Designing Magnetic Properties in CrSBr through Hydrostatic Pressure and Ligand Substitution

Magnetic van der Waals (vdW) materials are a promising platform for producing atomically thin spintronic and optoelectronic devices. The A‐type antiferromagnet CrSBr has emerged as a particularly exciting material due to its high magnetic ordering temperature, semiconducting electrical properties, and enhanced chemical stability compared to other vdW magnets. Exploring mechanisms to tune its magnetic properties will facilitate the development of nanoscale devices based on vdW materials with designer magnetic properties. Here it is investigated how the magnetic properties of CrSBr change under pressure and ligand substitution. Pressure compresses the unit cell, increasing the interlayer exchange energy while lowering the Néel temperature. Ligand substitution, realized synthetically through Cl alloying, anisotropically compresses the unit cell and suppresses the Cr‐halogen covalency, reducing the magnetocrystalline anisotropy energy and decreasing the Néel temperature. A detailed structural analysis combined with first‐principles calculations reveals that alterations in the magnetic properties are intricately related to changes in direct Cr–Cr exchange interactions and the Cr–anion superexchange pathways. Further, it is demonstrated that Cl alloying enables chemical tuning of the interlayer coupling from antiferromagnetic to ferromagnetic, which is unique among known two‐dimensional magnets.

