This is the accepted version of the journal article: Sattar, Shahid; Larsson, J. Andreas; Canali, C.M.; [et al.]. «Giant valley- polarized spin splittings in magnetized Janus Pt dichalcogenides». Physical review B, Vol. 105, issue 4 (Jan. 2022), art. A100. DOI 10.1103/PhysRevB.105.L041402 This version is available at https://ddd.uab.cat/record/269765 under the terms of the license Giant Valley-Polarized Spin Splittings in Magnetized Janus Pt Dichalcogenides Shahid Sattar,1, ∗ J. Andreas Larsson,2 C. M. Canali,1 Stephan Roche,3, 4 and Jose H. Garcia3, † 1 Department of Physics and Electrical Engineering, Linnaeus University, Kalmar SE-39231, Sweden 2 Applied Physics, Department of Engineering Sciences and Mathematics, Luleå University of Technology, Luleå SE-97187, Sweden 3 Catalan Institute of Nanoscience and Nanotechnology (ICN2), CSIC and BIST, Campus UAB, Bellaterra, 08193 Barcelona, Spain 4 ICREA, 08101 Barcelona, Spain (Dated: December 20, 2021) We reveal giant proximity-induced magnetism and valley-polarization effects in Janus Pt dichalco- genides (such as SPtSe), when bound to the Europium oxide (EuO) substrate. Using first-principles simulations, it is surprisingly found that the charge redistribution, resulting from proximity with ′ EuO, leads to the formation of two K and K valleys in the conduction bands. Each of these valleys displays its own spin polarization and a specific spin-texture dictated by broken inversion and time- reversal symmetries, and valley-exchange and Rashba splittings as large as hundreds of meV. This provides a platform for exploring novel spin-valley physics in low-dimensional semiconductors, with potential spin transport mechanisms such as spin-orbit torques much more resilient to disorder and temperature effects. One of the key aspects of van der Waals (vdW) het- one of the dichalcogenides of the TMD is replaced by erostructures is the proximity effect, where interlayer a different one) [35] are interesting low-symmetry mate- hybridization combines with the electronic properties rials since they possess an intrinsically broken inversion of their individual constituents to produce synergistic symmetry that yields to significant Rashba splittings and behaviors [1–4]. A salient illustration of such emerg- spin-momentum locking, and then offering SOT mecha- ing properties occurs in graphene-based heterostructures, nisms [35, 38]. These two features are essential elements since graphene has exceptional transport properties due for realizing spin-orbit torques (SOTs) [39, 40], a phe- to its linear dispersion at two nonequivalent valleys in nomenon where the magnetization direction of a mag- the Brillouin zone, but lacks spin functionality owing to netic system is electrically-controlled via the SOC, and its very small intrinsic spin-orbit coupling (SOC). How- that is very promising for efficient nonvolatile memories ever, it displays gate-tunable spin-dependent phenomena with nanosecond dynamics [41, 42]. at room temperature [5–8] and spin-valley coupling [9– Ultrathin Pt dichalcogenides (PtX2 (X=S, Se, Te)) 11] when combined with high SOC materials. Graphene constitute a particularly interesting class of materials also displays proximity-induced magnetism which is evi- with a very strong and highly tunable SOC that bestow it denced by a plethora of interesting gate-dependent mag- with exotic electronic and spin properties [43–47]. Their netoresistive phenomena [12–18]. The incorporation of most stable geometrical phase is the 1T-phase (P3̄m1) recently discovered materials with exotic individual prop- which displays a semiconducting behavior [43]. Mono- erties into vdW heterostructures is a unique way to dis- layer (1L) SPtSe was recently synthesized in a Janus cover and engineer disruptive material functionalities, form [48], enabling strong spin-momentum locking due and to efficiently realize complex effects, such as, val- to their low-symmetry nature [45]. To fruitfully exploit ley polarization, SOC-exchange swapping [19–22], and such spin-momentum locking for SOT applications, it is symmetry-enhanced