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Dmitry Lebedev, J. Tyler Gish, Ethan S. Garvey, Thomas W. Song, Qunfei Zhou, Luqing Wang, [Kenji Watanabe](https://orcid.org/0000-0003-3701-8119), [Takashi Taniguchi](https://orcid.org/0000-0002-1467-3105), Maria K. Chan, Pierre Darancet, Nathaniel P. Stern, Vinod K. Sangwan, [Mark C. Hersam](https://orcid.org/0000-0003-4120-1426)

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[Photocurrent Spectroscopy of Dark Magnetic Excitons in 2D Multiferroic NiI<sub>2</sub>](https://mdr.nims.go.jp/datasets/b1d70145-1021-47ae-88bb-19bc27210896)

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Photocurrent Spectroscopy of Dark Magnetic Excitons in 2D Multiferroic NiI2RESEARCH ARTICLEwww.advancedscience.comPhotocurrent Spectroscopy of Dark Magnetic Excitons in 2DMultiferroic NiI2Dmitry Lebedev, J. Tyler Gish, Ethan S. Garvey, Thomas W. Song, Qunfei Zhou,Luqing Wang, Kenji Watanabe, Takashi Taniguchi, Maria K. Chan, Pierre Darancet,Nathaniel P. Stern, Vinod K. Sangwan,* and Mark C. Hersam*Two-dimensional (2D) antiferromagnetic (AFM) semiconductors arepromising components of opto-spintronic devices due to terahertz operationfrequencies and minimal interactions with stray fields. However, the lack ofnet magnetization significantly limits the number of experimental techniquesavailable to study the relationship between magnetic order andsemiconducting properties. Here, they demonstrate conditions under whichphotocurrent spectroscopy can be employed to study many-body magneticexcitons in the 2D AFM semiconductor NiI2. The use of photocurrentspectroscopy enables the detection of optically dark magnetic excitons downto bilayer thickness, revealing a high degree of linear polarization that iscoupled to the underlying helical AFM order of NiI2. In addition to probing thecoupling between magnetic order and dark excitons, this work providesstrong evidence for the multiferroicity of NiI2 down to bilayer thickness, thusdemonstrating the utility of photocurrent spectroscopy for revealing subtleopto-spintronic phenomena in the atomically thin limit.D. Lebedev, J. T. Gish, T. W. Song, V. K. Sangwan, M. C. HersamDepartment of Materials Science and EngineeringNorthwestern UniversityEvanston, IL 60208, USAE-mail: vinod.sangwan@northwestern.edu;m-hersam@northwestern.eduE. S. Garvey, N. P. SternDepartment of Physics and AstronomyNorthwestern UniversityEvanston, IL 60208, USAQ. Zhou, L. Wang, M. K. Chan, P. DarancetCenter for Nanoscale MaterialsArgonne National Laboratory9700 South Cass Avenue, Lemont, IL 60439, USAQ. Zhou, L. Wang, M. K. Chan, P. DarancetNorthwestern-Argonne Institute of Science and Engineering2205 Tech Drive, Evanston, IL 60208, USAThe ORCID identification number(s) for the author(s) of this articlecan be found under https://doi.org/10.1002/advs.202407862© 2024 The Author(s). Advanced Science published by Wiley-VCHGmbH. This is an open access article under the terms of the CreativeCommons Attribution License, which permits use, distribution andreproduction in any medium, provided the original work is properly cited.DOI: 10.1002/advs.2024078621. IntroductionThe coupling between magnetic order andoptically excited states, such as excitons,has become a central topic of researchfor van der Waals two-dimensional (2D)magnets.[1] This coupling allows magneticproperties to be probed by studying exci-tons, which provides opportunities beyondtraditional methods such as magnetome-try or diffraction-based tools. E.g., photo-luminescence spectroscopy of NiPS3 hasrevealed ultranarrow emission (linewidthsless than 0.4 meV) with a high degreeof linear polarization.[2] This emission isassociated with coherent many-body ex-citons that are entangled with antiferro-magnetic (AFM) order.[2a] In this manner,photoluminescence measurements have al-lowed investigation of the magnetic prop-erties of NiPS3, such as the orientationK. WatanabeResearch Center for Functional MaterialsNational Institute for Materials Science1-1 Namiki, Tsukuba 305-0044, JapanT. TaniguchiInternational Center for Materials NanoarchitectonicsNational Institute for Materials Science1-1 Namiki, Tsukuba 305-0044, JapanM. C. HersamDepartment of ChemistryNorthwestern UniversityEvanston, IL 60208, USAM. C. HersamDepartment of Electrical and Computer EngineeringNorthwestern UniversityEvanston, IL 60208, USAAdv. Sci. 2024, 11, 2407862 2407862 (1 of 8) © 2024 The Author(s). Advanced Science published by Wiley-VCH