Layer-Dependent Mechanical Properties and Enhanced Plasticity in the Van der Waals Chromium Trihalide Magnets

The mechanical properties of magnetic materials are instrumental for the development of magnetoelastic theories and the optimization of strain-modulated magnetic devices. In particular, two-dimensional (2D) magnets hold promise to enlarge these concepts into the realm of low-dimensional physics and ultrathin devices. However, no experimental study on the intrinsic mechanical properties of the archetypal 2D magnet family of the chromium trihalides has thus far been performed. Here, we report the room temperature layer-dependent mechanical properties of atomically thin CrCl3 and CrI3, finding that the bilayers have Young’s moduli of 62.1 and 43.4 GPa, highest sustained strains of 6.49% and 6.09% and breaking strengths of 3.6 and 2.2 GPa, respectively. This portrays the outstanding plasticity of these materials that is qualitatively demonstrated in the bulk crystals. The current study will contribute to the applications of the 2D magnets in magnetostrictive and flexible devices.

T he magnetic moment of a crystal is susceptible to the application of external strain, 1 as a consequence magnetostriction has had a big technological relevance in the past century. 2−4 The recent isolation of free-standing 2D magnets, 5−9 has settled long-standing fundamental questions 7 and enabled ultrathin magnetoelectric devices. 10−12 However, despite recent works that have demonstrated a strong modulation of 2D magnetism in atomically thin CrI 3 under high-pressure values, 13,14 direct-strain modulation has only been attempted for <0.3% strain values, 15 and the prospects of the modulation of magnetism in the 2D limit have therefore not been fully explored. This can be attributed to a lack of fundamental understanding of the intrinsic mechanical properties of 2D magnets, which proves vital to realize their various applications. Indeed, although CrCl 3 was first studied by Kamerlingh Onnes 16 at the beginning of the last century, no experimental data on the mechanical properties of the magnetic chromium trihalide (CrX 3 , X = I, Cl, Br) bulk or few-layer crystals has been reported to date.
The mechanical properties of 2D materials have been shown to be different from those of their bulk counterparts. Graphene, for instance, has Young's modulus of ∼1 TPa and breaking strength of 130 GPa, 17 significantly higher than in graphite. 18,19 A similar trend has been observed in other 2D materials, such as atomically thin hexagonal boron nitride (hBN) (0.87 TPa in Young's modulus and 70 GPa in breaking strength) and molybdenum disulfide (MoS 2 ) (0.33 TPa in Young's modulus and 30 GPa in breaking strength). 20,21 It is worth mentioning that these strength values are far beyond the yield strength measured in conventional materials (i.e., ∼3 GPa for that of silicon), 22 demonstrating the capability of 2D materials to sustain an enormous strain without failure, 23 for example, up to 25% in the case of graphene. 17 On the other hand, the multilayer forms of these van der Waals crystals can benefit from their layered structure to achieve large plasticity. Such exceptional behavior has been recently reported in InSe, portraying this material as a strong candidate for near-future deformable electronics. 24,25 It is therefore timely to explore the layer-dependent intrinsic mechanical properties of the chromium trihalides as archetypal magnetic 2D materials.
In our experiment, we obtained atomically thin CrI 3 and CrCl 3 flakes down to the bilayer (2L) by mechanical exfoliation of bulk crystals. The exfoliation was directly performed on substrates with prefabricated microwells for atomic force microscopy (AFM) nanoindentation (see Supporting Information for details). Figure 1a,d shows an optical micrograph of atomically thin CrI 3 and CrCl 3 covering several holes in a 90 nm-SiO 2 /Si substrate. Figure 1b and e shows the corresponding AFM images in contact mode, portraying a thickness of 1.7 and 1.4 nm (Figure 1c,f), respectively, which corresponds to 2L CrCl 3 and CrI 3 .
