The sampled barite-bearing fractures are from Proterozoic crystalline bedrock at Forsmark, Laxemar, and Äspö (Southeastern Sweden) (see Drake et al. (2018) for details on the geological setting). Laxemar and Äspö are situated on the Baltic Sea coastline, and only ca. three kilometers apart; hence we consider them as one site (i.e., Laxemar) in this study. Drill cores were mainly obtained by triple-tube drilling conducted by the Swedish Nuclear Fuel and Waste Management Co. This drilling technique preserves fragile minerals on fracture surfaces, facilitating the investigation of ancient biological activity in deep fracture systems. Barite was sampled from fractures in a total of 40 drill cores. The samples represented depths ranging from 60 to 1660 m below sea level. The exact locations of the boreholes are provided in Runge et al. (2026). Sample characterization and mineral identification were performed directly on the fracture surfaces using a FEI QUANTA FEG 650 Scanning Electron Microscope (SEM) equipped with an integrated energy-dispersive spectroscopy (EDS, Oxford T-Max 80 detector) under low-vacuum conditions. The acceleration voltage was 20 kV, and the instrument was calibrated with a cobalt standard. The barite grains were hand-picked from the fracture surface under a microscope, embedded in several epoxy mounts (2.5 cm diameter), and polished to expose cross-sections of the grains. The polished grains were examined using SEM prior to SIMS analysis to detect growth zonation and avoid impurities and cracks.

Secondary-ion mass spectrometry (SIMS) was conducted on a CAMECA IMS1280 ion probe at the NordSIMS lab, Swedish Museum of Natural History, Stockholm. The analytical routines for S and O isotope analyses of barite follow those described by Drake et al. (2024), which are based on the approaches by Whitehouse (2013) for S and Heinonen et al. (2015) for O. The samples were sputtered using a 133Cs+ primary beam with 20 kV incident energy and a beam current of ∼ 3 nA, which was rastered over a 5 µm × 5 µm area during analysis. Each analysis comprised 40 s of pre-sputtering to remove the gold coating over a 15 µm × 15 µm area, centering of the secondary beam in the field aperture, and data acquisition in 12 four-second integration cycles. Secondary ion signals (32S and 34S or 16O and 18O) were detected simultaneously using two Faraday detectors with a common mass resolution of 4860 (M/ΔM) for S and 2430 (M/ΔM) for O. Data were normalized for instrumental mass fractionation using the S0327 reference material, with a conventionally determined δ34S value of +22.0 ± 0.3 ‰ and δ18O value of +11.0 ± 0.1 ‰ (Liseroudi et al., 2021). All results are reported as δ34SV-CDT (Ding et al., 2001) for S and δ18OV-SMOW (Coplen, 1995) for O. The typical uncertainties after propagating the within-run and external uncertainties from the standard measurements were ± 0.2 ‰ (1σ) for δ34S and between ± 0.2 ‰ and ± 0.6 ‰ (1σ) for δ18O values. The previously published calcite δ18OV-PDB values were converted to δ18OV-SMOW for comparability with barite using the formula δ18OV-SMOW = 1.03092 × δ18OV-PDB + 30.92. All SIMS data, including previously published data, are compiled in Runge et al. (2026).

Statistical analysis of 366 paired δ18Obarite/δ34Sbarite data was conducted using a Gaussian Mixture Model (GMM), which is a useful tool for classifying multivariate stable isotope data (Göhring et al., 2016). Notably, GMM is highly sensitive to outliers; hence, they need to be excluded before GMM to prevent adverse effects on the clustering performance. We identified outliers in the paired δ34S–δ18O data using density-based spatial clustering of applications with noise (DBSCAN; Ester et al., 1996). DBSCAN identifies data points that do not belong to any dense region as noise without assuming a predetermined number or shape of clusters, making it useful for outlier detection in bivariate isotope datasets (Valentine et al., 2015). The parameters for DBSCAN are the minimum number of points (minPts) required to form a dense region and the neighborhood radius (ϵ). We tested the sensitivity of our outlier detection to these parameters over a range of minPts values (2 to 15). For each minPts value, ϵ was set at the point of maximum curvature of the sorted k-distance curve (k = minPts) (Ester et al., 1996) (Fig. S1 in the Supplement). The δ34S/δ18O data were converted to z-scores before clustering to ensure neither variable dominated ϵ, and DBSCAN was run for each parameter pair (Fig. S2 in the Supplement). The stability of the identified parameter combinations was quantified using the Jaccard index (the number of outliers identified in two neighboring minPts settings divided by the number identified in each), and the number of dense clusters was tracked across settings (Fig. S3 in the Supplement). The number of clusters was stable at 2 for minPts ≥ 6, and neighboring minPts settings from 13 to 14 identified identical points as outliers (Jaccard = 1.00), indicating that DBSCAN using minPts values of 13 and 14 yields stable outlier detection results. Therefore, we used minPts = 13 and the associated ϵ = 0.586. This parameter combination identified 21 of 366 data points as outliers that were excluded before GMM.

