per Co atom at a compressive strain of ‐2% and a tensile strain of 5%, respectively. The tunable electronic and magnetic properties of Janus single‐layer CoClBr has potential application in low‐dimensional spintronics devices.