Full superconducting dome of strong Ising protection ingated monolayer WS2Jianming Lua, Oleksandr Zheliuka, Qihong Chena,b, Inge Leermakersc,d, Nigel E. Husseyc,d, Uli Zeitlerc,d, and Jianting Yea,1

aDevice Physics of Complex Materials, Zernike Institute for Advanced Materials, University of Groningen, 9747 AG Groningen, The Netherlands;bDepartment of Physics, Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong, China; cHigh Field Magnet Laboratory–EuropeanMagnetic Field Laboratory (HFML-EMFL), Radboud University, 6525 ED Nijmegen, The Netherlands; and dInstitute for Molecules and Materials, RadboudUniversity, 6525 ED Nijmegen, The Netherlands

Edited by Zachary Fisk, University of California, Irvine, CA, and approved February 21, 2018 (received for review September 26, 2017)

Many recent studies show that superconductivity not only exists inatomically thin monolayers but can exhibit enhanced properties suchas a higher transition temperature and a stronger critical field.Nevertheless, besides being unstable in air, theweak tunability in theseintrinsically metallic monolayers has limited the exploration of mono-layer superconductivity, hindering their potential in electronic applica-tions (e.g., superconductor–semiconductor hybrid devices). Here weshow that using field effect gating, we can induce superconductivityin monolayer WS2 grown by chemical vapor deposition, a typicalambient-stable semiconducting transition metal dichalcogenide(TMD), and we are able to access a complete set of competingelectronic phases over an unprecedented doping range from bandinsulator, superconductor, to a reentrant insulator at high doping.Throughout the superconducting dome, the Cooper pair spin ispinned by a strong internal spin–orbit interaction, making thismaterial arguably the most resilient superconductor in the exter-nal magnetic field. The reentrant insulating state at positive highgating voltages is attributed to localization induced by the char-acteristically weak screening of the monolayer, providing insightinto many dome-like superconducting phases observed in field-induced quasi-2D superconductors.

transition metal dichalcogenides | Ising superconductivity | spin-orbitcoupling | monolayer | ion-gated transistor

The last decade has witnessed the flourishing development ofisolating layered materials to their 2D limit (1). Reducing the

dimensionality of an electronic system from three to two di-mensions often conserves its fundamental electronic propertieswhile simplifying the theoretical description; hence, a number ofexact solutions of important physical models exist in 2D (2, 3).Although quantum confinement is gradually enhanced with re-duced thickness, significant modifications to the electronic statessometimes are observed when the system approaches the mono-layer limit such as the massless Dirac band in graphene (4, 5) andindirect-to-direct band gap transition in MoS2 (6). On the otherhand, the dimensionality of a system is not an invariable but israther related to specific phases (7), determined by the ratio of thegeometrical thickness d to fundamental electronic length scalessuch as the phase or superconducting coherence length ξ. For in-stance, 2D superconductivity is well established in amorphous filmsof superconducting metals (8) far thicker than a single atom be-cause ξ can easily exceed d. However, due to the large carrierdensity in metals, the corresponding Fermi wavelength λF of dif-fusive electrons appearing after a quantum phase transition is typ-ically smaller than d. This means that the transition coincides with adimensional crossover from a 2D superconductor to a quasi-2D or3D diffusive system. Such a dimensional crossover has also beenobserved in superconducting interfaces and cuprates whenapproaching the optimal gating and doping, respectively (9, 10).These constraints have motivated the search for truly mono-

layer superconductors (11, 12). Recently, epitaxial growth onoptimized substrates has given rise to elemental monolayerfilms (13, 14) (Pb, In, Ga, etc.), monolayer FeSe (15), as wellas monolayer cuprate (16), heavy fermion (17), and organic

superconductors (18). The interaction between these monolayersand their substrates appears to be strong, with the electronic andvibrational couplings in the third dimension believed to be re-sponsible for a reduced critical temperature Tc in metallic mono-layers and a significantly enhanced Tc in FeSe, respectively. Van derWaals layered materials (19–21) are 2D systems where electrons aremainly confined in a covalently bonded crystalline plane. Therefore,by breaking the van derWaals stacking, monolayer superconductingtransition metal dichalcogenides (TMDs) [such as NbSe2 (22, 23)]and high-Tc cuprates Bi2Sr2CaCu2O8 (24) could exhibit truly 2Dcharacteristics. However, due to their large intrinsic carrier density,switching electronic phases in these superconductors appears to belimited (25). Another strategy is to induce superconductivity in asemiconducting TMD monolayer such as MoS2 in ref. 26, thoughhere, the availability of possible electronic phases and their varia-tion by field effect has yet to be explored.Here we demonstrate that monolayers of the semiconducting

