Two-dimensional transition metal halide PdX2(X =F,Cl,Br,I):A promising candidate of bipolar magnetic semiconductors

Miao-Miao Chen(陈苗苗), Sheng-Shi Li(李胜世), Wei-Xiao Ji(纪维霄), and Chang-Wen Zhang(张昌文)

School of Physics and Technology,Institute of Spintronics,University of Jinan,Jinan 250022,China

Keywords: PdX2 (X =F,Cl,Br,I),bipolar magnetic semiconductors,first-principles calculations

1.Introduction

Recently, the development of high-performance twodimensional (2D) spintronic nanodevices has attracted widespread attention, with the current mainstream trend of miniaturization of electronic information devices.[1-8]The generation of 100% spin-polarized currents and manipulation of carriers’ spin polarization at the Fermi level (EF) are two key challenges for the development of high-performance 2D spintronic nanodevices.Half-metals (HMs),[9]with one metallic spin channel and another semiconducting channel,are highly desired because they provide 100%spin-polarized currents, but they have a fixed spin direction.Conventionally,the directions of spin polarization in materials can be manipulated by a magnetic field,whereas it is hard to be complicated in operation and useful only for certain materials and has an adverse impact on adjacent device parts.[10-18]The proposal of bipolar magnetic semiconductor(BMS)[19]material solves the problems, which allows us to achieve HM with different conductive spin channels by applying a gate voltage.This depends on their unique electronic structure: the valence band(VB)and the conduction band(CB)have opposite spin polarizations near theEF.[20,21]However,the method requires persistent electrical control which is volatile and achieved by applying a gate voltage.[19,20,22]So far,although there are many theoretically predicted BMS materials,[23-27]the experimental realization of BMS[28]is still lacking,as the large leakage current hinders its application in memory storage devices.[29]Recently,Li and Denget al.[30]proposed a new method to manipulate both spin-polarized orientations in BMS materials by the introduction of a ferroelectric(FE)gate with proper band alignment.Compared with traditional electrical control approaches, the method can overcome volatility, which is more energy-efficiency.Thus,it is emergent to search for and design experimentally reachable 2D BMS.

In this work,we first study the geometric,electronic,and magnetic properties of PdX2(X=F,Cl,Br,I)monolayers.It is found that PdCl2,PdBr2,and PdI2monolayers are outstanding candidates for spintronic materials and are possible to construct different spin-polarization transport channels in a single material by carrier doping.Hence, they are highly likely to become a material for spin field effect transistors(FET).Then we explore the robustness of PdCl2, PdBr2, and PdI2under external strains and strong electric fields and find that only the BMS properties of PdCl2and PdBr2are robust against external strains and strong electric fields.Furthermore, we introduce Ga2S3and Ga2Se3with different ferroelectric polarization to realize the nonvolatile spin polarization regulation of PdCl2and PdBr2.Finally, based on this, we design a multiferroic memory device and a spin filter device.Our research provides theoretical support for the experimental implementation of BMS.

2.Computational details

All of our density theory functional (DFT) calculations use the projection-enhanced wave (PAW) method,[31]which is implemented in the Viennaab initiosimulation package (VASP).[32,33]The paper uses Perdew-Burke-Ernzerhof(PBE)functional[34]to describe the correlation and exchange interactions of PdX2.The strong correlation effects for the Pd-4d electrons use the PBE+Umethod[35]and the HubbardUparameter is 3.5 eV.Then we employ the Heyd-Scuseria-Ernzerhof hybrid functional method(HSE06)[36]to obtain the accurate band structures.The cutoff energy is set to 400 eV.The Brillouin zone is sampled by using a 9×9×1k-mesh.To avoid interactions between adjacent layers,a vacuum space of 20 ˚A is applied along thez-axis [001] direction.The convergence criteria for the energy and residual force on each atom are 1×10-8eV and 0.001 eV/˚A.The phonon calculations are carried out by using density-functional perturbation theory as implemented in the PHONOPY code[37]combined with VASP.Theab initiomolecular dynamics(AIMD)[38]simulation is performed with a 4×4×1 supercell at 100 K temperature.The van der Waals(vdW)[39,40]is employed and a vacuum space greater than 30 ˚A or 40 ˚A is applied for the bilayer or three-layer heterostructures.The VASPKIT code is used to process some of the VASP data.[41]The Curie temperature is estimated by using the Monte Carlo simulation package MCSOLVER code[42]based on the Wolff algorithm.