While intralayer superexchange interactions in CrSBr are FM, analogous interactions in the isostructural compounds VOCl [47], CrOCl [48], and FeOCl [49] are AFM, suggesting that the sign of magnetic exchange in this family of materials may be highly sensitive to Cr-halogen-Cr and Cr-chalcogen-Cr bond angles. With this in mind, we chose hydrostatic pressure as an initial route to modify the magnetic properties of CrSBr, as pressure provides a medium to modify the structure without changing chemical properties. For measurements of CrSBr under hydrostatic pressure (P), samples were prepared by grinding bulk single crystals in liquid nitrogen (see methods for details). The powder was then mixed with Daphne oil and loaded into a highpressure cell along with a small piece of Pb acting as a manometer (figures s1-s3 and methods for details). We performed magnetic measurements on the randomly-oriented powder as a function of temperature (T), magnetic field (μ0H), and P. Figure 2A presents the magnetic susceptibility (χ) of CrSBr versus T for various P up to 1.39 GPa. TN manifests as a peak in χ vs. T and is extracted numerically by finding the zerocrossings of dχ/dT (figure s4). The ambient-P TN = 135 ± 3 K is in agreement with previous reports [17-20, 23, 35, 42, 43, 50-52]. Upon the application of P, TN decreases linearly at a rate of dTN/dP = -12.6 ± 1.0 K·GPa -1 (inset of figure 2A). Curie-Weiss analysis reveals that the Weiss temperature (θW) also decreases with increasing P, while the Curie constant (C) is independent of pressure (figure s5), indicating a weakening of the intralayer FM coupling strength with no change in the S = 3 /2 Cr 3+ moments. Further measurements of χ vs T with a large applied μ0H = 3 T (where all spins in the magnetic state are polarized along the field direction) (figure s6) show a paramagnetic-to-FM phase transition with a decreasing Curie temperature with increasing P, supporting the conclusion that increasing P weakens the intralayer FM coupling. In figure 2B, we plot magnetization (M) versus μ0H with increasing P. Because the CrSBr samples were measured as a randomly-oriented powder, we expect the M vs. μ0H traces to be an average of the axial-oriented M vs. μ0H traces (figure s7, s8). At ambient P, M vs. μ0H is approximately linear at low μ0H followed by a change in slope at μ0H = 0.28 ± 0.05 T (b-axis saturation field) and a subtle kink at μ0H = 0.46 ± 0.05 T (a-axis saturation field) followed by saturation at μ0H = 1.05 ± 0.05 T (c-axis saturation field). With increasing P, the low-field slope decreases, resulting in an increasing saturation magnetic field HSAT (defined here as the μ0H at which M = 0.9·MSAT). HSAT increases at a rate of dHSAT/dP = 0.49 ± 0.03 T·GPa -1 (inset of figure 2B). For consistency, we repeated all measurements on a second CrSBr growth batch, which show quantitatively similar results (insets of figures 2A, B and figure s9). We note that powder X-ray diffraction (PXRD) measurements showed no evidence of irreversible phase transitions after grinding or applying maximum P (figure s10).
To interpret the changes in magnetic properties of CrSBr under P, we measured the lattice parameters of CrSBr under P (figures s11-s15 and methods for details) and performed complementary theoretical simulations to calculate both the relaxed structural parameters and magnetic properties of CrSBr under P (see methods for details). In figure 2C, the experimental lattice parameters are plotted versus P. All lattice parameters decrease, with the most significant change along the c-axis. Our density functional theory calculations well-predict the experimental change in lattice parameters under P (figure s12) and find that, as the c-axis compresses, the corresponding interlayer AFM coupling drastically strengthens (by 340% at 1.5 GPa -inset of figure 2D). From this, one might expect TN to increase under P. However, all primary intralayer FM couplings weaken (J1, J2, and J3 - figure 2D and table s1) and the magnitude of the strongest intralayer coupling, J2, is more than 30 times that of JIL for the entire P range, indicating that the intralayer magnetic exchange is the dominant contribution to the ordering temperature. The calculations fully support this conclusion, correctly predicting a decreasing TN with increasing P ( figure 2E and table s1). Furthermore, the experimental observation of an increase in HSAT with increasing P is explained by the strengthening of the interlayer AFM coupling, in agreement with our calculations ( figure 2E and table s1, figure s7).
Using the computed high-pressure structures, we can begin to rationalize the observed magnetic properties and derive magneto-structural correlations for CrSBr. Looking first at the interlayer spacing, we find the calculated vdW gap decreases significantly (~10% at 1.5 GPa) with P, leading to an increase in Cr-Br-Br-Cr overlap and thus JIL (table s1). The intralayer magnetic exchange is more complex. The intralayer exchange interactions in CrSBr represent a competition between FM superexchange interactions and weaker AFM direct exchange interactions. Changes in the superexchange interactions should be explained by the Goodenough-Kanamori-Anderson rules[53-55] for a Cr 3+ ion. These would predict the strongest FM coupling for bond angles near 90° and the strongest AFM coupling for bond angles near 180°. In contrast, the strength of AFM direct exchange interactions increases exponentially as the distance between magnetic ions shrinks.
To understand the magnetic behavior of CrSBr under pressure, the effects of both direct exchange and superexchange must be considered. With increasing pressure, the magnitude of direct exchange should increase for J1, J2, and J3, as all Cr-Cr distances (dCr-Cr) shrink (table  s1). These changes should be most pronounced for J1 and J2, which have experimentallydetermined dCr-Cr of ~3.51 and ~3.59 Å, respectively, whereas dCr-Cr for J3 is much larger (~4.76 Å). Because dCr-Cr remains well outside the range of Cr-Cr bonding for all pressures studied here, we would expect the direct exchange interactions to remain small relative to superexchange interactions, which agrees with our experimental and computational data where the net intralayer coupling remains FM. However, the relative changes in the calculated exchange energies at 1.5 GPa compared to ambient pressure (ΔJ1 ~ ΔJ3 > ΔJ2) are inconsistent with the expectations for direct exchange alone (ΔJ1 ~ ΔJ2 > ΔJ3), suggesting that superexchange pathways are also affected by lattice compression. Zero-field-cooled magnetic susceptibility (χ) versus temperature (T) for various applied hydrostatic pressures (P). A measuring field of 250 Oe was used for all traces. Inset shows extracted percentage change in TN versus P for multiple measurement runs and growth batches. The extracted slope of TN versus P is given in the inset. B) Magnetization (M) versus applied magnetic field (μ0H) at 2 K for various P. μ0H is randomly oriented along all crystal axes. The saturation field (HSAT) is defined as the μ0H at which M is 90% of the saturation M (denoted by a black dashed line). Inset shows extracted HSAT versus P along with the extracted slope of HSAT versus P. C) Percentage change in lattice constants and the unit-cell volume versus P, as determined by powder X-ray diffraction. The dashed black line is a fit to an equation of state (see methods for details). D) Calculated percentage change in intralayer magnetic couplings versus P. Inset: calculated percentage change in interlayer magnetic coupling (JIL) versus P. E) Calculated HSAT (left axis, orange, purple, and green dots) and TN (right axis, solid black dots) versus P.
As noted above, changes in superexchange pathways under pressure should be most sensitive to changes in the Cr-S-Cr and Cr-Br-Cr bond angles. At 1.5 GPa, all of these angles are predicted to change by less than 1° compared to the relaxed ambient-pressure structure, suggesting that the modulation of the superexchange energies should be smaller or similar in magnitude to the changes in direct exchange (table s1). The largest change is observed in the Cr-S1-Cr bond angle (θ3, figure 1D), which increases towards 180°, enhancing the contribution of AFM exchange pathways and weakening the overall FM coupling (table s1). Consequently, both direct exchange and superexchange contributions contribute to the reduced magnitude of J3 with increasing P. In contrast, for J1 and J2, all of the relevant Cr-S-Cr (θ2 and θ1B) and Cr-Br-Cr (θ1A) (figure 1D) bond angles trend towards 90° with increasing P (table s1), which should enhance the FM superexchange interactions. Since the changes in bond angles are relatively small, the magnitude of these effects is likely minimized and could be less than the corresponding increase in AFM direct Cr-Cr exchange. Collectively, these results reveal the balance between superexchange and direct exchange that must be considered when designing new materials in this family.
