Introduction

Speleothems (eg stalagmites, stalactites, and flowstone) are secondary sedimentary deposits that can act as records of paleomagnetic secular variation, or the spatial and temporal variability of the prehistoric magnetic field. Sedimentary materials are useful for paleomagnetic secular variation studies as they provide near-continuous records of geomagnetic field behavior. In particular, stalagmites and flowstones have been used in paleomagnetic studies. These speleothems have a unique formation process compared to other sedimentary materials. Stalagmites are formed when water drips from the ceiling of a cave onto the ground. The lower \(CO_2\) concentration inside the cave causes degassing of the water, resulting in carbonate precipitation. The degassing and precipitation is further promoted by splashing on the stalagmite surface by reducing the surface area of the water droplets forming thin, concave-down, stacked layers. Each layer is approximately horizontal in the middle and thins out at the vertical edges. Flowstones precipitate as water flows along cave walls, with the low cave \(CO_2\) driving degassing. As these speleothems grow, factors such as the drip rate, saturation, and impurities affect what kind of carbonate fabric precipitates1. On precipitation, impurities in the water (eg. magnetic materials, aluminosilicates, silicates) can get entrapped within the stalagmite structure.

Perkins and Maher2 enumerated some of the advantages that speleothems have over traditional sedimentary material used for paleomagnetic studies. These advantages include a sub-annual lock-in time, no compaction or slumping, identifiable recrystallization, and the ability to be dated via U-series methods. Since the seminal study by Latham et al.3, speleothems have been used for paleodirectional studies. The field directions recorded by the tops of actively growing speleothems reflect the modern day field3. Additionally, Morinaga et al.4 used a mixture of molten sodium thiosulphate and magnetic separates from natural cave deposits to show that artificial stalagmites crystallized in the lab accurately record the ambient field direction. Although there are significant differences from the natural process of speleothem formation, this is one of very few studies that attempts to recreate speleothem magnetic remanence acquisition in a laboratory setting.

As speleothems have become an increasingly popular choice for paleomagnetism, it is necessary to understand the unique mechanics of their remanence acquisition process. In this study, we precipitate speleothem analogs under different field intensities to understand their ability to record magnetic field information. By introducing clay minerals, we study how flocculation affects the remanence acquisition process.

Speleothem paleointensity

Basic detrital remanent magnetization (DRM) theory5 suggests that isolated magnetic particles in a water column should fully align with the ambient field very rapidly; however, most sedimentary samples have a relatively low alignment efficiency. Multiple post-depositional processes and flocculation are usually invoked as the reason for the low intensity DRMs measured. Speleothems are unique in their remanence properties because they have a relatively high alignment efficiency compared to other sedimentary recorders (Fig. 1). Alignment efficiency is approximated here as a ratio of the magnitude of their natural magnetization to the magnetization gained when exposed to a large magnetic field, or the natural remanent magnetization (NRM) to the isothermal remanent magnetization (IRM). The alignment efficiency of speleothems falls mainly between 0.5 and 10%, which is on average 1-2 orders of magnitude higher than that of other sediments. This is an important consideration since estimates of paleointensity rely on a linear relationship between alignment efficiency and ambient field strength. In materials with a high degree of particle alignment, like in speleothems, this quality could lead to a general insensitivity to variations in magnetic field intensity.

Multiple studies have used speleothems as recorders of relative paleointensity6,712,13,14. In particular, speleothem paleointensity studies have been successful in characterizing brief intervals of very high or low intensities6,12. The main methods for calculating relative paleointensity are normalization of the NRM using IRM or anhysteric remanent magnetization (ARM) and the pseudo-Thellier method15. Ponte et al.7 found good agreement between all three of these methods for a mid-Holocene speleothem from Portugal. However, while the records follow similar trends, absolute paleointensity is harder to determine. Trindade et al.13 calculated paleointensity using the pseudo-Thellier method on two contemporary stalagmites from the same cave system. While the trends follow those predicted by global geomagnetic field models, both stalagmites required different scaling factors in order to match the expected range of intensity variation. To directly calculate past field intensities, we have to determine what factors drive remanence acquisition.

