Controlling the anisotropy of a van der Waals antiferromagnet with light

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Science Advances  02 Jun 2021:
Vol. 7, no. 23, eabf3096
DOI: 10.1126/sciadv.abf3096


Van der Waals magnets provide an ideal playground to explore the fundamentals of low-dimensional magnetism and open opportunities for ultrathin spin-processing devices. The Mermin-Wagner theorem dictates that as in reduced dimensions isotropic spin interactions cannot retain long-range correlations, the long-range spin order is stabilized by magnetic anisotropy. Here, using ultrashort pulses of light, we control magnetic anisotropy in the two-dimensional van der Waals antiferromagnet NiPS3. Tuning the photon energy in resonance with an orbital transition between crystal field split levels of the nickel ions, we demonstrate the selective activation of a subterahertz magnon mode with markedly two-dimensional behavior. The pump polarization control of the magnon amplitude confirms that the activation is governed by the photoinduced magnetic anisotropy axis emerging in response to photoexcitation of ground state electrons to states with a lower orbital symmetry. Our results establish pumping of orbital resonances as a promising route for manipulating magnetic order in low-dimensional (anti)ferromagnets.


The recent discoveries of van der Waals (vdW) two-dimensional (2D) layered magnets have led to a surge of interest due to their potential applications in constructing atomically thin spin-processing devices and nonvolatile magnetic memories (1, 2). Unique phenomena and effects are foreseen in 2D magnetic systems because of their reduced dimensionality (3). In contrast to 3D magnets, long-range magnetic order cannot exist in 2D at any finite temperature without the presence of magnetic anisotropy (4, 5). In 2D magnets, the anisotropy not only sets a preferred direction for spins but also protects the magnetic order against dimensionality-enhanced thermal spin fluctuations. This intimate relationship between magnetic order and anisotropy in 2D motivates the ongoing search for efficient pathways to manipulate the magnetic anisotropy in such systems. Since the magnetic anisotropy in most materials is determined by the coupling of electronic orbitals and spins, stabilizing and controlling 2D magnetism are actively pursued through the manipulation of orbital degrees of freedom, using, for example, mechanical strain (68) and electrostatic gating (9, 10). However, a large anisotropy is normally associated with an unquenched orbital moment, which is limited to specific oxidation states and to low-symmetry crystal environments, most notably for rare-earth ions (11). In most 2D magnets, magnetism arises from transition metal ions, which typically have a quenched orbital moment in their ground state. In these systems, magnetic anisotropy originates from the spin orbit–driven mixing of the ground state with higher-energy orbital states characterized by an unquenched momentum, a rather small effect. Optical pumping of the electronic transitions toward the higher-level orbital states (orbital resonances) provides the most direct access to the admixing and subsequent control of the magnetic anisotropy as manifested by the excitation of spin precession in 3D magnets (1215) even to the extent of the subcycle coherent switching of the spin orientation (1618). Resonant pumping of orbital transitions in 2D magnets, characterized by the subtle interplay between anisotropy and magnetic order, offers unique insights into dynamics of their highly nontrivial elementary excitations, such as, for example, topological magnons (19, 20).

Here, we study resonant optical control of magnetism in nickel phosphorus trisulfide (NiPS3), a vdW layered magnet with XY-type antiferromagnetism (2123). The energetic competition between charge transfer and Coulomb repulsion makes this system an intriguing example of a strongly correlated 2D magnet, with pronounced spin-charge correlations (24), spin-orbit entangled excitons (25), and strong spin-lattice coupling (26). We optically pump NiPS3 using ultrashort pulses of light and probe the ensuing spin dynamics on the picosecond time scale. Continuously varying the pump photon energy across orbital resonances, we identify a transition to the orbital state responsible for the anisotropic magnetic properties in equilibrium. By resonant optical pumping of this transition, we demonstrate the selective activation of a hitherto unreported 2D magnon mode with a terahertz (THz) frequency demonstrating the XY critical scaling with temperature. By studying the mode’s excitation as a function of the pump polarization and photon energy, we show that the activation proceeds as a result of the light-induced magnetic anisotropy emerging in response to the resonant photoexcitation of the higher-energy orbital states of Ni2+ ions. We also find that optical pumping in the region of optical transparency impulsively activates another high-frequency coherent mode, a previously unreported candidate for the complementary magnon mode in NiPS3.