spin-orbit torques (SOT) [23–26], imperative to determine the spin physics of the Janus- where the combination of magnetism, SOC and valley TMD coupled to a magnetic material. Such a coupling control are required. should be sufficiently strong to allow for the magnetiza- The recent synthesis of low-symmetry materials such tion control via the electronic spins propagating inside as Fe3 GeTe2 [27], 1T’-WTe2 [28] and Janus SMoSe [29], the TMD, but weak enough to at least partially preserve has shown new ways to control the spin degree of freedom the spin-momentum locking [40]. In Pt-based TMDs, by removing symmetry constraints and led to the obser- some studies suggest the formation of magnetism [49, 50], vation of unusual phenomenon such as canted quantum but to date the consequences of proximity effects between spin Hall effect [30], persistent spin-textures [31], multi- platinum-based TMDs and magnetic substrates have not directional spin Hall effect [32–34], and interface-free yet been explored. Rashba effect [35]. However, these systems are typically In this letter, we predict that low-symmetry Janus metastable [36, 37], a challenge that can be overcome by SPtSe on EuO is a suitable material combination encapsulation or via the substrates, and that also open a that generates large exchange coupling and valley- door for novel collective effects. Transition metal dichal- polarization, while preserving spin-momentum locking. clogenides (TMDs) in their Janus configuration (where Specifically, the EuO substrate induces the formation of 2 two time-reversal related valleys with C3v symmetry at (a) low symmetry points along the Γ-K/Γ-K ′ paths. These valleys display a large spin-splitting of several hundreds (c) (d) (e) meV, which are traced back to the joint contributions of Zeeman-like and Rashba interactions. We also dis- S cuss how the combination of these effects could lead to Se a giant spin-orbit torque and a current-driven magnetic Pt anisotropy, originating from the valley’s special point (b) K’ group symmetry. Since these materials possess a modest M lattice mismatch amenable to epitaxial growth and a low growth temperature similar to other recently synthesize . Γ K Eu O systems [51, 52], we propose them as a potential 2D sys- H tem with all ingredients required for efficient spin-orbit torques. FIG. 1: (a) Top and side views of 1L PtSe2 (black To start with, we aim at clarifying if the strong SOC rectangle shows unit cell). (b) Hexagonal Brillouin zone and broken inversion symmetry in SPtSe can lead to with high-symmetry points. Minimum energy a large spin-splitting and spin-momentum locking. Be- configurations of (c) PtS2 , (d) Janus SPtSe, and (e) 2L sides, one key question is whether a magnetic insulat- PtSe2 on EuO substrate. ing substrate such as EuO can induce a strong exchange coupling in SPtSe which will be essential for SOT appli- cations. To answer those questions, we performed fully- presents a very small amount of strain of 0.3%, while relativistic first-principles calculations using the Vienna all the other symmetric structures have strains of about Ab-initio Simulation Package (VASP) [53] to determine 3% [54]. After the relaxation procedure, we determined the geometrical, electronic, and spin properties of the that Pt-atoms prefer to sit on top of the Eu-atoms, re- Pt-dichalcogenides in the proximity to the magnetic sub- sembling the MoTe2 /EuO structure [19]. We found that strate EuO. Technical details of the simulations are pre- EuO has a ferromagnetic ground state, and a lattice con- sented in the Supplementary Information [54]. We found stant of 3.65 Å on its (111) hexagonal face. To identify that all freestanding TMDs are stable in the configura- the proximity-induce exchange interaction, we have per- tion shown in Fig. 1.a. Both PtSe2 and PtS2 have similar formed calculations in the absence of SOC and found electronic structures displaying a semiconducting behav- the typical exchange interactions to be very large, ∼ 400 ior with an indirect band-gap and no band-splitting [54]. meV [54]. We also observed the unexpected