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Farsane Tabataba-Vakili, Huy P. G. Nguyen, Anna Rupp, Kseniia Mosina, Anastasios Papavasileiou, [Kenji Watanabe](https://orcid.org/0000-0003-3701-8119), [Takashi Taniguchi](https://orcid.org/0000-0002-1467-3105), Patrick Maletinsky, Mikhail M. Glazov, Zdenek Sofer, Anvar S. Baimuratov, Alexander Högele

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[Doping-control of excitons and magnetism in few-layer CrSBr](https://mdr.nims.go.jp/datasets/108ce203-a099-4e7f-953f-b3194935c1ee)

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Doping-control of excitons and magnetism in few-layer CrSBrArticle https://doi.org/10.1038/s41467-024-49048-9Doping-control of excitons and magnetismin few-layer CrSBrFarsane Tabataba-Vakili 1,2 , Huy P. G. Nguyen1, Anna Rupp1,Kseniia Mosina 3, Anastasios Papavasileiou3, Kenji Watanabe 4,Takashi Taniguchi 5, Patrick Maletinsky 6, Mikhail M. Glazov 7,Zdenek Sofer 3, Anvar S. Baimuratov 1 & Alexander Högele 1,2Magnetism in two-dimensional materials reveals phenomena distinct frombulk magnetic crystals, with sensitivity to charge doping and electric fields inmonolayer and bilayer van der Waals magnet CrI3. Within the class of layeredmagnets, semiconducting CrSBr stands out by featuring stability underambient conditions, correlating excitons with magnetic order and thus pro-viding strong magnon-exciton coupling, and exhibiting peculiar magneto-optics of exciton-polaritons. Here, we demonstrate that both exciton andmagnetic transitions in bilayer and trilayer CrSBr are sensitive to voltage-controlled field-effect charging, exhibiting bound exciton-charge complexesand doping-induced metamagnetic transitions. Moreover, we demonstratehow these unique properties enable optical probes of local magnetic order,visualizing magnetic domains of competing phases across metamagnetictransitions induced by magnetic field or electrostatic doping. Our work iden-tifies few-layer CrSBr as a rich platform for exploring collaborative effects ofcharge, optical excitations, and magnetism.Recent experimental realization of two-dimensional (2D) magnetswith ferromagnetic (FM) order down to the monolayer limit1,2 hasinitiated extensive research on van der Waals magnets, with obser-vation of magnons3,4, magnetic proximity coupling5,6, and giantmagnetoresistance7,8. With additional electrostatic control of mag-netism as in CrI39–11, 2D magnets promise novel applications inspintronics or magnetic memories, including high-speed magneticswitching. More recently, antiferromagnetic (AF) semiconductorCrSBr with a bandgap of 1.5 eV12,13, intralayer FM order and AFinterlayer coupling14, and high Néel temperatures of 132 and 140 Kfor bulk15 and bilayer16 crystals has received particular attention dueto its intriguing magnetic14,17 and magneto-optical properties13,18,with demonstrations of strongly linearly polarized excitons sensitiveto the magnetic order18, magnon-exciton coupling19,20, exciton-polaritons21–23, and large negative magnetoresistance12,24,25. To date,however, electric control of magneto-optical phenomena in CrSBrhas remained elusive.In thiswork, wepresent an elaborate study of electrostatic controlof the coupled excitonic and magnetic properties of few-layer CrSBr.To this end, we embedmonocrystalline few-layer CrSBr in a field-effectdevice andperformcryogenicmagneto-optical studies as a function ofvoltage-induced doping and in the presence of magnetic fields alongthe magnetic hard (crystallographic c), easy (b), and intermediate (a)axes. Upon electron doping, we observe the emergence of chargedexciton complexes in bi- and trilayer crystals, and investigatetheir origins both experimentally and theoretically. The parabolicReceived: 18 December 2023Accepted: 22 May 2024Check for updates1Fakultät für Physik, Munich Quantum Center, and Center for NanoScience (CeNS), Ludwig-Maximilians-Universität München, Geschwister-Scholl-Platz 1,80539 München, Germany. 2Munich Center for Quantum Science and Technology (MCQST), 80799 München, Germany. 3Department of InorganicChemistry, University of Chemistry and Technology Prague, Technická 5, 166 28 Prague 6, Czech Republic. 4Research Center for Functional Materials,National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan. 5International Center for Materials Nanoarchitectonics, National Institute forMaterials Science, 1-1 Namiki, Tsukuba 305-0044, Japan. 6Department of Physics, University of Basel Basel, Switzerland. 7Ioffe Institute, 194021 SaintPetersburg, Russian Federation. e-mail: f.tabataba@lmu.de; anvar.baimuratov@lmu.de; alexander.hoegele@lmu.deNature Communications |         (2024) 15:4735 11234567890():,;1234567890():,;http://orcid.org/0000-0001-5911-7594http://orcid.org/0000-0001-5911-7594http://orcid.org/0000-0001-5911-7594http://orcid.org/0000-0001-5911-7594http://orcid.org/0000-0001-5911-7594http://orcid.org/0000-0003-3570-5337http://orcid.org/0000-0003-3570-5337http://orcid.org/0000-0003-3570-5337http://orcid.org/0000-0003-3570-5337http://orcid.org/0000-0003-3570-5337http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0003-1699-388Xhttp://orcid.org/0000-0003-1699-388Xhttp://orcid.org/0000-0003-1699-388Xhttp://orcid.org/0000-0003-1699-388Xhttp://orcid.org/0000-0003-1699-388Xhttp://orcid.org/0000-0003-4462-0749http://orcid.org/0000-0003-4462-0749http://orcid.org/0000-0003-4462-0749http://orcid.org/0000-0003-4462-0749http://orcid.org/0000-0003-4462-0749http://orcid.org/0000-0002-1391-4448http://orcid.org/0000-0002-1391-4448http://orcid.org/0000-0002-1391-4448http://orcid.org/0000-0002-1391-4448http://orcid.org/0000-0002-1391-4448http://orcid.org/0000-0001-8708-2405http://orcid.org/0000-0001-8708-2405http://orcid.org/0000-0001-8708-2405http://orcid.org/0000-0001-8708-2405http://orcid.org/0000-0001-8708-2405http://orcid.org/0000-0002-0178-9117http://orcid.org/0000-0002-0178-9117http://orcid.org/0000-0002-0178-9117http://orcid.org/0000-0002-0178-9117http://orcid.org/0000-0002-0178-9117http://crossmark.crossref.org/dialog/?doi=10.1038/s41467-024-49048-9&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-024-49048-9&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-024-49048-9&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-024-49048-9&domain=pdfmailto:f.tabataba@lmu.demailto:anvar.baimuratov@lmu.demailto:alexander.hoegele@lmu.dedispersions