While these results motivate studies of the magnetic behavior of CrSBr at even higher pressures where larger bond angle changes may affect superexchange pathways more drastically, chemical modification could induce larger structural changes than were obtained in the pressure range studied here. Specifically, we hypothesized that substitution of Br with Cl could induce a large lattice compression, while simultaneously allowing us to study the effects of changing Cr-halogen covalency on the magnetic properties. Furthermore, theoretical studies on ligand engineering[56] and strain[44] on chromium chalcohalides demonstrate changes to the magnetic properties with these perturbations. To explore this hypothesis, we synthesized a series of mixed-halogen compounds CrSBr1-xClx with x = 0 -0.67 (from now on referred to as "Cl-x") using the chemical vapor transport approach (see methods for details). The crystal structure of each compound was determined through single-crystal X-ray diffraction (SCXRD) ( figure 3A and table s2). Within the examined compositional range, the mixed-halogen alloys are isostructural to the parent compound CrSBr with the space group Pmmn (figure 3A). Because Cl is smaller than Br, Cl alloying has a significant impact on the lattice parameters, causing the lattice to "accordionize" along the a-axis, resulting in a decrease of the a-and clattice parameters with no significant change to the b-axis ( figure 3B and figure s16). The incompressibility of the structure along the b-axis stems from the Cr-(Cl/Br) bonds lying parallel to the ac-plane. At the highest Cl content (Cl-67), the a-and c-axes have compressed by 2.2% and 4.9%, respectively, compared to CrSBr, with the a-axis compression exceeding the effects of pressure at 1.5 GPa (figure s12). We note that despite the structural changes resulting from Cl alloying, the crystals with the highest concentration of Cl remain exfoliatable down to the monolayer limit (figure s17). corresponding EDX elemental mapping. Blue, yellow, red, and green maps correspond to Cr, S, Br, and Cl elemental mapping, respectively. In each elemental map, the top-left inset shows the average concentration relative to Cr. The error bar is the standard deviation between multiple measurements and crystals. In all images, the scale bar is 100 μm. D) Halogen content determined using SCXRD and EDX versus Cl content used in chemical vapor transport reactions. The dashed black line demarcates 1:1 measured Cl content to Cl content used in chemical vapor transport reactions. E) Photoluminescence intensity versus photon energy for all synthesized Cl concentrations. The corresponding Cl content for each trace is given in the inset. All data were taken at 70 K.
The chemical compositions of all new materials were determined through a combination of refining the Cl/Br occupancy on the mixed anion site on SCXRD data and energy dispersive X-ray spectroscopy (EDX) ( figure 3C, figures s18-s23 and table s3). The percentages of Cl atoms substituted on the Br sites are close to the nominal stoichiometric amount of bromine and chlorine used in the synthesis ( figure 3D). Importantly, the chemical composition maps measured using EDX ( figure 3C and figures s18-s23) show no evidence of Cl or Br clustering on the micron scale. Polarized Raman spectroscopy on all alloys supports this, demonstrating a continuous frequency increase of characteristic CrSBr modes with increasing Cl concentration (figure s24), consistent with the homogeneous substitution of the lighter Cl atoms on Br sites [57][58][59][60]. Despite the significant structural changes upon Cl alloying, photoluminescence measurements on the various compositions show negligible changes in the optical band gap ( figure 3E). This is consistent with previous band-structure calculations for CrSBr and CrSCl monolayers[61] and establishes our ability to tune the lattice and (as will be seen below) magnetic structure without significantly changing the electronic structure. Given the strong coupling between magnetism and optical and electronic properties in CrSBr, Cl alloying offers an entirely new space for designing magneto-optical and magneto-electronic properties without drastically affecting the band structure.
We now turn to explore how the magnetic properties of the mixed-halogen compounds change with increasing Cl content. In figure 4A, we plot χ vs T for all compounds. For Cl concentrations up to Cl-41, we observe a clear AFM transition with a peak in χ at TN, followed by a decrease in χ at low T with no difference between zero-field-cooled (ZFC) and field-cooled (FC) traces. TN for each stoichiometry up to Cl-41 was extracted numerically by finding the zerocrossings in dχ/dT (figure s25, s26) and is found to decrease linearly at a rate of dTN/dx = -61.8 K·x -1 (inset of figure 4A). The corresponding Curie-Weiss analysis (Figure s27) for this compositional range reveals that θW also decreases with increasing Cl content while the Curie constant remains constant, indicating a weakening of the intralayer FM coupling without a change in the S = 3 /2 Cr 3+ moments.
At high temperature, Cl-57 and Cl-67 follow a similar trend to the lower Cl concentrations. Specifically, θW lowers with increasing Cl content. Near the magnetic ordering temperature, however, the χ of Cl-57 and Cl-67 show distinctly different behavior from the lower Cl concentrations. For both compounds, the χ vs. T traces display a small kink (at T = 100 and 86 K for Cl-57 and Cl-67, respectively), a broad maximum (at T = 89 K and 42 K), and a clear divergence between the FC and ZFC traces at low temperature. These features suggest the possibility of multiple magnetic phase transitions, and further indicate that the magnetic ground state of Cl-57 and Cl-67 cannot be described as a trivial antiferromagnet (figure s26 for additional axial orientations). Complementary ac magnetic susceptibility measurements on Cl-57 and Cl-67 at zero dc field confirm the presence of multiple magnetic transitions and reveal frequency-dependent behavior (figure s28, s29), suggesting these compounds are best described as spin glasses or glassy magnets, wherein magnetic disorder emerges from competing FM and AFM interlayer interactions (see discussion below). Regardless, the magnetic critical temperatures (identified by peaks in the in-phase magnetic susceptibility) follow the same trend as the lower Cl concentrations (figures s27-s29 for details). This indicates that, over the entire compositional range, increased Cl alloying leads to decreased magnetic ordering temperatures and weakened intralayer coupling.
To better understand the origin of this unusual magnetic behavior at high Cl content, we performed axial-oriented M vs μ0H traces at 2 K for each stoichiometry ( figure 4B-D). For μ0H along the easy b-axis (figure 4C), we observe a clear AFM-to-FM spin-flip transition for Cl doping up to Cl-41. The HSAT, which we define as the midpoint of the transition where M = 0.5×MSAT to better illustrate the transition at higher Cl concentrations, decreases sharply with increasing Cl content, indicating a weakening of the interlayer AFM coupling. For Cl-57 and Cl-67, we observe s-shaped M vs μ0H traces with no observable hysteresis. We propose that this change in behavior arises from competing interlayer FM Cr-Cl-Cl-Cr interactions and AFM Cr-Br-Br-Cr interactions. In the aggregate, this leads to negligible interlayer coupling for Cl-57 and Cl-67, and causes these two compositions to behave as ferromagnets under small applied fields. For μ0H along the a-and c-axes (figure 4B and 4D, respectively), all alloys display similar behavior -a continuous spin canting process whereby the b-axis aligned spins cant towards the applied field direction. We observe a reduction in a-and c-axis HSAT, defined as the point where M = 0.9×MSAT, signifying a lowering of the magnetic anisotropy energy. A summary of the dependence of all axial saturation fields on Cl doping is given in the bottom inset of figure 4A. Remarkably, the a-and b-axis HSAT approach zero, indicating a diminishing anisotropy between the two inplane directions, while the out-of-plane anisotropy only decreases by ~50% (see also figure s30 for a detailed comparison between CrSBr and Cl-57). This reduction in the effective anisotropy between the a-and b-axes motivates further study of the critical behavior of these high Clcontent materials, specifically the possibility that they could display 2D-XY behavior at the monolayer limit [8,33].
The large unit cells needed to adequately model random distributions of halogens in the alloys precluded detailed computational studies of specific compositions. Instead, we modeled the magnetic properties of the theoretical end-member of this series, CrSCl, to better understand the experimental trends. Because CrSCl is not currently experimentally accessible, we simulated and relaxed the structure using CrSBr as a model lattice ( figure s31 and table s4). The relaxed CrSCl structure agrees remarkably well with an extrapolation of the experimental data up to 100% Cl content (figure 3B and table s4).