formation of The lack of spin-splitting, despite the presence of large valleys in the vicinity of high-symmetry K and K’ point SOC, is the result of time-reversal-symmetry Kramer’s of the BZ. To our knowledge, this is the first example degeneracy combined with inversion symmetry (one of of proximity-induced valley formation in 2D materials. the symmetries of the lattice 3̄m point group), which Since Eu and Pt are very heavy elements, we expect leads to two-fold degenerate bands over the whole BZ. strong possible SOC effects at these induced K-points It is pertinent to mention that the calculated band-gaps that could be used for purely electrical manipulation of values are underestimated; for example, 1L PtSe2 dis- the magnetic moments in EuO. Systems displaying val- plays an indirect band-gap of 1.20 eV which is signifi- leys at the K-points with 3m point group symmetries cantly smaller than the experimentally reported value of are very important for SOT since they allow for optimal 2.2±0.1 eV [46]. Therefore, an energy shift of ∼0.9 eV in Rashba-Edelstein effect and efficient SOT [26, 56] due the conduction band is needed to compensate and match to the possibility of vertical spin-splitting and symmet- the experimental values [55]. We also highlight the lack ric spin-momentum locking in the vicinity of two time- of valleys at the K and K ′ points in the BZ defined in reversal symmetric K-points, which also enables a novel Fig. 1.b, which is a significant difference between these kind of anisotropy-like SOT [24] hitherto only observed structures and the more commonly found TMDs in the in Fe3 GeTe2 [57]. 2H-phase. The origin of the large proximity-induced magnetism is In the Janus TMD SePtS, the presence of dissimilar actually understood by the observed significant charge re- chalcogen atoms breaks inversion symmetry by remov- distribution between the proximitized materials and the ing a vertical mirror plane reducing the point group to surface of the EuO substrate. Fig. 2.a shows the charge 3m; this lifts the band degeneracy with a significant split- density difference which evidences a substantial charge ting in the range of 10-100 meV [54]. An analysis of dif- accumulation on the bottom chalcogen atom compared ferent kinds of stacking showed that the rock-salt crys- to the top one with charge-density extending inside the tal structure of EuO oriented along the (111) hexago- van der Waals gap. By further performing a Bader charge nal face, sketched in Fig. 1.c, is the ideal orientation analysis, one demonstrates that bottom S atom acquires for epitaxial growth, since in this case the Janus SPtSe 0.52 |e| charge from the surrounding atoms (Eu loses 3 PtS2 SPtSe large value of Eb = -1.70 eV (-1.84 eV for 2L PtSe2 on (a) (b) (c) (d) EuO) confirms the presence of strong interlayer interac- tions. We note that the binding energy is even larger for the lower atomic-size chalcogen PtS2 relatives of PtSe2 with lesser interlayer distance, providing a stronger at- tachment of the former to EuO substrate albeit perturb- ing the electronic dispersion as discussed below. These results are consistent with experimental data on Pt (111) substrate where an interlayer distance of 2.28 Å is ob- served [43]. In Fig. 3.(a-d) the band structures for all the three cases are reported, and unveil a novel effect not present in previous calculations, namely a valley- FIG. 2: (a,c) Charge density difference (isovalue: dependent band splittings highlighted in Fig. 3.b for 1L 2.5 × 10−3 electrons/bohr3 ), and (b,d) Spin density Janus SPtSe. Such an effect provides convincing evidence (isovalue: 3.0 × 10−3 electrons/bohr3 ) of 1L PtS2 and of the simultaneous action of exchange and SOC inter- Janus SPtSe on EuO substrate, respectively. In (a,c), actions. We estimate the (Zeeman) exchange strength blue and yellow colors represent charge accumulation by computing the average of the splitting at each val- and depletion, wheres in (b,d), blue and yellow colors ley ∆ex ≈ (δΓ→K + δΓ→K ′ )/2, which leads to values be- represent spin-up and spin-down densities, respectively. tween 