in magnetic fields along the c and a axes18 allow us toestablish a self-consistent description of the neutral and chargedexciton complexes in the presence of coupling between intralayer andinterlayer excitons mediated by hole interlayer tunneling. We utilizethis understanding to demonstrate electric control of the metamag-netic transitions induced by magnetic field along the b axis, withpronounced exciton energy jumps correlated with themagnetic orderin bi- and trilayer18. Finally, we demonstrate how the coupling betweenexcitons and magnetism can be utilized for local sensing of magneticphases, which depend on both magnetic field and charge doping, andextend the technique to optical raster-imaging of magnetic domains.Results and discussionOur field-effect device incorporates a CrSBr flake with mono-, bi-, andtrilayer regions, exfoliated from a bulk crystal grown by chemicalvapor transport (details in Methods). The CrSBr flake shown in theoptical micrograph of Fig. 1a has a characteristic shape, extendedalong the crystallographic a axis18,26,27. Using the conventional dry-transfer method28, we fabricated a single-gated device with hBN asdielectric and few-layer graphene as top gate and contact layer (seeschematic in Fig. 1b, andMethods for fabrication details). To study thesample by low-temperature differential reflectance (DR) and photo-luminescence (PL) spectroscopy at 3.2 K as a function of electrostaticdoping, we identifymono-, bi-, and trilayer regions with strong excitonresonances, marked by diamonds in the DR map of Fig. 1c.The spectrum of the neutral monolayer at 0 V in the top panel ofFig. 1d shows a feature in DR at 1.342 eV, which corresponds to a broadabsorption peak (see Supplementary Fig. 1a for absorption spectradetermined by Kramers-Kronig relation) and low-intensity PL (toppanel of Fig. 1e). The negligible energy shift between DR, absorptionand PL indicates amomentum-direct exciton transition18 labeled as XA.Our theoretical analysis assigns the XA exciton to the transitionbetween the topmost valence band (v) and the lowest conductionband (c1) at the Γ point of the first Brillouin zone, without clear con-sensus on oscillator strength1314,17,1829,30. We adopt the notion of anominally dipole-forbidden transition v↔ c113 (see Methods fordetails), brightened by the asymmetry of our structure and the highsurface-to-volume ratio of the monolayer and persisting in the DRspectra of the neutral bi- and trilayer in the top panels of Fig. 1f, h,respectively (see Supplementary Fig. 2 for exciton layer assignment).The assignment of the transition to the top valence and bottomconduction band is substantiated by the absence of striking signatures-0.030.000.03DR0 V 30 V5 µm1.30 1.35 1.40200-20V G)V(Energy (eV)1.30 1.35 1.40200-20Energy (eV)1.30 1.35 1.40200-20Energy (eV)1.30 1.35 1.40200-20Energy (eV)1.30 1.35 1.40200-20Energy (eV)1.30 1.35 1.40200-20V G)V(Energy (eV)d03006000 V 30 V-0.6-0.30.00 V 30 V05001000  0 V  30 V-0.6-0.30.00 V 30 V0240 V 30 V)s/stc(LPgef hi-0.70.1DR0.1DR-0.050.05DR05PL (cts/s)0900PL (cts/s)0700PL (cts/s)XBXB XBXBXBXBXBXBML BL TL5 µma chBNVGbXA XAXA XAXB−XB'XB'XB−XB−XB−XB'XB− XB−XB− XB−XB'abc-0.7XAXAXAXAXAXAFig. 1 | CrSBr field-effect device and spectral signatures of doping. a Opticalmicrograph of the few-layer CrSBr crystal, with crystal axes and layer numbersindicated (ML:monolayer, BL: bilayer, andTL: trilayer; dashed linesmark the crystalboundaries, the rectangle corresponds to the region in c). b Field-effect devicelayout with few-layer graphene top gate and contact (dark grey). The CrSBr layers(blue and red indicating spin polarization in antiferromagnetic order) are encap-sulated by two hBN flakes (light grey). c Differential reflectance (DR) map of theregion marked in a in the energy range of 1.3−1.4 eV (same color bar as f, h), withblue areas corresponding to strong exciton resonances (dotted lines mark the few-layer graphene contact, and black diamonds indicate the positions on mono-, bi-and trilayer where all data were acquired; the two rectangles indicate the regionsstudied in Fig. 4). d, eMonolayer DR and photoluminescence (PL) spectra at 0 and30V (top panels) and the corresponding sweeps of the gate voltage VG (bottompanels), respectively. f–i Same as d, e, but for bilayer (f, g) and trilayer (h, i). XA, XB,and X0B label neutral and X�B charged exciton transitions.Article https://doi.org/10.1038/s41467-024-49048-9Nature Communications |         (2024) 15:4735 2upon electrostatic doping in the FMmonolayer, with data in Fig. 1d, e.Due to complete spin polarization of the bands, a bound exciton-charge state can not form with spin-aligned electrons, and we onlyobserve a gradual red-shift of the XA resonancewith the gate voltage inFig. 