3.Result and discussion

The PdX2(X=F, Cl, Br, I) monolayers share two possible phases,which are similar to classical 2D material PbBr2and PbI2,[43-52]namely,T(Fig.1(a))and H(Fig.1(b))phases.The Pd atomic layer is sandwiched by the upper and lower F/Cl/Br/I atomic layers, with atoms in each layer forming a 2D hexagonal lattice.In order to study more optimal configurations in terms of energy, the energy difference is calculated between the T and H configurations (∆ET-H).The lattice constant (a) and the ∆ET-Hof PdX2monolayers are shown in Table S1.The optimized lattice constants (T/H) of PdF2, PdCl2, PdBr2, and PdI2monolayers are 3.30/3.38 ˚A,3.70/3.54 ˚A,3.87/3.72 ˚A,and 4.11/3.97 ˚A,respectively.With the increase of theXatomic order, the lattice constant is increasing,meeting the positive correlation between lattice constants and atomic radius.All ∆ET-Hof the PdX2monolayers are negative, which indicates that the PdX2monolayers tend to form in the 1T configuration.Our works only consider the PdX2(X=F, Cl, Br, I) monolayers that are formed in the T phases.

Before confirming the magnetic and electronic properties of PdX2,we explore their stabilities(including dynamic stability,thermal stability,and mechanical stability).The formation energyEformis evaluated as

whereµPdis the chemical potential of the Pd bulk andµX2is the energy of theXmolecule.The calculated formation energies are listed in Table S1.The positive values demonstrate that the iodination is an exothermal process,suggesting the feasibility of the experimental synthesis of these materials.The phonon dispersion curves are calculated with a 5×5×1 supercell using the PHONOPY package through the density functional perturbation theory.[53]As indicated in Fig.S1,all the phonon frequencies of PdX2monolayers are positive in the first Brillouin zone,which proves the excellent dynamic stabilities of PdX2monolayers.To examine the thermal stabilities of the PdX2monolayer,the AIMD simulations are evaluated in the canonical ensemble on a 5×5×1 supercell.Four images of Fig.S2 indicate the total energies of PdF2, PdCl2, PdBr2,and PdI2monolayers, respectively.It can be seen that total energies have slightly fluctuated around the equilibrium value during the simulations and there is no destruction for the materials after 10000 fs, indicating the thermal stabilities of the PdF2, PdCl2, PdBr2, and PdI2monolayers under 100 K.Because of thep¯3m1 space group, by using Voigt symbols, the elastic tensor of PdX2can be reduced to[54]

The independentC11,C12, andC11-C12of PdX2are shown in Table S1.It can be found that the PdX2(X= F, Cl,Br, I) monolayers satisfy the Born-Huang criterion for twodimensional hexagonal planes(C11>0 andC11-C12>0),[56]which means that the PdX2monolayers are mechanically stable.

Fig.1.The crystal structures of PdX2 (X =F,Cl,Br,I)monolayers in T(a)and H(b)phases: top and side views.The electron localization functions for PdF2 (c),PdCl2 (d),PdBr2 (e),and PdI2 (f).Pd,F,Cl,Br,and I atoms are annotated accordingly.

To determine the magnetic ground states of the PdX2monolayers,the total energy differences(Table S1),including the ferromagnetic (FM) and three antiferromagnetic (AFM)states (Fig.S3(a)), are compared by using the supercell.Table S1 shows that the calculated total energies of the AFM are higher than that of the FM state for PdF2, PdCl2, PdBr2, and PdI2monolayers, which indicates the magnetic ground states of the PdX2monolayers are FM state.While PbBr2is an inherently nonmagnetic semiconductor,[52]this is due to the different electronic configurations of the Pd and Pb atoms.We track the physical originations of FM coupling in PdX2monolayers by the super-exchange interactions,which can be comprehended by the Pd-X-Pd bond angleθ(Table 1).The values ofθare 97.88◦, 93.49◦, 92.64◦, and 92.56◦for PdF2, PdCl2,PdBr2, and PdI2, respectively, closed to 90◦.According to the Goodenough-Kanamori-Anderson(GKA)rules,[55]PdX2monolayers possess FM coupling.