We performed GMM on the outlier-cleaned data set using the Python module Scikit-learn (Pedregosa et al., 2011). To select the appropriate number of clusters for GMM in our δ18Obarite/δ34Sbarite dataset, we identified the best-fit model by calculating the Bayesian Information Criterion (BIC) as a function of the number of clusters. The minimum BIC value indicated our dataset contained two clusters (Fig. S4A in the Supplement). Random state optimization for GMM was performed over a range of zero to ten, yielding a random state of zero at the minimum BIC. York regression was used to calculate the slopes and r2 values of the resulting clusters (Fig. S4B) (York et al., 2004). Notably, our dataset contains data points from two localities (i.e., Laxemar and Forsmark), whereas Laxemar provides the dominant fraction (323 vs. 21 for S). Deriving robust and meaningful clusters requires consistent behavior of these clusters across localities. Hence, we tested the sensitivity of our GMM approach to differences between localities by excluding Forsmark and repeating the same GMM procedure described for the entire dataset. After excluding the Forsmark data, the BIC-guided decision for a two-cluster model remained robust (Fig. S4C). Additionally, the resulting slopes of the individual clusters changed minimally after excluding Forsmark data (Fig. S4B and D). This suggests our clusters were independent of the localities. Thus, we used the cluster assignment and slopes resulting from GMM of the whole dataset to interpret our dataset. In concert, these observations strongly support a two-cluster GMM approach for classifying our δ18Obarite/δ34Sbarite dataset. Nevertheless, the resulting clusters should not be regarded as globally representative and may differ for barite from other areas.

Coupled δ34Spyrite and δ13Ccalcite signatures provide evidence of ancient organotrophic sulfate reduction (OSR) and sulfate-dependent anaerobic oxidation of methane (AOM) in deep subsurface fractures at Forsmark and Laxemar (Drake et al., 2013, 2015, 2018, 2021). The compiled data from Forsmark and Laxemar showed a δ34Spyrite range of -53.9 ‰ to +131.7 ‰, a δ18Ocalcite range of +10.5 ‰ to +28.1 ‰, and a δ13Ccalcite range of -93.1 ‰ to +36.5 ‰ (Drake et al., 2017, 2018) (Table 1, Figs. 2 and 3). A prominent role of thermochemical sulfate reduction (TSR) in these localities has been ruled out because of the large apparent 34ϵ between plausible δ34Ssulfate values of fracture fluids in these systems and pyrite (55 ‰ to 66 ‰: Drake et al., 2021). Moreover, TSR generally occurs at temperatures > 100 °C (Machel, 2001), which is inconsistent with fluid inclusion homogenization temperatures and clumped isotope thermometry indicating formation temperatures < 100 °C of coeval calcite (Drake et al., 2018; Herlambang et al., 2023). Thus, the wide δ34Spyrite range (-53.9 ‰ to +131.7 ‰) was interpreted to reflect Rayleigh distillation during microbial sulfate reduction (MSR) in semi-closed fracture systems, producing 34S-depleted sulfide and extremely 34S-enriched sulfate (Drake et al., 2018). The overall ranges of δ18Obarite (-0.9 ‰ to +19.7 ‰) and δ34Sbarite (+7.6 ‰ to +52.0 ‰) across both localities are consistent with MSR, which can produce 18O- and 34S-enrichment in the residual sulfate pool (Antler et al., 2013, 2014, 2015; Brunner et al., 2005; Drake et al., 2018; Han et al., 2025; Jørgensen et al., 2004; Rudnicki et al., 2001; Wortmann et al., 2007; Zaback et al., 1993). These observations strongly suggest MSR could be recorded in co-genetic barite from Forsmark and Laxemar.