190 meV to 360 meV as reported in Table I. Val- ley polarizations are actually quite typical of magnetized TMDs in their 1H structural phase, being a consequence 0.49 |e| and Pt loses 0.06 |e|) resulting in n-doping of of the hexagonal symmetry (D3h point group) and bro- the system. Fig. 2.b clarifies that such a charge redis- ken inversion symmetry that create a specific SOC term tribution is accompanied by a transfer of spin-polarized named valley-Zeeman, which behaves as an effective Zee- electrons from Eu to Pt atoms, which leads to the for- man field opposite sign at each valley. Therefore, the mation of a magnetic moment of magnitude +0.2µB lo- combined effect of this valley-Zeeman interaction with a cated on the Pt d-orbitals. We also observe S atoms to true Zeeman-field yields a valley-dependent Zeeman split- be anti-ferromagnetically coupled to it by having mag- ting with a splitting strength piloted by the SOC. We netic moments of +0.1µB and −0.02µB located on p- note that in principle, Pt-based TMDs are most stable orbitals for the top and bottom S atoms, respectively. In in the tetragonal phase (D3d point group), a phase pre- other words, non-magnetic few-layer PtX2 (X=S, Se) be- serving inversion symmetry, which forbids such a type comes magnetic on the EuO substrate due to the unique of valley-Zeeman SOC term. However, the presence of anti-ferromagnetic coupling of the S atoms. Looking at the substrate breaks such a symmetry whereas the pre- the EuO substrate itself, Eu and O atoms are also anti- served three-fold rotational symmetry induces the forma- ferromagnetically coupled to each other having a total tion valley-Zeeman SOC terms at the K points. Conse- magnetic moment of +7µB and −0.1µB sitting on f - and quently, the valley-polarization predicted by our calcu- p-orbitals, respectively. The system also become n-doped lations demonstrate large proximity-induced magnetism due the charge transfer between the chalcogen and sur- and lifting of the inversion symmetry in these Pt-based rounding atoms. These results are further validated by TMD supported by a EuO substrate. the atom-projected density of states that shows a strong The strength of the valley-Zeeman interaction is esti- orbital hybridization between Pt(d), S(p) and Eu(d) or- mated by computing the average difference in the split- bitals [54]. Since it is quite difficult to grow monolayer systems in general, and the electronic properties of PtSe2 are remarkably dependent on the crystalline structure TABLE I: Binding energy (Eb ), interlayer distance (d), [43–47], we also evaluated the bilayer case in the AA- conduction band spin-splittings along the Γ→K (δ Γ→K ) stacking. and Γ→K’ (δ Γ→K’ ) paths, Zeeman exchange strength We now discuss the results of the calculations when (∆ex ) and average difference in splittings (λvz ). both magnetism and SOC are included, for the mono- layer and bilayer cases of PtSe2 and SPtSe on the Eb d δ Γ→K δ Γ→K’ ∆ex λvz EuO substrate. The binding energy and interlayer (eV) (Å) (meV) (meV) (meV) (meV) distance for these calculations are given in Table I. 1L -1.94 2.05 362 355 358.5 3.5 The binding energy is calculated using the definition: PtS2 2L -2.05 2.04 331 270 300.5 30.5 Eb = E(PtSe2 /EuO) − E(PtSe2 ) − E(EuO), where 1L -2.04 2.07 313 372 342.5 29.5 SPtSe E(PtSe2 /EuO) is the total energy of the combined sys- 2L -1.87 2.05 185 345 265 80 tem, E(PtSe2 ) is the total energy of detached PtSe2 , and 1L -1.70 2.20 215 253 234 19 PtSe2 E(EuO) is the total energy of the EuO substrate. The 2L -1.84 2.18 171 214 192.5 21.5 4 PtSe2 SPtSe metric or Janus structure. In Table I a substantial valley 1 (a) (b) polarization is observed, that is 160 meV and 60 meV for the bilayer and monolayer structures respectively. This Monolayer (1L) is three to ten times larger than their symmetric counter- E-EF (eV) 0 parts. Since the structures are formed by the same atoms, such a change can be attributed to the giant Rashba ef- δΓ K δΓ K’ fect expected in this phase. It is pertinent to mention -1 that Janus SPtSe on EuO show these effects regardless