NiPS3 crystallizes in the monoclinic space group C/2m (27) (see Fig. 1A). In the ab plane, it features a network of edge-sharing NiS6 octahedra arranged on a honeycomb lattice, each having a small trigonal distortion perpendicular to this plane (see Fig. 1B). Below the Néel temperature, TN = 155 K, the magnetic moments of Ni2+ ions arrange into a complex compensated antiferromagnetic pattern. The pattern is formed by zigzag ferromagnetic spin chains along the a axis, which are coupled antiferromagnetically within the single layer (28) (see Fig. 1A). A large spacing, c = 6.63 Å, between adjacent layers leads to a negligible orbital overlap between the magnetic ions of different layers, thereby suppressing interlayer exchange such that the antiferromagnetic order acquires a 2D character already in the bulk form.

Fig. 1 Ultrafast light-induced dynamics in vdW antiferromagnet NiPS3.

(A) Crystallographic and magnetic structure of NiPS3. Green/fade orange/light pink spheres represent nickel/sulfur/phosphorous atoms. The green and red triple vectors are crystallographic and magnetic frames, respectively. (B) Left: Ni2+ ion in the trigonally distorted octahedral sulfide environment. Right: Crystal field splitting of the ground state and first excited triplet state for Ni2+ ion (Oh, octahedral field) in a trigonally distorted octahedral environment (D3h); S.-O., spin-orbit coupling. (0, ±1) correspond to the projection of the spin moment along the trigonal distortion axis. (C) Schematic of the time-resolved pump-probe experiment. The pump (violet) and near-infrared probe (gray) pulses are collinearly focused onto the NiPS3 sample with variable time delay Δt. The pump-induced dynamics is measured by tracking the pump-induced polarization rotation θ and intensity I of the probe pulses. (D) Optical absorption spectrum of NiPS3 displaying the 3A2g3T2g and 3A2g3T1g absorption bands due to the d-d orbital resonances of Ni2+ ions (in pink and red, respectively) and the onset of the above bandgap absorption due to Ni-S charge transfer transitions (black band). (E) Experimentally detected polarization rotation signal θ as a function of the delay time Δt after excitation with pump pulses at various photon energies.

The orientation of magnetic moments in NiPS3 is governed by a biaxial magnetocrystalline anisotropy consisting of two distinct contributions: a dominant easy-plane anisotropy that locks the orientation of the spins to a magnetic plane (xy), slightly inclined from the crystallographic ab plane, and a secondary weaker anisotropy that orients the spins in the magnetic (xy) plane along the x axis. Microscopically, the easy-plane anisotropy develops as a result of a zero-field splitting [D ≈ − 1.1 meV (29)] of the 3A2g ground state of the Ni2+ ion (S = 1) in the crystal field of the trigonally distorted NiS6 octahedra (see Fig. 1B). Note that 3A2g is an orbital singlet and alone cannot develop the splitting. The splitting and anisotropy arise indirectly as a consequence of spin-orbit–driven intermixing of the ground state with the first excited orbital triplet state 3T2g, which is split by the trigonal lattice distortion (29, 30) into a set of low-symmetry doublets 3Eg and singlets 3A1g separated by an energy gap of around 110 meV, as schematically shown in Fig. 1B. Although there are no reports on the origin of the in-plane magnetic anisotropy along the x axis in NiPS3, it likely stems from a rhombic distortion of the NiPS6 octahedra, which further splits the 3A2g levels. Hence, an anisotropic Hamiltonian considering not only the axial distortion of the octahedron but also an in-plane distortion may be needed to take this observation into account (see section S6).

The orbital resonances in NiPS3 correspond to a pair of d-d transitions 3A2g3T2g and 3A2g3T1g emerging within the 3F ground state multiplet of the Ni2+ ion split by the octahedral crystal field (Oh) (see fig. S1). In NiPS3, these transitions result in a pair of two broad optical absorption bands centered at 1.07 (3A2g3T2g) and 1.73 eV (3A2g3T1g). Note that in contrast to other transition metal ions, the d-d resonances in Ni2+ are spin-parity allowed (ΔS = 0), i.e., they do not involve a spin-flip, and thus cannot directly affect the exchange interaction between adjacent spins. To selectively address these resonances, we used ultrashort (~100 fs) pump pulses with photon energy tunable in a broad spectral range of 0.1 to 1.9 eV. The pump-induced dynamics were measured by tracking the intensity I and the rotation of the polarization plane θ of time-delayed copropagating near-infrared probe pulses at a photon energy of 1.55 eV, as schematically shown in Fig. 1C. Whereas I is considered as a measure of the nonmagnetic components of the dielectric tensor, θ is sensitive to the magnetic order via magneto-optical effects, such as the Faraday effect and magnetic linear birefringence.