The electron localization functions(ELF)[56-58]are plotted to investigate the bonding character of PdF2,PdCl2,PdBr2,and PdI2monolayers in Fig.1.The(001)section of the ELF confirms that electrons are highly localized around the Pd and F/Cl/Br/I atoms and that electrons are absent between them,indicating the typical ionic character between the Pd-Xbonds.Our Bader charge analyses[59]further reveal that the significant electrons respectively transfer 1.2, 0.74, 0.53, and 0.20 electrons from the Pd to F/Cl/Br/I atoms(Table 1),which fall with the electronegativity of F,CI,Br,and I reduced.

Table 1.The Pd-X-Pd bond angle θ and charge transfer number(∆e-)per unit cell for PdX2 (X =F,Cl,Br,I)monolayers.

We used the PBE+Umethod for the calculations of the electronic structures (Fig.2).The VBs of the PdF2, PdCl2,PdBr2, and PdI2monolayers possess spin-up polarization when they approachEF, while their CBs possess spin-down polarization when they approachEF.The PdF2monolayer is a direct bandgap semiconductor with a value of 2.14 eV(Fig.2(a)).The PdCl2, PdBr2, and PdI2monolayers are the indirect bandgap semiconductors,and their band gaps are 1.33 eV,0.88 eV,and 0.34 eV,respectively(Figs.2(b)-2(d)).The above results show that the PdF2,PdCl2,PdBr2,and PdI2monolayers are BMS.To confirm the results, the more accurate HSE06 calculations (Figs.S4(a) and S4(b)) further display that although the band gaps increase to 3.56 eV,2.24 eV,1.65 eV, and 1.01 eV for PdF2, PdCl2, PdBr2, and PdI2, respectively, the VBs and the CBs have opposite spin polarizations near theEF,indicating that the BMS remains in the four systems.

Fig.2.The electronic band structures based on the PBE+U functional for PdF2 (a),PdCl2 (b),PdBr2 (c),and PdI2 (d).

After having demonstrated the bipolar magnetic properties, we now turn to the formation mechanism of BMS for PdX2monolayers by crystal field theory.Under the octahedral crystal fields of PdX2(Fig.3(a)),the d orbitals of Pd split into t2g(dxy/dyz/dxz) and eg(dx2-y2/dz2) with a splitting gap(∆c).According to the electronegativity and nominal valence state Pd2+, the t2gorbitals and the egorbitals of the spin-up channel are occupied by six electrons and two electrons, respectively, consistent with the calculated magnetic moment 2µB.Here, the spin splitting exchange interactions lead the electronic states of the magnetic atom in VBMs and CBMs to belong to different spin channels.It can be attested by their density of states(DOS;Fig.S4(b)).The DOS shows that the spin-exchange splitting (∆s) of them are the primary causes of bandgap and the CBM and VBM of PdX2are mainly contributed by Pd atoms.The BMSs in PdX2are derived from the strength of on-site Coulomb repulsion and the crystal field effect,which are coincident with the report.[60]The d electronic states of the PdX2monolayer near the Fermi surface, which usually leads to ferromagnetism, verifying the FM ground state.

The influence of temperature on magnetism is crucial for the practical application of spin electronic devices.Based on the following formulas,the spin Hamiltonian can be described as

whereJ,Si,D, andSZiare the nearest magnetic exchange interaction parameter, the spin vector of each atom, the anisotropy energy parameter,and theZcomponent of the spin vector,respectively.The positive and negative values ofJdepend on the FM and AFM orders,respectively,

Fig.3.(a)The schematic diagram of the d-orbital electron occupation of Pd atoms.(b)-(e) The density of states (DOS) for PdF2, PdCl2, PdBr2 and PdI2.The gray,orange,and green solid lines represent the total DOS rotated up or down, the DOS contributed by Pd-4d, and the DOS contributed by X-p orbitals,respectively.