Fig. 1
Fig. 1
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Comparison of NRM versus IRM for different paleomagnetic samples6,7,8,9,10,11. The grey lines mark orders of magnitude of alignment efficiencies.

Accessory minerals in speleothems

During the formation of a speleothem, a minor fraction of accessory minerals are incorporated into the speleothem’s carbonate structure. These accessory minerals may originate from four separate sources. One source is drip water, which picks up grains from the soil and epikarst as it percolates through cracks and fissures, eventually falling onto the wet surfaces of actively growing speleothems. Another source can be periodic flooding of the cave that deposits coarse detrital material or splashing of cave sediments onto the flanks of the speleothems. Third, detrital material may come from windblown sediment for speleothems near cave entrances. Lastly, minerals incorporated into speleothems may be authigenic16,17,18,19,20,21. Here, we will be focusing on detritus entering the system via drip water, as that is the main continuous source of magnetic material for most speleothems.

The majority of detritus in speleothems is non-magnetic17,22,23,24. In a study of speleothems from localities in England and Wales, less than 1 wt% of the speleothem mass came from detrital content, and of that, the majority was quartz, with lesser amounts of chlorite, muscovite, and other unidentified aluminosilicates17. In a study on speleothems from southern Minnesota, 5-6 g of the speleothem had about 50 mg of non-carbonate minerals, of which about 0.1 mg was magnetic23. Measurements of stalagmites from caves near the Yantze River in China found less than 60 ppm of iron22.

The primary magnetic remanence holders in speleothems are magnetite, maghemite from soils, and allochthonous titanomagnetite. Although other magnetic minerals, such as goethite and hematite, are commonly found, most of the NRM signal of most speleothems comes from low coercivity minerals18. Both magnetite and titanomagnetite have morphologies ranging from euhedral to heavily abraded18. Because cave conditions are not thermodynamically favorable for magnetite formation18,25,26, both the abraded and euhedral magnetite are likely detrital with the difference in abrasion due to distance traveled17. Titanomagnetite forms exclusively in igneous environments, so it must be detrital as well. Strauss et al.18 found that the grain sizes ranged from superparamagnetic to multi-domain. However, the remanence is dominated by single domain and pseudo-single domain grains with bulk coercivities ranging from 5 to 20 mT.

An essential observation for the acquisition of remanence in speleothems is that their constituent magnetic minerals are unlikely to occur as isolated grains. Instead, iron oxides are incorporated into speleothems through low density aggregates of natural organic material and aluminosilicates27 (Fig. 2a). Imaging of the detritus in stalagmites show clay grains associated with iron oxides28,29. The size of aggregates transported through drip water is limited by that of the pores and fissures within the epikarst. Bull16 found very few grains exceeding 45 \(\mu m\) that were deposited through cracks and fissures, with the vast majority much smaller27.

Alignment and deposition of magnetic grains

Magnetic materials introduced to a stalagmite via drip water must settle through a film of water \(0.05 - 0.2\) mm thick30,31 on the stalagmite surface. Our understanding of magnetic alignment in speleothems is based on the model proposed by Nagata5, in which the aligning torque is countered by the viscosity of the fluid. According to this model, a speleothem’s water column is thick enough that single-domain sized magnetite grains should completely align with the field within their settling time. One way of slowing down the rapid alignment with the field is to introduce flocculation, which increases the mass of a settling unit relative to its magnetization. As the co-occurrence of alumnosilicates and magnetic minerals have been noted in both cave dripwaters27 (Fig. 2a) and preserved in stalagmites directly28, it is reasonable to assume that flocculation contributes to lower alignment efficiencies in speleothems. Models show that that flocculation can result in a lowering of alignment efficiency that results in a sensitivity to field intensity32,33,34.Variations in flocculate size also significantly affect the magnitude of the relative paleointensity signal34.