GmbHhttp://www.advancedscience.commailto:vinod.sangwan@northwestern.edumailto:m-hersam@northwestern.eduhttps://doi.org/10.1002/advs.202407862http://creativecommons.org/licenses/by/4.0/http://creativecommons.org/licenses/by/4.0/http://crossmark.crossref.org/dialog/?doi=10.1002%2Fadvs.202407862&domain=pdf&date_stamp=2024-08-09www.advancedsciencenews.com www.advancedscience.comFigure 1. Crystal and magnetic structures, device architecture, and photocurrent spectroscopy of NiI2. a) Crystal structure of NiI2. The schematic of theground state helical magnetic order, viewed along [110] direction (b) and [001] direction (c). The spins are perpendicular to the propagation vector Q(0.138a*,0,1.457c*). The view along [001] shows in-plane component of Q and the direction of electric polarization P along the two-fold rotation axis.d) Optical micrograph of a FET device fabricated from a bulk NiI2 flake. e) Schematic of the photocurrent spectroscopy measurement on the NiI2 FETdevice. f) Photocurrent spectrum of bulk NiI2 (black curve) recorded at 7 K, which shows sub-bandgap transitions, including the magnetic exciton.of the Néel vector and critical exponents that characterize the spindimensionality class.[2b] In addition, the interplay between exci-tons and magnetic order allows for magnetic field control over ex-citonic emission. For the aforementioned NiPS3, the linear polar-ization angle of photoluminescence has been controlled throughthe application of an external magnetic field.[3] Another 2D mag-netically ordered semiconductor, CrSBr, has exhibited stronglycoherent exciton-magnon coupling, which can be tuned by theapplication of strain or an external magnetic field.[4]Despite these demonstrations, studies exploring the cou-pling of excitons with magnetic order in the atomically thinlimit remain scarce, primarily due to the limited number of2D magnetically ordered semiconductors, most of which orderantiferromagnetically.[1b,c] While AFM materials are more ro-bust against external parasitic magnetic fields and enable higheroperating frequencies compared to ferromagnetic (FM) mate-rials, their lack of net magnetization limits options for detect-ing and controlling AFM order.[1a,d] NiI2, a recently discoveredgate-tunable 2D van der Waals magnetic semiconductor,[5] hasa helical AFM ground state below the second Néel tempera-ture TN2 ≈ 59 K (TN1 ≈ 76 K). The helix has a propagationvector Q (0.138a*,0,1.457c*) such that the spins make an an-gle of ≈55° with the [001] direction (Figure 1a–c).[6] The emerg-ing helical magnetic order at the TN2 transition breaks inver-sion symmetry and drives in-plane ferroelectricity due to strongDzyaloshinskii-Moriya interactions, making NiI2 a multiferroicmaterial (Figure 1c).[7] Although early reports suggested thatthis multiferroicity persists down to monolayer thickness,[7a] re-cent studies have concluded that multiferroicity may only persistdown to bilayer thickness.[8]Recent absorption spectroscopy and resonant inelastic X-rayscattering (RIXS) studies detected an excitonic peak in bulk NiI2crystals at an energy of 1.384 eV with a linewidth as narrowas 5 meV.[9] This peak showed a small degree of linear polar-ization (<0.2) and by optical absorption measurements disap-peared above TN2, which suggests that it is coupled to the un-derlying magnetic order of NiI2. However, unlike NiPS3, mag-netic excitons in NiI2 are dark with no observable photolumines-cence, which has hindered studies of these magnetic excitons infew-layer 2D NiI2 samples. Moreover, domains and defects (e.g.,stacking faults) likely result in the emergence of multiple spinhelix propagation directions coexisting within a bulk crystal, thusfurther complicating the study of correlations between the polar-ization of excitons and magnetic order NiI2.Here, we employ photocurrent spectroscopy to study the darkquantum-entangled excitons in the 2D AFM semiconductor NiI2down to bilayer thickness. Although photocurrent spectroscopyhas been previously used to study excited states in 2D semicon-Adv. Sci. 2024, 11, 2407862 2407862 (2 of 8) © 2024 The Author(s). Advanced Science published by Wiley-VCH GmbH 21983844, 2024, 38, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/advs.202407862 by National Institute For, Wiley Online Library on [16/10/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons Licensehttp://www.advancedsciencenews.comhttp://www.advancedscience.comwww.advancedsciencenews.com www.advancedscience.comductors [10] and light helicity detectors have been realized us-ing tunneling photocurrent measurements of 2D magneticallyordered CrI3,[11] photocurrent spectroscopy has not yet been ap-plied to 2D AFM semiconductors due to limited electrical con-ductivity at the cryogenic temperatures where magnetic order