Contrasting Ferromagnetism in Pyrite FeS 2 Induced by Chemical Doping versus Electrostatic Gating
CContrasting Ferromagnetism in Pyrite
FeS Induced by Chemical Doping versusElectrostatic Gating
Ezra Day-Roberts, Turan Birol, and Rafael M. Fernandes School of Physics and Astronomy, University of Minnesota, Minneapolis, MN 55455, USA Department of Chemical Engineering and Materials Science,University of Minnesota, Minneapolis, Minnesota 55455, USA
Recent advances in electrostatic gating provide a novel way to modify the carrier concentration inmaterials via electrostatic means instead of chemical doping, thus minimizing the impurity scatter-ing. Here, we use first-principles Density Functional Theory combined with a tight-binding approachto compare and contrast the effects of electrostatic gating and Co chemical doping on the ferromag-netic transition of FeS , a transition metal disulfide with the pyrite structure. Using tight-bindingparameters obtained from maximally-localized Wannier functions, we calculate the magnetic sus-ceptibility across a wide doping range. We find that electrostatic gating requires a higher electronconcentration than the equivalent in Co doping to induce ferromagnetism via a Stoner-like mech-anism. We attribute this behavior to the formation of a narrow Co band near the bottom of theconduction band under chemical doping, which is absent in the electrostatic gating case. Our resultsreveal that the effects of electrostatic gating go beyond a simple rigid band shift, and highlight theimportance of the changes in the crystal structure promoted by gating. I. INTRODUCTION
Transition metal disulfides, (TM)S , with the pyritestructure host a wide variety of electronic ground states[1]. Varying the transition metal TM tunes the bandfilling over a wide range, from a 3 d electronic configu-ration in the case of MnS to a 3 d configuration forZnS . As the carrier concentration changes, a rich land-scape of electronic states emerges, including: an an-tiferromagnetic insulator (MnS )[2–4], a semiconductor(FeS ) [5, 6], a ferromagnetic metal (CoS ) [5, 6], anantiferromagnetic Mott insulator (NiS ) [7–9], a super-conductor (CuS ) [10, 11], and another semiconductor(ZnS ) [12]. Tuning continuously across these phaseswould provide a unique avenue to elucidate the interplaybetween different electronic orders. While it is possible touse chemical doping to move across most of the transitionmetal disulfides’ phase diagram, this approach introducesdisorder and local inhomogeneity, which complicates thetheoretical picture [13].Electrostatic gating offers a promising alternative tochemical doping as a means to tune the carrier con-centration, while avoiding the steric and chemical (elec-tronegativity, etc.) effects associated with the additionof dopants. While the effects achievable using a con-ventional gate dielectric are often limited, novel gatingapproaches such as using a polar oxide or ferroelectricgating are quite promising [14, 15]. Also exciting arethe recent advances in electrostatic gating with ionic liq-uids or gels, which provide access to much higher elec-tron concentrations than those attainable by dielectric-based gating [13, 16, 17], opening new avenues to ex-plore different regions of electronic phase diagrams [18–21], including wide regions of the disulfide pyrite electron-density phase diagram. Indeed, in dielectric-based gat-ing devices, breakdown voltages restrict the added car-rier densities to values < − cm − [13]. In con- trast, the ability to achieve carrier concentrations of up to8 × cm − [22] via electrolyte gating has been widelyemployed to study a variety of phenomena in oxides,such as the structural transformation in VO [23–25],the metal-insulator transition in SrRuO [26, 27], andsuperconductor-insulator transitions in multiple materi-als [19, 28–31]. These studies, however, revealed an im-portant issue associated with electrolyte gating: often,electrochemical effects beyond simple electrostatics areat play [16, 32–34]. For example, in La . Sr . CoO − δ ,oxygen vacancies are formed under positive gating volt-ages [35]. These vacancies, which are formed in responseto gating, enhance the sensitivity of the electronic struc-ture to gating. However, they also introduce a significantdegree of irreversibility. While this irreversibility can beundesirable for certain applications, many attempts havebeen made to take advantage of these electrochemicaleffects for many applications as well [35–39]. In con-trast to oxides, strong sulfur-sulfur bonding in the pyritestructure [40] makes the formation energy of single sul-fur vacancies prohibitely high [41] while multi-vacancydefect complexes dominate the electrochemical response[42]. How these defect complexes