The extremely high δ34Spyrite values at Forsmark and Laxemar imply the presence of an even more 34S-enriched sulfate reservoir potentially archived in co-genetic barite. To detect this archive and investigate its relationship with OSR and AOM, we analyzed δ34Sbarite and δ18Obarite in the same drill cores that were previously sampled for δ34Spyrite and δ18Ocalcite, and δ13Ccalcite analysis (Drake et al., 2017, 2018) (Figs. 2 and 3; Table 1). The δ34Ssulfate values of the paleo-fracture fluids are unknown and likely changed over time. However, the δ34Ssulfate values of the current fracture fluids (+14 ‰ to +27 ‰: Drake et al., 2013) are similar to the median δ34Sbarite values at Forsmark (+26.6 ‰) and Laxemar (+18.3 ‰), suggesting dissolved sulfate in such fluids is a plausible source for barite. The total range of δ34Sbarite (+7.6 ‰ to +52.0 ‰) is consistent with processing of such fracture fluids by MSR under closed-system conditions (Paytan et al., 2002). However, this range is much narrower than that of δ34Spyrite (-53.9 ‰ to +131.7 ‰) across Forsmark and Laxemar (Figs. 2 and 3; Table 1). The ancient barite from Forsmark and Laxemar does not record the extreme 34S-enrichment expected from the δ34Spyrite data. This agrees with barite that recently precipitated on drill core equipment within a deep borehole at Äspö (Fichtner et al., 2024), and carbonate-associated sulfate from the Forsmark and Laxemar drill cores (Fichtner et al., 2026). Therefore, a record of extremely 34S-enriched sulfate in the deep subsurface remains undetected.

The co-variation of the δ18Obarite and δ34Sbarite values exhibited substantial scatter (Fig. 4A), implying a mixture of different sulfate sources and/or an overlap of different fractionation processes. Since the δ18O/δ34S systematics of dissolved sulfate in the low-temperature groundwater systems at Forsmark and Laxemar are affected by OSR and AOM (Drake et al., 2017, 2018; Fichtner et al., 2024), we aimed to identify whether our dataset contains groups of barite associated with either OSR or AOM. To identify barite associated with these groups, we classified our dataset using Gaussian Mixture Modeling (GMM) and compared the linear regression slopes of the resulting clusters with known sulfate δ18O/δ34S trends in MSR-affected settings. We identified a steeper trending “Group 1” cluster (slope: 0.95 ± 0.01; r2 = 0.39) and a shallower trending “Group 2” cluster (slope: 0.55 ± 0.01; r2 = 0.38) (Fig. 4A; Table 2). The clusters resulting from GMM are statistical entities and cannot be interpreted as continuous fractionation trends in our study. This is because our dataset contains multiple barite growth generations from different locations and records different fractionation trends, non-coeval sulfate reservoirs between growth zones, or local fluid mixing. Therefore, our statistical analysis can only detect average δ18O/δ34S trends of overlapping fractionation or mixing processes involving fracture water sulfate that was processed by OSR and AOM at different points in space and time. These overlapping trends likely explain the low r2 values. There was no correlation between Group 1 or Group 2 barite and the δ18O values of co-genetic calcite (Fig. 4B). This suggests that the difference between Group 1 and Group 2 does not simply reflect isotopically distinct water sources (Pedersen et al., 1997). Instead, they most likely record different processes affecting the respective sulfate reservoirs from which barite precipitated.