isestablished. By leveraging recent advances in the processing ofNiI2,[5] we demonstrate that photocurrent spectroscopy can beperformed on 2D NiI2 field-effect transistors (FETs). Contrary tothe previous report on bulk crystals,[9] we reveal a high degreeof linear polarization for magnetic excitons in ultrathin NiI2 andshow that the polarization direction is correlated with the helicalAFM propagation vector. Measurements of few-layer samples fur-ther show that magnetic excitons in NiI2 persist down to bilayerthickness with a blue-shifted exciton energy by 18 meV comparedto bulk NiI2.2. ResultsIn our experiments, NiI2 was micromechanically exfoliatedusing Scotch tape, and FETs were assembled by combiningpolymer-assisted flake transfer and lithography methods (seeExperimental Section and Figure 1d,e). When processed in amanner that avoids chemical degradation, graphene-contactedNiI2 FETs show ambipolar transport at room temperaturewith electron (hole) field-effect mobilities of ≈1 cm2 V−1 s−1(0.01 cm2 V−1 s−1).[5] After confirming high-quality charge trans-port characteristics, we acquired photocurrent spectra of bulkNiI2 by measuring the FET source-drain current under opticalirradiation over an excitation wavelength range of 500–1000 nm(≈1.2–2.5 eV). At room temperature, the photocurrent is ob-served to increase with photon energy above 1.38 eV (Figure S1,Supporting Information). By assuming an indirect bandgap forbulk NiI2 and fitting the linear region of the Tauc plot of thephotocurrent spectrum,[12] an energy bandgap of 1.40 eV was ex-tracted (Figure S1, Supporting Information), which agrees wellwith values obtained by absorption and photocurrent measure-ments of bulk NiI2 crystals.[13]Low-temperature photocurrent spectroscopy measurementsreveal an increase in the energy bandgap up to 1.577 eV forbulk NiI2 at 7 K, as extracted from the photocurrent Tauc plot(Figure 1f; Figure S1, Supporting Information). In addition,four sub-bandgap peaks are observed at 1.389, 1.400, 1.413, and1.510 eV (Figure 1f; Figure S2, Supporting Information). Basedon absorption measurements of bulk NiI2 crystals, these peakscan be assigned to the magnetic exciton (1.389 eV), two-magnonsideband absorption (1.40–1.41 eV), and the 3A2g → 3T1g tran-sition (1.510 eV).[9,14] Our photocurrent data yield the best fitswhen the two sidebands are included (Figure S2, SupportingInformation), similar to the magnetic exciton in NiPS3 that isalso accompanied by several sideband peaks.[2a] The magneticexciton at 1.389 eV is of particular interest due to its narrowlinewidth (≈6 meV) and entanglement with the underlying AFMorder in NiI2.[2a,9] While magnetic excitons can be detected inNiPS3 via photoluminescence spectroscopy,[2] the magnetic ex-citons in NiI2 are dark and thus have only been observed usingabsorption spectroscopy and RIXS in bulk crystals in previouswork.[9] Therefore, photocurrent spectroscopy measurements of-fer a unique opportunity to probe the magnetic excitons in exfo-liated 2D NiI2 flakes.Photocurrent spectroscopy allows the polarization of the mag-netic exciton in NiI2 to be measured by irradiating with linearlypolarized light. For this experiment, we employed vertical FETsto ensure that the current passes through a single domain ofNiI2. The vertical FET consists of a NiI2 flake sandwiched be-tween two monolayer graphene strips (Figure 2a). Photocurrentmeasurements reveal that the two-magnon sidebands and 3A2g→ 3T1g transitions are independent of the polarization of the in-cident light. However, the magnetic exciton peak shows signif-icant anisotropy with twofold symmetry (Figure 2b; Figure S3,Supporting Information). Fitting the data with a sinusoidal func-tion and calculating the degree of linear polarization as:𝜌 =I⊥ − I∥I⊥ + I∥(1)gives 𝜌 = 0.81, suggesting strong linear polarization and thus ahighly anisotropic magnetic exciton in NiI2. Here, I⊥(I∥)repre-sents the intensity of photocurrent with vertically (horizontally)polarized linear excitation.To probe the origin of the linear polarization, we first deter-mined the crystal orientation of the NiI2 flake by linear dichro-ism measurements. As established previously, the electric polar-ization of NiI2 (due to its ferroelectricity below the Néel tempera-ture) is pointing along the [110] direction (Figure 2a) and can beprobed by linear dichroism.