1d, e, with amaximumshift of 7meV at 30 V. Even though couplingof electrostatic field and doping effects can not be ruled out in oursingle-gated device and could account in part for the shift via the Starkeffect, we observe clear signatures of doping in bi- and trilayer for thesame voltage range both in DR (Fig. 1f, h) and PL (Fig. 1g, i).Themost striking spectral features of layer charging in Fig. 1f–i arethepronouncedenergy shifts at elevatedpositive gate voltages around15 V, converting the spectrally narrow peaks XB with energy near1.370 eV into X�B peaks just below 1.350eV. The energy difference of19meV, as well as the blue-shift of the XB resonance upon doping, arereminiscent of negatively charged trions31,32 or Fermi-polarons33–37 inmonolayer transition-metal dichalcogenides, indicating enhancedCoulomb interactions due to reduced dielectric screening in the 2Dsemiconducting magnet. We assign the neutral exciton XB in Fig. 1f, h,with narrow absorption of ~3meV full-width at half-maximum line-width and negligible Stokes shift to the transition between the topvalence band ν and the higher-energy conduction subband c2, which isdipole-allowed for linear polarization along the b axis13 (Supplemen-tary Fig. 3 shows linearly polarized out-of-plane emission). The corre-sponding PL spectra in Fig. 1g, i stem from hot excitons, withincomplete relaxation of electron constituents from subband c2 to c1.In the trilayer, the pronounced spectral feature just below XB,labelled as X0B in Fig. 1h, i, deserves a separate discussion. The transi-tion, red-shiftedby 5.4meV fromXB, is strong inDRandclearly presentin PL, yet without signatures of doping. Our theoretical analysis (seeMethods) identifies the corresponding exciton as being localizedexclusively in themiddle layer, where enhanced screening changes theenergy of X0B excitons. Remarkably, the exciton shows no signature ofcharge-bound states (note the prevalence of its spectral features atvoltages above the XB to X�B cross-over in Fig. 1h, i). This observationindicates that excitons in the middle layer are not subjected to intra-layer charge. The top and bottom layers of the trilayer host field-induced electrons in their lowest-energy c1 states, downshifted by themagnetic layer interactions with respect to the c1 band of the middlelayer. We note that a second sample reproduces all discussed neutraland charged exciton transitions in mono-, bi-, and trilayers (see Sup-plementary Fig. 4).To elucidate the rich exciton multiplicity in bi- and trilayer crys-tals, we performed magneto-optical studies in magnetic fields alongthe c axis (perpendicular to the layers), and analyzed the respectiveexciton dispersions in the framework of the states introduced above.The data in Fig. 2a, b show the evolution of DR with magnetic field forthe neutral and charged bilayer at 0 and 30 V, respectively, with thecorresponding data for the trilayer shown in Fig. 2c, d. We first notethat all states involved exhibit symmetric energy red-shifts from 0Ttowards increasing absolute values of the magnetic field, before theylevel off beyond a saturation field of ~2 T13,18,38. This behavior can beunderstood by considering spin canting from the AF state at 0 T to theFM state at sufficiently high magnetic fields18,38, as indicated by thearrows in the top panels of Fig. 2a–d.In the neutral bilayerwith data in Fig. 2a, the energies of XA andXBreduceparabolically with the samedispersion to settle in the saturatedFM regime with a broader linewidth and nearly preserved contrast inDR. The same magneto-dispersion of both excitons is consistent withdifferent conduction bands and a shared valence band. In the electron-doped limit at 30 V of Fig. 2b, X�B exhibits a parabolic energy red-shiftsimilar to XB with the same saturation field, but the dispersion is flatterin the vicinity of 0 T. Themagneto-dispersions of XA, XB, and X�B in theneutral and charged trilayer (with data in Fig. 2c, d) are similar to thebilayer, whereas the curvature of the dispersion of X0B is twice as largeand unaffected by doping. The magneto-dispersions along the a axisreproduce these observations with a lower saturation field of 1 T (seeSupplementary Figs. 5 and 6).Such negative diamagnetic shifts of neutral and charged exitonsare highly unusual in conventional semiconductors39. They can beunderstood in the framework of our analysis, invoking interlayerexcitons with smaller binding energy and, consequently, higherabsolute energy40, in addition to intralayer excitons and their chargedcounterparts introduced above. With magnetic field along the c axiscausing gradual spin canting from b axis AF to c axis FM order, spin-conserving hole tunneling sets in to mix intra- and interlayer excitonstates. Our analysis (see Methods) shows in Fig. 2e that the magneto-1.301.351.40)Ve(ygrenE1.301.351.40)Ve(ygrenE-2 0 21.301.351.40Bc (T))Ve(ygrenE-2 0 2Bc (T)-2 0 21.301.351.40Bc (T))Ve(ygrenE-0.60.1ba c dDR-0.60.1DRfe g hXB XB0 V 30 V 0 V 30 VXA XAXB XB-2 0 2Bc (T)XB'XB− XB−XB'XB'XB−XBXAXB'XBXAXB−XBXAXBXAFig. 2 | Magneto-optical spectroscopy of neutral and charged bi- and trilayer inmagnetic field along the c axis. a, b Evolution of bilayer differential reflectance(DR) with magnetic field along the c axis (Bc) in the neutral and negatively chargedregime at 0 and 30 V, respectively. The top panels illustrate the spin orientation,where blue and red colors indicate antiferromagnetic order with opposite spins,while all other spin orientations are grey. c, d Same as a, b, but for the trilayer.e–h Calculated dispersions of the corresponding neutral and charged excitons inmagnetic field along the c axis.Article https://doi.org/10.1038/s41467-024-49048-9Nature Communications |         (2024) 15:4735 3dispersions of XA,B excitons can be represented for magnetic fieldsB <Bsat (with the saturation fieldBsat corresponding to the FMorder) asEA,BðBÞ= EA,Bð0Þ � tB2, with the fitting parameter t ≈ 2meV/T2 relatedto the interlayer hole tunneling and the energy splitting between theintralayer and interlayer excitons.Within the minimal model of Fermi-polarons (see Methods fordetails), where we account for the Fermi-sea mediated coupling ofintralayer excitons and trions36,37, the magneto-dispersion of X�B inFig. 