diffuse and determinethe electrochemical response in pyrites is far from clear.Among the pyrite transition metal disulfides, FeS hasattracted interest both as a potential photovoltaic ma-terial, characterized by a high optical absorption, a lowtoxicity and a low cost to manufacture [43–45], and asa metallic ferromagnet when doped with cobalt [6, 46].FeS is often unintentionally doped, and a great amountof work has been performed on the nature of nativedopants [41, 47] as well as the role of surface vs. bulkconduction [48, 49]. While the “doping puzzle” aboutthe nature of native dopants in single crystals vs. films ofFeS seems to be resolved [42, 50], there are several openquestions about the electronic properties of FeS thatremain unsettled, such as the impact of the conductingsurface states [51], the nature of the ferromagnetic tran- a r X i v : . [ c ond - m a t . m t r l - s c i ] J a n sition in the doped compounds [52], and the role of Codoping in inducing ferromagnetism even at very smalldoping concentrations [53].To shed new light on some of these issues, in this pa-per we perform a first-principles study of electrostaticallygated FeS and CoS with pyrite structure, systemati-cally comparing their electronic and magnetic propertieswith those of chemically doped Fe − x Co x S . To modelelectrostatic gating, we go beyond the rigid-band shiftparadigm and account for changes in the band structureand in the crystal structure arising from the change in thecarrier concentration [54]. By computing the magnetiza-tion, we find that ferromagnetism appears for a smalleradded carrier concentration in the case of chemical dop-ing as compared to electrostatic gating. We attributethis behavior to the different energy ranges of the widesulfur anti-bonding band in the two cases, as well as tothe existence of a narrow Co band near the bottom ofthe conduction band in the case of chemical doping.By comparing the carrier-concentration evolution ofthe magnetization with that of the density of states,we propose that the ferromagnetism is promoted by theStoner mechanism. This naturally accounts for the sen-sitivity of the ferromagnetism to the changes in the bandstructure caused by chemical doping and electrostaticgating. We go beyond the first-principles analysis bycomputing the Lindhard function from a multi-orbitaltight-binding model derived from the maximally local-ized Wannier functions. We find that the non-interactingmagnetic susceptibility is peaked at the Γ point of theBrillouin zone, confirming the Stoner-character of the fer-romagnetic instability and ruling out finite wave-vectormagnetic states.The paper is organized as follows: In section II wesummarize our methods. In section III we present ourfirst-principles results on the magnetic, electronic, andcrystalline structures of the chemically doped and elec-trostatically gated cases. In section IV we fit a tightbinding model to our first-principles results to calculatethe non-interacting magnetic susceptibility. We concludewith a summary of our main results in section V. II. METHODS
DFT+U calculations were done using the VASP imple-mentation of the projector-augmented-wave (PAW) ap-proach [55, 56]. The exchange-correlation functional wasapproximated using the PBEsol set generalized gradientapproximation (GGA), which is developed for accuracyin crystal structure relaxations [57]. To correct the un-derestimation of on-site interactions between electrons,DFT+U approach was used [58]. A value of U = 5 eVwas selected as a compromise to achieve good agreementwith the experimental lattice constant and sulfur-sulfurdistance for both FeS and CoS (see Appendix). ForFeS alone, a lower value of approximately 2 eV is op-timal, in agreement with previous works [59]. For CoS alone, a much larger value of U is preferred, because thelattice constant is underestimated and the sulfur-sulfurdistance is overestimated for all values below 7 eV. The U value of 5 eV gives an error in each lattice constant ofless than 1% and an error in the sulfur-sulfur distance ofabout 2 . k -point grid of 8 × × is found to not be spinpolarized in its ground state while for all other chemicaldoping levels the ground state is found to be spin polar-ized, consistent with previous reports [60, 61]. A tight-binding model is constructed by calculating the Max-imally Localized Wannier Functions by employing thewannier90 package [62]. The wannierization calculationis done in the non-spin polarized state with the samevalue of U , since we are concerned with the emergenceof the magnetic instability and not with the behavior ofthe materials in their ferromagnetic state.In order to compare the effects of electrostatic gatingwith chemical doping we performed two sets of calcu-lations. To simulate electrostatic gating (EG) we con-sider undoped FeS (or CoS ) and vary the total num-ber of electrons in the unit cell by adding electrons (orholes) [63]. The highest level of EG we considered was1 removed electron or 0.5 added electrons per transitionmetal atom. This is almost an order of magnitude largerthan the experimentally achievable values, and leads tovery large changes in the crystal structure. Thus, theresults presented for the highest levels of EG serve justto illustrate trends for comparison with chemical doping.To simulate chemical doping (CD), we replaced one, two,or three of the Fe ions in the unit cell with Co ions, cor-responding to x = 0 . , . , and 0 .