[7] We found that the positive lobeson the linear dichroism polar plot are oriented parallel to theNiI2 flake edge, allowing that direction to be assigned to [110](Figure 2c). Since the helix propagation vector Q lies in the (110)plane (Figure 1b), the polarization of the magnetic excitons inNiI2 is along its in-plane component, Qin (Figure 2d).Next, we studied the influence of external factors, such as mag-netic field or electrostatic gating, on the magnetic excitons inNiI2. The application of an out-of-plane magnetic field up to 2.5T does not change the position or width of the magnetic excitonpeaks (Figure S4, Supporting Information). This insensitivity tomagnetic field can be explained by the fact that the metamagnetictransitions in NiI2 (spin-flop or spin-flip) require application ofsubstantially higher out-of-plane magnetic fields (>14 T) that arenot accessible in our experimental apparatus.[7b] Therefore, therigid magnetic order of NiI2 translates into a highly robust na-ture of the magnetic excitons. Application of an electric field viathe gate electrode revealed that the magnetic exciton decreases inenergy at both large positive and large negative gate voltages (i.e.,80 V and –60 V, respectively, through a combined dielectric stackof 300 nm thick SiO2 and 20 nm thick bottom hBN), althoughthe change in energy is within 1 meV (Figure S5, SupportingInformation). Similar to externally applied magnetic fields, theminimal response to electric fields and charge carrier modula-tion highlights the robustness of the AFM order and magneticexcitons in NiI2.Photocurrent spectroscopy was further employed to study thethickness dependence of the spectral response for few-layer NiI2(Figure 3; Figure S6, Supporting Information). These measure-ments revealed a negligible shift in magnetic exciton energydown to trilayer thickness. In contrast, the magnetic exciton peakis blue-shifted by 18 meV in bilayer NiI2 (Table S1, Support-ing Information). The persistence of the magnetic exciton downto bilayer thickness confirms the multiferroicity of bilayer NiI2Adv. Sci. 2024, 11, 2407862 2407862 (3 of 8) © 2024 The Author(s). Advanced Science published by Wiley-VCH GmbH 21983844, 2024, 38, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/advs.202407862 by National Institute For, Wiley Online Library on [16/10/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons Licensehttp://www.advancedsciencenews.comhttp://www.advancedscience.comwww.advancedsciencenews.com www.advancedscience.comFigure 2. Polarization-dependent photocurrent characterization. a) An optical micrograph of a vertical FET device fabricated from a bulk NiI2 flake.b) Photocurrent as a function of energy and polarization angle of the excitation laser. Optical transitions are marked with triangles; only the magneticexciton peak shows a polarization-dependent photocurrent response. c) Linear dichroism data for the bulk NiI2 flake shown in (a). Positive lobes (bluecolor) indicate the direction of the C2 rotation axis and electric polarization. d) Polar plot of the magnetic exciton photocurrent extracted from (b); dashedline is the sinusoidal fit. The direction of linear polarization lies along the Qin component of the magnetic modulation vector, which is orthogonal to theelectric polarization.in agreement with recent optical studies.[8c] On the other hand,the magnetic exciton and magnon peaks were not observed inthe photocurrent spectra for monolayer NiI2 FETs. Instead, pho-tocurrent measurements on monolayer NiI2 only revealed onebroad peak, likely corresponding to the 3A2g → 3T1g transition(Figure 3d).To understand the shift of the magnetic exciton to higher en-ergies for thin NiI2 flakes, we analyzed the photocurrent spectraof NiI2 of different thicknesses using Tauc plots (Figure S1, Sup-porting Information). A slight increase in the bandgap for bilayerand trilayer NiI2 by ≈10 meV is observed compared to bulk NiI2,which further increases to ≈30 meV for monolayer NiI2. Theseresults are consistent with density functional theory modeling ofthe NiI2 bandgap using DFT+U calculations with a classical elec-trostatic model of the quasiparticle corrections and exciton bind-ing energies that incorporate the heterogeneous dielectric screen-ing effects of hBN.[15] Ultimately, this increase in bandgap energycontributes to the increased energy of the magnetic exciton forthinner NiI2 flakes.The computed band structure for monolayer NiI2 is providedin Figure 4 using a Hubbard value U = 5 eV calculated usinglinear response theory (Figure S7, Supporting Information).