The sample was cooled down to 10 K, well below TN, and pumped using linearly polarized pulses at variable photon energies. The time-resolved polarization rotation θ reveals a notable sensitivity of the pump-induced dynamics to the photon energy of the excitation (see Fig. 1, D and E). When excited at the 3A2g3T2g resonance (hν = 1.8 eV), θ displays a damped oscillation as a function of the pump-probe time delay Δt, with frequency f1 = 0.30 THz (see fig. S2 for the Fourier spectra). No coherent oscillations were observed when exciting at the higher photon energy (hν = 0.97 eV) corresponding to the 3A2g3T1g resonance. Detuning the photon energy below the absorption lines of the resonances (hν = 0.8 eV) shows no signal associated with the frequency f1 but reveals instead another higher-frequency mode at f2 = 0.92 THz. We note that the oscillations seen in the polarization rotation dynamics were not observed in the probe intensity dynamics I (see fig. S3), thus hinting at their magnetic origin. In addition, we found no match for the frequencies of these oscillations in the phonon spectrum of NiPS3, which was well studied in recent years (26, 3133).

To understand the significance of the orbital resonances, we tracked the ultrafast dynamics while varying the pump photon energies across the subgap states down to the phonon Reststrahlen band edge at 0.1 eV. The amplitudes of both oscillations at f1,2 were retrieved, and their relative values (normalized on the pump fluence) were plotted as a function of the pump photon energy. Figure 2A shows that the f2 mode is excited in the broad window of optical transparency 0.1 to 0.9 eV, indicating the off-resonant character of the excitation and impulsive stimulated Raman scattering (ISRS) process as a plausible mechanism. In notable contrast, the excitation of the lower-frequency f1 mode only occurs in a relatively narrow photon energy range, showing a pronounced resonance with the 3A2g3T2g transitions (see Fig. 2A). The lineshape of the resonance reveals a fine structure indicative of the trigonal splitting of the 3T2g manifold (3Eg, 3A1g) (see fig. S1). Despite a nearly order of magnitude stronger optical absorption, no oscillations were seen upon resonant pumping of the 3A2g3T1g higher-energy orbital resonance, underscoring the exceptional sensitivity of the oscillations to the photoexcitation of the 3T2g states. Whereas the amplitude of the mode at f2 reveals a linear dependence on the pump fluence (Fig. 2B), the amplitude of the f1 mode saturates above 5 mJ/cm2 (Fig. 2C), indicating a possible saturation of the 3A2g3T2g transition.

Fig. 2 Selective excitation of the light-induced coherent dynamics.

(A) Amplitudes of the coherent oscillations corresponding to the modes at frequencies f1,2 normalized to the maximal value of the f1 mode as a function of the pump photon energy. Solid lines are guides to the eye. Inset: Schematic illustration of the optical transition at which the f1 mode is observed. (B and C) Amplitude of the oscillation as a function of the pump fluence for the (B) f2 and (C) f1 modes. The solid lines are linear fits, including saturation.

The temperature (T) dependence of the frequencies f1,2 evidences that these modes are sensitive to the magnetic ordering. Figure 3A shows that as T increases, the damping of the first mode goes up, while the frequency f1 gradually decreases and ultimately converges to zero at a temperature close to TN. Although the application of a relatively weak in-plane magnetic field H up to 7 kOe produced no observable shift in f1 (see fig. S4), the observation of the critical softening is a strong indication that the oscillation is of magnetic origin (34, 35). The softening can be characterized by a power law f1(T) ∝ (TNT)β (see Fig. 3C and fig. S5), with TN ≈ 155 ± 1 K, in full agreement with literature data, and a critical exponent β = 0.23 ± 0.01 valid down to the temperature T0 = 0.65 TN (see fig. S5). Note that the β value also matches remarkably well with the critical exponent of the XY model (βXY = 0.23) previously proposed to describe the temperature evolution of the 2D magnetic ordering in NiPS3 (3638). This remarkable observation is an unambiguous and, at the same time, unexpected indication of the intrinsically 2D character of the mode observed in the bulk form of NiPS3.