Fig. 2
Fig. 2
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(a) TEM image of a flocculate in cave dripwater containing aluminosilicates and iron oxides reproduced from Hartland et al.27 (b) SEM image of the surface of a stalagmite with a columnar fabric reproduced from Frisia et al.1 (c) cross-section of experimental stalagmite.

Speleothems, such as stalagmites and flowstones, frequently show banding parallel to paleo-growth surfaces. Previous magnetic studies of speleothems have proposed using this banding as a basis for applying bedding corrections to remanence directions in an effort to ameliorate inclination shallowing7,22. Although these studies document a relationship between the orientation of the banding and the inclination acquired within a speleothem, corrections based on “unfolding” of the remanence directions using this banding do not lead to improved clustering of paleomagnetic directions22.

While it is tempting to think of such banding as smooth paleogrowth surfaces, in reality, growth surfaces of stalagmites and flowstones are highly textured surfaces influenced by carbonate crystal fabrics. As suspended magnetic flocculates settle, the surface texture is likely to play an important role in particle alignment and ultimately on the direction and intensity recorded by the material. Speleothem fabrics have been differentiated into five categories, mainly based on the size and shapes of the carbonate crystals1 and fabrics can further be affected by the carbonate mineralogy28,34. As climate and hydrology change, the actively growing fabric will also change. High-resolution scanning electron microscope (SEM) images of these different fabrics show surface topography on the order of and much larger than the size of flocculates found in cave dripwater (Fig. 2b). For example, surfaces of speleothems with columnar fabric have pores on the order of tens of microns1,38. Frisia et al.37 proposed a model of calcite growth that supports detrital accumulation in the pore spaces between calcite crystals. In the candle-like, columnar stalagmites that are the focus of most paleomagnetic studies, the fast-growth direction of calcite (the c-axis) tends to be oriented nearly perpendicular to the growth surface. In the center of a stalagmite, this would result in vertically oriented pore spaces where particles would settle on highly tilted surfaces. Along the flanks of a stalagmite, such pore spaces will be more shallowly oriented. Landing on a slope affects the direction recorded38 and, on a speleothem, there is a range of tilted surfaces facing different directions.

In this study, we precipitate speleothem analogs to explore the relationship between clay availability and the sensitivity of paleointensity measurements. These experiments focus on recreating flocculates of clay and magnetite settling through a water column and interacting dynamically with an actively growing crystalline matrix with a range of oriented surfaces. We do not produce stalagmite-like morphologies on a large scale, but these experiments capture the essential processes thought to occur within stalagmites. We then use numerical simulations to further explore the effects grain size, length of the water column, and interactions with the speleothem surface.

Experimental results

Artificial speleothems (Fig. 2c) were precipitated from ammonium dihydrogen phosphate (ADP) in four different field intensities (15, 30, 50, 70 \(\mu T\)) and with four different ratios of magnetite to kaolinite (Table 1). In order of decreasing mass ratios of magnetite to kaolinite, the four ratios are: 1:0, 1:2, 1:3, and 1:4. A full description of the precipitation process and the materials used is provided in the Methods section.

Directional analyses

Calculated Fisher mean and \(\alpha _{95}\) values for each growth type overlap with the applied field direction during growth (Fig. 3a). The magnetite-only samples (1:0 mixture) had an average inclination slightly steeper than the applied field. With increasing amounts of clay, there was a slight shallowing of the inclinations and an increased spread of recorded inclinations (Fig. 3b). With the exception of the 1:4 mixture growth at \(15\mu T\), the artificial speleothems were able to faithfully record the applied field direction within a 95% confidence interval.