[16]In order to assess the role of electronic correlations, monolayerNiI2 is modeled using an FM configuration. In particular, fol-lowing the Ni 3d8 electronic configuration, the conduction bandis comprised of the spin-down components of the half-filled egbands with each Ni atom carrying a magnetic moment of 2𝜇B.The valence band has a strong I 5p character, with the half-filledNi eg orbitals within 1 eV of the valence band maximum. DFTcalculations indicate that the bandgap is correlation-driven, withAdv. Sci. 2024, 11, 2407862 2407862 (4 of 8) © 2024 The Author(s). Advanced Science published by Wiley-VCH GmbH 21983844, 2024, 38, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/advs.202407862 by National Institute For, Wiley Online Library on [16/10/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons Licensehttp://www.advancedsciencenews.comhttp://www.advancedscience.comwww.advancedsciencenews.com www.advancedscience.comFigure 3. Photocurrent spectroscopy of few-layer NiI2. a) Photocurrent spectra of FET devices fabricated from few-layer NiI2 flakes (open symbols)and their fits (solid lines); the spectra are offset for clarity. The Gaussian peaks represent the magnetic exciton. b) Thickness-dependent energy of themagnetic exciton in NiI2 extracted from the fits of the photocurrent spectra in (a). c,d) Photocurrent spectral fits for bilayer NiI2 at 6 K and monolayerNiI2 at 2 K, respectively.Figure 4. Density functional theory modeling of NiI2 band structure. a) Spin-polarized band structure of monolayer NiI2 from DFT+U with U = 5.0 eV.The insets show the wavefunctions for the top valence band and the bottom conduction band at the Γ point, as marked by the black and red arrows,respectively. b) Bandgap of NiI2 at different thicknesses as a function of Hubbard U values.Adv. Sci. 2024, 11, 2407862 2407862 (5 of 8) © 2024 The Author(s). Advanced Science published by Wiley-VCH GmbH 21983844, 2024, 38, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/advs.202407862 by National Institute For, Wiley Online Library on [16/10/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons Licensehttp://www.advancedsciencenews.comhttp://www.advancedscience.comwww.advancedsciencenews.com www.advancedscience.comthe bandgap varying approximately linear with the Hubbard term(Figure 4b). The deviation from a purely linear behavior can beexplained by the hybridization of the filled eg orbitals, which arepredicted to be the valence band for U < 3 eV with a similar be-havior found for bulk NiI2 (modeled using AFM configuration;Figures S7 and S8, Supporting Information).In accordance with the small dispersion of NiI2, minimalchanges to the bandgap are expected due to quantum confine-ment. However, the correlation-driven quasiparticle bandgap andeffective values of U are strongly increased as the dielectricscreening decreases, with linear response calculations leading toU values of 1.7 eV for bulk NiI2 compared to 5 eV for mono-layer NiI2 in vacuum, leading to a quasiparticle bandgap openingof 0.72 eV (Table S2, Supporting Information; a similar changeof 0.87 eV is also predicted by classical electrostatic models [15]).The predicted quasiparticle bandgap opening is strongly reduced(0.09 eV) by the presence of the hBN substrate (𝜖|| = 6.9). Impor-tantly, the computed exciton binding energies (Table S2, Support-ing Information) are increased by comparable values, resulting inthe small increase of the bandgap observed experimentally.3. DiscussionThrough the use of cryogenic photocurrent spectroscopy on FETdevices, we have studied the magnetic excitons in thick and few-layer NiI2. Previous optical absorption measurements of bulkNiI2 crystals showed a minor degree of linear polarization of mag-netic excitons (<0.2) and were not able to correlate the polariza-tion with the underlying magnetic order or ferroelectric polar-ization, likely due to the polycrystalline nature of the samples.[9]In contrast, our photocurrent spectroscopy measurements wereperformed on high-quality isolated microscopic flakes, which al-lowed us to reveal the high degree of linear polarization of themagnetic excitons in NiI2 (>0.8) and detect the linear polariza-tion orientation with respect to the non-collinear magnetic or-der of NiI2, namely along the in-plane component of the he-lix propagation vector, Qin (Figure 2). These results highlightthe power of photocurrent spectroscopy measurements for prob-ing the interplay between optical, electrical, and magnetic prop-erties of 2D magnetic semiconductors. Since the electrical po-larization of NiI2 pointing along the [110] direction is perpen-dicular to the linear light polarization that gives the largestexciton photocurrent, we conclude that the ferroelectricity ofNiI2 does not play a significant role in the properties of themagnetic excitons.Revealing the high degree of linear polarization of excitonsand their correlation to the NiI2 magnetic order (i.e., direction ofthe spin helix propagation vector) has important consequences.First, probing the magnetic order of van der Waals antiferromag-nets remains a grand challenge due to the absence of net magne-tization. Therefore, development of methods for studying mag-netism in atomically thin AFM materials is highly important forthe future progress of AFM opto-spintronics.