75 in Fe − x Co x S .For each different carrier concentration in EG we fullyrelaxed both the ionic positions and the lattice vectors.For the CD configurations, the dopants break the sym-metry of the crystal structure, so cell shape distortionsaway from cubic are in principle permitted by symme-try. Since the average structure with disorder has cubicsymmetry, such distortions were not allowed in our cal-culations. This was achieved by iteratively relaxing cellsize and ionic positions separately until convergence wasobtained.The entire conduction band manifold that consists of 2 e g orbitals and 1 sulfur anti-bonding orbital per FeS for-mula unit was used for wannierization. This manifold isisolated from other bands so no disentanglement was nec-essary [64]. The tight binding models we obtained fromthe wannierization procedure reproduce the DFT bandstructure extremely well (see the Appendix for details),but this requires using a very large number of hoppingparameters. As a result, we do not report our hopping FIG. 1. (a) The simple-cubic primitive unit cell of FeS . Thetransition metal atoms occupy the corners and the face cen-ters of this cell. Each transition metal atom is in the centerof a sulfur octahedron. (b) The transition metal octahedraare corner sharing in the pyrite structure. In addition, everysulfur is part of a dimer connecting neighboring octahedra.Lattice Constant (˚A) Internal parameter (u)FeS Exp 5.428 0.385FeS Theory 5.421 0.387CoS Exp 5.535 0.395CoS Theory 5.510 0.391TABLE I. Experimental crystal structure parameters for pureFeS and CoS compared with our calculations [65, 66]. parameters. III. FIRST-PRINCIPLE RESULTSA. Magnetization
The pyrite structure has a simple cubic cell, consistingof a face-centered lattice of transition metal atoms eachsurrounded by a distorted sulfur octahedron (see Fig. 1).The sulfur atoms form covalently bonded dimers, with
Chemical Doping ( This Work ) FeS gated ( This Work ) CoS gated ( This Work ) DFT ( supercell ) [ Ref 58 ] DFT ( VCA ) [
Ref 58 ] Experimental [ Ref 67 ] M a g n e t i z a t i o n p e r a dd e d e - p e r T M i o n ( μ B ) / f.u. FIG. 2. Magnetization per added free electron as functionof the number of added electrons. Our DFT+U results arecompared with previous first-principles and experimental re-sults on doped Fe − x Co x S [60]. Note that electrostaticallygated systems do not achieve 100% spin polarization until ap-proximatelly 0 . . Furthermore,electrostatic gating requires a higher added electron concen-tration to achieve ferromagnetism as compared to chemicaldoping. the center point of the dimers forming another FCC lat-tice shifted from the transition metal lattice by half alattice vector [67]. Because the sulfur atoms share twoelectrons in these dimers, the sulfur charge state is − − valence. This is in contrastto oxides and most other transition metal dichalcogenideswhere the chalcogens have a − valence [68]. In FeS , the dimer anti-bonding states areunoccupied and overlap with the empty Fe e g bands.These dimers are thus an important ingredient of theelectronic structure. The sulfur-sulfur distance controlsthe energy of the sulfur anti-bonding bands that makeup the bottom of the conduction band in FeS . Thereis only one internal crystallographic parameter, u , whichcontrols the sulfur atoms’ positions at ( u, u, u ) and atthe symmetry-equivalent positions. This parameter con-trols both the distortion of the octahedra and the relativesulfur-sulfur and transition metal-sulfur distances. TableI lists the previously reported experimental lattice con-stant and internal parameter [65, 66] , comparing themto the relaxed values found in this work. The discrepen-cies come from our choice to use a single value of U forboth FeS and CoS .The magnetic transition that takes place on going fromFeS to CoS allows access to a large range of spin polar-izations [6], making this possibly the best studied transi-tion in the pyrite disulfides family. In early experiments,ferromagnetism was found already at very low dopinglevels of less than x = 0 .