where theEFMandEAFMrepresent the total energy of systems with FM and AFM ordering.The values ofJcan be estimated as

The computedJfor 2D PdX2(X=F,Cl,Br,I)are 0.67 meV,8.67 meV, 10.30 meV, and 13.10 meV, respectively.Then their magnetic anisotropy energies(MAE)are calculated.The MAE is defined as the energy difference MAE=E001-E100between the out-of-plane (001) and the in-plane (100) magnetization directions by incorporating the SOC effect.The MAE are 61 µeV, 77 µeV, 60 µeV,-982 µeV for the PdF2,PdCl2,PdBr2,and PdI2monolayers,respectively.It indicates that there are the Berezinskii-Kosterlitz-Thouless (BKT)[61]magnetic transition at a critical temperature (TC) for PdF2,PdCl2, and PdBr2monolayers, which can be estimated asTC=0.89J/kB.HerekBis the Boltzmann constant.We get that theTCfor PdF2,PdCl2,and PdBr2monolayers are around 7 K, 90 K, and 106 K with theirJ, above the boiling point of liquid nitrogen (77 K) for PdCl2and PdBr2monolayers.Figure S4(b)shows that the PdI2monolayer has an estimated Curie temperature of 503 K, notably far above room temperature (300 K).Overall, except for PdF2, all others are apparently outstanding candidates for spintronic materials.The PdCl2,PdBr2,and PdI2monolayers will be studied in the following.

Having evaluated the magnetic properties of PdCl2,PdBr2, and PdI2monolayers, we further turn to whether spin polarization can be controlled through electron/hole doping since introducing an FE gate to control the spin polarization of BMS is equivalent to carrier doping,as shown in Fig.S5.We take Fig.S5(a)for example,when 0.1-0.5 electrons are doped,the CBs of PdCl2are crossed by the Fermi energy level, and the material becomes an HM with the spin-up channel.Doping 0.1-0.5 holes will drive theEFto transverse with VBs,and become the HM of the spin-down channel.The introduction of a FE gate is expected to realize the control of spin polarization.

In device fabrication, it is likely to introduce strain due to the lattice mismatch between the 2D material and the substrate,and there may be the electric interference from the environment or neighboring electric device.Therefore,we rationalize the robustness of PdCl2, PdBr2, and PdI2monolayers under the electric fields and strains.Firstly,the biaxial strains are applied to PdCl2, PdBr2, and PdI2monolayers (Fig.S6).Strains are defined asε=(a1-a0)/a0, wherea1anda0are lattice constants of PdX2with and without deformation, respectively.The negatively and positively valuedεrepresent compression and tension, respectively.The BMS characteristics are well preserved at-10%<ε<10% for PdCl2and PdBr2(Figs.S7(a) and S7(b)).With 2%-10% compressive strain, the semiconductor PdI2firstly changes to HM, then metallic,but that remains unchanged with tensile strain.Secondly, we investigate the robustness of the BMS property to electrical interference from the environment or a neighboring electrical device.Figures S7(a)-S7(c)displays the band structures of PdCl2,PdBr2,and PdI2under the electric field of 0.1-0.5 V/˚A, respectively.Clearly, under the strong electric field of 0.5 V/˚A, the Fermi energy levels of PdCl2and PdBr2are vibrated between the VBM and the CBM.The semiconductor changes to metal for PdI2under the electric fields(Fig.S7(c)).Moreover,the calculation of the value of ∆EFM-AFM(Fig.S8)is performed to check the magnetic ground states of PdCl2,PdBr2,and PdI2monolayers,and we find that the energetically favorable magnetic configurations are still the FM coupling in the cases of the electric fields and strains.In short,only PdCl2and PdBr2monolayers exhibit robustness under the electric fields and strains and are likely to become the experimentally achievable devices.Therefore, we have only conducted research on nonvolatile electric control of spin polarization for PdCl2and PdBr2structures below.