[1b,e] Next, the inter-play between magnetic and optoelectronic properties allows thecontrol of excitonic transitions through applied magnetic fields.Indeed, in the case of NiPS3, the application of an in-plane mag-netic field results in a spin-flop transition, which translates intothe rotation of the magnetic exciton polarization by 90°.[3] SinceNiI2 has a more complex helical magnetic order than NiPS3, itsmetamagnetic transitions are less explored. We do not see anymetamagnetic transitions and hence no change in the energy orwidth of magnetic exciton peaks with an out-of-plane magneticfield up to 2.5 T (Figure S4, Supporting Information). However,the study by Kurumaji et al. on bulk NiI2 crystals observed a spin-flop transition induced by in-plane magnetic field (starting from9 T at 50 K), which likely constitutes a rotation of the helical prop-agation vector by 90° (from Qin ⊥ [110] to Qin ∥ [110]).[7b] Fur-ther investigations are needed to probe whether such a spin-floptransition results in the corresponding rotation of polarization di-rection of the magnetic excitons. Last, the observation of a highdegree of linear polarization and correlation to the magnetic or-der is an important addition to the ongoing studies of the natureof the transition at 1.389 eV. A recent RIXS study of nickel di-halides assigns this transition to a d-d excitation of octahedrally-coordinated Ni2+, suggesting its independence of the presence oflong-range AFM order.[17] However, another RIXS study of mag-netic excitons in NiPS3 revealed exciton-spin interactions, andfound that the propagation of excitons through the AFM lattice issimilar to the propagation of a double-magnon excitation.[18] TheRIXS studies together with our polarization-resolved photocur-rent spectroscopy measurements call for future experimental andtheoretical studies on the nature of the sharp excitonic transitionsand their coupling to the underlying long-range magnetic orderin Ni-based van der Waals AFM semiconductors.Application of a gate voltage has been shown to be an effec-tive way to change the magnetic coupling between layers andthus magnetism in few-layer van der Waals magnets such as CrI3and Cr2Ge2Te6.[19] However, in the case of NiI2, we do not find astrong influence of gate voltage on the magnetic excitons, whichhighlights the robustness of these transitions with respect to out-of-plane electric fields and modulation of the Fermi level. Ourprobing of the excitons in the lateral FET geometry further allowseven stronger electrostatic gating schemes (such as ionic liquidsor solid-state ionic conductors) for modulating the magnetic andoptoelectronic properties of NiI2.[20] Expanding this method be-yond a single-material FET geometry to heterostructure samplesalso holds promise for studying interfacial effects, proximity cou-pling, and manipulation of many-body excitons in the atomicallythin limit.Last, by studying few-layer NiI2 FET devices, we observe themagnetic excitons down to bilayer thickness, which implies thatbilayer NiI2 has a similar helical magnetic order to bulk NiI2. Inthe case of monolayer NiI2, we could only detect the 3A2g →3T1gtransition, and do not observe the magnetic exciton or magnonsideband peaks (Figure 3). One potential reason for this observa-tion is the broadening of the magnetic exciton and magnon tran-sitions in monolayer NiI2 flakes such that their detection is oc-cluded due to the overlap with the neighboring 3A2g →3T1g transi-tion. Similar broadening was recently observed for the magneticexciton in bilayer NiPS3, although the exciton in NiPS3 is brightand well-separated from other bands in the spectrum, making iteasier to detect via photoluminescence spectroscopy.[2b] Anotherpossible explanation is the absence of the magnetic exciton inmonolayer NiI2, which would point to differences in the long-range magnetic or ferroelectric order in the monolayer limit forNiI2.[7a,21] This possibility is consistent with recent optical studiesthat have questioned the originally postulated multiferroicity ofmonolayer NiI2.