Figure 4: Magnetic properties of CrSBr1-xClx. A)
Magnetic susceptibility (χ) versus temperature (T) for various Cl contents (x). A measuring field of 250 Oe was used for Cl-00, Cl-11, and Cl-27, whereas a measuring field of 100 Oe was used for Cl-41, Cl-57, and Cl-67. For Cl-00, Cl-11, Cl-27, and Cl-41, only the zero-field trace is shown as it overlaps the field-cooled trace. For Cl-57 and Cl-67, both zero-fieldcooled and field-cooled traces are shown. Top inset shows extracted critical temperature versus Cl content. Grey, blue, and yellow regions correspond to experimentally identified PM, AFM, and spin-glass regions, respectively. Green region corresponds to the predicted FM state for CrSCl (table s4). Up to Cl-41 the critical temperature depends linearly on Cl doping. The linear fit parameters are given in the inset. Bottom inset shows the extracted saturation magnetic fields at 2 K for fields parallel to the a-, b-, and caxes. B-D) Magnetization normalized to the saturation magnetization (M/MSAT) versus applied magnetic field (μ0H) at 2 K for μ0H oriented along the a-(B), b-(C), and c-(D) axes. The saturation magnetic field is defined as the magnetic field when the magnetization is 90%, 50%, and 90% of the saturation magnetization for the a-, b-, and c-axes, respectively.
As with the high-pressure data above, the combination of experimental magnetic data and computed magnetic and structural parameters allows us to derive magneto-structural correlations for halogen alloying in CrSBr. Increasing Cl content leads to a reduction in the interlayer spacing (figure 3B), which could naively be expected to strengthen the interlayer magnetic exchange. Our experimental data, however, reveal that the interlayer coupling weakens with increasing Cl content ( figure 4C). This behavior can be explained by the reduced orbital overlap of interlayer Cr-Cl-Cl-Cr exchange compared to Cr-Br-Br-Cr. Consistent with this hypothesis, calculations predict a change in the interlayer coupling from AFM in CrSBr to FM in CrSCl (table s4 and figure s31), confirming that orbital overlap between the halogens across the vdW gap, rather than the interlayer Cr-Cr distance is responsible for directing the sign and strength of interlayer exchange. These results can also explain the glassy behavior of Cl-57 and Cl-67, which arises from competing interlayer FM Cr-Cl-Cl-Cr and AFM Cr-Br-Br-Cr interactions. We note that the change in sign of the interlayer coupling upon Cl substitution in CrSBr is distinctly different from what is observed in bulk chromium trihalides, where interlayer coupling is always AFM in the high temperature monoclinic structure and FM in the low temperature rhombohedral structure, independent of the identity of the halide[33]. The weak interlayer coupling emerging from competing FM and AFM interactions in Cl-57 and Cl-67 should make the magnetic ground state in these materials particularly susceptible to external stimuli, such as strain, pressure, and magnetic field, making these materials promising candidates for switchable 2D devices.
The largest change in the calculated intralayer coupling upon Cl substitution is the magnitude of J1, which decreases by ~80% while remaining FM (table s4). The shorter calculated dCr-Cr in CrSCl compared to CrSBr should increase the contributions of AFM direct exchange, though this is unlikely to fully explain the marked drop in the magnitude of the exchange energy. While the Cr-S2-Cr and Cr-X-Cr bond angles associated with J1 do change with halogen substitution (figure s16 and table s4), the large reduction in the superexchange contribution to J1 is most likely driven by the more ionic nature of the Cr-Cl bond compared to the more covalent Cr-Br bond. This predicted decrease in J1 for CrSCl compared to CrSBr explains a majority of the reduction in θW with increasing Cl content. However, examination of the other exchange pathways is useful to better distinguish the relative contributions of structural and electronic changes on magnetism, in addition to the relative effects of direct exchange and superexchange.
Because Cl substitution induces an expansion along the b-axis, the reduced magnitude of J3 cannot be explained by direct exchange, and must instead be rationalized by the shift in the Cr-S1-Cr bond angle towards 180°, which enhances the AFM contributions in the superexchange pathway (table s4 and figure s16). Similarly, because Cl substitution has little effect on the dCr-Cr relevant to J2, direct exchange is unlikely to contribute strongly to changes in J2. Surprisingly, while J2 is calculated to become more strongly FM, the Cr-S-Cr bond angles relevant to J2 increase away from 90° (table s4), suggesting that electronic, rather than structural modifications, must drive the changes in magnetic exchange. Here, we propose that the reduced covalency of the Cr-Cl interaction (compared to Cr-Br) leads to an increase in the Cr-S bond covalency (indicated by a reduction in dCr-S 2 ), which enhances the magnitude of the J2 superexchange. Further, this change in the Cr-halogen covalency helps explain the changes in magnetic anisotropy with Cl substitution. Our experimental and computational data support large reductions in the magnetic anisotropy energy when Cl is substituted for Br (table s4), in line with previously predicted results [56]. The combined effects of reduced Cr-halogen covalency and smaller spin-orbit coupling for Cl compared to Br should dramatically weaken magnetocrystalline anisotropy in these materials, which is largely derived from anisotropic exchange interactions mediated by the halogens.
Intriguingly, a comparison of the Curie-Weiss analyses performed at the highest pressure (1.39 GPa -figure s5) and at the highest Cl substitution (Cl-67 -figure s27) reveal nearly identical changes in the θW, implying similar changes in the overall magnitude of the intralayer FM exchange. However, the effects on the magnetic ordering temperature are much more dramatic for Cl substitution (-43.5 K vs. CrSBr) compared to pressure (-16.6 K at 1.39 GPa vs. ambient P), indicating that other factors play a key role in the magnetic ordering temperature of CrSBr and its analogues. The presence of interlayer frustration in the Cl-substituted compounds may partly explain the reduced critical temperatures, but the small magnitude of interlayer exchange compared to the intralayer exchange suggests this effect should play a small role in dictating the ordering temperature. Instead, we propose that the reduced magnetic anisotropy between the a-and b-axes in the alloys suppresses the magnetic ordering temperature. An intermediate magnetic regime with short-range FM correlations has been observed previously in CrSBr, and these results could support claims that this regime hosts 2D-XY-like behavior (figure s32)[42, 43], motivating further study of the magnetism of the mixed-halogen compounds at the 2D limit. More broadly, the effects of anisotropy observed here indicate that strong uniaxial anisotropy is required to maximize magnetic ordering temperatures for in-plane, orthorhombic 2D magnets and that 2D-XY-like magnetic regimes may be accessible outside of materials with high rotational symmetry.
In summary, we have demonstrated two routes to tune the magnetic properties of the layered semiconductor CrSBr: hydrostatic pressure and halogen substitution. Both strategies are found to reduce the magnetic ordering temperature. The combined experimental and computational analyses suggest a complex interplay between structural effects, weakly modulating both direct exchange and superexchange pathways, and changes to the Cr-halogen covalency, which strongly affects the strength of the FM superexchange. Additionally, in the Clsubstituted phases, we have identified a strong suppression of the anisotropy energy between the two in-plane axes, while maintaining a large anisotropy for the spins to remain in-plane. Preliminary optical and exfoliation experiments indicate that these Cl-substituted analogues retain the semiconducting properties and ambient stability of the parent CrSBr phase, motivating further characterization of the coupling between magnetism and optical, electronic, and structural properties across the series. More generally, these results highlight that the CrSBr family of 2D magnets offers the ability to chemically or mechanically control magnetic coupling and anisotropy, similar to the more thoroughly studied chromium trihalide family. The enhanced tunability of the interlayer coupling, improved stability in ambient conditions, and semiconducting transport properties strongly motivate the incorporation of CrSBr and its analogues into functional 2D spintronic devices. Further modulation of the properties of CrSBr through chalcogen alloying or iodine-substitution can expand upon the rich phase space of these materials, which includes diverse magnetic ground states (FM, AFM, spin glass) and spans a wide range of ordering temperatures, with the additional possibility to access 2D-XY magnetic phases hosting topological magnetic vortices. Finally, the demonstration that hydrostatic pressure, in addition to uniaxial strain, can tune the magnetism of these materials postsynthetically provides a new handle to modify the magnetic properties both in the bulk and at the 2D limit. These chemical and mechanical tools make the CrSBr family an ideal platform for future developments in 2D magnetism and spintronic devices.
Supporting information is available from the Wiley Online Library or from the authors.