2f is weaker: it contains an additional factor of EF=Etr, given by theratio of the Fermi energy EF to the trion binding energy Etr. WithEF = 10meV and Etr = 19 meV extracted from the data in Fig. 1, themodel predicts a slightly flatter trion dispersion than observed in theexperiment of Fig. 2b, possibly because of disregarded intra-interlayertrion coupling. The dispersions in the neutral and charged trilayer canbe understood along the same lines, as shown in Fig. 2g, h for the sameset of fit parameters, by taking into account that XB stems from theouter layers and X0B exclusively resides in the middle layer. The maindifference is that hole tunneling to both the top and bottom layers isnot suppressed, which results in E0BðBÞ≈ E0Bð0Þ � 2tB2 with twice aslarge curvature in the dispersion of X0B as compared to XA,B, in fullagreement with experimental data.The gradual spin canting transition along the c axis is contrastedby an abrupt metamagnetic spin-flip transition18,41 along the b axisparallel to the magnetic moment. At a critical magnetic field near0.17 T, the spins flip from AF to FM order in both the neutral andcharged bilayer, when swept upward from negative to positive valuesas in Fig. 3a, b. Unlike inmagneto-dispersions along the hard c axis, thecritical field along the easy axis depends hysteretically on the sweepdirection (Fig. 3c), which is indicative of a first-order magnetic transi-tion well known from optical spectroscopy18 and magneto-transportstudies12,24,25.The critical field is determined by the spin-lattice energy, which inturn is governed by the interplay between the interlayer exchangeenergy J and magnetic field interaction24. From the data, we estimatethe spin-lattice energy for AF and FM states as a function of the mag-netic field, as shown in Fig. 3d, assuming the crossing points betweenFM and AF states at the center of the hysteresis (see Methods fordetails). In the upward direction and with initialization in the FM state-20 -10 0 101.361.381.40)Ve(ygrenEVG (V)-20 -10 0 101.361.381.40)Ve(ygrenEVG (V)-0.3 0.0 0.3-6-4-202ygreneecittalnipSfos tin uniJBb (T)-0.3 0.0 0.3-6-4-202ygreneecittalnipSfostinuniJBb (T)0.10 0.15 0.20ygrenE)kcit/Vem05(Bb (T)0.2 0.3ygrenE)kcit/Vem05(Bb (T)-0.3 0.0 0.31.301.351.40)Ve(ygrenEBb (T)-0.3 0.0 0.3Bb (T)-0.3 0.0 0.31.301.351.40)Ve(ygrenEBb (T)-0.3 0.0 0.3Bb (T)-20 0 200.10.2/  FM-AF  / AF-FM VG (V)B b (T)-0.60.1a b g hDRc-20 0 200.20.3AF-mixed mixed-AFAF-FM    FM-AFB b (T)VG (V)i j-0.60.1DRXBXB0 V 30 V 0 V 30 V203025151050-5-10-15-20-25VG(V)203025151050-5-10-15-20-25VG(V)XA XAXBXB− XB−XB'XB'XB0.165 TXB'defkl0.160 TXB1.35 eV 1.35 eVXB−XB /XB−XB /Fig. 3 | Effect of doping on excitons andmetamagnetic transitions inmagneticfield along the b axis. a, b Differential reflectance (DR) as a function of increasingmagnetic field along the b axis (Bb) at 0 and 30V, respectively. The top panelsindicate the bilayer spin orientation. c Energy of XB (brown/orange) and X�B (dark/light purple) at different gate voltages for upward and downward magnetic fieldsweep directions indicated by right and left arrows in the corresponding colors,respectively. The hysteresis loops at each gate voltage VG are offset by 50meV forclarity; note that both XB and X�B coexist at 15 and 20V. d Calculated bilayer spinlattice energy as a function of Bb for the antiferromagnetic (AF, black line) andferromagnetic (FM, blue and red lines) phases indicated by the arrows. The brownline shows theupward sweepwith jumpscorresponding to the experimental data ina. e Evolution of the critical magnetic field of the AF-FM metamagnetic transitionwith gate voltage. f Doping-induced metamagnetic switching from AF to FM at amagnetic field of 0.165 T, with arrows indicating spin orientations. g–l Same asa–f, but for the trilayer. iHysteresis loops of X0B. j Spin lattice energy for trilayer AF(solid black), FM (solid blue/red), and mixed (dashed blue/red) phases. k Criticalmagnetic fields of the metamagnetic transitions observed in the trilayer. l Doping-induced switching in the trilayer from AF to mixed state at a magnetic field of0.160 T. Blue and red colored arrows in a, b, d, g, h, j, l illustrate layers with left andright spin orientation, respectively.Article https://doi.org/10.1038/s41467-024-49048-9Nature Communications |         (2024) 15:4735 4at a negative magnetic field, the spins flip from FM to AF order andback to FM, as illustrated by the brown trace in Fig. 3d extracted fromthe data in Fig. 3a. The hysteretic behavior near AF-FM degeneracy isresponsible for abrupt jumps in the brown trace of Fig. 3d. Crucially,our device allows to tune the criticalfieldof the spin-flip transitionwithgate voltage, as evident from the data in Fig. 3c, e. This effect, alsoobserved in bilayer CrI39,10, is consistent with an inverse scaling of theinterlayer exchange energy with doping, which reduces the criticalfield upon negative doping. According to the Kugel-Khomskii model,the interlayer exchange energy is inversely proportional to the on-siteCoulomb interaction42, which in turn is proportional to the electrondensity. This implies that the metamagnetic AF-FM transition near thecritical field can be equivalently induced by doping, as demonstratedin Fig. 3f.The neutral and charged trilayer exhibit a similarly abrupt AF-FMtransition as the bilayer, however, at larger critical fields near 0.32 T(Fig. 3g, h). Surprisingly, we also observe an additional transition intoan intermediate or mixed state near 0.16 T, which is stable for 30mTbefore switching back to AF order. In this regime, the X0B resonancefirst jumps to lower energy (still above its energy in the FM state) andthen back, while the energy of XB remains unaffected. This intricatesignature corresponds to mixed order in the trilayer, resulting in twoadjacent layers with FM and AF order illustrated in the top panelof Fig. 3g.The corresponding spin-lattice energies for AF, FM, and mixedstates shown in Fig. 3j provide some intuition for the spin-flip transi-tions as a function of the magnetic field. In the upward direction, withinitialization in the FM state at a negative magnetic field, the trilayer isin an energetically favorable FM state (solid blue line). With increasingmagnetic field, the spins of the middle layer flip to AF order, which ispreserved beyond 0T as a metastable state, where its time-reversalcounterpart would be energetically more favorable. An energy-reducing transition, however, would require the simultaneous spin-flip in all three layers. With increasing field, the spin-lattice energy ofthe AF state crosses the FM and themixed states (solid and dashed redline, respectively), where the trilayer transitions into a metastableFig. 