Previous studies established that sulfate reduction rates (SRR) control the δ18O/δ34S slope in residual sulfate during the early stages of MSR (Brunner et al., 2005; Han et al., 2025; Wortmann et al., 2007). At a lower SRR, δ18O rises rapidly relative to δ34S leading to a steeper slope, whereas at a higher SRR, δ18O rises slowly relative to δ34S, leading to a shallower slope (Fig. 1). Thus, the difference in δ18O/δ34S slopes could reflect a lower SRR in Group 1 than in Group 2 barite (Fig. 4A). Moreover, differences in metabolic pathways (OSR vs. AOM) can lead to variable δ18O/δ34S trends in sulfate at similar SRR (Antler et al., 2013, 2014, 2015). To clarify the effects of SRR and MSR pathways on δ18O/δ34S systematics recorded in barite at Forsmark and Laxemar, we correlated our GMM-classified δ18Obarite and δ34Sbarite data (i.e., excluding outliers) with the δ13C values of calcite in the same samples (Figs. 2C, 3C, and 4C). When petrographic correlation of barite with individual calcite generations was not possible, we used average δ13Ccalcite values from the barite-bearing samples. Out of all classified barite data, 71 spots in Group 1 and 81 spots in Group 2 had associated δ13Ccalcite data. Strongly 13C-depleted calcite (δ13C < -40 ‰) was almost exclusively associated with Group 1 barite (28 out of 71) (Fig. 4C). The δ13C values of this calcite (-70 ‰ to -40 ‰) cannot be explained by oxidation of organic matter via OSR alone and suggest variable input of inorganic C from the oxidation of primarily microbial methane (Drake et al., 2015, 2017). This implies that some Group 1 barite associated with such calcite was affected by AOM. In contrast, only 2 out of 81 spots in Group 2 barite were associated with strongly 13C-depleted calcite. Instead, Group 2 was almost exclusively associated with calcite that has a δ13C ≈ -30 ‰ or higher (Fig. 4C), suggesting methane was not the main C source (Whiticar, 1999). This calcite likely reflects a more prominent contribution from organic matter rather than methane oxidation, implying that the associated barite was affected by OSR (Drake et al., 2017). Notably, such OSR-related barite not only dominates Group 2, but also widely occurs in the AOM-affected Group 1 (Fig. 4C). Thus, it seems unlikely that the different MSR pathways are the only control on the different slopes of both groups. Instead, we interpret the different δ18O/δ34S trends to result from an interplay of MSR pathways and SRR: Group 1 reflects AOM and OSR at a relatively low SRR, whereas Group 2 dominantly reflects OSR at a relatively high SRR.

The outliers identified via DBSCAN (n = 21) are strongly heterogeneous and do not follow a common δ18O/δ34S trend (Fig. 4A, Table 2). Thus, the outliers do not form a coherent group and likely reflect highly variable fluid compositions and fractionation processes. Moreover, a relationship of the outliers with fluid sources and MSR pathways is unclear because only four outliers have associated δ18Ocalcite and δ13Ccalcite values (Fig. 4B and C).

The major control on SRR is the availability and quality of electron donors (i.e., H2, CH4, or organic matter) (Leavitt et al., 2013; Lyons and Gaudette, 1979; Westrich and Berner, 1984). SRR is high when electron donors are more bioavailable and abundant, and vice versa. The abundances of electron donors in the parent fluids from which our ancient barite precipitated are unknown. However, low SRR due to nutrient limitation was inferred based on the large apparent 34ϵ associated with pyrite formation at these sites (Drake et al., 2018), consistent with the common free energy limitation in deep subsurface habitats in general (Hoehler and Jørgensen, 2013). Thus, a relatively lower availability of electron donors in Group 1 could have caused the lower inferred SRR than in Group 2 (Fig. 5A). Moreover, the typical range of sulfate concentrations in modern anoxic fracture fluids at Forsmark and Laxemar (< 1 to 10 mM: Hallbeck and Pedersen, 2008; Laaksoharju et al., 2008; Drake et al., 2013) is much lower than in marine environments (28 mM in seawater: Jørgensen et al., 2019). Such sulfate concentrations may additionally limit SRR in the deep subsurface (Boudreau and Westrich, 1984; Pallud and Van Cappellen, 2006). Sulfate concentrations in these subsurface habitats also vary around the threshold at which sulfate reducers outcompete methanogens for substrate utilization (ca. 1–10 mM: Iversen & Jorgensen, 1985; Glossner et al., 2016; Sela-Adler et al., 2017). If sulfate concentrations exceed this threshold, OSR can be favored, inhibiting methanogenesis and AOM. Thus, δ13C evidence for AOM indirectly supports sulfate limitation in Group 1 (Fig. 4c). Thus, a combined effect of electron donor limitation and low sulfate concentrations could have favored methanogenesis and AOM at relatively low SRR (Fig. 5A). Conversely, a higher abundance of electron donors could explain a higher inferred SRR in Group 2 than in Group 1 (Fig. 5B). At higher sulfate availability, methanogenesis is inhibited, possibly resulting in a lack of evidence for AOM in Group 2 (Fig. 5B). Instead, OSR is favored and SRR is high, resulting in a shallower trend in Group 2 (Fig. 5B). Thus, we interpret the relative abundances of sulfate and electron donors to control the observed δ18O/δ34S trends in ancient subsurface barite by modulating SRR and MSR pathways.