01 in Fe − x Co x S [69], an ob-servation that has been confirmed by many later exper-iments [6, 40, 52] (see experimental points in figure 2).Magnetization measurements show that Fe − x Co x S is a FIG. 3. Calculated density of states at the Fermi level ρ F asfunction of the number of added electrons for electrostati-cally gated FeS (red squares) and CoS (blue diamonds),and chemically doped Fe − x Co x S (green circles). nearly perfect half-metal across a large range of dopingconcentrations ( x ≈ . − . x ≈ . − .
15, and a half-metal with 100%spin polarization emerging at and above x ≈ . − . − x Co x S (green circles), are shownin Fig. 2. In agreement with previous results, we finda ferromagnetic transition occuring for 0 < x < . (red squares), ferromagnetism onsets only at larger car-rier concentrations, equivalent to x ≈ . − .
30, withhalf-metallicity appearing only at x ≈ .
40. Conversely,starting from CoS and adding holes (blue diamonds),half-metallicity starts disappearing around 1 − x ≈ . B. Density of States
To shed light on the origin of the ferromagnetic state,we plot in Fig. 3 the DOS at the Fermi level, ρ F , asfunction of the added carrier concentration. Comparisonwith the behavior of the magnetization in Fig. 2 suggeststhat a Stoner mechanism is likely at play [60]. Indeed, atlow carrier concentrations, the CD material has a higherDOS at the Fermi level than the EG material, consistentwith the fact that the former is ferromagnetic at low dop-ing levels. Similarly, the DOS of the EG materials showa significant increase around x ≈ .
25, which coincideswith the onset of ferromagnetism in Fig. 2.The key difference between EG and CD compoundsis which bands are being filled. Figure 4(a) shows aschematic representation of the density of states for EGFeS , whereas the calculated DOS is shown in Fig. 5(a). The valence band consists of fully occupied t g orbitals,and the conduction band consists of unoccupied e g statessurrounded by a wide sulfur p -band [70]. This wide bandhas sulfur-sulfur antibonding character, as shown in Fig.4(b) [71]. Gating affects the relative bandwidth of thesulfur bands, which decreases for increasing x . Introduc-ing electrons to FeS initially fills this sulfur band, whichhas a low density of states. Fe e g states start being occu-pied only after around 0 .