4 | Optical imaging of magnetism in bi- and trilayer CrSBr. a Raster-scanmaps of a bilayer (BL) region (left rectangle in Fig. 1c; the white areas delimit thecrystal top edge) with bias at 0 V for five consecutive magnetic fields along the baxis, with false-color contrast given by the energy of the XB transition in differentialreflectance (DR) with corresponding antiferromagnetic (AF, purple) and ferro-magnetic (FM, orange) phases indicated on the right of the color bar. b Same asa, but for a constant field of 168mT and five different gate voltages. c, d Equivalentmaps of the trilayer (TL) region (right rectangle in Fig. 1c, with the dashed anddotted lines indicating the bi- to trilayer boundary and the edge of the graphenecontact, respectively; grey pixels correspond to vanishing exciton DR due to localdisorder) for magnetic fields across the metamagnetic one-flip transition (c) andvoltage-controlled magnetism at a constant field of 156mT (d). In all panels, thepixel color derives from the energies of XB in the bilayer and X0B in the trilayer,respectively, and the corresponding magnetic states are indicated on the right ofthe color bar, with blue and red arrows representing layers with left and right spinorientation, respectively.Article https://doi.org/10.1038/s41467-024-49048-9Nature Communications |         (2024) 15:4735 5mixed state. Eventually, as this state becomes less favorable withincreasing magnetic field, a double spin-flip occurs into the energeti-cally favorable AF order (solid black line) and finally into the FM state(solid red line). Overall, this intricate sequence of spin-flips in the tri-layer with magnetic field is driven by the minimization of the energycosts for spin-flips inmagnetically ordered layers. As in the bilayer, thecritical fields of the respective transitions in the trilayer depend on thecharge doping, as evident from Fig. 3i, k, l for the AF-FM, FM-AF, andAF-mixed transitions, shifting towards lower values with increasingdoping. Analogously to the bilayer, the metamagnetic transitions canalso be induced by doping, as shown explicitly for the AF-mixed statetransition in Fig. 3l.With theobservation that the exciton energy is correlatedwith theunderlying magnetic order as in Figs. 2 and 3, the exciton transitionscan be employed for all-optical detection of local magnetic order. Inthe following, we demonstrate this feature bymapping out domains ofmagnetic phases and their sensitivity to doping near metamagnetictransitions. We start out with the bilayer, initialized in its AF groundstate at zeromagneticfield and zero doping (leftmost panel of Fig. 4a),imaged by hyperspectral raster-scan DR mapping with purple andorange colors representing AF and FM domains, respectively. Withincreasing field, the AF domain shrinks, and the FM domain emergesnear the critical field at the top edge of the crystal (maps of Fig. 4a atconsecutive fields of 164, 168, and 172mT), until full coverage isreached at 176mT (rightmost panel of Fig. 4a), with the bottom leftcorner next to the monolayer flipping last. Remarkably, the char-acteristic local nucleation and propagation of FM domains can beinduced by doping, as highlighted for five increasing gate voltages inFig. 4b at a constant field of 168 mT.Weuse the technique to visualize themagnetic transition from theAF to themixed state in Fig. 4c (see also Supplementary Fig. 7 for large-areamapping of all trilayer transitions).With increasingmagneticfield,the mixed state nucleates at the edge of the few-layer graphene con-tact and spreads along the a axis (x direction). We note that the AF-mixed transition in the trilayer and the AF-FM transition in the adjacentbilayer happen at the same field within the resolution limit, whichindicates that the flip in the trilayer is induced by intralayer exchangecoupling to the proximal bilayer. Remarkably, the trilayer mixed stateis clearly discerned from the AF state despite nominally identicalmagnetization, which renders their discrimination difficult with con-ventional methods12,16,18. As in the bilayer, related phenomena of phasetransitions can be induced by doping and detected all-optically, asdemonstrated in Fig. 4d.Our work identifies few-layer CrSBr as an intriguing platform tostudy and control excitons and magnetism with electrostatic doping.The rich phenomena observed are intertwined, providing a route tonovel devices involving not only coupled electric and magnetic phe-nomena, but also adding optical means to control and exploit mag-netism via neutral and charged excitons. The aspects highlighted inour work indicate the existence of rich magnetic phases in trilayercrystals beyond just AF or FM order, which can potentially be utilizedin novel devices for spintronics and magnetic memories featuringlayer-selective initialization, control, and read-out by combined elec-trostatic and optical means. Finally, the features cooperatively man-ifest optical imaging of magnetic order in CrSBr as an efficient andsensitive local probe of magnetic domains, providing insight com-plementary to other techniques43–45.MethodsCrSBr synthesisCrSBr bulk single crystals were synthesized by chemical vapor trans-portmethod using chromium (99.99%, −60mesh, Chemsavers), sulfur(99.9999%, 