Fig. 3
Fig. 3
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(a) Equal area plot of all specimens grouped by growth type with a Zjiderveld plot39 of an example AF demagnetization (b) Inclinations of all specimen. The dotted line indicates the applied field direction. The Fisher mean inclination (white triangles) of each growth type are also indicated. The colored bars highlight the inclination values that fall within the \(\alpha _{95}\) angle of the Fisher mean. (c) Total angular misfit from the growth direction as a function of growth field. The dotted line indicates the cutoff value for samples used in the intensity analysis.

Figure 3c shows the angular misfit as a function of the growth field. Angular misfit was calculated as the total angle between the applied field and measured remanence. As the applied field increased, the variation in angular misfit decreased. A \(15^\circ\) cutoff was used to filter the specimens for intensity calculations.

Alignment efficiency and intensity relationship

The alignment efficiency of the artificial speleothems is calculated as the ratio of the NRM to the IRM. For our artificial speleothems, it ranges between 1 and 30%. When grouped by growth type, the 1:0 mixtures have the highest alignment efficiencies with a mean value close to 21% and a standard deviation of 5%. This is higher than the alignment efficiencies found in natural speleothem samples. The mean values for alignment efficiency of the other mixtures range between 1 - 10%. These values overlap with the efficiencies found for natural speleothems (Fig. 1).

The relationship between the applied intensity of the growth field and the calculated intensity is explored by plotting the alignment efficiency as a function of the applied growth field (Fig. 4). Intensity was calculated using only specimen that passed the directional filter (Fig. 3c). The 1:0 mixtures have no distinguishable dependence on the applied field. With decreasing ratios of magnetite to clay, the average alignment efficiency decreases but the sensitivity to changes in field increases. The moderate magnetite to clay ratios (1:2, 1:3) resulted in a slightly positive trend. Due to its greater amount of magnetite, the 1:2 mixture had NRM intensities about four times higher than those of the 1:3 mixture. However,the sensitivity to the field is higher for the 1:3 mixtures than for the 1:2 ones. Finally, the mixture with the lowest magnetite to clay ratio (1:4) had a very low dependence on growth field. Hence, field dependence appears to be optimized for a certain range of ratios.

Fig. 4
Fig. 4
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Alignment efficiency (NRM/IRM) as a function of the applied field for each set of growth types. Each growth type was fit with a Langevin function with higher \(\beta\) values corresponding to a greater field dependence. The 1:4 mixture was not fit due to the lack of low field data.

Modeling alignment of flocculates in a water column

We used numerical models to better understand the dominant influences on speleothem remanence acquisition. Acquisition of DRM via flocculates has been modeled by numerous studies32,33,34,40,41, but not specifically for the physical and mechanical properties of speleothems.

Flocculate sizes were set by sampling from a log normal distribution with a mean radius of \(0.5 \,\mu m\) to match the size of flocculates imaged in cave dripwater27 and a sigma of 1. To get a magnetization, flocculate size was mapped to an integer number of associated magnetic grains between 1 and 6, resulting in more magnetic grains on larger flocculates. Magnetite grain sizes were pulled from one of two log-normal distributions, one based on coercivity measurements and one based on magnetic separates. These two distributions allow us to compare our artificial speleothems with natural ones. Based on measurements of magnetic separates from a speleothem, the magnetization of the detrital material is approximately \(3 \, A/m\)18,23. This is about an order of magnitude greater than the \(0.33 \, A/m\) volume magnetization used for other flocculate models33, but this bulk sample includes flood layers enriched in magnetic material, so it is not surprising that the magnetization is high. Assuming the magnetization comes from a single prolate magnetite particle with an axial ratio of 1.33 and a saturation magnetization of \(92 \, Am^2/kg\)42, this corresponds to a grain diameter near 30 nm. To stay within the range of single domain magnetite, we used prolate magnetite particles with an axial ratio of 1.33 and pulled from a log normal distribution with a mean width of 40 nm and a sigma of 0.1. This results in flocculates with magnetizations ranging between \(10^{-18}\) and \(10^{-19} \, Am^2\). Alternatively, magnetite grains were pulled from a log normal distribution with a mean radius of \(0.22 \, \mu m\) and a sigma value of 0.1 and given an axial ratio of 1.33, which matches the distribution of magnetite powder43 used in the experimental section. Because these grains are larger than single domain, the magnetization was calculated by approximating the saturation magnetization as 12% of the standard value for magnetite. This resulted in flocculates with magnetizations on the order of \(10^{-15} \, Am^2\). Each magnetite grain was assigned a random direction, and the magnetization of each flocculate was found by vector addition of the grains. This method of creating flocculates results in a positive correlation between magnetization and flocculate size, as suggested by Tauxe et al.33.