TMD WS2, where both carrier tunability and true 2D charac-teristics are accessible, provide an extremely versatile option forfield effect control of various quantum phases. By field effectgating, WS2 flakes evolve from a direct band insulator into ametal that exhibits superconductivity (27–35) at low tempera-tures. The significant spin–orbit coupling in the conduction bandleads to so-called Ising superconductivity (23, 36, 37) that is re-markably robust against external in-plane magnetic fields. Be-yond the peak of the superconducting dome, the normal statebecomes more resistive with increasing gate bias, eventually

Significance

Compared with 3D superconductors, atomically thin super-conductors are expected to be easier to engineer for electronicapplications. Here, we use field effect gating to induce super-conductivity in a monolayer semiconducting transition metaldichalcogenide, WS2, grown by chemical vapor deposition. Theremarkable doping range allows access to a cascade of elec-tronic phases from a band insulator, a superconductor, to areentrant insulator at high doping. The large spin-orbit cou-pling of ∼30 meV makes the Ising paring in WS2 arguably themost strongly protected superconducting state against exter-nal magnetic field. The wide tunability revealed by spanningover a complete superconducting dome paves the way for theintegration of monolayer superconductors to functional elec-tronic devices exploiting the field effect control of quantumphases.

Author contributions: J.L., O.Z., U.Z., and J.Y. designed research; J.L., O.Z., Q.C., I.L., N.E.H.,and J.Y. performed research; J.L., O.Z., Q.C., and J.Y. analyzed data; and J.L. and J.Y. wrotethe paper.

The authors declare no conflict of interest.

This article is a PNAS Direct Submission.

Published under the PNAS license.1To whom correspondence should be addressed. Email: j.ye@rug.nl.

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1716781115/-/DCSupplemental.

Published online March 19, 2018.

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quenching the superconductivity, and a second distinct insulatingground state develops beyond the superconducting dome.

MethodsThe monolayer WS2 flakes used in our experiments are grown by chemicalvapor deposition (CVD). The high quality of the as-grown crystalline sheets isconfirmed by the observation of strong photoluminescence (PL) and a mo-bility of μ ∼ 300 cm2/Vs at 10 K and at optimal gating, which is comparable toor higher than for its cleaved counterparts (38) (Fig. S1). An electronicallyhomogeneous part exhibiting a uniform PL is isolated by etching a standardHall-bar from a pristine triangular monolayer (Supporting Information,section 1) and fabricated into a dual-gate configured device composed of anionic liquid top gate (VTG) and a dielectric back gate (285 nm SiO2 on a highlydoped silicon substrate, VBG) as shown in Fig. 1A. This dual-gating methodallows both coarse and fine electrostatic control of quantum phases (Sup-porting Information, section 2). Applying first an ionic gate at T ∼220 K, wecan introduce an extremely strong electrostatic field effect, which is sub-sequently fixed by freezing the ionic liquid below its glass transition tem-perature Tg ∼ 190 K. By grounding the ionic gate and sequentially warmingthe device slightly above Tg, we are then able to create dense coarse dopingstates (color coded in Fig. 1B), which can be seamlessly linked at low tem-peratures by VBG. The quasi-continuous transfer curve thus obtained (blackcurve in Fig. 1B) defines electronic phases as a function of effective gatevoltage Veff (Supporting Information, section 4). Note that on both sides ofoptimal doping, the dependence of Hall carrier density on Veff is opposite:positive on the left, but negative on the right, relating to the reentrantinsulating phase at low temperatures (for more discussion see Fig. 4).Around optimal doping, there is a crossover linking two monotonic corre-spondences (as elaborated in Fig. S5). Therefore, we use Veff instead of Hallcarrier density to label states across the whole spectrum. Although a simplecapacitance model cannot be applied directly to our dual gated device (39),Veff generally scales linearly with the number of charge carriers injected into

the sample, which is equivalent to the nominal stoichiometry of in-tercalated/doped bulk compound.

