Sonication-assisted liquid exfoliation and size-dependent properties of magnetic two-dimensional α-RuCl3

Originating from the hexagonal arrangement of magnetic ions in the presence of strong spin orbit coupling, α-RuCl3 is considered as model system for the Kitaev-Heisenberg model. While the magnetic properties of α-RuCl3 have been studied in bulk single crystals or micromechanically-exfoliated nanosheets, little is known about the nanosheets’ properties after exfoliation by techniques suitable for mass production such as liquid phase exfoliation (LPE). Here, we demonstrate sonication-assisted LPE on α-RuCl3 single crystals in an inert atmosphere. Coupled with centrifugation-based size selection techniques, the accessible size- and thickness range is quantified by statistical atomic force microscopy. Individual nanosheets obtained after centrifugation-based size selection are subjected to transmission electron microscopy to confirm their structural integrity after the exfoliation. The results are combined with bulk characterisation methods, including Raman and x-ray photoelectron spectroscopy, and powder diffraction experiments to evaluate the structural integrity of the nanosheets. We report changes of the magnetic properties of the nanomaterial with nanosheet size, as well as photospectroscopic metrics for the material concentration and average layer number. Finally, a quantitative analysis on environmental effects on the nanomaterial integrity is performed based on time and temperature dependent absorbance spectroscopy revealing a relatively slow decay (half-life of ∼2000 h at 20 °C), albeit with low activation energies of 6–20 kJ mol−1.


Introduction
Layered ruthenium chloride (α-RuCl 3 ) is a candidate for the Kitaev-Heisenberg model due to a triangular arrangement of magnetic ions and strong relativistic spin-orbit coupling. The spin-1/2 model with bond-dependent spin interactions features a quantum spin liquid (QSL) ground state, which can be considered as topological state with the potential for coherent transport of quantum information and fractional excitations [1][2][3][4]. The latter can be understood as exotic phenomenon which splits an electron into well-defined quasiparticles. In case of a Kitaev 2D-honeycomb lattice, this supports the formation of gauge fluxes and Majorana fermions [5]. While fractional excitation is only reported in theory as yet, the prospect of experimental realisation of such interactions in α-RuCl 3 (or any material) could be considered as breakthrough in quantum computation technology [6].
However, apart from such exotic interactions, non-Kitaev interactions in RuCl 3 yield long-range antiferromagnetic order at low temperatures [1]. The ordering in single crystals has previously been found to proceed via a single sharp phase transition at a Neel temperature of T N = 7 K as seen in magnetic susceptibility and specific heat measurements [1] or via a sequence of two phase transitions occurring at T N1 ≈ 14 K, and T N2 ≈ 8 K, respectively [7][8][9][10]. It has been argued that the number, position, and shape of the magnetic transitions changes as a function of stacking order and stacking faults of the hexagonal layers of Ru 3+ ions in single-crystalline samples. In polycrystalline samples however, single antiferromagnetic phase transitions are reported at T N = 11 K [11], T N = 13 K [12], and T N = 15.6 K [13], respectively.
While the majority of studies on the optical and magnetic properties α-RuCl 3 has focused on the bulk material, only little is known about the materials' properties after exfoliation. This is an important aspect, as the delamination of the crystal goes in hand with a reduction of the stacking disorder, which is discussed to be responsible for an enhanced onset of the antiferromagnetic ordering [1,10]. Although it was recently demonstrated that α-RuCl 3 can be exfoliated by chemical [10], and electrochemical exfoliation [14], in both examples the material loses its pristine electronic and magnetic properties due to electron doping. To avoid this, an alternative liquid exfoliation strategy is sonication assisted liquid phase exfoliation (LPE), which relies on mechanical delamination by forces exerted on the starting material, created upon collapse of cavitation bubbles [15][16][17][18] and colloidal stabilisation through suitable surfactants or solvents [19][20][21]. This methodology has been applied to over 15 classes of layered materials, which have been successfully exfoliated into 2D-nanostructures, including transition metal dichalcogenides (TMDs) [22][23][24], transition metal hexathiohypodiphosphates (M 2 P 2 S 6 ) [25,26], III-VI and IV-VI semiconductors [27][28][29], pnictogens [30][31][32], silicates [33], oxides [34,35], hydroxides [36], and other minerals [37], as well as synthetic structures, such as organic polymers [38], 2D covalent organic frameworks [39,40] and others. Typically, no phase transition or strong doping is observed so that it might be a suitable approach to study layer number dependent properties of α-RuCl 3 .