25 electrons per iron are added.Once the e g band starts being filled, the DOS increasessignificantly, and ferromagnetism emerges. This qualita-tive picture also applies to EG CoS , although it has anarrower sulfur bandwidth as compared to EG FeS .The DOS evolution with carrier concentration is ratherdifferent in the case of CD Fe − x Co x S . The reason isbecause, in the 2+ valence state, iron is slightly moreelectronegative than cobalt (1.390 vs 1.377 in the scaledefined by Yuan et al. [72]), which means that the sameelectronic orbitals will be at lower energies in cobalt rela-tive to iron. As a result, occupied Co e g states are lowerthan the unoccupied e g states of Fe. These states, whichhave a large DOS, make up the lower edge of the con-duction band as illustrated schematically in Fig. 4(c)and shown quantitatively in Fig. 5(b). Thus, in con-trast to the electrostatically gated case, where the addedelectrons start by occupying low DOS sulfur states, theextra electrons in Fe − x Co x S occupy high DOS cobalt e g states immediately. This is related to the appearanceof ferromagnetism at a much lower added carrier concen-tration. C. Crystal Structure
The changes in the electronic structure discussed aboveare also accompanied by changes in the crystal struc-ture, highlighting the importance of effects beyond a sim-ple rigid-band shift in the case of electrostatically gatedcompounds. Figure 6 shows the evolution of the crystalstructure with increasing electron count, contrasting thecases of electrostatic gating (red and blue curves) andchemical doping (green curves). The former is modeledeither as electrons added to the FeS structure (red) oras holes added to the CoS compound (blue). There arenoticeable changes in the trends of multiple structuralparameters near 0 . .
30 added electrons per formulaunit (f.u.). While some changes might seem unphysicallylarge, we emphasize that large values of added carriersare not experimentally feasible via electrostatic gating,and are only included here to illustrate the trends.These effects are mainly driven by the Fermi level en-tering the e g bands at this doping, as discussed in the pre-vious subsection. For less than 0 .
25 added electrons perf.u., the states that are being filled have sulfur antibond-ing character, which causes the sulfur-sulfur distance toincrease (panel (b)). Once 0 .
25 electrons per f.u. areadded, the e g bands begin filling, which is reflected inthe sharp upturn in the transition metal-sulfur distance FIG. 4. (a) Schematic representation of the DOS for electrostatic gated FeS . The red (green) bands are iron (sulfur) bands.(b) DFT band structure of FeS , with red denoting greater iron character and green, greater sulfur character. (c) Schematicrepresentation of the DOS for chemically doped Fe − x Co x S . A cobalt d -band (blue) emerges at the bottom of the wide sulfurband. FeS - E - E F ( e V ) DOS ( eV - )( a ) FeS CoFeS - - E - E F ( e V ) DOS ( eV - )( b ) Fe Co S FIG. 5. Calculated densities of states for (a) pure FeS and(b) chemically doped Fe . Co . S . The character of thebands are colored according to the legends. Note the promi-nent peak originating from the Co orbitals at the bottom ofthe conduction band in the doped case. in the case of FeS (panel (a)). In the case of CoS ,there is a much less steep change, although an increaseis also observed. At the same time, since there are stillsome sulfur-sulfur antibonding states at the Fermi level,the lattice constant increases at a faster rate (panel (d))to compensate for the effects of the internal parameter u (panel (c)). This behavior of the lattice constant un- der electrostatic gating strongly deviates from a linearinterpolation that would be expected from Vegard’s law[73], which is well followed under chemical doping. In-deed, adding 0 .
25 electrons per Fe increases the latticeconstant by more than 4%, whereas 25% Co doping onlychanges the lattice constant by ≈ . u , shown in panel (c). This parameterand the lattice constant a are related to the sulfur-sulfurand metal-sulfur distances as d S − S = a √ − u ) and d TM − S = a (cid:113) − u + 3 u . For these values of u there isa tradeoff: higher u gives a larger transition metal-sulfurdistance but a smaller sulfur-sulfur distance. These com-peting effects lead to the clear non-monotonic behaviorof u . For less than 0 .