We screen Ga2S3and Ga2Se3from the family of 2D FE III2-VI3 materials[62]by comparing the lattice mismatch.The optimized lattice constant of the Ga2S3and Ga2Se3with vdW corrections are 3.70 ˚A and 3.88 ˚A,respectively.Subsequently, we construct two multiferroic vdW heterostructures(PdCl2/Ga2S3and PdBr2/Ga2Se3),whose lattice mismatch are 0.02%and 0.36%.Three possible stacking patterns are investigated as shown in Fig.4,denoted as configurations I-III.Our calculations show that configuration-III(Figs.4(c)and 4(f))is energetically the most favorable configuration for both upward polarization(P↑)and downward polarization(P↓), this stacking pattern will be researched in the following sections.The binding energy of multiferroic vdW heterostructure is defined as

whereEBMS/FE,EBMSandEFErepresent the energies of the BMS/FE heterostructure, BMS layer and the FE layer,respectively.The cohesive energies of PdCl2/Ga2S3(P↑),PdCl2/Ga2S3(P↓),PdBr2/Ga2Se3(P↑),and PdBr2/Ga2Se3(P↓)are about-1.89 eV,-1.25 eV,-2.14 eV, and-1.41 eV, respectively, indicating that the heterostructure can be feasible to explore experimentally and stably exist.

Fig.4.Three possible stacking modes with upward polarization (a)-(c)and downward polarization (d)-(f) for PdCl2/Ga2S3 and PdBr2/Ga2Se3 heterostructures.

Then we discuss the density of states (DOS) of the PdCl2/Ga2S3and PdBr2/Ga2Se3heterostructures.Here red and blue symbols denote the contributions from spin-up and spin-down electronic states of PdCl2, PdBr2, Ga2S3, and Ga2Se3, respectively.Figures 5(a) and 5(c) display that theEFcrosses the minority spin-down bands of the PdCl2and PdBr2for PdCl2/Ga2S3(P↑) and PdBr2/Ga2Se3(P↑), respectively, leading to a half-metal behavior in PdCl2and PdBr2.Figures 5(b) and 5(d) show that the semiconductor natures of PdCl2and PdBr2are retained for PdCl2/Ga2S3(P↓) and PdBr2/Ga2Se3(P↓),respectively.

Fig.5.DOS of PdCl2/Ga2S3 and PdBr2/Ga2Se3 for P↑and P↓.The solid red and blue lines represent the DOS contributed by BMS and FE,respectively.

Next, the plane-average potential and the charge density difference of different heterointerfaces are calculated for understanding the mechanism of the electrically controlled semiconductor/half-metal transition.For the P↑,the potential energies of the BMS layer PdCl2and PdBr2are lower than that of the FE layer Ga2S3and Ga2Se3,respectively(Figs.6(a)and 6(c)), which can generate that the spin-down CBM of PdCl2and PdBr2is lower than the VBM of Ga2S3and Ga2Se3, respectively,meaning that there are electrons transfer at the heterostructure interface.

The charge density difference suggests that electron transfer occurs only at the interface between Ga2Se3(P↑)and PdBr2(Fig.S9(c)), while there are almost no electrons accumulating around the interface between Ga2S3(P↑) and PdCl2(Fig.S9(a)).This is consistent with the DOS(Fig.5(a))showing that theEFcrosses minority spin-down bands of PdCl2.On the contrary,although the potential energies of the BMS layer PdCl2and PdBr2are lower(Figs.6(b)and 6(d)),the CBMs of Ga2S3and Ga2Se3are still slightly higher than the spin-down VBM of PdCl2and PdBr2, respectively.This can hinder the spontaneous diffusion of holes for the P↓.The charge density difference suggests that a small number of holes is still insufficient to make theEFof PdCl2and PdBr2cross the spinup bands (Figs.S9(b) and S9(d)).Hence, the realizations of the half-metallicity are dependent upon the polarization fields of the FE layer Ga2S3and Ga2Se3and the charge transfer at the interface between the FE and BMS layers for PdCl2and PdBr2.

Fig.6.Plane-averaged potential of PdCl2/Ga2S3 and PdBr2/Ga2Se3 bilayer heterostructures along the z-direction for P↑and P↓.