To this end, we apply the additive free delamination of α-RuCl 3 by sonication assisted LPE under inert conditions. To address the impact of the layer number on the optical and magnetic response, samples were size-selected following previously established centrifugation-based techniques [41]. The lateral size and thickness distribution of the α-RuCl 3 nanosheets in the fractions was quantified by statistical atomic force microscopy (AFM). The structural integrity of the nanosheets was confirmed by a combination of transmission electron microscopy (TEM), Raman spectroscopy, xray diffraction (XRD) and x-ray photoelectron spectroscopy (XPS) measurements. In addition, the magnetic susceptibility of α-RuCl 3 was studied for three samples of different nanosheet size distributions in dispersion and for drop-cast samples, respectively. Furthermore, extinction and absorbance measurements on nanosheet dispersions were used to reveal systematic changes of the photo spectroscopic response. This allows to extract metrics for the material concentration, and the average layer number. Finally, time and temperature dependent absorbance measurements were used to study and to quantify the environmental stability for different nanosheet sizes.

Preparation and characteristics of the nanomaterial
α-RuCl 3 crystals were grown by chemical vapour transport as reported in literature (see SI, experimental section for details) [42]. The layered character can be observed by SEM, revealing crystallites up to a size of approximately 1 mm (see SI, figure S1). The crystallinity of the starting material is confirmed by Raman spectroscopy and powder XRD (see SI, figure S2). Ground single crystals were exfoliated under inert gas conditions in dried, distilled, and degassed N-cyclohexyl-2-pyrrolidone (CHP) assisted by bath sonication. CHP was chosen as exfoliation medium as pyrrolidone-based solvents are known to be suitable stabilising solvents for LPE of various layered crystals and additionally can promote surface passivation supressing material decomposition [25,43]. The latter is associated to strong interactions of the solvent with the nanosheet surface and the formation of a protective solvation shell [43,44]. After exfoliation, the as-obtained stock dispersion of the nanomaterial was size-selected by liquid cascade centrifugation (LCC) [41] to split the initially polydisperse nanosheet mixture of different sizes and thicknesses into fractions of well-defined size distributions. To this end, consecutive centrifugation steps were applied, starting with a step at low centrifugal acceleration (i.e. 100 g), which leads to sedimentation of large and thick nanosheets. The resulting supernatant was separated from the sediment and used for the subsequent step at higher centrifugation speed (i.e. 400 g). After this, and the following centrifugation steps, the sediment was redispersed in reduced volume of fresh solvent to yield a concentrated nanosheet dispersion for further analysis. Note that the unit g refers to a relative centrifugal force (RCF) expressed in multiples of the earth's gravitational acceleration. The same procedure was followed for centrifugation at 1k g, 3k g, 6k g, 12k g, 22k g, and 50k g, whereas the first sediment and the final supernatant were both discarded, as they contain mostly unexfoliated, and defective material, respectively. Following this method, seven fractions of α-RuCl 3 nanosheets with different size and thickness distributions were produced, suitable for further analysis. For consistency with previous reports, we label the fractions by the lower and upper boundary of the centrifugal acceleration used for trapping nanomaterial between two consecutive steps. For example, the sediment from centrifugation of the supernatant after 3k g at 6k g is labelled as 3-6k g.
To quantify the size and thickness distribution in the individual fractions of the size selection, statistical AFM measurements were performed on drop-cast nanosheets on Si/SiO 2 wafer fragments after dilution of the concentrated samples with isopropanol (see SI, experimental section for details). For measuring the dimensions of the nanosheets, line profiles are extracted. We define the nanosheet length as the longest dimension of a sheet, while the width is the dimension perpendicular to the length. The height of a sheet is extracted from the average height from both profiles. An example is given in the SI, figures S3(A) and (B) (for further details, see [23,45]). Representative images of the fractions containing the largest (0.1-0.4k g) and the smallest (22-50k g) nanosheets isolated within the boundaries of the size selection are shown in figures 1(A) and (B). The corresponding distributions of the lateral sizes and the nanosheet layer number of the same two fractions are shown in direct comparison in figures 1(C) and (D), respectively. Note that for the accurate determination of the layer number from the measured apparent AFM thickness, additional contributions from impurities, solvent residues, chemical potential, and the measurement parameters must be considered. The measured apparent height in liquid-exfoliated nanosheets is thus typically overestimated, but proportional to the expected crystallographic thickness [25,40,[46][47][48][49][50][51]. This issue can be overcome by a step height analysis on incompletely exfoliated nanosheets to convert apparent AFM thickness to layer number [25,40,46,47,52]. In brief, the AFM height of a single layer is determined by measuring line profiles on nanosheets with suitable steps and terrace structures (see SI, figure S3(C) for an example). Plotting the step height on >100 structures in ascending order reveals regular steps with a height of multiples of 1.5 nm in the case of LPE α-RuCl 3 (see SI, figure S3(D)). Hence, the measured, apparent nanosheet height is divided by 1.5 nm for conversion into layer number.