Acknowledgments:
E.J.T. and D.G.C. contributed equally to this work.
We thank Dr. Yue Meng and Rich Ferry for assistance with DAC assembly and high-pressure X-ray diffraction measurements. Research on tunable vdW magnetic semiconductors was supported as part of Programmable Quantum Materials, an Energy  Note: All compositions were synthesized through chemical vapor transport (CVT) reactions using a stoichiometric amount of chromium(III) bromide/chloride, sulfur, and chromium. CVT reactions rely on all the elements having large enough partial pressures for effective mass transport through the formation of volatile transport effective species which were generated in situ at the crystal growth temperatures (850C -950C). The temperatures used in the synthesis allowed for both halogens species to transport effectively and be incorporated into the final product; though, the final composition of the product was typically deficient in chloride (i.e., the nominal ratio of chlorine to bromine used in the synthesis was greater than the ratio derived from SCXRD and EDX). CVT reactions with higher chlorine concentrations were attempted though only resulted in the deposition of Cr(Cl/Br)3 and Cr2S3 phases on the sink side limiting the highest chlorine alloy level to Cl-67. Note that the original synthesis [2] for Cl-alloyed CrSBr required the use of S2Cl2 and S2Br2. Because these reagents are liquid, using the original method limits the precise control of the stoichiometry compared to solids which can be mass accurately. Additionally, the original synthesis incorporated only 1/3 Cl onto the Br sites while the method described in this work can incorporate double the amount of Cl.

