pubs.acs.org/JPCL Letter Origin of Rashba Spin Splitting and Strain Tunability in Ferroelectric Bulk CsPbF3 Preeti Bhumla,* Deepika Gill, Sajjan Sheoran, and Saswata Bhattacharya* Cite This: J. Phys. Chem. Lett. 2021, 12, 9539−9546 Read Online ACCESS Metrics & More Article Recommendations *sı Supporting Information ABSTRACT: Spin−orbit coupling (SOC) in conjunction with broken inversion symmetry acts as a key ingredient for several intriguing quantum phenomena, viz., Rashba−Dresselhaus (RD) effect. The coexistence of spontaneous polarization and the RD effect in ferroelectric (FE) materials enables the electrical control of spin degrees of freedom. Here, we explore the fi FE lead halide perovskite CsPbF3 as a potential candidate in the eld of spintronics by employing state-of-the-art first-principles-based methodologies, viz., density functional theory (DFT) with semilocal and hybrid functional (HSE06) combined with SOC and many-body perturbation theory (G0W0). For a deeper understanding of the observed spin splitting, the spin textures are analyzed using the k.p model Hamiltonian. We find there is no out-of-plane spin component indicating that the Rashba splitting dominates over Dresselhaus splitting. We also observe that the strength of Rashba spin splitting can be substantially tuned on application of uniaxial strain (±5%). More interestingly, we notice reversible spin textures by switching the FE polarization in CsPbF3 perovskite, making it potent for perovskite-based spintronic applications. ead halide perovskites have evolved as an excellent choice studied as promising functional materials for spin-based − in optoelectronics owing to their exotic properties, viz., applications.29 33 Recently, a significant Rashba effect has L ffi suitable optical band gap, high absorption coe cient, low trap been reported in the tetragonal phase of MAPbI3 (MA = 1−9 + 34,35 ff density, and reasonable manufacturing cost. These alluring CH3NH3 ) due to the rotations of the MA ion. The e ect materials exhibit great applications as absorbers for high power has also been predicted in CsPbBr and MAPbBr perov- − 3 3 conversion efficiency solar cells.10 12 In the past few decades, skites.36,37 Lately, there are several reports on a ferroelectric- ff ff β β consistent research e orts have led to the revolutionary growth coupled Rashba e ect in halide perovskites (viz. -MAPbI3, - ffi 13,14 + of power conversion e ciency to over 25%. Additionally, MASnI3,ortho-MASnBr3,FASnI3 (FA = HC(NH2)2 )), the large spin−orbit coupling (SOC) tied to the presence of opening new possibilities for perovskite-based spin devices.29,38 the heavy element Pb plays a decisive role in determining the However, because of the volatile nature of organic molecules, electronic properties of lead halide perovskites.15,16 Over the these perovskites suffer from poor stability toward heat and years, the influence of SOC is well documented on the band moisture.39 Downloaded via INDIAN INST OF TECH DELHI- IIT on October 1, 2021 at 18:24:37 (UTC). structures of these perovskites.16 Intriguingly, SOC in Therefore, in our present work, we intend to explore See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles. conjunction with broken inversion symmetry acts as a key inorganic FE perovskites in terms of RD splitting. Note that ingredient for several exotic phenomena such as persistent spin the interplay between ferroelectricity and the Rashba effect textures,17,18 topological surface states,19 and Rashba− ff − gives rise to electric control of the bulk Rashba e ect, leading Dresselhaus (RD) effects.20 24 to an exciting class of ferroelectric Rashba semiconductors − In the absence of the inversion symmetry, the crystal feels an (FERSCs).40 42 This effect can be theoretically quantified by effective magnetic field due to SOC. This field coupled with employing the k.p perturbation theory. According to this spin moment leads to the momentum-dependent splitting of theory, the lowest-order RD Hamiltonian is given by43,44 bands, known as Rashba−Dresselhaus (RD) splitting. 25 26 ff Dresselhaus and Rashba e ects were originally reported HRD()()()k =−+−ασ Rxykk σ yx ασ D xx kk σ yy (1) in zinc-blende and wurtzite structures, respectively. The primary difference between both these effects resides in the origin of the non-centrosymmetry. In the Rashba effect, there Received: August 8, 2021 is site inversion asymmetry, whereas in the Dresselhaus effect, Accepted: September 23, 2021 bulk inversion asymmetry is present. During the past decade, the RD effect has been the subject of intense research due to its potential applications in the emergent field of spin- tronics.27,28 In view of this, lead halide perovskites have been © XXXX American Chemical Society https://doi.org/10.1021/acs.jpclett.1c02596 9539 J. Phys. Chem. Lett. 2021, 12, 9539−9546 The Journal of Physical