of the presence of S or Se adjacent to the substrate [54]. It is complicated to extract the Rashba splitting since its -2 contribution is mixed with different interactions. There- 1 fore, we assume no Rashba interaction in the symmetric structure and further subtract the average spin polar- 0.5 ization for the Janus case. Following this procedure, we evaluate a Rashba coupling ranging between 30 meV and E-EF (eV) Bilayer (2L) 60 meV, which is again much larger than any other stud- 0 ied Janus-like system to date. To determine whether the systems in indeed subject -0.5 to a strong Rashba SOC, the spin-textures are computed (c) (d) using a 2D k-mesh (kx × ky : 15 × 15) centered at the Γ- -1 point (kz = 0) and are presented for the energy contours K Γ K’ M ΓK Γ K’ M Γ E = −0.20 eV and E = −0.85 eV in Fig. 4. The colors indicates opposite spin-polarities along the projected x, FIG. 3: (a,c) Electronic band structure of 1L and 2L y, and z directions, represented also in the labels above. PtSe2 and (b,d) Janus SPtSe on EuO substrate, In the valence bands, around the Γ point, we see a close respectively. The SOC effects are included for each case. contour which points to a mexican-hat shaped dispersion, although it is tilted due to the effect of the exchange in- teraction. This contour displays spin-momentum locking ting at each valley λvz ≈ |δΓ→K − δΓ→K ′ | /2. The values which is opposite for the two concentric bands and hints in Table I show Zeeman interactions ranging from 3 meV at potentially observing large spin-orbit torque in exper- to 80 meV in the symmetric structures. These values iments. However, in the conduction bands, the contour are extraordinarily large compared to other conventional crosses the K/K ′ points showing two distinct features: TMDs, as a consequence of the strong SOC introduced (i) strong spin-momentum locking in isolated bands, (ii) by the heavy metals. We however note that such esti- an energy contour with C3v point group symmetry. The mation does not include possible additional contribution first feature allows optimal spin-to-charge conversion via from Rashba SOC stemming from the interaction with the Rashba-Edelstein effect which is a precursor of SOT the substrate, which should slightly renormalize the band [26, 56]. The out-of-plane spin component reinforces the splitting. idea of a concomitant existence of exchange and Rashba interactions. The presence of a Fermi-contour with three- Sx Sy Sz fold rotational invariance is a necessary condition for a K novel kind of anisotropy-like SOT [24] hitherto observed only in Fe3 GeTe2 [57]. . Γ K’ In conclusion, we employed first-principles calculations to investigate proximity effects in ultrathin Pt dichalco- genides and Janus SPtSe on magnetic EuO substrate. Substantial charge redistribution was found within these systems, resulting in shifting CBMs in the vicinity of FIG. 4: 2D spin-textures of Janus 2L SPtSe on EuO ′ high-symmetry K and K points, with the formation of substrate. Refer to brown lines in Fig. 3.d, inner multiple valleys. Very importantly, the broken inver- contours corresponds to valence bands passing through sion and time-reversal symmetries, together with prox- an energy E = −0.85 eV whereas the outer contours imity effects from the magnetic substrate, generate huge (corners) belongs to conduction bands passing through spin-splittings (of the order of several hundred meV) in an energy E = −0.20 eV, respectively. The red/blue the conduction band of few-layer PtX2 (X=S, Se) and colors indicate spin up/down. Janus SPtSe. Moreover, these ultrathin systems become magnetic, hosting magnetic moments at different atomic We finally discuss the results obtained for the asym- sites with an anti-ferromagnetic coupling between op- 5 posite S atoms demonstrating spin-valley polarization. [14] Z. Wang, C. Tang, R. Sachs, Y. Barlas, and J. Shi, Phys. These findings provide a versatile platform to explore Rev. Lett. 114, 016603 (2015). spin-valley physics in Pt dichalcogenides and leads to [15] P. Wei, S. Lee, F. 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