Fig. 3 Critical behavior of the light-induced coherent dynamics.

(A and B) Temperature dependence of the time-resolved polarization rotation after pump-induced excitation with photon energies of 1.08 (A) and 0.2 eV (B). Irregularities at ~13 ps in (B) are related to an artifact of the measurement setup. (C and D) Frequency (left axis) and damping factor α (right axis) of the oscillations as extracted from the damped sine fits of the time-domain data in (A) and (B). The solid lines represent the best fit of (TNT)β (C), which gives TN = 155 ± 1 K and β = 0.23, and a linear function (D) to the frequency data. (E and F) Schematics of the in-plane (E) and out-of-plane (F) magnon modes.

The temperature evolution of the higher-frequency oscillation at f2 is substantially different. As T increases, the central frequency f2 shows a slight increase, which above 75 K is followed by a steep, nearly linear, softening. A linear extrapolation of the frequency decrease versus T suggests that a complete softening of the mode occurs at T = 170 K, in proximity to TN (see Fig. 3D). The softening indicates that the oscillation is either of magnetic origin itself or strongly sensitive to the magnetic ordering. This is further corroborated by the significant growth of the damping constant upon heating. Such highly damped behavior is typical for soft modes in the vicinity of their associated phase transitions (39).

We now analyze the spin dynamics possible in NiPS3 from a phenomenological theory perspective. Two magnon modes are expected in a compensated antiferromagnet, featuring a biaxial magnetic anisotropy (40, 41). The modes correspond to orthogonal deflections of the Néel vector defined as L = S(S1 − S2), where S = S(T) is the average value of the Ni2+ spin, and S1,2 is a pair of antiferromagnetically coupled spins. In equilibrium, L is oriented along the x axis, and deflections are expected in (∥) and out of (⊥) the magnetic easy plane (xy), in such a way that the dynamical components ΔLy and ΔLz emerge (see Fig. 3, E and F). The frequencies f∥,⊥ of the magnons are defined by the geometric mean of the respective magnetic anisotropy (D∥,⊥) and exchange energy Jex (see section S6) and, in addition, proportional to S(T). Hence, both should experience a power-law temperature scaling inherent to the magnetic order parameter L similarly to the one observed for the f1 mode. Because the out-of-plane anisotropy is typically more substantial for easy-plane antiferromagnets such as NiPS3, ff is expected. Note that although there is no net magnetization in the ground state: M = S(S1 + S2) = 0, a finite magnetization component M[L·,L] emerges due to the dynamics of the Néel vector L (42). As a consequence, the in- and out-of-plane magnetic modes can be fully described by the orthogonal pairs (Ly, Mz) and (Lz, My), respectively.

In (43), it was recently shown that the application of an in-plane magnetic field larger than Hsf = 100 kG promotes a spin-flop transition in NiPS3, during which the spins suddenly rotate in the easy-plane and, in addition, cant along the field orientation. It can be easily shown (see section S7) that the magnitude of the spin-flop field Hsf is a direct measure of the frequency of the in-plane dynamics f = γHsf = 280 GHz, where γ = 28·10−4 GHz/G is the gyromagnetic ratio. This estimate agrees particularly well with f1 and thus provides another strong indication that the coherent oscillation excited upon resonant pumping of the 3A2g3T2g transition is the in-plane magnon mode characterized by Ly and Mz and a 2D critical scaling. We note that even though there is an oscillating out-of-plane magnetic component Mz, the experimentally observed oscillations show a strong phase and amplitude dependence on the orientation of the probe polarization plane with respect to the crystal axes, indicating that the detection of this mode is given by linear magnetic birefringence due to the Ly component rather than Faraday rotation, sensitive to Mz (44).

Having identified f = f1, we put forward the assumption that the higher-frequency oscillation at f2 can be assigned to the complementary out-of-plane magnon (f = f2). Our phenomenological theory (see section S8) suggests that excitation of the out-of-plane magnon mode with linearly polarized light is possible in NiPS3 due to the low-symmetry (monoclinic) distortion of the crystal lattice. However, these assumptions do not agree with the recently reported, although mutually conflicting, values for the zone-center magnon at the significantly higher frequencies of 1.69 and 2.4 THz from (45) and (25), respectively. To unambiguously establish the origin of the coherent mode f2, time-resolved measurements in high magnetic fields, HHsf, are of primary importance.