Both fractions shown in figure 1 exhibit a lognormal lateral size (length L, figure 1(C)) and thickness (layer number N, figure 1(D)) distribution which is shifted towards significantly smaller sizes for the fraction isolated at higher centrifugation speed (22-50k g). A comparison of the size and thickness distributions of all fractions isolated by LCC is shown in the SI (figures S3 and S4). Upon further analysis, the arithmetic mean values of the nanosheet length, <L> and layer number, <N> are plotted as a function of the midpoint of the two consecutive centrifugation steps used to produce the fraction (central RCF) on a logarithmic scale (figures 1(E) and (F)). In both cases, a clear decrease of both dimensions is observed with increasing centrifugal acceleration, following a power law dependence. Fitting the data reveals proportionalities for <N> ∝ RCF −0. 34 and <L> ∝ RCF −0.39 . Note that a similar behaviour is observed for other 2D-material systems [53], even though an exponent of −0.5 is typically expected for <L> due to the correlation between <L> and the cut size, which is found to be proportional to the inverse rotation rate, as reported elsewhere [41,54]. To further visualise the change of the dimensionality of the nanomaterial in each fraction of the size selection sequence, the area of individual nanosheets found in the different size fractions is shown as function of their layer number in a scatter plot where each data point represents an individual sheet (figure 1(G)). The graph clearly shows the decrease of the average nanosheet size with increasing centrifugation speed, as well as some overlap of the nanosheet dimensions represented in adjacent fractions. In addition, it shows that thinner nanosheets tend to be smaller and thicker nanosheets tend to be larger. This is typical for LPE nanosheets and due to both delamination and nanosheet tearing occurring [55].
To confirm the crystallinity and structural integrity of the nanosheets, a combination of TEM, Raman spectroscopy, XPS and XRD measurements was performed on the exfoliated nanomaterial. The results of the microscopic and spectroscopic characterisation are summarised in figure 2. For TEM, a nonsize selected dispersion, where only unexfoliated material was removed as sediment at 100 g, was drop-cast on Quantifoil TEM grids in N 2 atmosphere. This sample was chosen to avoid exposure to ambience as much as possible, since centrifugation had to be performed (in sealed vials) outside the glovebox. We note that CHP residues were removed in the prevacuum of the microscope (∼2 × 10 −5 mbar) at 150 • C for 40 min prior to low dose high resolution (HR)-TEM measurements (see SI, figures S5(A)-(D) for further details). A TEM overview image, including a relatively large nanosheet of several µm in length is shown in figure 2(A). The nanosheets shown on the image exhibit sharp edges, in good agreement with the morphology of the material characterised by AFM measurements. Selected area electron diffraction (SAED) was measured on the region indicated by the dashed circle and is shown in the inset of figure 2(A). The diffraction pattern shows sharp and bright spots confirming the crystallinity of the exfoliated nanomaterial. Figures 2(B) and (C) show HRTEM images of exfoliated α-RuCl 3 nanosheets, revealing the atomic lattice. The results from HRTEM are in good agreement with a simulated trigonal lattice structure (see SI, figures S5(E)-(H) for direct comparison of the measurement to expected patterns for different simulated RuCl 3 polymorphs) and previously reported literature [56]. The inset in figure 2(B) shows a fast Fourier transformed reciprocal space pattern of the probed region, further emphasising the crystalline character of the sample. In addition to SAED, scanning transmission electron microscopy (STEM) energy-dispersive x-ray (EDX) mapping was performed on free-standing nanosheets. The magnified high-angle annular dark field (HAADF) STEM image and the elemental distribution maps for ruthenium (red), chlorine (green) and oxygen (white) are shown in figure 2(D). The measurements confirm the material's stoichiometry, and suggest only minute oxidation. This finding is further supported by core-loss electron energy loss spectroscopy (see SI, figures S6(A)-(C)). The average EDX spectrum on the sample shown in figure 2(D) and EDX measurements on additional nanosheets are shown in the SI (figures 6(D)-(F)). Based on EDX measurements, the material stoichiometry is suggested to be RuCl 2.6 O 0.02 , RuCl 2.7 O 0.3 and RuCl 3.1 O 0.01 for the different probed areas, respectively. Note that small and thin nanosheets show high electron beam sensitivity at 80 kV indicated by substantial changes of the nanosheet lattice upon beam irradiation. Hence, no further quantitative analysis is possible on ultrathin samples. Examples on the impact of the electron beam on thin α-RuCl 3 nanosheets are shown and discussed in the supporting information (see figures S6(G) and (H)).