The mechanical properties of the few-layer CrI 3 and CrCl 3 were probed by the nanoindentation technique performed with the same AFM used for topographic inspection. 17,20 The load− displacement curves were obtained by applying a load at the center of each suspended region until fracture for a minimum of five indentations per thickness per material to ensure the repeatability of the results. The curves were then fitted by a well-established model 17  Young's modulus and breaking strength of 2L CrI 3 and 2L CrCl 3 were E = 43.4 ± 4.4 GPa and σ = 2.2 ± 0.5 GPa and E = 62.1 ± 4.8 GPa and σ = 3.6 ± 0.4 GPa, respectively. The ultimate strain was found directly under the tip and its values for 2L CrI 3 and 2L CrCl 3 were 6.09% and 6.49%, respectively. A direct comparison between the two materials indicates that both the Young's modulus and the breaking strength of CrCl 3 were larger than those of CrI 3 , depicting that the chromium trihalide materials with a heavier halide exhibit a lower  Nano Letters pubs.acs.org/NanoLett Letter mechanical stiffness. This trend correlates nicely with the ionic character of the Cr−X bond, which is stronger in the Cr−Cl interaction compared to Cr−I. 26 Remarkably, as the thickness of the flakes increases, both atomically thin materials show a drop in Young's modulus and breaking strength. For example, 9L CrI 3 had E = 15.8 ± 1.2 GPa and σ = 1.6 ± 0.04 GPa, representing a 64% and 27% decrease in Young's modulus and breaking strength compared to 2L, respectively. Similar trends were observed in CrCl 3 , where 10L CrCl 3 had E = 27.1 ± 2.5 GPa and σ = 2.2 ± 0.2 GPa. To provide further insights into the layer-dependent mechanical properties of the chromium trihalides, we have Nano Letters pubs.acs.org/NanoLett Letter undertaken van der Waals-corrected density functional theory (vdW-DFT) calculations to unveil the energy landscape of interlayer sliding shifts during the mechanical tests (see section 6 in the Supporting Information for details). Figure 3a shows a schematic of the atomic structure of bilayer CrX 3 along the crystallographic c axis (direction of the AFM tip motion during indentation) in the monoclinic phase (space group C2/m) present at room temperature, with the definition of the two interlayer sliding paths utilized in the simulations: along [100] and along [010]. We apply a fractional lateral shift on one chromium-trihalide layer relative to the other starting from the AB stacking order (Figure 3b,c). The FEM simulations predict that the suspended 2L CrX 3 crystals are mostly under small inplane strain in the area far from the contact region even under the fracture loads. This picture changes in the region close to the indentation center where out-of-plane compression starts to play a key role in the fracture mechanism. Figure 3d and 3g shows the in-plane strain (solid lines) and out-of-plane compression (dashed lines) distributions close to the indentation center under different fracture loads for 2L CrCl 3 and 2L CrI 3 , respectively. On the vdW-DFT calculations, three distinct regions were chosen to evaluate the sliding energy barriers. In the region far away from the indentation center, the equilibrium interlayer interaction occurs at 0 GPa out-of-plane compression and 0% in-plane strain (i.e., 0 GPa and 0% for both CrCl 3 and CrI 3 ). This choice of strain conditions is a valid approximation to our experiments, where extremely low values of strain, <0.5%, are found at the membrane edges (see Figure S3). The area just outside of the contact region is under a large in-plane strain but without any out-of-plane compression (5.35% and 0 GPa for CrCl 3 ; 4.79% and 0 GPa for CrI 3 ). The tip contact region experiences the highest in-plane strain and out-of-plane compression under the fracture loads (0.49 GPa and 6.49% for CrCl 3 ; 0.36 GPa and 6.09% for CrI 3 ). Figure 3e, 3f, 3h, and 3i summarizes the sliding energy per formula unit obtained for CrI 3 and CrCl 3 at different values of interlayer pressure and inplane strain as provided by FEM simulations. In the regions of the membranes beyond ∼8.5 nm from the indentation centers (see Table S2), where no pressure and small strain are present in the systems, the individual layers of 2L CrI 3 and CrCl 3 tend to slide over each other despite the path considered, that is, . This indicates that the layers can displace almost freely with little energetic opposition (Figure 3f and 3i). As pressure and strain are applied (see Table S2), there is an increment of the energetic barriers at 2/3 along [100] for CrCl 3 (168 meV) and CrI 3 (209 meV) which indicates that the layers may find difficulties to slide over at that particular position (Figure 3e and 3h). The main driving force for such enhancement of the energies is the strong overlap of the charge density at 2/3 ( Figure S5). Conversely, along [010] at 0.49 GPa and 6.49%, and 0.36 GPa and 6.09% for both CrCl 3 and CrI 3 , respectively, the energies at 2/3 and their multiple positions (0, 1/3, 1) are below kT (Figure 3f and 3i) Figure S7), the layers will follow a downhill energy profile from ∼76 (CrCl 3 ) and ∼98 meV (CrI 3 ) to 0 meV on both cases rather than increase their energy following the same path along [100]. These results are consistent with the variation of mechanical properties versus the number of layers which follows our previous analysis on graphene and hBN 20 providing a plausible explanation for the layer-dependence of the mechanical properties in CrX 3 . It is worth mentioning that the energetic barriers observed in the sliding of the layers are particularly sensitive to the relaxation of the atoms involved (Cr, Cl, I) during the computation. Figure S8 shows results without any relaxation in the layers, which resulted in larger barriers. Indeed, lower energies than those shown in Figure 3e−f and Figure 3h−i can be achieved when the relaxation of the Cr atoms is also taken into account (see Figure S9) with a consequent expansion of the interlayer distance (see Figure  S10). This correlates well with the positions where the energies increase during the sliding and suggests that changes of stacking order should be followed by expansion or contraction of the interlayer distance as recently measured. 