Flocculate rotation is governed by

$$\begin{aligned} \underbrace{I{\frac{d^2 \theta }{dt^2}}}_{\text {inertial}} = \underbrace{-8 \pi \mu r^3 {\frac{d \theta }{dt}}}_{\text {viscous}} - \underbrace{mB\sin \theta }_{\text {magnetic}} \end{aligned}$$
(1)

where I is the moment of inertia, \(\theta\) is the angular misalignment between the magnetic moment and the magnetic field, \(\mu\) is the translational viscosity of water, m is the magnetic moment, and B is the magnetic field. The viscosity term used here is that for a spherical particle, as the viscosity term gets complicated very quickly when non-spherical shape parameters are introduced44. Following Nagata5, the inertial term is dropped resulting in the following equation of motion

$$\begin{aligned} \tan {\frac{\theta }{2}} = \tan {\frac{\theta _o}{2}} e^{{-mBt}/{8 \pi \mu r^3}} \end{aligned}$$
(2)

where \(\theta _o\) is the initial angular misalignment. Time, which is correlated to water column length, is the limiting factor to complete alignment with the applied field direction. Speleothems have a water column thickness of approximately \(100 \, \mu m\)31 and our artificially grown stalagmites had a water column thickness of approximately 5mm. Velocity of the flocculates was calculated according to the empirical relationship found by Gibbs45 for estuarine flocculates of

$$\begin{aligned} v = 1.1 r^{0.78}. \end{aligned}$$
(3)

This relationship takes into account the decreasing density of flocculates with increasing size. By combining the equation of motion with the velocity equation, the angle of misalignment as a function of the depth of the water column is:

$$\begin{aligned} \tan {\frac{\theta }{2}} = \tan {\frac{\theta _o}{2}} \exp {\left( {\frac{-mBl}{8.8 \pi \mu r^{3.78}}}\right) }, \end{aligned}$$
(4)

where l is the length of the water column in meters.

The applied field for each simulation is downward in the \(+90^\circ\) inclination direction. In this approach, only the inclination of the flocculates changes during alignment. Solving Equation 4 gives the final inclination of the flocculate. Each simulation included 500 flocculates, all of which were vector summed to calculate the total DRM intensity and direction. To normalize it, we calculated a saturating IRM. The flocculate’s rotation was applied to each magnetite grain associated with it. The magnetite grains were assumed to have uniaxial anisotropy, so the moment of any grain with a negative inclination was reversed to simulate an IRM applied in the +Z (\(90^\circ\) inclination) direction. The vector sum of the moments is the IRM.

Fig. 5
Fig. 5
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Alignment efficiency of simulations of 500 flocculates settling in a water column as a function of ambient field. Each black dot represents a simulation, the red triangle is the mean alignment efficiency for each scenario, and the grey bars indicate one standard deviation around the mean. The dashed line is a Langevin fit to the mean values with higher \(\beta\) values corresponding to a greater field dependence. Graphs a, c, e used a smaller grain size of magnetite while varying water column lenth (a,c) or flocculate size (e). Graphs b and d were run for larger magnetite grains. f is a schematic that shows how alignment efficiency (NRM/IRM) and field sensitivity (\(\beta\)) vary as different parameters are changed.