Results and DiscussionThe Veff dependence of the sheet resistance Rs (Fig. 1B) at 2 K(diamond), 10 K (triangle), 70 K (square), and 150 K (circle) givesan overview of the whole spectrum of electronic states. Betweentwo insulating phases, metallic transport appears at intermediatevalues of Veff accompanied by a transition into a superconductingstate. At Veff = 1,130 V, optimal transport shows the lowest Rs andthe highest superconducting transition temperature Tc.The temperature dependence of Rs on the left and right sides

of optimal doping is shown in Fig. 1 C and D, respectively. Thecurves reveal that superconductivity emerges from a nonmetallicstate (dRs/dT < 0, Fig. 1C) when approaching optimal dopingfrom the low gating side and quenches into another insulatingstate at high gating (Fig. 1D). In this way, a full spectrum ofelectronic phases can be prepared using a single tuning param-eter Veff, allowing the properties of different quantum phases—such as the quantitative dependence of superconductivity on Veff(Insets in Fig. 1 C and D)—to be analyzed in detail.The full phase diagram is shown in Fig. 2, with the super-

conducting dome spanning the range 0.8 kV ≤ Veff ≤ 1.6 kV.(Throughout, Tc is defined as the temperature at which Rs falls to50% of its normal state value.) The Veff dependence of the Hallcarrier density nHall (Fig. 2, Lower) indicates that Tc is mainlydriven by changes in the carrier density. However, the separationbetween the maxima of Tc and nHall (10 K) suggests that Tc mayalso be affected by electron-impurity scattering, as inferred fromthe opposite Veff dependence of carrier mobility μ (T = 10 K,right axis in Fig. 2, Lower) extracted from Rs (Fig. 1B) above and

Fig. 1. Electrical transport of ion-gated monolayer WS2. (A) Schematic of measurement set-up with both ion liquid VTG and solid back gates VBG. (Inset)Optical image of the monolayer etched into standard Hall-bar geometry. (B) Transfer characteristics measured by scanning VBG at 70 K with various VTGs wereconcatenated, as indicated by the black line. The origin of effective gate voltage Veff was extrapolated using gate dependence of Hall carrier density (Fig. S4).Square resistance Rs at typical temperatures (150 K, circle; 70 K, square; 10 K, triangle; 2 K, diamond) are shown for many different Veffs to reveal theevolution from an insulator to a superconductor and finally, to the reentrant insulator. Each color represents a specific VTG. (C and D) Temperature-dependentRs is plotted for regimes before (C) and after (D) the peak of the superconducting dome, where each curve corresponds to one Veff of the same color in B.(Insets) Details around the superconducting–insulating transition on a linear scale.

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below the Tc maximum. Notably in MoS2 (27), a similarly gatedsuperconducting dome follows Tc ∝ (n2D − n0)

zv, where zv ∼ 0.6is the product of exponents for correlation length (z) and cor-relation time (v) in scaling theory (3, 7), in analogy to that foundfor LaSrO3/SrTiO3 interfaces (40). In the present monolayersuperconductor, the limited temperature range precludes a res-olution of the scaling exponents and the exact locations of thetwo quantum critical points (QCPs, denoted roughly by twodashed circles). Nevertheless, within the experimentally accessi-ble phase space, the voltage dependence of Tc does not contra-dict the relationship seen in the other two systems.In many quasi-2D superconductors, quasi-metallic (qM) re-

gions have been inferred (7, 40, 41), in which Rs exhibits atemperature dependence weaker than exponential althoughoverall dRs=dT < 0. Here, we define Tmin as the temperature atwhich Rs reaches a minimum (Fig. 1 C and D) presumably fromcompetition between electron-phonon scattering and Andersonlocalization. In Fig. 2, the trace of Tmin (empty squares, Upper)marks the boundary of the qM regime. It is worth noting that theqM region here is manifest in a finite-size sample at intermediatetemperatures, which might cross over to insulating behavior atlower temperatures and/or in larger samples. We leave thisquestion open to future investigations to be conducted atmilliKelvin temperatures.An outstanding feature of the 2D superconductivity in TMD

materials is the Ising pairing (23, 36, 37) that originates from thevalley coupled spin texture found in monolayer TMDs. In this cir-cumstance, the spins of the Cooper pairs become pinned by a strongout-of-plane effective magnetic field that is generated by an intrinsic