25 added electrons per f.u. the effecton the sulfur-sulfur distance is more important, and u de-creases. However, for larger numbers of added electrons,once the e g states begin filling, the transition metal-sulfurdistance becomes more important and u increases. IV. TIGHT-BINDING MODEL
While DFT is able to determine the ground state en-ergy of a specific magnetic configuration, testing all possi-ble types of magnetic order to find the lowest energy stateis infeasible. Instead, to screen the possible magneticwave-vectors, we compute the non-interacting magneticsusceptibility via the Lindhard function. In a weakly in-teracting system, which should describe doped FeS , thisquantity provides a good indicator of the different insta-bilities of the system. While more sophisticated calcula-tions that account for electronic interactions are possible, Chemical DopingFeS gatedCoS gated ( a ) T M - S d i s t a n c e ( Å ) Chemical DopingFeS gatedCoS gated ( b ) S - S d i s t a n c e ( Å ) FeS gatedCoS gated ( c ) I n t e r n a l p a r a m e t e r u Chemical DopingFeS gatedCoS gated ( d ) L a tt i c e C o n s t a n t ( Å ) / f.u. FIG. 6. Plots of several structural parameters as a function ofadded electrons (per formula unit) for electrostatically-gatedFeS (red), electrostatically-gated CoS (blue, in which casethe added carriers are actually holes), and chemically dopedFe − x Co x S (green). The panels display (a) the sulfur-sulfurdistance, (b) the transition metal-sulfur distance, (c) the in-ternal sulfur parameter u , and (d) the lattice constant. Chem-ical doping reduces the symmetry and leads to multiple dif-ferent TM–S and S–S distances, which are shown as separatedatapoints in panels (a) and (b) FIG. 7. Illustraton of the sulfur-dimer centered Wannier func-tion (left) and transition metal centered Wannier function(right). The sulfur-dimer function has p anti-bonding charac-ter, which is the character of the wide band at the bottom ofthe conduction band shown in Fig. 4(a). for the scope of this work it suffices to consider the non-interacting susceptibility.To efficiently compute the Lindhard function, we firstconstruct a tight-binding model from the Wannier func-tions, which are obtained from a unitary transformationof the Bloch wavefunctions into a new basis. The re-sulting functions are maximally spatially localized andentirely real [74]. In practice, we calculate an approx-imate unitary transformation that minimizes the realspace spread of the wavefunctions. This additionallygives a maximum ratio of the real and imaginary parts ofthe wavefunction of less than 10 − . Wannier models areregularly used to interpolate band structures [75], to mapFermi surfaces [76], and to calculate Fermi surface inte-grals [77]. Figure 7 shows an example of a Wannier func-tion centered on a sulfur dimer with some hybridizationto the six transition metal atoms neighboring the sulfurdimer. The other Wannier functions have well-localized e g character on the transition metal atoms, as also shownin Fig. 7. This Wannier function further emphasizesthe covalency between the S atoms in dimers, since thefunction is centered at the bond center and not on anindividual S ion. These dimer orbitals are important tothe overall band structure, as discussed above. The en-tire conduction manifold that consists of the transitionmetal e g and sulfur anti-bonding states is used for ourWannier calculations, generating twelve Wannier func-tions per cell, with no need for disentanglement.These functions allow us to efficiently derive a tight-binding model of the form: H = (cid:88) (cid:126)R,st t (cid:126)Rst (cid:16) ˆ c † (cid:126)R,s ˆ c (cid:126) ,t + c.c. (cid:17) . (1)from the Wannier basis, where ˆ c † , ˆ c are creation and an-nihilation operators, (cid:126)R is the vector connecting the unitcells of two orbitals, and s, t are orbital indices within acell (spin indices are omitted for simplicity). The hop-ping terms t (cid:126)Rst = (cid:104) (cid:126) s | ˆ H | (cid:126)Rt (cid:105) are directly computed as thematrix element between the s th Wannier function in thehome cell and the t th Wannier function in the cell at (cid:126)R .Because we are not interested in finding a minimal model,twenty distinct hopping vectors are kept corresponding toapproximately 700 separate terms. This large number ofterms allows us to obtain almost exact agreement withthe DFT band structure for all bands (see the Appendixfor all DFT and tight binding bandstructures). Withthis model we can very efficiently compute energies atarbitrary k-points.From the tight-binding model we calculate the mag-netic susceptibility in the first Brillouin zone by comput-ing the Lindhardt function. The general non-interactingmagnetic susceptibility is given by [78] χ pqst ( q , ω ) = − N (cid:88) k ,µν a sµ ( k ) a p ∗ µ ( k ) a qν ( k + q ) a t ∗ ν ( k + q ) ω + E ν ( k + q ) − E µ ( k ) + i + (2) × [ f ( E ν ( k + q )) − f ( E µ ( k ))] , where a sµ ( k ) are the matrix elements corresponding tothe change from orbital basis (latin indices) to band ba-sis (greek indices), E µ ( k ) is the energy of band µ at mo-mentum k , and N is the number of sites. The staticsusceptibility is [78] χ ( q ) = 12 (cid:88) sp χ ppss ( q , . (3)Figure 8 shows the susceptibilities for EG FeS andCoS , as well as for CD Fe − x Co x S . In agreement withthe spin-polarized DFT calculations, we observe a sharpincrease in the magnetic susceptibility at the Γ point(i.e. q = 0) starting at 0 .