1−6mm Wuhan Xinrong New Material Co. Ltd), and bro-mine (99.9999%, Sigma Aldrich), combined with a stoichiometry of1:1:1, sealed in a quartz tube under high vacuum, and then placed into atwo-zone tube furnace. The material was pre-reacted in an ampoule at700 °C for 25 h until most of the bromine was reacted. During thisprocedure one part of the ampoule was kept under 200 °C to avoidpressure disruption of the ampoule. The crystal growth by the vaportransport method was performed in a two-zone horizontal furnace.First, the source and growth ends were kept at 800 and 900 °C,respectively. After 25 h, the temperature gradient was reversed, andthe temperature at the hot end was gradually increased from 880 to930 °C for an 8-day period while the growth zone was kept at 800 °C.The high-quality CrSBr single crystals were removed from the ampoulein an Ar glovebox.Field-effect devicesCrSBr, few-layer graphene, andhBN (NIMS)flakeswere exfoliated frombulk single crystals at ambient conditions onto SiO2/Si substrates.Suitable CrSBr flakes were identified by optical contrast and atomicforce microscopy. A PDMS/PC stamp was used to sequentially pick upthe hBN, few-layer graphene, and CrSBr layers employing the dry-transfer method28. Poly-(Bisphenol A-carbonate) pellets (SigmaAldrich) were dissolved in chloroform with a weight ratio of 6. Themixturewas stirred overnight at room temperature at 500 rpmusing amagneton bar. The well-dissolved PC film was mounted on a PDMSdomeon a glass slide. First, the top hBN layerwith a thickness of 64 nmwas picked up with the stamp, followed by the CrSBr flake, a few-layergraphene contact layer, and 84 nm bottom hBN. The stack wasreleased at a temperature of 190 °C onto a pre-patterned SiO2/Si targetsubstrate with Ti/Au metal pads, then soaked in chloroform solutionfor 2 min to remove PC residues and cleaned by acetone and iso-propanol. Next, the top gate few-layer graphene flake was picked upand placed on top of the heterostack, followed by another cleaningstep. The pick-up temperature for CrSBr was around 110 °C, for theother flakes ~100 °C. The sample was annealed at 200 °C under ultra-high vacuum for 15 h. Then, Ti/Au contact stripes were fabricated toconnect the few-layer graphene gates to the contact pads using laserlithography and electron-beam evaporation. The second sample wasfabricated in the same way but using hBN flakes with 28.5 and 26 nmfor the topandbottomencapsulating layers, respectively. Electrostaticdopingwas controlled by applying a gate voltagewith aprogrammableDC-source (Yokogawa7651) between the gate and the groundedcontact layer.Magneto-optical spectroscopyCryogenic PL and DR spectroscopy were performed in back-scatteringgeometrywith a lab-built confocalmicroscope in a close-cycle cryostat(attocube systems, attoDRY1000)with a base temperatureof 3.2 K anda solenoid with magnetic fields of up to ±9 T. Magnetic field sweepsalong the b axis in upward (downward) direction were performed byinitializing the magnet at −500mT (500mT) and then ramping to thetarget field. We estimate the magnetic field inaccuracy to 2mT forsweeps in steps of 2mT, as deduced from repeated measurementsunder nominally identical conditions. Measurements with magneticfield along the c axis were conducted by positioning the sample withrespect to a low-temperature apochromatic objective (attocube sys-tems, LT-APO/NIR/0.81) with piezo-units (attocube systems, ANPx101,ANPz101, and ANSxy100). For measurements along the b and a axes, acustom-built Voigt adapter was used, consisting of a mirror mountedat 45∘ and an aspheric lens (Geltech 350330) glued onto a Ti part. Thesample holder was mounted on an L-shaped adapter with the crystal-lographicbora axis of the sample alignedwith the axis of the solenoid.The L-shaped adapter was mounted on piezo-units (attocube systems,ANPx101, ANPz101, and ANSxyz100) for nanopositioning and scan-ning. Momentum-space imaging in 4f and telescope configurationemployed four achromatic doublet lenses (Edmund Optics, VIS-NIR)and was performed in an attoDRY800 close-cycle cryostat with 4 Kbase temperature.Article https://doi.org/10.1038/s41467-024-49048-9Nature Communications |         (2024) 15:4735 6In experiments on sample 1, PL was excited at 870 nmand 100μWwith a Ti:sapphire laser (Coherent,Mira) in continuous-wavemode andSemrock tunable short-pass and long-pass filters were used (887 nmVersaChromeEdge) in excitation and detection. DR, defined asDR = (R−R0)/R0, where R was the reflectance from the sample and R0 was thereference reflectance on the nearby substrate with hBN, was recordedwith a Tungsten-Halogen lamp (Thorlabs, SLS201L or Ocean Insight,HL-2000-HP). The signal was dispersed by a monochromator (RoperScientific, Acton SpectraPro 300i or Acton SP250 or Teledyne Prince-ton Instruments, IsoPlane SCT320) with a 300 grooves/mm gratingand detected by a Peltier-cooled (Andor, iDus 416 or Teledyne Prin-ceton Instruments, PIXIS 1024) or liquid nitrogen-cooled (Spec-10:100BR) charge-coupled device. A set of linear polarizers (Thorlabs,LPVIS), half- or quarter-waveplates (B. Halle, 310−1100 nm achromatic)mounted on piezo-rotators (attocube systems, ANR240) were used tocontrol the polarization in excitation and detection. For sample 2,excitation and detection were circularly polarized, and PL was excitedat 800 nm and 100 μW with a Ti:sapphire laser (SolsTiS, M Squared)with 842 nm short-pass (Semrock 842/SP BrightLine HC Short-passFilter) and 808 nm long-pass (Semrock LP Edge Basic Long-pass Filter)filters in excitation and detection.Fermi-polaron modelWe develop the Fermi-polaron model for multilayer CrSBr based onthe approach used for 2D semiconductors35–37, taking into account thespin-polarized band structure of CrSBr. We recall that bothmonolayerand multilayer CrSBr are described by a centrosymmetric D2h pointsymmetry