Zeeman-type spin–orbit interaction (SOC) pointing oppositely in K/K′ valleys (Fig. 3B, Inset). The Zeeman field—normally the uni-versal pair-breaking mechanism in superconductors—here stronglyprotects the Cooper pair against an orthogonal (in-plane) externalmagnetic field. Compared with other quasi-2D Ising superconduc-tors such as ion-gated multilayer MoS2, where the electronic wavefunction is confined to the uppermost layer and Ising pairing isprotected by SOC ∼6 meV (36), the much heavier transition metalin WS2 creates SOC that is five times larger (∼30 meV) (42),pointing to an even higher in-plane upper critical field Bc2. Thisstronger SOC in WS2, and hence larger spin splitting, can result inan archetypal spin texture for Ising pairing, which avoids thecrossing of two lower lying spin-split conduction bands in MoS2when the Fermi level moves further away from the band edge at K/K′ points (43). More importantly, the SOC in WS2 is more than oneorder of magnitude larger than the superconducting order param-eter calculated from maximum Tc. In this sense, monolayer WS2may provide an elegant platform to probe unconventional Isingpairing theoretically predicted for this system (44, 45).Guided by the phase diagram established in Fig. 2A, we suc-

ceeded to induce superconductivity in another sample B with anoptimal Tc = 3.15 K (Fig. 3A, Inset). The observed lower Tc hereis possibly due to the more defective crystal, as the interactionbetween electrons and charged scatterers would renormalize thesuperconducting order parameter (46). This is also consistentwith the lower mobility of sample B. The Bc2s were measured inthree representative regions of the dome, as shown in Fig. 3.Interestingly, the strongest Ising protection was measured nearthe lower edge of the dome, where relatively weak electric fields

Fig. 2. Phase diagram of monolayer WS2 and criticalscaling of quantum phases. (Upper) Superconductingcritical temperatures TC are plotted (solid circle) as afunction of the effective back gate. Quasi-metal (qM)regime is bounded by metal–insulator crossover tem-perature (empty square). The initiation and sup-pression of the superconducting dome are indicatedby dashed circles. (Lower) Hall carrier density mea-sured at 160 and 10 K are plotted on the left axis;Hall mobility at 10 K on the right axis.

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cause a minimum Rashba effect (36) (Fig. 3A, Upper: Tc = 1.54 Konly shifted by ΔTc = 0.08 K for an in-plane field B// as high as35 T). Following mean-field theory (36) (also see Supporting In-formation, section 6), we can estimate the contribution fromZeeman-type SOC and Rashba splitting to the enhancement ofBc2 (relative to the Pauli limit Bp = 1.86 Tc). The comparison withexperimental data (solid red points) is shown in Fig. 3B (red line).Assuming a Rashba effect created through ionic gating of order0.7 meV—that is, as found near the left QCP of MoS2 (36)—theobtained Zeeman-type SOC is found to be 30 meV, consistentwith theoretical calculations. Neglecting the Rashba contribution,our data set a lower bound of 19.5 meV for Zeeman SOC. Be-cause of the very large Bc2 for states at the peak (Fig. 3A, Middle)and the upper edge (Fig. 3A, Lower) of the dome, the change of Tcat a maximum field of 12 T is below the measurement accuracy forextracting quantitative values of the SOC.In Fig. 3B, we compared the ratio Bc2/Bp of other supercon-

ductors where the Pauli limit is significantly violated. For thegated monolayer WS2, Bc2/Bp is at least as large as those in theUCoGe (47) and the submonolayer Pb film (48) protected bytriplet pairing and Rashba splitting, respectively. It is much largerthan other recently discovered Ising-protected superconductorssuch as multilayer MoS2 (36) and monolayer NbSe2 (23). It isnoteworthy that the Zeeman SOC in the NbSe2 (∼70 meV,valence band) is even larger than that in both MoS2 (∼6 meV)and WS2 (∼30 meV), yet the level of protection in monolayerNbSe2 and bulk (LaSe)1.14(NbSe2) (49) (resembling decoupledmonolayers at low temperatures) merely approaches that found ingated MoS2. A similar mismatch also appears in TaS2(Py)0.5 (50),where the pairing occurs also in the valence band. This reductionin Ising protection could be influenced by a competing chargedensity wave (CDW) phase and the contributions from a spin