Powderization of CrSBr crystals for magnetometry measurements under pressure:
CrSBr was powderized through the following process: large crystals of CrSBr were placed in a thin porcelain crucible along with enough liquid N2 to fully submerge the crystals. The crystals were ground with a thermally equilibrated pestle for 5 mins. The material was rinsed with acetone to remove residual moisture from condensation.

Determination of applied hydrostatic pressure for magnetometry measurements under pressure:
Since the superconducting critical temperature (TC) of Pb is well-known to linearly depend upon the applied hydrostatic pressure at a rate of dTC/dP = 0.379 K·GPa -1 [3], we can use the measured TC of Pb to determine the applied hydrostatic pressure on CrSBr. The Pb plus CrSBr sample is first zero-field cooled below the transition to 6 K, then the magnetic susceptibility ( ) versus temperature (T) is measured with a small measuring field of 5 Oe (such that the measuring field is much less than the zero-temperature upper critical field [4], which for lead is 800 Oe). versus T is measured at a rate of 0.05 K/min to ensure the transition is precisely resolved and traces with increasing and decreasing T were measured to check for measurement precision. The Pb TC is extracted by finding the condition where = 0.5 N (where N is the susceptibility in the normal state) and correlated to the measured pressure-cell compression.

Vibrating sample magnetometry under hydrostatic pressure:
All vibrating sample magnetometry was conducted on a Quantum Design PPMS DynaCool system using the commercially-available HMD high pressure cell. Multiple single CrSBr crystals were selected, and powderized in liquid nitrogen using a mortar and pestle. Before and after the VSM measurements, PXRD was used to confirm there was no significant change in structure upon powderizing or after applying maximum pressure. The powder was then combined with Daphne 7373 oil and a ~1-2 mm long wire of Pb in a Teflon capsule was inserted into the pressure cell. The variable temperature scans and fielddependent magnetic susceptibility curves for each pressure were measured during the same measurement cycle. The measurements performed at different pressures were done sequentially with increasing pressure (from zero applied pressure up to the maximum achievable pressure). After the final maximum pressure measurement, the capsule containing the CrSBr powder, Daphne 7373 oil, and the Pb manometer was removed, fixed to a brass paddle with GE varnish, and re-measured as a consistency check of the zero-pressure measurement.
Vibrating sample magnetometry on CrSBr1-xClx: All vibrating sample magnetometry was conducted on a Quantum Design PPMS DynaCool system. For each stoichiometry, a pristine single CrSBr1-xClx crystal was selected and attached to a quartz paddle using GE varnish (which was cured at room temperature under ambient conditions for 30 minutes) and oriented with the a-, b-, or c-axis parallel to applied field direction. The same crystal was used for all axialorientated measurements. The variable temperature scans and field-dependent magnetic susceptibility curves for each axis were measured during the same measurement cycle. Between axial-oriented measurements, the crystal was removed using a 1:1 ethanol/toluene solution, dried in air and then reoriented and reattached using GE varnish.

Ac magnetometry on CrSBr1-xClx:
All ac magnetometry was conducted on a Quantum Design PPMS DynaCool system with the ACMSII module. For each measured stoichiometry, a pristine single CrSBr1-xClx crystal was selected and attached S4 to a quartz paddle using GE varnish (which was cured at room temperature under ambient conditions for 30 minutes) and oriented with the a-or b-axis parallel to the applied magnetic field. An ac magnetic field excitation of 4 Oe was used for all measurements. The variable temperature and frequency-dependent magnetic susceptibility curves for each axis were measured during the same measurement cycle.

Ambient-pressure powder X-ray diffraction:
Powder diffraction patterns were collected on a Malvern Panalytical Aeris diffractometer with a Cu Kα xray source energized to 40 kV and 15 mA. The X-ray beam was filtered with a Niβ filter. The LNpowderized sample of CrSBr was mounted on a Si-zero background holder which was spun during the collection to reduce preferred orientation.

Single-crystal X-ray diffraction:
Single crystal diffraction measurements were collected on CrSBr1-xClx crystals using an Agilent Supernova single crystal diffractometer. The crystals were mounted onto a MiTeGen MicroLoops™ holder with paratone oil. The X-ray source was a Mo Kα micro-focus energized to 50 kV and 0.8 mA.
The collection temperature was maintained at 250 K using an Oxford instruments nitrogen cryostat. The data collection, integration, and reduction were performed using the Crysalis-Pro software suite. The crystal structure was solved and refined using ShelXT and ShelXL respectively.

Details of diamond anvil cell (DAC) assembly.
We used Boehler-Almax diamond anvils with 300 μm culets set in tungsten carbide seats with a conical aperture of 80°. The anvils and seats were loaded into DacTools iBX-80 type cells. A stainless-steel gasket with a starting thickness of 250 μm was pre-indented to a thickness of ~40 μm. A sample space with a diameter of ~200 μm was then created in the center of the indented gasket via electro-discharge machining using a Boehler μDrill with a copper wire electrode.

High pressure powder X-ray diffraction measurements.
To reduce texture effects in powder X-ray diffraction measurements, single crystals of CrSBr were first cooled to 77 K in liquid nitrogen and then ground with a mortar and pestle. The resulting powder was sieved to remove large, unground crystals. The sieved powder was further ground between two glass slides prior to loading in the diamond anvil cell.
The sample chamber prepared as described above was loaded with CrSBr powder, a small piece of gold foil to serve as a pressure calibrant during diffraction measurements, and two ruby microspheres (BETSA®) to serve as a pressure calibrant during gas loading. A representative photograph of one of the loaded cells is shown in figure s11. The cell was subsequently loaded with neon as the pressure transmitting medium using the COMPRES gas loading system as GSECARS, at the Advanced Photon Source at Argonne National Laboratory [5].
High pressure powder X-ray diffraction experiments were conducted at beamline 16-ID-B, within HPCAT at the Advanced Photon Source (APS). High intensity monochromatic synchrotron radiation with a fixed wavelength of 0.406626 Å was used as the source in all diffraction measurements. The cell was loaded into a diaphragm gas membrane assembly, which enables diffraction measurements over very small pressure increments (~0.1 GPa). At each pressure step, separate diffraction images were collected S5 without rotation on the CrSBr sample and the Au foil to enable determination of lattice parameters and sample-space pressure, respectively. Diffraction images were masked and integrated using the Dipotas 0.5.1 software package to produce the corresponding 1D diffraction patterns [6].