In a word, the generated electric polarizations for Ga2S3(P↓) and Ga2Se3(P↓) can drive the downward shift of theEFof PdCl2and PdBr2, which offers an opportunity to achieve nonvolatile electrical control of spin polarization in PdCl2and PdBr2by enhancing polarization field.[63,64]Then we add the Ga2S3and Ga2Se3to the bottom of PdCl2/Ga2S3and PdBr2/Ga2Se3(Figs.7(a)and 7(b)),respectively.The vdW heterostructures are named PdCl2/bi-Ga2S3and PdBr2/bi-Ga2Se3, respectively.Two different polar configurations are taken into account for bi-Ga2S3and bi-Ga2Se3,i.e.,the polarization directions of FE layers were both pointing upward(P↑↑)or downward(P↓↓).

Fig.7.The vdW heterostructures of PdCl2/bi-Ga2S3 and PdBr2/bi-Ga2Se3 for P↑↑and P↓↓.

The binding energies of PdCl2/bi-Ga2S3(P↑↑),PdCl2/bi-Ga2S3(P↓↓), PdBr2/bi-Ga2Se3(P↑↑), and PdBr2/bi-Ga2Se3(P↓↓) are-2.71 eV,-2.64 eV,-2.97 eV, and-2.88 eV, respectively, testifying that they are stable.As expected, the DOS of PdCl2/bi-Ga2S3and PdBr2/bi-Ga2Se3trilayer heterostructures(Fig.8)show that the BMS PdCl2and PdBr2become the spin-up (spin-down) HM for P↑↑(P↓↓),manifested that the nonvolatile spin polarization regulation of PdCl2and PdBr2can be achieved by introducing the bilayer FE gates.

After the above discussion,we find that the PdCl2/Ga2S3and PdBr2/Ga2Se3heterostructures possess the capacity to control the HM,and the PdCl2/bi-Ga2S3and PdBr2/bi-Ga2Se3possess the capacity of controlling the spin polarization of BMS.

Fig.8.DOS of PdCl2/bi-Ga2S3 or PdBr2/bi-Ga2Se3 for P↑and P↓.The solid red and blue lines represent the DOS contributed by BMS and FE,respectively.

Therefore,the multiferroic memory device(Figs.9(a)and 9(b)) are designed for the bilayer heterostructures.The P↑is equivalent to the“1”state(Fig.9(a)),while the P↓is equivalent to the“0”state(Fig.9(b)).In this context,the data reading process is accessible by detecting the electrical signals,and the data reading process is accessible by switching the FE polarized states, thus avoiding the destructive effect caused by detecting the polarized state.Then the spin filter device(Figs.9(c)and 9(d))is constructed for the trilayer heterostructures.The electron would travel through the BMS layer, becoming the HM with 100%spin-down polarization at the P↑↑,which is n-type doped.Conversely, the spin-up electrons can pass through the BMS layer at the P↓↓.In short,the manipulation of spin-polarized current can be achieved in this device.

4.Conclusion

In summary, we predict that the PdX2(X= F, Cl, Br,I) monolayers are 2D FM BMS with dynamic stability, thermal stability, and mechanical stability by first-principles calculations.The critical temperatures of both PdCl2and PdBr2monolayers are higher than the boiling point of liquid nitrogen (77 K).Moreover, the BMS characteristics of PdCl2and PdBr2are robust against external strains and strong electric fields, which is conducive to their applications.The carrier doping can induce the change between the semiconductor and half metal.Furthermore, we manipulate the spin polarization of PdCl2and PdBr2by introducing the FE gate to enable magnetic half-metal/semiconductor switching and spin-up/down polarization switching control.Finally, based on this, we realize two kinds of spin devices(multiferroic memory and spin filter).As well as proposing two novel BMS materials: PdCl2and PdBr2, this study provides a theoretical basis for the development of spin devices.

Acknowledgments

Project supported by the Taishan Scholar Program of Shandong Province, China (Grant No.ts20190939), the Independent Cultivation Program of Innovation Team of Jinan City (Grant No.2021GXRC043), the National Natural Science Foundation of China (Grant No.52173283), and the Natural Science Foundation of Shandong Province (Grant No.ZR2020QA052).