14 In addition, the magnitudes of the barriers for CrI 3 are moderately larger than those for CrCl 3 , which suggests a slightly more stable dependence of the mechanical properties with the thickness, in agreement with the overall experimental trend observed. Overall, the measured mechanical values are among the smallest ones observed within the family of 2D materials, that is, much less stiff than 2D transition metal dichalcogenides and mica. 21,27,28 Figure 4 shows a map of the mechanical properties of atomically thin CrX 3 compared to other materials. The position of CrX 3 on this chart can be qualitatively explained by taking into account the bonding energies inside of the crystal, which scale according to the magnitudes of Young's modulus and breaking strength. While the dissociation energy for the honeycomb of C atoms in graphene yields a value of 805 kJ/ mol, 29 our DFT calculations indicate a formation energy of 260.9 kJ/mol for CrI 3 and 597.7 kJ/mol for CrCl 3 , depicting a weaker interatomic interaction than that of the graphene lattice. In addition, within the chromium halide family, the Nano Letters pubs.acs.org/NanoLett Letter smaller the ionic character the larger the bond energies, 26 with a variation of the electronic localization function across the different Cr-halides. 30 These results underline the soft nature of the chromium trihalides, which makes them extremely sensitive to small stress changes and very effective for strain modulation.
Although these results place the chromium trihalides as one of the softest 2D materials that have been experimentally measured so far, their breaking strength up to 10L is larger than that of silicon (∼2 GPa), 22 showcasing the general outstanding mechanical properties of 2D materials. It is also important to consider the significance of the presence of imperfections in the crystals, which affects the elastic behavior. Griffith described how the breaking strength in brittle materials (see also section 7 on the Supporting Information) is governed by defects and imperfections, 31 establishing a limit of σ ∼ E/9 by experimental extrapolation. In the limit of an ideal material, mechanics are governed by its molecular tensile strengths. In both chromium trihalides, the bilayers (σ ∼ E/20) and the multilayers (σ ∼ E/10) follow a behavior close to this limit. These results suggest that the mechanical behavior in CrX 3 thin crystals is determined by the interatomic interactions rather than defects, indicating a high crystallinity and a low density of impurities in the suspended regions. In comparison, polycrystalline classical materials like silicon 22 or tungsten alloys, 32 σ < E/100, report much lower values. 31 The nonlinear elastic constitutive behavior was assumed for modeling CrX 3 few layer crystals in FEM, and the derived maximum strains are close to ∼6−6.5% for the bilayers (see section 5 on the Supporting Information). The prospects of the combination of the exceptional flexibility and strengths with the intrinsic magnetism of atomically thin CrX 3 nature hold promise for an enhanced strain-tunability in ultrathin magneto-mechanical devices. 33 Considering the remarkable flexibility of few-layer CrCl 3 and CrI 3 , and the interlayer sliding origin of the layer-dependent Young's moduli, we investigated the plastic behavior of the two magnetic van der Waals materials in their bulk form. This property is of great relevance for future flexible devices, and it has recently been observed in bulk crystals of InSe. 25 The deformability factor (Ξ) proposed by Wei T-R et al. can be useful as a way to frame the plastic behavior of a material, it is related to the sliding (E s ) and cleavage (E c ) energies of layered materials via where E is the volumetric Young's modulus. The magnitudes of Ξ for bulk CrCl 3 and CrI 3 are plotted in Figure 5a and 5b as a function of the Young modulus and bandgaps for different materials with different electronic properties (semiconducting, insulators and metals). The cleavage energies were defined as the energies to separate bilayer CrX 3 systems to two monolayers (see Figure S6), the sliding energies were taken from the most energetically favored sliding path in the equilibrium state, that is, along [010] direction (Figure 3), and the Young's modulus values were extracted from the experimental data for 2L CrCl 3 and CrI 3 . For both bulk CrCl 3 and CrI 3 the cleavage energies are larger than their sliding energies (see Table S3). Interestingly, the magnetic CrX 3 showed one of the highest deformability factors of the 2D materials, even larger than that of the recently reported InSe ( Figure 5). 25 This outstanding capability for deformation is experimentally illustrated by macroscopically folding bulk CrI 3 and CrCl 3 crystals in Figure 5c.   Figure S12). The scale bars are 1 mm.