Analysis of Powder X-ray Diffraction Data.
For each pressure step, the cell pressure was obtained by comparison of the lattice parameters of the Au foil with the established equation of state [7]. Powder X-ray diffraction data were then analyzed using the GSAS-II software package [8]. Due to the weak intensity of the (00l) reflections and the possible overlap of the (011) and (002) reflections, we observed that lattice parameters obtained using the Pawley method were highly sensitive to the initial parameters used in the refinement. To obtain reasonable initial parameters, we extracted the estimated b-lattice parameter by inspection of the (020) reflection, and subsequently estimated a-and c-lattice parameters by inspection of the (110) and (011) reflections, respectively. Using these lattice parameters as the initial values, we then fit the patterns over the 2θ range 3° to 23° using the Pawley method to extract accurate unit cell parameters at each pressure. We note that it was necessary to constrain the b-axis lattice parameter during initial refinements of the background, line shape, and a-and c-axis lattice parameters to obtain reasonable fits of the (020) reflection.
We then used the software package EoSFit7 [8] to fit the unit cell volume as a function of pressure. We used a third-order Birch-Murnaghan equation of state to fit the data [9,10]: Where P is the pressure, V is the unit cell volume, V0 is the initial unit cell volume at ambient pressure, B0 is the bulk modulus, and B0' is the derivative of the bulk modulus with respect to pressure. A single equation of state was sufficient to fit the data at room temperature up to 3.5 GPa, suggesting no phase transition occurs in the pressure range where magnetic analyses were performed. A small anomaly is possibly observed in the b-axis lattice parameters near 0.6 GPa, though we attribute this anomaly to the necessary constraints applied to the b-axis lattice parameter during refinements, as described above.

Scanning electron microscopy:
Scanning electron micrographs were collected on a Zeiss Sigma VP scanning electron microscope (SEM) using a beam energy of 5 kV. Energy dispersive X-ray spectroscopy (EDX) of the CrSBr crystals was performed with a Bruker XFlash 6 | 30 attachment. Spectra were collected with a beam energy of 15 kV. Elemental compositions and atomic percentages were estimated by integrating under the characteristic spectrum peaks for each element using Bruker ESPRIT 2 software.

Raman spectroscopy:
Raman spectroscopy for all CrSBr1-xClx single crystals was performed under ambient conditions in a Renishaw InVia™ micro-Raman microscope using a 532 nm wavelength laser. A 50x objective was used with a laser spot size of 2-3 µm. A laser power of ~2 mW was used with a grating of 2400 g/mm for all spectra. An acquisition time of 20s was used for each measurement. For each crystal, 5 independent spectra were acquired and averaged after subtracting a dark background. The dark background was a spectrum acquired with no laser excitation and the same acquisition parameters.

Photoluminescence (PL) spectroscopy:
PL measurements were carried out with a 450-nm continuous-wave (CW) laser with a power of 900 µW. The PL spectra were collected by a Princeton Instruments PyLoN-IR detector cooled with liquid nitrogen. All samples were prepared by exfoliating single crystals of CrSBr1-xClx onto SiO2/Si+ substrates passivated with 1-dodecanol. The exfoliation was done under inert conditions in an N2 glovebox with < 1 ppm O2 and < 1 ppm H2O content. Thin-bulk flakes were identified by optical microscopy and loaded into an Oxford Instruments Microstat HiRes2 cryostat inside the glovebox to avoid exposing the samples to air before measurements.

Exfoliation:
CrSBr1-xClx flakes were exfoliated onto 285 nm SiO2/Si+ substrates using mechanical exfoliation with Scotch ® Magic TM tape [11,12]. Before exfoliation, the substrates were cleaned with a gentle oxygen plasma to remove adsorbates from the surface and increase flake adhesion [13]. The exfoliation was done under inert conditions in an N2 glovebox with < 1 ppm O2 and < 1 ppm H2O content. Flake thickness was identified using optical contrast and then confirmed with atomic force microscopy.

Atomic Force Microscopy:
Atomic force microscopy was performed in a Bruker Dimension Icon ® using OTESPA-R3 tips in tapping mode. Flake thicknesses were extracted using Gwyddion to measure histograms of the height difference between the substrate and the desired flake.

Theoretical Calculations:
Ab initio calculations of bulk CrSBr and CrSCl were performed using DFT implemented in the QUANTUM ESPRESSO package [14]. Norm-conserving pseudopotentials with a plane-wave energy cutoff of 85 Ry were employed. For structural optimization, the spin-polarized Perdew-Burke-Ernzerhof exchangecorrelation functional was employed, with dispersion corrections within the D2 formalism [15] (PBE-D2) included to account for the van der Waals interactions. The structures were fully relaxed until the force on each atom was < 0.005 eV Å '( . The calculated lattice constants for bulk CrSBr and CrSCl are 3.5 and 3.4 Å along the axis, respectively, and both 4.7 Å along the axis. The calculated interlayer distance for bulk CrSBr and CrSCl are 8 and 7.5 Å, respectively. For each hydrostatic pressure applied, the intraand interlayer Heisenberg magnetic exchange couplings were calculated in 3 × 3 × 1 and 3 × 3 × 2 supercells respectively, by a four-state mapping method [16] within the local spin density approximation (LSDA). The Curie temperature was calculated using metropolis Monte Carlo (MC) methods implemented in the VAMPIRE package [17]. The critical exponent was determined by fitting the temperature dependent with and denote the top and bottom layers in a unit cell, ℎ represents the external magnetic field. The ground state energy differences between the FM and AFM states ( 78 − 978 ) under different hydrostatic pressure were calculated with spin-orbit coupling (SOC) taken into account within LSDA, based on the structures revealed by PBE-D2. The corresponding cell compression is given in the inset. All traces were offset and normalized for clarity. A measuring field of 5 Oe was used. B) Extracted superconducting transition temperature (TC) of lead versus cell compression. TC was defined as the temperature at which the magnetic susceptibility was 50% of the normal-state susceptibility. C) Corresponding applied pressure versus cell compression. The applied pressure was determined from the well-known dTC/dP = 0.379 K/GPa for lead [3].