To additionally assess the nanomaterials' structural integrity after the exfoliation and size selection, in particular for small/thin nanosheets that cannot be reliably probed in TEM, measurements on ensembles of nanosheets were performed. To this end, samples of different nanosheet sizes were dropcast in an inert atmosphere on a gold coated aluminium support for Raman spectroscopy and XPS measurements (figures 2(E) and (F)) and on a quartz substrate for powder XRD measurements (figure 2(G)). The Raman spectra of three different sizes representative for large, intermediate, and small nanosheets (i.e. 0.1-0.4k g, 6-12k g and 22-50k g) are shown in figure 2(E), together with an average spectrum measured on a single crystal. The spectra are shown with horizontal offset for clarity. While all modes from the bulk material can also be observed in the exfoliated nanosheets, a significant broadening of the modes is observed for the exfoliated material, which can be attributed to finite size-effects, and random orientation of the drop-cast material. We note that a similar effect has also been observed for micromechanicallycleaved nanosheets [4]. As no additional modes appear in the spectra of the nanosheets, no clear indications for material decomposition after LPE and LCC can be observed by Raman measurements. However, species formed upon decomposition may not be Raman active or resonant with the excitation wavelength.
Hence, XPS measurements were additionally performed. The ruthenium 3d core level spectrum is shown in figure 2(F) , intermediate (6-12k g, green) and small (22-50k g, blue) nanosheet sizes, respectively. Similar modes are observed for the exfoliated nanomaterial as for bulk material. We note that a significant broadening of the modes is observed, which can be attributed to random orientation of the material upon drop casting. (F) Ruthenium 3d core level x-ray photoemission spectrum of a fraction containing the smallest nanosheets (22-50k g). Data fitting suggests that only ∼50% of the material surface is composed of α-RuCl 3 at the time of the measurement. (G) In-plane PXRD measurements (λ = 1.54059 Å) of a bulk crystal (grey) compared to different size-selected fractions of exfoliated nanosheets deposited on a quartz support in transmission geometry. Reported data on restacked RuCl 3 nanosheets is shown for comparison. The data for restacked nanosheets was modified and reproduced with permission from [10].
for the sample containing the smallest fraction of nanosheets (22-50k g). In addition to the expected signals from RuCl 3 , additional contributions from carbon, elemental ruthenium, ruthenium oxide, -hydroxide and -oxyhydroxide (RuO 2 , Ru(OH) 3 , and RuO(OH) 2 ) are identified. The spectra suggest that only about 50% of the initial RuCl 3 is retained on the surface of the sample. Fitting of the data to the response from the individual components implies that ∼10% of the signal stems from elemental ruthenium, ∼21% from RuO 2 and 16% from Ru(OH) 3 . A similar composition was found for a sample prepared the same way as the dispersion used for TEM (only removal of unexfoliated material), as shown in figure  S7. This seems to disagree with TEM analysis on individual flakes. However, we note that XPS is surface sensitive and that the samples might have been exposed to ambient atmosphere (oxygen and water) prior to the measurement during sample transport even though they were sealed in a vacuum bag in the glovebox (see SI methods). Further, we note striking changes in the ruthenium 3d core level spectra on prolonged exposure. A set of four subsequent measurements on the same sample area is displayed in figure S7. Clearly, the RuCl 3 nanosheets are extremely sensitive also to the x-ray irradiation in spite of the ultrahigh vacuum conditions. Overall, the percentage of oxides and hydroxide species increases, while the feature assigned to RuCl 3 drops to ∼30% relative contribution to the ruthenium core level spectrum ( figure S7(E)). Hence, the contribution of decomposition products from XPS measurements is likely overestimated. Unfortunately, it is not possible to infer whether beam damage has already occurred during the first acquisition so that the composition of the smallest/thinnest nanosheets cannot be assessed.
