How to produce spin-splitting in antiferromagnetic materials.

Antiferromagnetic (AFM) materials have potential advantages for spintronics due to their robustness, ultrafast dynamics, and magnetotransport effects. However, the missing spontaneous polarization and magnetization hinders the efficient utilization of electronic spin in these AFM materials. Here, we propose a simple way to produce spin-splitting in AFM materials by making the magnetic atoms with opposite spin polarization locating in the different environment (surrounding atomic arrangement), which does not necessarily require the presence of spin-orbital coupling. We confirm our proposal by four different types of two-dimensional AFM materials within the first-principles calculations. Our works provide an intuitional design principle to find or produce spin-splitting in AFM materials.

Piezoelectric ferromagnetism in Janus monolayer YBrI: a first-principles prediction.

Coexistence of intrinsic ferromagnetism and piezoelectricity, namely piezoelectric ferromagnetism (PFM), is crucial to advance multifunctional spintronic technologies. In this work, we demonstrate that Janus monolayer YBrI is a PFM, which is dynamically, mechanically and thermally stable. The electronic correlation effects on the physical properties of YBrI are investigated by using generalized gradient approximation plus U (GGA+U) approach. For out-of-plane magnetic anisotropy, YBrI is a ferrovalley (FV) material, and its valley splitting is larger than 82 meV within the considered U range. The anomalous valley Hall effect (AVHE) can be achieved under an in-plane electric field. However, for in-plane magnetic anisotropy, YBrI is a common ferromagnetic (FM) semiconductor. When considering intrinsic magnetic anisotropy, the easy axis of YBrI is always in-plane, and its magnetic anisotropy energy (MAE) varies from 0.309 meV to 0.237 meV (U = 0.0 eV to 3.0 eV). However, the magnetization can be adjusted from the in-plane to out-of-plane direction by an external magnetic field, and then lead to the occurrence of valley polarization. Moreover, the missing centrosymmetry along with broken mirror symmetry results in both in-plane and out-of-plane piezoelectricity in the YBrI monolayer. At a typical U = 2.0 eV, the piezoelectric strain coefficient d11 is predicted to be -5.61 pm V-1, which is higher than or comparable with the ones of other known two-dimensional (2D) materials. The electronic and piezoelectric properties of YBrI can be effectively tuned by applying biaxial strain. For example, tensile strain can enhance valley splitting and d11 (absolute value). The predicted magnetic transition temperature of YBrI is higher than those of experimentally synthesized 2D FM materials CrI3 and Cr2Ge2Te6. Our findings of these distinctive properties could pave the way for designing multifunctional spintronic devices, and bring forward a new perspective for constructing 2D materials.

Importance of magnetic shape anisotropy in determining magnetic and electronic properties of monolayer VSi2P4.

Two-dimensional (2D) ferromagnets have been a fascinating subject of research, and magnetic anisotropy (MA) is indispensable for stabilizing the 2D magnetic order. Here, we investigate magnetic anisotropy energy (MAE), magnetic and electronic properties ofVSi2P4by using the generalized gradient approximation plusUapproach. For largeU, the magnetic shape anisotropy (MSA) energy has a more pronounced contribution to the MAE, which can overcome the magnetocrystalline anisotropy (MCA) energy to evince an easy-plane. For fixed out-of-plane MA, monolayerVSi2P4undergoes ferrovalley (FV), half-valley-metal (HVM), valley-polarized quantum anomalous Hall insulator (VQAHI), HVM and FV states with increasingU. However, for assumptive in-plane MA, there is no special quantum anomalous Hall (QAH) state and spontaneous valley polarization within consideredUrange. According to the MAE and electronic structure with fixed out-of-plane or in-plane MA, the intrinsic phase diagram shows common magnetic semiconductor, FV and VQAHI in monolayerVSi2P4. At representativeU = 3 eV widely used in references,VSi2P4can be regarded as a 2D-XYmagnet, not Ising-like 2D long-range order magnets predicted in previous works with only considering MCA energy. Our findings shed light on importance of MSA in determining magnetic and electronic properties of monolayerVSi2P4.

A piezoelectric quantum spin Hall insulator VCClBr monolayer with a pure out-of-plane piezoelectric response.

The combination of piezoelectricity with a nontrivial topological insulating phase in two-dimensional (2D) systems, namely piezoelectric quantum spin Hall insulators (PQSHI), is intriguing for exploring novel topological states toward the development of high-speed and dissipationless electronic devices. In this work, we predict a PQSHI Janus monolayer VCClBr constructed from VCCl2, which is dynamically, mechanically and thermally stable. In the absence of spin orbital coupling (SOC), VCClBr is a narrow gap semiconductor with a gap value of 57 meV, which is different from Dirac semimetal VCCl2. The gap of VCClBr is due to a built-in electric field caused by asymmetrical upper and lower atomic layers, which is further confirmed by the external-electric-field induced gap in VCCl2. When including SOC, the gap of VCClBr is increased to 76 meV, which is larger than the thermal energy of room temperature (25 meV). The VCClBr is a 2D topological insulator (TI), which is confirmed by Z2 topological invariant and nontrivial one-dimensional edge states. It is proved that the nontrivial topological properties of VCClBr are robust against strain (biaxial and uniaxial cases) and external electric fields. Due to broken horizontal mirror symmetry, only an out-of-plane piezoelectric response can be observed, when a biaxial or uniaxial in-plane strain is applied. The predicted piezoelectric strain coefficients d31 and d32 are -0.425 pm V-1 and -0.219 pm V-1, respectively, and they are higher than or compared with those of many 2D materials. Finally, Janus monolayer VCFBr and VCFCl (dynamically unstable) are also constructed, and they are still PQSHIs. Moreover, the d31 and d32 of VCFBr and VCFCl are higher than those of VCClBr, and the d31 (absolute value) of VCFBr is larger than one. According to out-of-plane piezoelectric coefficients of VCXY (X ≠ Y = F, Cl and Br), CrX1.5Y1.5 (X = F, Cl and Br; Y = I) and NiXY (X ≠ Y = Cl, Br and I), it is concluded that the size of the out-of-plane piezoelectric coefficient has a positive relation with the electronegativity difference of X and Y atoms. Our studies enrich the diversity of Janus 2D materials, and open a new avenue in the search for PQSHI with a large out-of-plane piezoelectric response, which provides a potential platform in nanoelectronics.