group. According toRef.13, in the set of axeswith z∥c (normalto the monolayer, magnetic hard axis), y∥b (magnetic easy axis), andx∥a (magnetic intermediate axis) the orbital Bloch function of thetopmost valence band v (we account for a single valence band v owingto its significant separation from the lower-lying bands) in the mono-layer is transformed according to the B3g (or Γ+4 , i.e., as yz) irreduciblerepresentation, and for two nearest conduction bands c1 and c2according to Ag (Γ+1 as x2 + y2 + z2) and B1u (Γ�3 as z), respectively.Intralayer FM spin-spin interactions result in the complete spinpolarization of the Bloch states with the spins aligned along the b (y)axis in the monolayer. In multilayers, spins are aligned anti-ferromagnetically along the positive and negative directions of the baxis in neighboring layers. Optical transition v↔c1 is forbidden in thedipole approximation and the transition v↔c2 is allowed for lightpolarized along the easy axis b∥y. Note that the predicted order of c1and c2 bands varies in the literature, cf. Refs. 13,18,46, due to the smallc1−c2 energy splitting and, correspondingly, its strong dependence onthe ab initio and model parameters.The lowest-energy optical transition in the monolayer, labeled asXA is linearly polarized along the b∥y axis, broad in absorption and faintin PL, without a sizable Stokes shift. The latter feature indicates amomentum-direct exciton transition, which, however, should benominally forbidden by dipolar selection rules. We speculate that dueto the asymmetry of the structure (inequivalence of z→−z) enhancedbythe large surface-to-volume ratio in the monolayer, the dipolar selec-tion rules are compromised and the v↔c1 transition becomes weaklyallowed. XA also prevails in the spectra of the bi- and trilayer, where itsfeatures in absorption and PL are contrasted by the much more pro-nounced and spectrally narrow resonances of XB, which we assign tothe dipole-allowed v↔c2 transition with linear polarization along theb∥y axis.With this understanding, we consider the manifold of relevantneutral and negatively charged exciton states as in the SupplementaryFig. 2. We assume that the difference of the binding energies of theintra- and interlayer excitons exceeds by far the c1−c2 conduction bandsplitting. We also neglect bound charge complexes of interlayer exci-tons (negative interlayer trions) due to much smaller bindingenergies40. Furthermore, we neglect interlayer electron and holetunneling at zero magnetic field where single-particle tunnelingbetween the same bands is spin-forbidden, while at finite fields thetunneling c1↔c2 is suppressed by the conduction band splitting. Atfinitemagneticfield along the c axis, the spins in the neighboring layersare canted, and hole tunneling between the layers becomes allowed18.In this framework, the bilayer systemHamiltonian breaks into twoidentical blocks describing electrons either in the top or in the bottomlayer:HBL =H 00 H� �: ð1ÞEach block accounts for both vc1 intra- and interlayer (A) excitons andvc2 intra- and interlayer (B) excitons, as well as their coupling with thecorresponding Fermi-sea in the bottom conduction subband c1:H =EA sB 0 0 0sB EIA 0 0 00 0 EB sBffiffiffiffiffiffiffiffiffiffiffiEtrEFp0 0 sB EIB 00 0ffiffiffiffiffiffiffiffiffiffiffiEtrEFp0 EB � Etr0BBBBBB@1CCCCCCA, ð2Þwhere EA(B) are the bare energies of A(B)-excitons (in absence of tun-neling and electron doping); EIA(IB) = EA(B) +Δ are the energies of theinterlayer A(B)-excitons with the difference in the binding energies Δ.The coefficient s quantifies the magneto-induced interlayer holetunneling; EF is the Fermi level and Etr is the trion binding energy. TheHamiltonian in Eq. (2) corresponds to the non-self-consistent approx-imation for the exciton-electron scattering matrix element, and we setthe couplingparameter to beffiffiffiffiffiffiffiffiffiffiffiEtrEFp, omitting anumerical coefficient ~1as well as the Fermi-sea effect on the trion binding energy47.In the weak doping regime (EF ≪ Etr) and moderate magneticfields (∣sB∣≪Δ), we obtain the energies of the A-excitons (decoupledfrom the Fermi-sea) and Fermi-polarons formed by B-excitons in theform:EAðBÞ≈ EA � tB2, ð3aÞERPB ðB,EFÞ≈ EB � tB2 + EF , ð3bÞEAPB ðB,EFÞ≈ EB � Etr � EF �EFΔEtrðΔ+ EtrÞtB2, ð3cÞwith t = s2/Δ. In this regime, the A-exciton and B-exciton (repulsivepolaron, RP) have the same magneto-dispersion, while the attractiveFermi-polaron (AP) has a smaller dispersion in magnetic field due tothe additional term EF=Etr≪1. In the main text we use the nota-tion EBðBÞ= ERPB ðB,0Þ.Due to a sizable spread in the calculated conduction band split-ting c1–c213,18, we take EA,B as two fitting parameters. By fitting theexperimental data to the eigenvalues of the Hamiltonian in Eq. (2), weobtain EA = 1344meV, EB = 1370meV, t = 2.2meV/T2, Bsat = 1.9 T, Etr = 19meV, and EF = 10meV. In Fig. 2e, f, we show the eigenenergies of XA, XB,and X�B in the neutral and negatively charged regime, respectively.In the trilayer, we also assume suppressed interlayer tunneling ofelectrons as well as the exciton as a whole quasiparticle. The relevantstates are shown in Supplementary Fig. 2c, and the Hamiltonian iswritten as:HTL =H 0 00 H0 00 0 H0B@1CA, ð4ÞArticle https://doi.org/10.1038/s41467-024-49048-9Nature Communications |         (2024) 15:4735 7where the blocks of the states related to the top pair of layers and thebottom pair of layers are identical to the bilayer Hamiltonian in Eq. (2),while the Hamiltonian H0 is different, describing electrons in themiddle layer.We assume that the states in the middle layer have a differentenergy due to a different dielectric environment as compared to theouter layers, and label such excitons with a prime (see SupplementaryFig. 