For further characterisation, powder XRD measurements were performed ( figure 2(G)). The diffractograms of the samples containing large, intermediate, and small nanosheets show patterns distinct from bulk α-RuCl 3 which is shown in grey for comparison. In order to understand these differences, reflexes are additionally compared to the recently reported pattern of randomly restacked RuCl 3 nanosheets (dark grey trace) [10]. The most intense Bragg reflexes of the exfoliated nanomaterial are found at similar angles as the restacked material. In addition, a signal broadening is observed which is assigned to structural distortion of restacked material after drop casting, similar to the effects observed in the Raman spectra. A closer analysis reveals that an increasing number of unassignable reflexes is observed with decreasing material size which could suggest that crystalline degradation products are formed, which are observed more clearly in the samples with higher surface to volume ratio. However, an alternative interpretation of the data could be that these are due to preferred orientation effects which are less prominent in the smaller sheets so that out-of-plane reflections become more dominant compared to larger sheets, where mostly reflections with (001) character can be observed due to the reflection geometry. This would imply that the other reflexes at higher angles (2Θ) are assignable to other RuCl 3 polymorphs or decomposition products. However, to confirm this, simulations for different crystal lattices and stacking orientation would be required, in particular because the reflexes cannot be assigned to the expected species from XPS measurements [10,57,58]. Overall, the bulk characterisation clearly shows that exfoliated α-RuCl 3 is prone to degradation which is discussed in more detail below. Since the material is exposed to ambient conditions during most measurements, unambiguous conclusions about the degree of oxidation cannot be obtained. However, results from TEM measurements, where the exposure to oxygen and water was minimised are encouraging and reveal only minute oxidation for the-as prepared-nanomaterial. Unfortunately, the smallest/thinnest nanosheets are very sensitive to beam damage both in TEM and XPS, so that their composition cannot be precisely assessed. However, as we will demonstrate below, absorbance spectra show the same spectral profile across all size-selected fractions which indicates a similar initial composition, also for the fraction of smallest/thinnest nanosheets. In the following, this will be analysed in more detail and also used to track degradation as function of time and temperature after exposure to ambient atmosphere which results in significant changes of the spectral profile. Overall, the results emphasize that extreme care must be taken upon preparation of liquid phase exfoliated nanomaterials due to significantly enhanced reactivity of the nanosheets compared to their bulk counterparts.

Magnetic characterisation of α-RuCl 3 nanosheets
As mentioned above, α-RuCl 3 is considered particularly interesting for fundamental studies of magnetic properties in lowdimensional structures and a possible realisation of a twodimensional QSL in its ground state [10,[59][60][61][62]. To date, the majority of work was carried out on micromechanicallyexfoliated (ME) nanosheets [4,56,63], with few examples of exfoliation in liquids [10,14] and no report on pristine, undoped nanosheets as produced by sonication-assisted LPE. To this end, measurements in a superconducting quantum interference device on three different sizes, representative for large, intermediate, and small (i.e. 0.1-0.4k g, 6-12k g and 22-50k g) α-RuCl 3 nanosheets were performed in liquid environment and on drop-cast nanosheets, deposited in an inert atmosphere. The results of the magnetic measurements are shown figure 3. The low-temperature magnetic response of the different sizes of CHP-dispersed nanosheets are shown for two separate batches of exfoliated material. For clarity, a measurement on the starting material is included. Due to background uncertainties, resulting from non-negligible contributions from the solvent, the data was scaled to the susceptibility of the crystal at 50 K for better comparability. The bulk material shows a smooth Curie-Weiss like increase of the magnetisation upon cooling from room temperature, followed by a broad anomaly, indicative for the evolution of long-range antiferromagnetic order at around 10 K. This anomaly is suppressed in the large (0.1-0.4k g) nanosheet dispersion, and instead, a sharp transition is visible at T = 2 K (figure 3(A), inset). No such transition is observed for the smaller nanosheet sample (22-50k g) within the accessible temperature range. However, a similar transition can be observed for one out of the two batches of intermediate sized nanosheets (6-12k g) in ∂(χT)·∂T −1 as illustrated in the inset of figure 3(A). We note that in general, the magnetic response at low temperatures differs between the respective batches for the small-and intermediate sized nanosheet dispersion, which we attribute to a combination of material decomposition, solvent effects and partial aggregation of dispersed nanosheets while approaching low temperatures.