[8]Adv. Sci. 2024, 11, 2407862 2407862 (6 of 8) © 2024 The Author(s). Advanced Science published by Wiley-VCH GmbH 21983844, 2024, 38, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/advs.202407862 by National Institute For, Wiley Online Library on [16/10/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons Licensehttp://www.advancedsciencenews.comhttp://www.advancedscience.comwww.advancedsciencenews.com www.advancedscience.com4. ConclusionsIn conclusion, photocurrent spectroscopy measurements enableelectrical probing of quantum many-body magnetic excitons inthe 2D AFM semiconductor NiI2. This optically dark magneticexciton is detected down to bilayer thickness, which is consistentwith the helical ground state magnetic order and multiferroicityof bilayer NiI2. Photocurrent spectroscopy also reveals a high de-gree of linear polarization of the magnetic excitons in NiI2 as wellas coupling to the underlying helical magnetic order. The mag-netoelectric nature of NiI2 enables potential polarization controlusing external magnetic and electric fields. For instance, the ap-plication of the in-plane magnetic field is known to transformNiI2 into another multiferroic phase, which is proposed to have aspin structure with Qin parallel to [110], as was observed in simi-lar multiferroics MnI2 and CoI2.[7b,22] Consequently, this work islikely to be of high interest for emerging efforts to realize andexploit opto-spintronic and related quantum phenomena in 2Dmagnetically ordered semiconductors.5. Experimental SectionNiI2 Crystal Growth and Exfoliation: NiI2 crystals were grown by thechemical vapor transport method according to previously published pro-cedures, and the quality of the crystals was verified by Raman spectroscopyand charge transport measurements of NiI2 FETs.[5,6] Few-layer NiI2 flakeswere micromechanically exfoliated from the bulk crystal onto 300 nm thickSiO2/Si substrates using Scotch tape inside an inert nitrogen atmosphereglovebox. The thickness of the resulting exfoliated NiI2 flakes was identi-fied based on optical contrast and variable temperature charge transportmeasurements described below.[5]Device Fabrication: FET device fabrication was performed usingpolymer-assisted flake transfer in an inert nitrogen atmosphere gloveboxand previously published lithography methods.[5] Device assembly wasinitiated by picking up the top hexagonal boron nitride (hBN) flake, fol-lowed by sequential pick-up of other flakes and landing the heterostructureon pre-patterned metal contacts.Electrical Transport, Photoconductivity, and Photocurrent SpectroscopyMeasurements: Device measurements were performed in Lakeshore CRX4K and Lakeshore CRX-VF probe stations using Keithley Source Meter2 400 units. Photocurrent spectroscopy measurements were performedusing a Lakeshore CRX-VF probe station and a SuperK Extreme EXR-20laser (NKT Photonics) by varying the wavelength of the incident beam from500 to 1000 nm using an LLTF-VIS monochromator. The laser was focusedusing a lens down to a spot size of ≈100 μm and global power on the or-der of 100 μW, translating to an intensity on the order of 1 μW μm−2 in thecenter of the spot. Identical photocurrent spectra were obtained using a50x long working distance objective with a spot size of 4 μm (with the laserspot aligned entirely within the channel of the NiI2 FET) at similar intensi-ties. The laser was modulated with a mechanical chopper, and the signalwas detected using an SR830 lock-in amplifier (Stanford Research). Thelaser was calibrated using an IntelliCal Ne/Ar source (Princeton Instru-ments) and iHR320 spectrometer equipped with a syn-plus CCD camera(Horiba Scientific).Linear Dichroism Measurements: Linear dichroism measurementswere carried out with samples mounted in a closed cycle variable tem-perature cryostat (Opticool, Quantum Design). The CW 2.33 eV laser wasfocused onto the sample with a long working distance 50x objective using ahomebuilt microscope setup. The laser was modulated with a mechanicalchopper before being linearly polarized and sent through a photo-elasticmodulator (PEM). The PEM was set to have a maximum retardance of0.5𝜆 with a fast axis at 45° with respect to the input polarization. A half-waveplate was used to rotate the modulated polarization with respect tothe crystal axes before being focused onto the sample with a 100x objec-tive. The linear dichroism signal was collected in reflection geometry anddirected to a Thorlabs avalanche photodiode for lock-in detection.Density Functional Theory Calculations: Structural optimization andelectronic band structures were obtained from density functional the-ory (DFT) and DFT+U calculations that were performed using the Vi-enna Ab initio Simulation Package (VASP) [23] with projector augmentedwave (PAW) pseudopotentials and Perdew-Burke-Ernzerhof (PBE) param-eterization of the generalized gradient approximation (GGA) exchange-correlation functional.