To further our understanding of the excitation mechanism of the in-plane (f1) magnon and its relation to the light-induced magnetic anisotropy, we varied the orientation of the pump polarization plane, set by the azimuthal angle ϕ (see Fig. 4A). Although the optical absorption at the 3A2g3T2g orbital resonance is nearly independent of ϕ, the amplitude and phase of the induced magnetic oscillations are strongly affected by variation of the angle. Figure 4B shows that the amplitude of the excited magnon follows a clear π-periodic sinusoid with maxima corresponding to the polarization oriented at ±45° with respect to the orientation of the Néel vector L. This dependency can be simply understood: The linearly polarized light incident at normal to the (ab) crystal plane promptly induces a magnetic anisotropy axis, directed along the orientation of the pump polarization plane. The axis breaks the magnetic symmetry in the basal plane (xy), providing an in-plane magnetic torque sufficiently short to impulsively trigger the planar motion of the spins (see Fig. 4C). The validity of this scenario is further supported by a phenomenological theory based on symmetry considerations and general principles of light-matter interactions in a magnetic medium (see section S8).

Fig. 4 Selection rules for the excitation of the in-plane magnetic mode.

(A) Pump-induced rotation of the probe polarization plane as a function of pump-probe delay time Δt for different orientations of the linear polarization of the pump. The pump photon energy is 1.0 eV. (B) The amplitude of the oscillations as a function of the azimuthal angle ϕ between the pump polarization plane and the a crystal axis. (C) Schematics showing that the electric field of light acts as an instantaneous photomagnetic anisotropy (dashed line) with a direction along the light polarization plane, resulting in a torque and subsequent oscillations of the Néel vector L and net magnetization M.


The azimuthal dependence of the oscillation amplitude on the orientation of the pump polarization allows us to attribute the excitation of the in-plane magnon mode to an ultrafast light-induced change of the magnetocrystalline anisotropy. This anisotropy emerges in response to resonant optical excitation of the Ni2+ electrons to the 3T2g orbital state, characterized by an unquenched net angular momentum. To estimate the lifetime of the photoinduced anisotropy, we performed a time-resolved analysis of the frequency of the spin precession at various fluences of the incident pump. A long-living change in the anisotropy should renormalize the magnon frequency within the lifetime of the excited state in agreement with (46, 47) and the derived formulas in sections S6 and S8 and thus can be seen as a measure of the magnetic anisotropy relaxation. Consequently, exciting with greater fluence would amplify this effect: The spin precession frequency would scale with the fluence. In contradiction to this, we observe that fluence affects only the amplitude but not the frequency of the spin precession (fig. S9), which indicates that the lifetime of the anisotropy is at least shorter than the period of the spin precession (<3 ps). The short lifetime of the anisotropy can originate from the short-lived photoexcited state, whose lifetime is given by the natural width of the 3A2g3T2g absorption line (0.2 eV) and is on the order of 20 fs. The observed polarization control of the spin precesion is strongly reminiscent of the inverse Cotton-Mouton effect (48), a particular variant of the magnetic ISRS also widely considered as an instantaneous photoinduced magnetic anisotropy (49, 50). In the magnetic ISRS scenario, the pump photon is scattered in an event where an electron momentarily gains orbital angular momentum from the higher-level orbital states typically having energy higher than the incident photon. Our experimental results can thus be interpreted alternatively as being indicative of the resonant enhancement of the scattering process upon approaching the transition to the higher-level 3T2g orbital state, underlining the strong impact of the low-symmetry trigonal 3T2g states on the magnetic anisotropy of NiPS3. Several works reported that magnetic ISRS processes in iron-based compounds can be significantly enhanced in the vicinity of the d-d transitions [see, for example, (14, 15)]. Our experiment shows that almost no magnon excitation is observed for the photon energies below the 3A2g3T2g resonance, contrary to what is expected for the ISRS process. The resonant enhancement picture must thus assume that the magnon amplitude falls below our detection limit away from the resonance. Regardless of the exact microscopic nature of the driving mechanism, we emphasize the crucial role of the d-d transitions for optical control of magnetic anisotropy in NiPS3.