To amend the magnetic response of the nanomaterial, freestanding nanosheet films of the individual sizes were prepared by drop casting of the dispersed material in a nitrogen atmosphere (see figure S8). The high-temperature magnetism for the different nanosheet size pellets is proportional to the bulk material, as evident by the susceptibility curves in figure 3(B). The platelets' susceptibilities deviate from that of the bulk material below ∼75 K, indicating stronger short range antiferromagnetic correlations in the bulk material than in the platelets. Both, the medium-and large-sized nanosheet films show a similar behaviour, exhibiting a broad plateau-like hump at around 4 K and a sharp decrease at the lowest accessible temperatures ( figure 3(B), inset 1). The broad hump evolves into a well resolved peak if a low magnetic field is applied (B = 0.01 T, see figure 3(B), inset 2). This implies the evolution of long-range antiferromagnetic order at T N = 3 K for the medium-and large-sized nanosheets, while the magnetic ordering is suppressed either completely or shifted towards temperatures below the accessible range when B = 1 T is applied. Further, size reduction stabilises the antiferromagnetic phase, as evidenced by a sharp peak in the susceptibility at B = 1 T at 2.2 K for the sample containing the smallest nanosheets ( figure 3(B), inset 1). Note that due to the limited amount of material, measurements at B = 0.01 T were not successful for the smallest nanosheets. Despite the fact that longrange magnetic order in the small-sized platelets appears to be more pronounced compared to fractions containing larger nanosheets, the broad hump is not observed, which indicates less pronounced short-range antiferromagnetic correlations in this temperature regime. Hence, the overall tendency is that high-temperature antiferromagnetic correlations are suppressed upon size reduction while at the same time a sharp, rather 3D-like antiferromagnetic phase transition appears to be stabilised. One may argue that the low-temperature antiferromagnetic phase appearing in the solid nanosheet samples is of similar nature as the phase indicated by the sharp decrease in susceptibility of the solution-dispersed samples.

Optical properties of α-RuCl 3 nanosheets
To further shine light on size and thickness-dependent properties, the size-selected fractions of the α-RuCl 3 nanosheets were subjected to extinction and absorbance spectroscopy. For this purpose, photo spectroscopic measurements were performed in transmission mode, where T = 10 −Ext with Ext = ε · c · d (ε = extinction coefficient, c = concentration of the nanosheets and d = depth of the light path). We note that the measured extinction (Ext) is the combination of the wavelength dependent absorption (Abs) and scattering (Scat) contributions of the material, where Ext (λ) = Abs (λ) + Scat (λ). The dispersions were therefore additionally measured in the centre of an integrating sphere for the absorption measurements, where scattered light is collected (see experimental section). For a quantitative analysis, the concentration of each size-fraction was determined by gravimetric weighing of the exfoliated material.
That the scattering contribution is typically more pronounced for larger than for smaller particles of similar geometry is best illustrated by a direct comparison: figures 4(A) and (B) shows the wavelength dependence of the extinction (ε), absorption (α), and scattering (σ) coefficient of dispersions containing large (0.1-0.4k g) and a small (22-50k g) nanosheet sizes, respectively. A significant difference between the extinction and the absorbance coefficient is observed for the large nanosheets ( figure 4(A)), which is almost negligible for the fraction containing the small nanosheets ( figure 4(B)). Note that, compared to other LPE nanosheets such as TMDs, Ni 2 P 2 S 6 , or layered hydroxides [22][23][24][25]36], the contribution from scattering to the extinction spectra is much less pronounced [64].
The absorption and extinction coefficient spectra of all nanosheet sizes are shown in direct comparison in figures 4(C) and (D). All nanosheet sizes show two broad features at ∼370 and ∼550 nm. The inset in figure 4(D) depicts the change of the extinction coefficient as function of nanosheet size for three distinct wavelengths (400, 500 and 600 nm), which shows no significant variation with nanosheet size. This is an unusual observation as typically various effects lead to significant characteristic changes to the spectra of nanosheets of different sizes, including contributions from size-dependent light scattering as well as edge and confinement effects and from dielectric screening [25,28,46,65,66]. Those different effects influence the spectra in a characteristic way depending on the impact of the nanosheet size on the nanosheet geometry, and the band structure of the material. While size-independent optical coefficients are not usually observed, they enable the reliable determination of the α-RuCl 3 nanosheet concentration using the Beer Lambert law.