degenerate Γ point (51), which might effectively weaken the strongIsing pairing formed at the K/K′ valleys of NbSe2 and TaS2.Another prominent feature of the data is the reversible re-

entrance into a strongly insulating state at high Veff, which isclosely related to how the superconductivity is suppressed beyondoptimal doping. First, we rule out the possibility of electrochemicalreaction between WS2 and ion liquid as seen from the high re-peatability of sample performances in consecutive gating processes(comparison of transport behavior is shown in Fig. S6, and more iselaborated in Supporting Information, section 3.). Second, recentadvances in studies of semiconducting WS2 (42) could safely ex-clude many exotic(intrinsic) mechanisms as well, such as theopening of a Mott, CDW, or Kondo gap, and the enhanced cor-relation effects (52, 53). Alternatively, extrinsic mechanisms, whichtake into account the charged ions on the sample surface (54), maybe more relevant. Typical examples include narrow-band materialssuch as rubrene (55) and ReS2 (56) where Mott- and Anderson-type localization were proposed, respectively, and wide-band ma-terials like silicon inversion layers (54, 57, 58) with Coulomb trapsand strong short-range scattering from rough surfaces. To addressthis universal insulating phase, in the following, we focus on thecommon fact that all of the above examples involve ionic gating(either by ion liquid or alkaline metal).Inspection of Arrhenius plots (Fig. 4A) yields similar in-

sulating behavior at high temperatures for both the low and highgating sides of the dome. Without knowledge of the underlyingtransport mechanism, we tentatively extract a characteristic en-ergy scale. As shown in Fig. 4B, although the two energy scalesare similar in magnitude, their dependences on Veff have theopposite sign. The temperature dependence of nHall also con-firms insulating behavior at large Veff, manifesting as a freeze-outof carriers within a large range of gate voltages including the

Fig. 3. Ising pairing over the entire superconducting dome. (A) Upper critical field Bc2 was measured on the left side (Upper), the peak (Middle), and rightside (Lower) of the superconducting dome (Inset to A). Superconducting critical temperature Tc is defined by 50% of normal state resistance denoted by thedashed line. Each state is highlighted by an empty circle in the dome. (B) Normalized Bc2 with respect to the Pauli limit in WS2 is denoted by the solid red circle,which exceeds that of many well-known superconductors with high Bc2, including TMDs, triplet pairing, and monolayer Pb film. (Inset) Schematic of Zeeman-type effective magnetic fields (green arrows) with alternating directions in K/K′ valleys in a hexagonal Brillouin zone, which stabilize electron spins (red/bluedenotes spin up/down) in a Cooper pair against external in-plane magnetic field Bex.

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whole superconducting dome (Veff from 0.8 to 1.6 kV, Fig. 4C).In contrast, a nearly temperature-independent nHall is observedonly in the qM region near the left QCP at low Veff.To account for the above observation about activation energy

and Hall carrier density, we adopt a scenario of a gate-induced bandvariation as sketched in Fig. 4D, which is based on the fact thatrandomly arranged charged ions can trap the induced carriers (54,58) as well as disturb periodic lattice potential (56). In such a truly 2Dsystem, weak out-of-plane screening exposes induced carriers directlyto the potential of ions lying on the surface. The localization effectdepends on the distance l between induced carriers and chargecenters of the cations (Fig. 4D). At low Veff << 1.1 kV, ions accu-mulated by the weak electric field create a uniform potential, while atlarge Veff>> 1.1 kV, the discreteness of the ions at a reduced l can nolonger be averaged out by the characteristically weak 2D screeningeffect. This increased randomness enlarges the band tail (Fig. 4E)where more carriers localize, reducing the number of free carriersavailable for band transport. In the high gating limit and low tem-perature, every induced carrier is localized/bounded on site by thepotential of an adjacent ion—that is, forming electron–cation pairsthat mimic the hydrogen impurity model (Fig. 4E, Right). Strongly