In conclusion, our work establishes selective pumping of orbital resonances as an efficient pathway to control magnetic anisotropy and to reveal high-frequency 2D coherent spin dynamics in vdW layered antiferromagnets. While ultrafast control of the magnetic anisotropy and sub-THz spin dynamics is demonstrated here, in bulk lamellar NiPS3, due to advances in exfoliating techniques and strong magneto-optical responses observed in our experiments, we anticipate the applicability of the suggested approach to atomically thin antiferromagnets (26, 51). Such systems can serve as an excellent test bed for the theoretical XY model, with further possibilities such as revealing dynamics of nontrivial topological vortex states associated with the Berezinskii-Kosterlitz-Thouless transition (3, 26).


Crystals of NiPS3 were grown by chemical vapor transport. First, polycrystalline NiPS3 was synthesized by mixing powders of S (99.998%, from Sigma-Aldrich), P (> 99.99%, from Sigma-Aldrich), and Ni (99.99%, from Sigma-Aldrich) in a stoichiometric ratio, pressed into a pellet, and sealed in a quartz ampoule (P ~ 5·10−5 mbar, length = 25 cm, internal diameter = 1.5 cm). The ampoule was kept at 400°C for 20 days and cooled down slowly (0.07°C/min). Next, the previous material was mixed with iodine (99.999% anhydrous beads from Sigma-Aldrich; [I2] ~ 5 mg/cm3), sealed in an evacuated quartz ampoule (P ~ 5·10−5 mbar, length = 50 cm, internal diameter = 1.5 cm), and placed in a three-zone furnace in a gradient of temperatures of 700°/650°/675°C for 28 days. Phase and compositional purity were verified by powder x-ray diffraction and inductively coupled plasma optical emission spectrometry. The materials were handled inside an argon glove box to avoid any possible oxidation. Exact details about temperature gradients and characterization of crystals from the same batch as the ones used in this work can be found in (6).

The pump pulses at the photon energies of 0.8 to 1.9 eV (~100 fs) were obtained using an optical parametric amplifier (OPA), and to access energies below 0.4 eV (~200 fs), we used difference frequency generation by mixing the outputs of two OPAs in a GaSe crystal (52). The pump pulses at a 500-Hz repetition rate were focused on the sample surface to a spot with a diameter of 200 μm. The time-delayed copropagating near-infrared probe pulses at a photon energy of 1.55 eV were focused to a spot of 130 μm, such that the spatial overlap between pump and probe pulses was satisfied.


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Acknowledgments: We thank A. V. Kimel for critically reading the manuscript, and R. V. Mikhaylovskiy for fruitful discussions. D.A. thanks R. Huber for continuous support. Funding: This work was supported by the EU through the European Research Council, grants no. 677458 (AlterMateria) and 788222 (MOL-2D), and by the COST action MOLSPIN CA15128, the Netherlands Organisation for Scientific Research (NWO/OCW) as part of the Frontiers of Nanoscience program (NanoFront), and VENI-VIDI-VICI program, the Spanish MICINN (project MAT-2017-89993-R and Unit of Excellence “Maria de Maeztu” CEX2019-000919-M). M.Š., M.L., H.S.J.v.d.Z., and P.G.S. acknowledge funding from the EU Horizon 2020 research and innovation program under grant agreement numbers 785219 and 881603. E.L. acknowledges funding from the EU Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement no. 707404. B.A.I. is supported in part by the National Research Fund of Ukraine within the competition program “Support for research of leading and young scientists,” and the project “Development of the physical basis of magnetic nanoelectronics” no. 2020.02/0261. Author contributions: D.A. conceived the project together with E.C. and A.D.C. D.A., J.R.H., and M.M. carried out the experiments and analyzed the data. S.M.-V. synthesized the crystal sample. B.A.I. developed the theoretical formalism to describe the magnetization dynamics and contributed to the interpretation of the data. M.Š., M.L., E.L., H.S.J.v.d.Z., and P.G.S. discussed the experimental results. The manuscript was written by D.A., J.R.H., M.M., B.A.I., and A.D.C. with feedback from all coauthors. Competing interests: The authors declare that they have no competing interests. Data and materials availability: All data needed to evaluate the conclusions in the paper are present in the paper and/or the Supplementary Materials. Additional data related to this paper may be requested from the authors. The source data for figures are publicly available with identifier 10.5281/zenodo.4570835.

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