The stronger 34S-enrichment in the OSR-dominated Group 2 than in the AOM-affected Group 1 contrasts with observations from marine sediments, where 34S-enriched barite is a commonly used proxy for AOM at the SMTZ (Torres et al., 1996; Wood et al., 2021; Yang et al., 2023; Zan et al., 2022; Zhou et al., 2015). This discrepancy could be due to the higher sulfate concentration in seawater (28 mM: Jørgensen et al., 2019) compared to the subsurface at Forsmark and Laxemar (< 1 to 10 mM), allowing sulfate to become strongly 34S-enriched before barite becomes undersaturated (Fichtner et al., 2024). The relatively steep slope of the AOM-affected Group 1 is comparable to some previous observations from marine methane-diffusion-limited AOM settings, such as sedimentary SMTZs, or OSR-dominated methane-devoid settings (Antler et al., 2013, 2015; Blake et al., 2006; Böttcher et al., 2006). At the same time, Group 2 shows little clear evidence of AOM but a shallow slope similar to marine methane-in-excess environments (i.e., the methane flux exceeds methane consumption via oxidation), such as cold seeps (Aharon and Fu, 2000, 2003; Antler et al., 2013, 2014; Rubin-Blum et al., 2014). These observations highlight a further discrepancy between marine environments and the deep subsurface. In marine environments, steeper δ18O/δ34S slopes tend to be found in settings affected by OSR or methane-limited AOM, whereas shallower slopes result from AOM at high methane concentrations. In our subsurface barite, steeper slopes tend to be more associated with evidence for AOM, whereas shallower slopes tend to occur in OSR-dominated settings. The relatively shallow slope of OSR-related barite in the subsurface implies a lesser extent of equilibrium isotope exchange of S intermediates with water compared to marine settings. This could be achieved via a higher overall SRR in the subsurface than in marine settings; however, this seems unlikely given the oligotrophic nature of subsurface habitats (Küsel and Dopson, 2026). Additional factors influencing the different behavior of δ18O/δ34S trends in the deep subsurface may be the increasing temperature and pressure with depth or factors within microbial communities, such as low cell densities or adaptations to extreme nutrient limitation. However, the impact of these factors on δ18O/δ34S relationships in residual sulfate during MSR remains speculative. Irrespective of this unresolved problem, the differences in δ18O/δ34S systematics between marine and subsurface barite highlight that interpretations cannot be extended from one system to the other without additional constraints.

The absence of extreme 34S-enrichment in barite from Forsmark and Laxemar is unexpected considering the corresponding δ34Spyrite values of up to +131.7 ‰, predicting an even more 34S-enriched sulfate reservoir during pyrite formation. The δ34Sbarite values of up to +52.0 ‰ observed among the outliers suggest that the SRR at times exceeded the sulfate resupply, decreasing the steady-state sulfate concentration (i.e., closed-system conditions) (Fig. 4A). Hence, Rayleigh distillation is locally recorded in subsurface barite, although not to the extreme degree observed in pyrite (Table 1). This discrepancy between the barite and pyrite records has been suggested to result from (i) the precipitation of barite and pyrite under separate microenvironmental conditions, involving the isolation of evolved 34S-enriched fluids, or (ii) late-stage barite undersaturation which may inhibit sulfate precipitation or favor its post-formation dissolution before the formation of a 34S-enriched sulfate reservoir (Fichtner et al., 2024, 2026). Barite undersaturation may arise from sulfate depletion at high degrees of Rayleigh distillation (Fichtner et al., 2024; Wood et al., 2021). Alternatively, barite precipitation during earlier stages may deplete Ba2+ (Aloisi et al., 2004), which in crystalline bedrock fractures is mainly supplied by feldspar dissolution. However, none of the δ34S analyses of carbonate-associated sulfate in the samples analyzed here detected this reservoir (Fichtner et al., 2026). This suggests that the mechanism limiting the precipitation of extremely 34S-enriched sulfate is more likely associated with the S cycle, rather than cation availability. Sampling biases cannot be excluded but have been mitigated by the large number of δ34S analyses (n = 505) of barite from multiple fractures at two localities. Notably, the strongest 34S-enrichment observed here occurs in the outlier group and is not associated with cogenetic calcite data (Fig. 4A–C; Table 2). This makes an interpretation of the associated MSR pathway and SRR difficult for these cases. However, it seems likely that these barites represent relatively late-stage precipitates that possibly formed in an environment where barite saturation was less limiting.