localized electrons in the reentrant regime would form an impurityband, thereby reducing the Fermi level with increasing gate voltage.When the temperature is lower, charge transport deviates from singlethermal activation from impurity band to conduction band, which islikely due to an additional conduction channel involving hoppingbetween localization centers.With this physical picture in mind, we can understand the shift

in maxima between nHall (10 K) and Tc in Fig. 2. Starting from Veff∼1,130 V, where Tc peaks, nHall decreases from 160 K to10 Kmore rapidly at higher Veff, due to the stronger localization orig-inating from more and deeper Coulomb traps. Such localization ofinduced carriers neutralizes Coulomb traps (Fig. 4D, dashed line),which then acts as short-range scattering centers and leads to adecrease in mobility (Fig. 2, Lower). As a result, compared with itscounterpart (with the same Tc) on the left side of the dome peak,the state on the right side resides in a more disordered environ-ment that cancels out the effect of higher carrier density on criticaltemperature. In other words, the interplay between carrier densityand disorder shapes the superconducting dome versus Veff.Considering that electrostatic gating by polarizing dielectrics

(polarized dipole) and ionic media (cation–anion pair) is similar

Fig. 4. Reentrant insulator induced in monolayerWS2 by ionic gating. (A) Arrhenius plot of conductance defined as 1/Rs in insulating (Left) and reentrant insulating(Right) regimes. The characteristic energy scales are extracted in terms of thermal activation transport (dashed lines). In Right, the long tail at low temperature maysuggest complicated hopping mechanisms along with the increasing Veff. (B) Extracted characteristic energy is plotted as a function of effective gate voltages. Blacksquares and blue triangles correspond to reentrant insulator and band insulator. (C) Normalized Hall carrier density at various gate voltages as a function oftemperature. Free carriers freeze out during cooling down in the reentrant insulating regime (red), while the carrier concentration almost remains constant in themetallic regime (blue and purple). (D) Schematics of electron (blue sphere) localization in the Coulomb traps (black curve) due to the poorly screened cations(organic molecular DEME+, the positive charge center is highlighted by a solid ball in purple) in proximity to monolayer WS2 film. (E) Representation of the densityof states (DOS) as a function of energy, E, in the insulating phase (left of the dome) and the reentrant insulator (right of the dome), in both of which a disorderpotential results in a localized band tail below the spin–split conduction band (red and blue denote spin up and down, respectively). The insulating side has a lowdensity of localization centers (Left), whereas overlapping of high-density localized states on the reentrant insulating side plausibly forms an impurity band.

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in principle, the competing quantum phases induced in the presentstudy represent the high field limit with respect to those super-conducting domes reported previously (27, 29, 31–33, 40, 53) (Fig.S7), where either a very strong field effect or an isolated mono-layer crystal was missing. In this truly 2D system, localized statescan now be easily formed because of the slow 1/r3 decay of the ionpotential, indicating that any disorder in the potential landscapehas a long-range effect. In contrast, in quasi-2D systems, gate-induced carriers always extend to a finite thickness; strong gat-ing populates multiple subbands, causing crossover to 3D, whichenhances screening and thereby reduces carrier localization. Inthis sense, the proposed scenario provides a clear understandingof the power law/logarithmic correction in the normal state re-sistance as the precursor of a reentrant insulator in ion-gatedbulky materials (silicon, rubrene, etc.) and universally observed

superconducting dome in gated multilayer MoS2 (27), TiSe2 (31),ZrNCl (32), as well as LaAlO3/SrTiO3 interface (40, 59), whereaccessing the right QCP and the insulating state subsequent to thesuperconducting dome is prohibited by the enhanced screening inthese quasi-2D systems.

ACKNOWLEDGMENTS. We thank J. Harkema for technical support. Q.C.thanks the scholarship from The Ubbo Emmius Fund. J.Y. and Q.C. thank theStichting voor Fundamenteel Onderzoek der Materie (FOM) (Grant FV157)and FlagERA iSpinText for financial support. J.Y. acknowledges fundingfrom the European Research Council (Consolidator Grant 648855, Ig-QPD).U.Z. acknowledges support of HFML-RU/FOM, member of the EuropeanMagnetic Field Laboratory (EMFL) and part of this work was supported byThe Netherlands Organization for Scientific Research (NWO) as part ofDESCO program no. 149 by FOM.

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