Due to the uncertainty in the masses extracted from gravimetry which have an impact on the coefficient spectra, sizedependent trends were additionally studied on normalised spectra. As shown in figures S9 and S10, the absorbance spectra only show very minor variations across the size-selected fractions. However, we note that exposure to ambience, in particular at elevated temperatures, induces significant changes (figure S9) in the spectral profile. This indicates that the sample initially have the same composition and that degradation can be monitored through absorbance measurements. While changes across fractions in the normalised extinction and absorbance spectra are subtle, they are nonetheless systematic with size (see SI, figure S10(B) inset). Changes of the intensity ratios in extinction or absorbance spectra typically scale with the nanosheet lateral sizes due to different electronic contributions from the nanosheet edges and planes. Hence, the peak intensity ratio ( 370 nm / 555 nm ) is plotted as function of the average lateral nanosheet size in each fraction as determined from the statistical AFM analysis (see SI, figure S10(C)). This enables to fit the change of the spectra to a previously reported model (see table 1) [66]. While the fits are reasonable, we note that the magnitude of the change of the intensity ratios is too small for a reliable size determination from UV-Vis spectroscopy alone.
In addition to the size-dependent variation of the intensity ratio, systematic shifts of the optical transitions are observed in the spectra. These are often attributed to confinement and dielectric screening effects of excitons and typically scale with the nanosheet layer number [25,46]. For a precise determination of the centre of mass peak position, the second derivative of the spectra is used, as shown in figure 4(E). A systematic redshift is observed for the peak at 375 nm in both, the extinction, and absorption spectra, as indicated by the arrow (for absorbance see SI, figure S10(D)). The resonance of the peak shows a well-defined scaling with the average nanosheet layer number, following an empiric equation, in agreement with previous reports (figure 4(F)) [24]. This is useful as it allows to quantify and compare phenomenological changes of electronic transitions with the average material layer number for different material systems, and to derive metrics for the layer number from extinction and absorbance spectroscopy. The results are shown in the table below  (table 1).
We note that the resonances extracted from the extinction spectra are increasingly red-shifted for thicker nanosheets opposed to transition energies extracted from absorption spectra. This is attributed to an increasing contribution of light scattering from larger nanosheets, which is red-shifted compared to the absorbance (see also figure 4(A)). Fitting parameters for systematic changes of the extinction and absorbance intensity ratio and peak position with the average lateral nanosheet dimensions, <L>, and arithmetic mean layer number, <N>, respectively. Note that the change of the intensity ratio with nanosheet length is subtle and does not allow for a reliable platelet length determination from UV-Vis spectroscopy alone.

Environmental stability of α-RuCl 3 nanosheets
Nanosheets are often more sensitive to environmental decomposition or degradation compared to their corresponding bulk counterparts due to the largely increased surface area. It is therefore important to study the material stability for different nanosheet sizes and hence varying effective surface area. This is particular the case of α-RuCl 3 , since some techniques suggested oxidation as discussed above. For a study on degradation kinetics, absorbance spectroscopy can be used to investigate the environmental impact on the nanosheets' optical properties as a function of size, time and temperature. To this end, dispersions containing nanosheets with different lateral sizes and thicknesses (being large-0.1-0.4k g, intermediate-6-12k g, and small-22-50k g) were exposed to ambient conditions and stirred at 20 • C, 40 • C and 60 • C, respectively, with absorbance spectra being acquired in defined time intervals. Prior to each measurement, samples were bath sonicated for ∼2 min to avoid potential impact from aggregation or material sedimentation. Absorption spectra of large-sized nanosheets, acquired at different stirring times, up to 672 h (28 days), at 60 • C are shown in figure 5(A). It is evident from significant changes of the spectral profile in the UV-region that the material undergoes substantial structural changes over time. In addition to obvious changes in the UVregion, the overall signal intensity of the material in the visible region (500 and 800 nm) decreases systematically over time where the initial shape of the spectral profile is retained. This suggests that within this wavelength range only contributions from RuCl 3 are detected, which can be used to quantitatively track the material decomposition as a function of time. We find that the change of the absorbance at 525 nm is best behaved for all nanosheet sizes and temperatures (for the full set of spectra, see SI, figure S11), following a single exponential decay (see SI, figures S12(A)-(C)).