Each simulation of 500 flocculates was run 20 times at each of the four fields that correspond to those of the artificial speleothem growth experiments (\(15, 30, 50, 70 \, \mu T\)). The results of these simulations are shown in Fig. 5.

Overall, these show a positive relationship between alignment efficiency and the intensity of the applied field. Smaller magnetite grains result in smaller grain moments and correspond to the largest sensitivity to applied field, with an \(\sim 30\%\) increase in the mean values between 15 and 70 \(\mu T\). Larger grain sizes result in less field dependence with only a 0.4-6% increase in mean value. The most analogous simulation to our experiments is the larger grain size with the longer water column length. The very small increase in efficiency seen in the experimental results matches that seen in the modeling results. None of these scenarios have a linear relationship. In all four, the slope flattens at high field values.

Additionally, these models were run for flocculates of varying sizes but with similar moments, with magnetite grain sizes pulled from the distribution centered around a 40 nm diameter. As flocculate size increased, the alignment efficiency decreased. Field sensitivity was similar for flocculates with radii between \(1-2 \, \mu m\) but decreased for flocculates outside that range.

Interacting with a highly textured surface

Another notable difference between simulations and experiments is that the average efficiency is still much higher for the simulations. There must be a secondary mechanism that lowers the overall alignment efficiency but does not necessarily have a field dependence. Here, we explore the effect of flocculate rotation upon landing on the actively growing carbonate surface.

As the flocculates settle onto the speleothem surface, they interact with a steeply sloping, textured surface. This causes them to roll and fall into the pore space between growing calcite grains. To approximate the effect of this process, we introduced a random nudge to all of the flocculates that account for landing-induced rotation. This was achieved by generating a random rotation angle (\(\alpha\)) for each flocculate and rotating the grain \(\alpha\) degrees around an axis in the horizontal plane with a random declination. The value \(\alpha\) was drawn from a linear uniform distribution between \(-\alpha _o\) and \(+\alpha _o\).

Fig. 6
Fig. 6
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(a) Alignment efficiency as a function of applied field for a simulation with a single domain sized distribution of magnetite grains on flocculates falling through a 0.1 mm water column. Each dot is the mean value for 10 simulations and the color of the dot corresponds to the \(\alpha _o\) randomization angles. (b) Mean alignment efficiency of the flocculates before randomization divided by that after randomization as a function of the \(\alpha _o\). (c) \(\beta\) value of the best Langevin fit a function of \(\alpha _o\).

As the randomization angle increases, the overall alignment efficiency decreases (Fig. 6). However, for randomization angles below \(120^\circ\), the overall shape of the function is similar. At higher values of \(\alpha _o\), the slope changes significantly, making it difficult to extract the applied field from the alignment efficiency.

Discussion

The incorporation of magnetic materials in speleothems can be described by a two-step process. The first step is alignment of grains within the water column, which is highly influenced by flocculation and has a dependence on growth field. The second step involves a relatively field-independent process related to the interaction of the flocculates with a very rough, actively growing crystal matrix. This lowers the alignment efficiency and also slightly obscures the field dependence.

An important observation is that the relationship between applied field and alignment efficiency is not linear. To quantify the relationship, we used a modified version of the Langevin function

$$\begin{aligned} L(B) = \coth {\frac{B}{\beta }} - \frac{\beta }{B} - \text {C} \end{aligned}$$
(5)

which describes the relationship between magnetization and field. B is the applied growth field and C is a constant. The main fitting parameter is \(\beta\), which scales with how angular the approach to saturation is. Lower values of \(\beta\) correspond to a sharper approach towards saturation and a lower overall sensitivity to the changes in field intensity at high field values. In the models, the simulations with the highest sensitivity had a non-linear dependence on field that flattened out within Earth-like field values. This agrees with previous modeling by Mitra and Tauxe34 which predicts a non-linear dependence on field with no inclination shallowing for the size of flocculates used in this study. This is consistent with what we found; our directions recorded matched the applied field, but the relationship with field intensity was non-linear both in modeling and experiments. As the length of the water column increased, \(\beta\) decreased, resulting in less sensitivity to the field. This non-linear relationship means that distinguishing between low field values is easier than doing so for high field values. Hence, it might be easier to identify periods of anomalously low field intensity6, than discriminate between multiple high field intensities. Osete et al.12 is an example of using a speleothem’s recording sensitivity to distinguish between low and high paleointensity regimes across a geomagnetic instability.