2c). Based on experimental observations (Figs. 1h and 2c) that (i)X0B has no charge-bound state upon doping, and (ii) no clear signatureof X0A is observed, we disregard these states in our model (Supple-mentary Fig. 2c). Consequently, themiddle blockH0 in theHamiltonianof Eq. (4) reduces to:H0 =E 0B sB sBsB E 0IB 0sB 0 E 0IB0B@1CA, ð5Þwhere E 0IB = E0B +Δ is the energy of the interlayer B-excitons in themiddle layer (note the multiplicity of two for such states).Thus, the spectrum of the trilayer is a superposition of the bilayerspectrum (Eqs. (3)) and the spectrum of the middle layer that for∣sB∣≪Δ approximates to:E0BðBÞ≈ E 0B � 2tB2: ð6ÞWe note that the curvature of its dispersion in magnetic field istwice that of the bilayer excitons described by Eq. (3b), as the twointerlayer excitons couplewith the intralayer exciton. By extracting thesplitting at 0 T (AF state) in the neutral regime (as in Figs. 1h and 2c)wedetermine E 0B = 1365 meV. The eigenenergies of XA, XB, X0B, and X�B inthe neutral and negatively charged regimes are shown in Fig. 2g, h,respectively.Estimation of the spin lattice energyTo understand the spin-flip transitions in magnetic field along the baxis as in Fig. 3a, g, we estimate the spin-lattice energy by the followingHamiltonians for bi- and trilayers42:HðsÞBL = Js1s2 +μBbðs1 + s2Þ, ð7ÞHðsÞTL = Jðs1s2 + s2s3Þ+μBbðs1 + s2 + s3Þ, ð8Þwhere Bb is the magnetic field along the b axis, s1,2,3 = ± 1 are the spinorientations along the b axis for the respective layers, J is the positiveinterlayer exchange between neighboring layers, and μ is themagneticdipole moment of one layer. We assume that each layer exhibitsintralayer FMorder and neglect the intralayer exchange energies in theHamiltonians of Eq. (7) and (8). The calculations are shown in Fig. 3d, jfor bi- and trilayer, respectively.Data availabilityThe data that support the findings of this study are available at https://doi.org/10.5282/ubm/data.45048.Code availabilityThe codes that support the findings of this study are available from thecorresponding authors upon request.References1. Gong, C. et al. Discovery of intrinsic ferromagnetism in two-dimensional van der Waals crystals. Nature 546, 265 (2017).2. Huang,B. et al. Layer-dependent ferromagnetism in a vanderWaalscrystal down to the monolayer limit. Nature 546, 270 (2017).3. Ghazaryan, D. et al. Magnon-assisted tunnelling in van der Waalsheterostructures based on CrBr3. Nat. Electron. 1, 344 (2018).4. Cenker, J. et al. Direct observation of two-dimensional magnons inatomically thin CrI3. Nat. Phys. 17, 20 (2021).5. Seyler, K. L. et al. Valley manipulation by optically tuning themagnetic proximity effect inWSe2/CrI3 heterostructures.Nano Lett.18, 3823 (2018).6. Lyons, T. P. et al. 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F.T.-V. acknowledgesfunding from the Munich Center for Quantum Science and Technology(MCQST) and the EuropeanUnion’s Framework Programme for Researchand Innovation Horizon Europe under the Marie Skłodowska-CurieActions grant agreement no. 101058981. A.R. acknowledges funding bythe Bavarian Hightech Agenda within the Munich Quantum Valley doc-toral fellowship program. A.P. was supported by theOnassis FoundationScholarship ID: F ZS 045-1/2022-2023 and Bodossaki Foundation Scho-larship. K.W. and T.T. acknowledge support from JSPS KAKENHI (grantNo. 19H05790, 20H00354 and 21H05233). P.M. acknowledges financialsupport from the ERC consolidator grant project QS2DM and SNF pro-ject no. 188521. Theoretical analysis by M.M.G. was supported by RSFproject 23-12-00142. Z.S.was supportedby theERC-CZprogram (projectLL2101) from the Ministry of Education, Youth and Sports (MEYS). A.S.B.acknowledges funding by the European Union’s Framework Programmefor Research and Innovation Horizon 2020 under the Marie Skłodowska-Curie grant agreement no. 754388 (LMUResearchFellows) and fromLMUexcellent, fundedby the FederalMinistry of Education andResearch(BMBF) and the FreeState of Bavaria under the ExcellenceStrategyof theGerman Federal Government and the Länder. A.H. acknowledgesfunding by the Bavarian Hightech Agenda within the EQAP project.Author contributionsK.M., A.P., and Z.S. synthesized CrSBr crystals, and K.W. and T.T. pro-vided hBN crystals. H.P.G.N. fabricated the field-effect devices. F.T.-V.,H.P.G.N., and A.R. performed the experiments. A.S.B. developed thetheoretical model with support fromM.M.G. F.T.-V., H.P.G.N., A.R., P.M.,M.M.G., A.S.B., and A.H. analyzed and discussed the data. F.T.-V.,M.M.G., A.S.B., and A.H. wrote the manuscript. All authors commentedon the manuscript.FundingOpen Access funding enabled and organized by Projekt DEAL.Competing interestsThe authors declare no competing interests.Additional informationSupplementary information The online version containssupplementary material available athttps://doi.org/10.1038/s41467-024-49048-9.Correspondence and requests for materials should be addressed toFarsane Tabataba-Vakili, Anvar S. Baimuratov or Alexander Högele.Peer review information Nature Communications thanks ShengweiJiang, and the other, anonymous, reviewer(s) for their contribution to thepeer review of this work. 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To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.© The Author(s) 2024Article https://doi.org/10.1038/s41467-024-49048-9Nature Communications |         (2024) 15:4735 9https://arxiv.org/abs/1310.6120https://doi.org/10.5282/ubm/data.450https://doi.org/10.1038/s41467-024-49048-9http://www.nature.com/reprintshttp://creativecommons.org/licenses/by/4.0/http://creativecommons.org/licenses/by/4.0/ Doping-control of excitons and magnetism in few-layer�CrSBr Results and discussion Methods CrSBr synthesis Field-effect devices Magneto-optical spectroscopy Fermi-polaron�model Estimation of the spin lattice�energy Data availability Code availability References Acknowledgements Author contributions Funding Competing interests Additional information