Chemistry Letters pubs.acs.org/JPCL Letter Figure 1. (a) Optimized crystal structure of CsPbF3 in the rhombohedral R3c phase. Cs, Pb, and F atoms are indicated by red, gray, and yellow colors, respectively. (b) The first hexagonal Brillouin zone showing the high symmetry path for band structure calculations in the R3c phase of CsPbF3. Electronic band structure of CsPbF3 for the R3c phase, calculated using (c) PBE and (d) PBE+SOC. The conduction and valence bands considered in the discussion are indicated by an orange color. (e) Schematic representation of bands showing Rashba splitting. (f) Splitting of conduction band minimum (CBm) and valence band maximum (VBM) of the chosen bands along the M-Γ-K path. The inset shows the enlarged view of CBm. (g) Projected density of states (pDOS) in the R3c phase of CsPbF3 calculated using HSE06+SOC. The Fermi energy is set to zero in the energy axis. σ σ Here, x and y are Pauli spin matrices, ki is the crystal using the climbing image nudged elastic band (CINEB) α α momentum (i = x, y, z), and R and D represent the Rashba method. ̅ and Dresselhaus coefficients, respectively. On solving the free- CsPbF3 mainly manifests in the cubic (Pm3m)and electron Hamiltonian with these terms, we get two spin-split rhombohedral (R3c) phases.52,53 The Pm3̅m phase is polarized states having opposite spin polarization. Though centrosymmetric, i.e., contains an inversion center. On the Rashba and Dresselhaus exhibit a similar type of splitting, other hand, the rhombohedral R3c phase (see Figure 1a) is projection of spin in momentum space, i.e., spin texture, gives non-centrosymmetric and exhibits FE behavior due to the 53 the idea of the nature of the splitting. Striving toward sizable distortion of cations away from anionic polyhedra. The calculated change in FE polarization of the rhombohedral Rashba-type splitting, CsPbF3 perovskite may be a desirable candidate. To the best of our knowledge, the available (R3c) phase relative to the centrosymmetric structure is 34 μ 2 literature does not encompass a detailed quantitative study C/cm along the [0001] direction in a hexagonal setting of the RD effect in this material. The presence of Pb and (along the [111] direction in a rhombohedral setting). The ferroelectricity in the non-centrosymmetric phase of CsPbF details of optimized crystal structures are provided in section I 3 of Supporting Information. Next, we have investigated the indicates the possibility of the RD effect in this material. electronic band structures of the Pm3̅m and R3c phases. The Motivated by this idea, we have undertaken a theoretical band structure of the Pm3̅m phase in the presence of SOC study based on the perturbative k.p formalism and backed by reveals that there is no momentum-dependent splitting owing first-principles calculations. In the present work, we have ̅ to its centrosymmetric structure (band structure and pDOS of studied the Pm3m and R3c phases of CsPbF3. First, we have the Pm3̅m phase are given in section II of Supporting examined the electronic band structures in the above- Information). In addition, the cubic Pm3̅m phase is not mentioned phases. After that, we have estimated the band dynamically stable (see section III for phonon band gap of these phases using first-principles-based approaches 45,46 structures). Therefore, we have explored RD splitting in the combined with SOC, viz., density functional theory (DFT) latter phase (i.e., R3c). We have plotted the band structure of ϵ 47 with semilocal exchange-correlation ( xc) functional (PBE ), 48,49 50,51 the FE R3c phase along the high symmetry path using a hybrid DFT with HSE06, and single-shot GW (G0W0) hexagonal setting (as shown in Figure 1b). First, we have under the many-body perturbation theory (MBPT). Sub- performed non-spin-polarized calculations. After that, we have sequently, we have analyzed the electronic band structure of considered SOC in the calculation of the electronic band the R3c phase in terms of Rashba splitting under the combined structure. Figure 1c,d shows the electronic band structures framework of DFT and perturbative k.p formalism. We have calculated using PBE and PBE+SOC, respectively. A direct also investigated the effect of strain on the electronic band gap band gap of 3.26 eV is observed without SOC, whereas upon and Rashba parameters of the R3c phase. Finally, we have including SOC, the band gap is reduced to 2.42 eV (indirect) determined the minimum energy pathway of the FE transition around the Γ point. This change in the band gap is attributed 9540 https://doi.org/10.1021/acs.jpclett.1c02596 J. Phys. Chem. Lett. 2021, 12, 9539−9546 The Journal of Physical Chemistry Letters pubs.acs.org/JPCL Letter to SOC arising from the presence of Pb-6p orbitals in the consequence, the CBm and VBM are located slightly off the Γ conduction band (see pDOS in Figure 1g).