Microscale observations of pyrite–calcite–barite assemblages could help investigate this interpretation further (Figs. 6 and 7). Sample KAS02 (802 m) can serve as an example of AOM-associated barite due to its association with calcite that has an average δ13C of -72.1 ‰ and pyrite with δ34S values spanning -23.5 ‰ to +42.5 ‰ (Fig. 6A and B). Additionally, all SIMS spots on barite in this sample belong to Group 1 (Fig. 7A). Together, these observations are consistent with a sulfate pool affected by AOM at relatively low SRR. Notably, this barite exhibited distinct crystallographic and isotopic zonation with only minor δ34S and δ18O variabilities between growth zones of ∼ 4 ‰ and ∼ 0.8 ‰, respectively (Fig. 7B). This low variability suggests relatively open system conditions during barite growth (Fichtner et al., 2024; Wood et al., 2021). In contrast, the much more pronounced core-to-rim δ34S increase in the co-genetic pyrite from -23.5 ‰ to +42.5 ‰ indicates MSR in a more closed system, meaning that SRR exceeded the resupply of sulfate during pyrite growth (Fig. 7C). Apparently, barite and pyrite in this sample record precipitation in distinct hydrogeochemical regimes, possibly at different stages of fracture fluid evolution or in separate microenvironments.

Sample KLX01 (220 m) serves as an example of OSR-related barite due to its association with calcite lacking a substantial δ13C depletion (-11.6 ‰) (Fig. 6C and D). Notably, barite in this sample exhibited a massive core and a porous rim (Fig. 7D). These texturally distinct growth zones were associated with a sharp core-to-rim δ34S and δ18O increase of ∼ 12 ‰ and ∼ 6 ‰, respectively (Fig. 7D and E). This sharp increase suggests that barite in the rim precipitated from sulfate that had already undergone 34S-enrichment via sulfate reduction elsewhere in the fracture system (e.g., Drake et al., 2018). Additionally, SIMS spots related to Group 1 predominated in the core, whereas spots related to Group 2 exclusively occurred in the rim (Fig. 7D). This implies that the processing of the respective sulfate reservoirs reflected by core and rim occurred under different SRR and/or MSR pathways. Thus, the distinct textural and isotopic differences demonstrate that the generations reflect two barite precipitation events, rather than continuous barite growth. The porosity in the rim suggests barite dissolution (Fig. 7D), possibly due to undersaturation via rapid sulfate depletion at the high SRR inferred for Group 2 (Fichtner et al., 2024). Thus, a relatively high SRR in a sulfate-poor environment may result in a preservation bias against extremely 34S-enriched barite in deep subsurface environments. The relatively minor core-to-rim δ34S increase of ca. 0 ‰ to 20 ‰ in co-genetic pyrite implies that sulfate did not become strongly depleted during pyrite formation in this microenvironment (Fig. 7F). While there was no evidence for AOM from δ13Ccalcite in this sample, it cannot be resolved petrographically whether the calcite and pyrite are co-genetic to the barite core or rim. Therefore, it remains unclear whether the shift from Group 1 to Group 2 during barite growth is due to different MSR pathways or SRR, or both. Nevertheless, the differences between the samples KAS02 (802 m) and KLX01 (220 m), as well as their evolution during barite growth, demonstrate a strong control of hydrogeochemical conditions on their isotopic composition in different microenvironments and over time. This highlights that the associated barite and pyrite record different environmental conditions and should be correlated with caution.