Plotting the natural logarithm of the absorption at 525 nm as a function of the stirring time for different temperatures reveals a clear linearisation of the data, consistent with a (pseudo) first order rate law for the material degradation. Note that degradation kinetics in solution can be quite complex due to the formation of a solvation cage around the reagents, which may control the reaction rate due to diffusion effects. In addition, here, various reaction sites (e.g. edges and basal plane) are possible and different reaction products were observed in XPS (oxides and hydroxides). Therefore, a simple (pseudo) first order reaction would be more than surprising. However, in spite of an underlying complexity on the molecular level, the average macroscopic behaviour can apparently be approximated well with the (pseudo) first order kinetics. Therefore, we use a linear fit on the semi-ln scale to extract the macroscopic half-lives for the material decomposition. Note that the linear fit allows less degrees of freedom compared to an exponential fit and is thus more reliable for this purpose. The data is exemplarily shown in figure 5(B) for large (0.1-0.4k g) α-RuCl 3 nanosheets (for all sizes, see SI figures S12(D)-(F)). This is useful as it gives an idea about suitable conditions and the available timeframe for material processing (see table 2) and allows to estimate the activation energy of the material Table 2. Half-lives of the nanosheet degradation extracted from fitting the (pseudo) first order decay kinetics obtained from following the absorbance as function of time for size-selected fractions of α-RuCl 3 containing large, medium and small nanosheets at three temperature. The activation energies of the degradation are also given. decomposition from an Arrhenius type plot. The result of the latter is shown in figure 5(C), where the natural logarithm of the macroscopic material half-live is shown as a function of the corresponding inverse temperature. While only three temperatures were studied for each material size, a reasonable linearisation is found, which allows to approximate the size-dependent activation energy (see table 2). The trend is illustrated in figure 5(D), where the decomposition activation energy extracted from figure 5(C) is shown as a function of the average nanosheet size as determined from statistical AFM analysis. It is evident that the activation energy for the α-RuCl 3 degradation increases with the material size, which implies a lower activation energy for the material decomposition at nanosheet edges as opposed to the nanosheets' basal planes. While activation energies of the degradation are lower than for WS 2 monolayers in aqueous surfactant or Ni 2 P 2 S 6 [25,67], we note that the half-lives are relatively long. This implies that, while the degradation of the material is observed at moderate temperatures already, the available timeframe until a significant portion of the material is affected from environmental impacts is reasonable for all material fractions studied within the scope of this work (t 1/2 > 30 days), and is in agreement with previously reported results on aging effects on micromechanically-cleaved RuCl 3 nanosheets [4].

Conclusion
In conclusion, we demonstrated the additive free liquid exfoliation of α-RuCl 3 into nanosheets of different sizes and thicknesses in an inert atmosphere. The nanomaterial was separated into fractions of different size and thickness distributions, following established cascade centrifugation protocols. The structural integrity and crystallinity of individual nanosheets is confirmed by TEM measurements and further supported by a combination of Raman spectroscopy, XPS and XRD measurements, averaging over a large number of nanosheets. For the first time, susceptibility measurements were performed on α-RuCl 3 nanosheets in a liquid medium and compared to randomly restacked nanosheets in drop-cast samples. No QSL state could be confirmed for any of the exfoliated nanosheet sizes. In contrast, hightemperature antiferromagnetic correlations are suppressed upon size reduction while a sharp, 3D-like antiferromagnetic phase transition seems to be stabilised. Further, the photo spectroscopic response of α-RuCl 3 nanosheets for different size fractions allows to establish spectroscopic metrics for the average material layer number and concentration in dispersion. We emphasize that an unusually small change of extinction and absorbance intensity ratio with material lateral size is observed. While qualitatively similar to previously reported material systems [25,66,68], it is not considered as reliable metric due to the magnitude of the observed changes. At last, the material sensitivity to ambient oxygen and water was studied by time and temperature dependent absorbance measurements for different material sizes. The results suggest a macroscopic (pseudo) first order rate kinetic for the material decomposition which allows to estimate the available timeframe for further material processing and the activation energy for the degradation which is well below room temperature. An increasing trend of the activation energy with material size implies a preferentially edge-centred decomposition mechanism. We note that the observation of a relatively slow reaction with low activation energy (i.e. below room temperature) strongly suggests that kinetics on the molecular level are relatively complex so that the analysis should be considered as approximation.
We consider the presented results important for future applications exploiting magnetic properties of nanosheets. The low activation energy for the material decomposition emphasises that the exfoliation, storage and processing parameters can lead to significant differences in material characteristics attributed to partial oxidation of the nanomaterial and have to be studied carefully before applications can be considered.

Data availability statement
The data that support the findings of this study are available upon reasonable request from the authors.