25 added electrons per f.u.in both gated compounds, consistent with a tendency to-wards ferromagnetism. Note that χ (Γ) is proportionalto the density of states at the Fermi level; thus, the non-monotonic behavior of the magnitude of χ ( q ) as functionof doping in the case of CD Fe − x Co x S is consistent withthe non-monotonic dependence of the DOS shown in Fig.3. The key point of this calculation is to show that, whenferromagnetism emerges upon adding 0.25 electrons performula unit, the non-interacting susceptibility displaysno competing peaks at other wave-vectors. This makesit less likely that competing magnetic states are realizedin this compound and, moreover, lends support to theproposal that the ferromagnetism is of Stoner-type. V. CONCLUSIONS
We performed first principles calculations for bothchemically doped Fe − x Co x S and electrostatically gatedFeS and CoS to elucidate how these different ways ofchanging the carreir concentration affect the magneticand electronic properties of these pyrite compounds. Wefound that electrostatic gating requires a larger concen-tration of added electrons to induce ferromagnetism ascompared to chemical doping. We attribute this behav-ior to the Stoner nature of the ferromagnetic instabil-ity, combined with the fundamentally different ways inwhich the band structure changes upon gating versus FIG. 8. Non-interacting magnetic susceptibilities in momen-tum space χ ( q ) for (a)gated FeS , (b) gated CoS , and (c)doped Fe − x Co x S . Note how in (c) the overall magnitude ofthe curves is not monotonic with doping. doping. Specifically, while Co e g bands with large DOSform at the bottom of the conduction band when FeS is doped with Co, these bands are not present in elec-trostatically gated FeS . Instead, in the latter case, alow DOS wide sulfur band must first be occupied beforethe e g Fe band becomes filled, thus delaying the onset offerromagnetism.Our structural relaxation calculations revealed signif-icant changes in several relevant crystalline parametersupon adding electrons via gating. This result demon-strates that electrostatic gating has a much richer im-pact beyond a rigid-band shift, altering both the crys-tal structure and the electronic structure. Finally, ourtight-binding parametrization allowed us to compute thenon-interacting magnetic susceptibility, which revealed asharp peak at the Γ point consistent with a leading fer-romagnetic Stoner-like instability.Our investigation shows that, even without consider-ing the impact of disorder introduced by dopants, elec-trostatic gating and chemical doping can affect the elec-tronic properties of a compound in rather different ways,resulting in distinct macroscopic properties. This alsosuggests that a combination of electrostatic gating andchemical doping may provide an interesting and efficientway to probe and tune electronic ground states. We notethat the current capabilities of ionic liquid or gel gatingof adding 10 cm − would correspond to adding ≈ . (assuminga penetration depth of one unit cell). Thus, our resultssuggest that electrolyte gating is a viable means to induceferromagnetism in FeS purely electrostatically. ACKNOWLEDGMENTS
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