[23a] For the Brillouin zone integration, a k-point den-sity of ≈40 Å−1 was used. Convergences of the total and electronic ener-gies were 10−5 eV/atom and <10−6 eV, respectively. A vacuum layer largerthan 16 Å was chosen to minimize spurious interactions between the pe-riodic layers. A plane-wave cutoff energy of 600 eV was used. The van derWaals dispersion energy correction used the Grimme D3 method.[24] TheHubbard U term was added to describe the strongly localized Ni 3d elec-trons. Its values for bulk and 2D NiI2 with different thicknesses were de-termined using a self-consistent approach [16a] based on a linear-responsemethod.[16b] In order to correct the self-energy errors in DFT calculationsand account for the dielectric screening effects of the hBN substrate, aclassical electrostatic image model [15] was used on top of PBE+U calcu-lations for the bandgap of NiI2. The dielectric constants for hBN and NiI2are 6.9 [25] and 9.65 (calculated from the random phase approximation),respectively. The exciton binding energies were computed using an effec-tive mass theory of the excitons,[15c] with consideration of the dielectricscreening effect with and without the hBN substrate. The determinationof the image plane position for NiI2 is shown in Figure S9 (SupportingInformation).Supporting InformationSupporting Information is available from the Wiley Online Library or fromthe author.AcknowledgementsThis research was primarily supported by the National Science Founda-tion Division of Materials Research (NSF DMR-2004420). In addition, D.L.acknowledges support from the Swiss National Science Foundation foran Early PostDoc Mobility Fellowship (P2EZP2_181614) and the Materi-als Research Science and Engineering Center of Northwestern University(NSF DMR-2308691) for charge transport measurements. J.T.G. acknowl-edges support from the Department of Energy (DOE DE-SC0019356) fordevice fabrication, and E.S.G. acknowledges support from the NationalScience Foundation Division of Materials Research (NSF DMR-1905986)for variable-temperature cryostat measurements. K.W. and T.T. acknowl-edge support from JSPS KAKENHI (Grant Numbers 19H05790, 20H00354and 21H05233) for hBN synthesis. This work made use of the North-western University NUANCE Center and the Northwestern University Mi-cro/Nano Fabrication Facility (NUFAB), which have received support fromthe SHyNE Resource (NSF ECCS-1542205), the International Institutefor Nanotechnology, and the Northwestern University MRSEC program(NSF DMR-2308691). The Lakeshore CRX-VF probe station, SuperK Ex-treme EXR-20 laser (NKT Photonics), and 2D crystal manipulation system(Graphene Industries) used in this work were supported by an Office ofNaval Research DURIP Grant (ONR N00014-19-1-2297).Conflict of InterestThe authors declare no conflict of interest.Author ContributionsD.L. and J.T.G contributed equally to this work. D.L., J.T.G., V.K.S., andM.C.H. devised the principal objectives of the project. D.L. grew the NiI2Adv. Sci. 2024, 11, 2407862 2407862 (7 of 8) © 2024 The Author(s). Advanced Science published by Wiley-VCH GmbH 21983844, 2024, 38, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/advs.202407862 by National Institute For, Wiley Online Library on [16/10/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons Licensehttp://www.advancedsciencenews.comhttp://www.advancedscience.comwww.advancedsciencenews.com www.advancedscience.comcrystals by the chemical vapor transport method. J.T.G., D.L., and T.W.S.exfoliated the NiI2 flakes and fabricated the FET devices. D.L., J.T.G., andT.W.S. performed the photocurrent measurements with the help of V.K.S.E.S.G. performed low-temperature linear dichroism measurements underthe supervision of N.P.S.. K.W. and T.T. provided the hBN crystals. L.W.and Q.Z. performed the DFT calculations under the supervision of M.K.C.and P.D.. M.C.H. supervised the project. 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Advanced Science published by Wiley-VCH GmbH 21983844, 2024, 38, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/advs.202407862 by National Institute For, Wiley Online Library on [16/10/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons Licensehttp://www.advancedsciencenews.comhttp://www.advancedscience.com Photocurrent Spectroscopy of Dark Magnetic Excitons in 2D Multiferroic NiI2 1. Introduction 2. Results 3. Discussion 4. Conclusions 5. Experimental Section Supporting Information Acknowledgements Conflict of Interest Author Contributions Data Availability Statement Keywords