Figure s2: Determination of applied pressure versus cell compression for measurement run 2. A)
Magnetic susceptibility versus temperature across the superconducting transition for the lead manometer for various applied pressures. The corresponding cell compression is given in the inset. All traces were offset and normalized for clarity. A measuring field of 5 Oe was used. B) Extracted superconducting transition temperature (TC) of lead versus cell compression. TC was defined as the temperature at which the magnetic susceptibility was 50% of the normal-state susceptibility. C) Corresponding applied pressure versus cell compression. The applied pressure was determined from the well-known dTC/dP = 0.379 K/GPa for lead [3].    Features are seen at each axial saturation field (a sharp kink at the b-axis saturation field, a peak at the a-axis saturation field, and a shoulder at the c-axis saturation field). C) Experimental derivative of the magnetization versus magnetic field at various applied pressures (taken from the data in figure  2B). There is close agreement between the calculated and experimental M vs μ0H curves.  Due to the pressure cell preparation, the magnetic field is randomly oriented along all crystal axes. The corresponding pressure is given in the inset. The saturation field is defined as the magnetic field at which the magnetization is 95% of the saturation magnetization (denoted by a black dashed line).     refinements for powder X-ray diffraction data. Powder X-ray diffraction data and Pawley refinements for CrSBr at 0.28 GPa (top) and 3.48 GPa (bottom). Black, red, and gray lines correspond to the observed data, the calculated fit, and the difference, respectively. The broad feature near 11.5° was caused by the sample holder and was modeled as part of the background.       In the Cl-57 and Cl-67 traces, TC is defined using the ac susceptibility measurements in figure s28 and figure s29, respectively. The extracted critical temperature for each Cl doping is denoted by black dashed lines.

Figure s26
: Additional magnetic susceptibility data on CrSBr1-xClx. A) Magnetic susceptibility versus temperature with the magnetic field aligned along the a-axis for various levels of Cl doping. The corresponding Cl doping is given in the inset. A measuring field of 250 Oe was used for Cl-00, Cl-11, and Cl-27, whereas a measuring field of 100 Oe was used for Cl-41, Cl-57, and Cl-67. For Cl-00, Cl-11, Cl-27, and Cl-41, only the zero-field trace is shown as it overlaps the field-cooled trace. For Cl-57 and Cl-67, both zero-field-cooled and field-cooled traces are shown. B) Magnetic susceptibility versus temperature with the magnetic field aligned along the c-axis for various levels of Cl doping. The corresponding Cl doping is given in the inset. A measuring field of 250 Oe was used for Cl-00, Cl-11, and Cl-27, whereas a measuring field of 100 Oe was used for Cl-41, Cl-57, and Cl-67. For Cl-00, Cl-11, Cl-27, and Cl-41, only the zero-field trace is shown as it overlaps the field-cooled trace. For Cl-57 and Cl-67, both zero-field-cooled and field-cooled traces are shown.  Figure s28: Ac magnetometry on CrSBr0.43Cl0.57. A) Dc magnetic susceptibility (solid black lines) and the derivative of magnetic susceptibility (solid red lines) versus temperature for magnetic fields aligned parallel to the b-axis. A measuring field of 100 Oe was used. Both field-cooled and zero-field-cooled traces are shown. B, C) Real (B) and imaginary (C) components of the ac magnetic susceptibility versus temperature for various ac field frequencies (denoted by different trace colors or line styles). The ac magnetic field was applied parallel to the b-axis. Zero ac magnetic field was applied. In all plots, vertical solid gray bars denote distinct features in χ, χ', or χ''. Figure s29: Ac magnetometry on CrSBr0.33Cl0.67. A) Dc magnetic susceptibility (solid black lines) and the derivative of magnetic susceptibility (solid red lines) versus temperature for magnetic fields aligned parallel to the a-axis. A measuring field of 100 Oe was used. Both field-cooled and zero-field-cooled traces are shown. B, C) Real (B) and imaginary (C) components of the ac magnetic susceptibility versus temperature for various ac field frequencies (denoted by different trace colors or line styles). The ac magnetic field was applied parallel to the a-axis. Zero dc magnetic field was applied. In all plots, vertical solid gray bars denote distinct features in χ, χ', or χ''. Magnetization versus magnetic field for CrSBr0.43Cl0.57 at various temperatures for magnetic fields oriented along the a-(red traces), b-(blue traces), and c-axes (green traces). B). Magnetization versus magnetic field for CrSBr at various temperatures for magnetic fields oriented along the a-(red traces), b-(blue traces), and c-axes (green traces). For each panel, the temperature ranges over which the magnetization traces were acquired is given in the inset. Here, TKT is also a fit parameter and represents the temperature below which magnetic vortices should bind. For CrSBr and Cl-67, we obtain fitted TKT of 99 K and 84 K, respectively. While the ordering temperature of CrSBr is much larger than the TKT predicted by its high temperature susceptibility, the freezing temperature of Cl-67 is comparable to its predicted TKT, consistent with its weaker interlayer interactions and suppressed anisotropy energy between the a-and b-axes. For both materials, the strong agreement between the Kosterlitz-Thouless fits and the magnetic susceptibility above the Weiss temperature suggest the possibility of XY-like behavior within the paramagnetic phase. -