Magnetite grain size in natural speleothems is closer to the finer grain size range modeled18. As the grain size increases, the sensitivity to growth field decreases, as seen by the barely resolvable relationship with growth field of the artificial stalagmites. In speleothems, the sizes of flocculates are limited by the porosity of the epikarst. Hence, the flocculates are likely to be of similar size and smaller than the ones modeled in this study. Both these cases result in a non-linear but relatively strong field dependence, however, the alignment efficiency of the models is significantly greater than that of the artificial and natural speleothems.

Our artificial growth experiments showed that flocculation decreased the overall alignment efficiency, lowering from near 20% for pure magnetite to between 1% and 15% for mixtures with clay. One possible result of increasing the amount of clay relative to magnetite is the creation of more flocculates that are the same size, but with fewer magnetite grains per flocculate, and hence lower moments. The effect of this can be seen by comparing the model runs in Fig. 5b,d to those in Fig. 5a,c. The smaller grain size of magnetite resulted in an effective overall smaller flocculate moment. These simulations had a lower alignment efficiency and a greater field dependence (higher \(\beta\)) than the simulations of flocculates with larger magnetic moments. The other possible result of increasing the total amount of clay relative to the amount of magnetite is to maintain flocculates with the same overall moments but much larger radii. This scenario is explored in the models shown in Fig. 5e. In general, larger flocculates result in lower alignment efficiencies. However, the \(\beta\) value is maximized for the \(2 \mu m\) case, indicating that field sensitivity is maximized at a certain ratio of magnetite to clay. This is in line with the numerical simulations done by Mitra and Tauxe34 that found that increasing the flocculate size from \(2\:\mu m\) to \(3\:\mu m\) significantly reduced the sensitivity to the field strength. If increasing the amount of clay results in both of these effects happening in tandem, it is reasonable to assume that there is a range of clay to magnetite ratios with an optimal sensitivity to Earth-like field strengths. As seen in the experimental results, the average alignment efficiency peaks for the 1:3 mixture. For natural speleothems, natural fluctuations in the delivery of clay grains will affect these two separate flocculation-related processes. This makes it difficult to directly compare the paleointensity recorded by sections within the same speleothems or between speleothems from the same cave system, even though these typically exhibit a highly uniform magnetic mineralogy.

The interaction between the clay-magnetite flocculates and the actively growing, highly textured crystals in a speleothem results in rotation and reorientation of the flocculates, which in turn decreases overall alignment efficiency. Here we model these flocculate-substrate interactions (FSIs) using the \(\alpha _o\) parameter. For example, lowering the alignment efficiency for \(1 \, \mu m\) flocculates settling through \(100 \, \mu m\) of water (Fig. 5a) from the 50% seen in simulations to the \(\sim\)15% seen in natural samples, corresponds to an \(\alpha _o\) of \(150^\circ\) (Fig. 6). At this degree of FSI randomization, the directional recording is still accurate (\(\alpha _{95} = 5^\circ\)), but the sensitivity to the strength of the applied field is diminished. The resulting sensitivity to field strength after FSI randomization may still allow researchers to distinguish between periods of very high and very low field intensity (e.g, geomagnetic excursions, reversals, and spikes), but subtle variations in field strength are unlikely to be resolvable from speleothems.

The highest alignment efficiencies are associated with the magnetite-only experiments. Theoretically, the size and magnetization of these magnetite grains should have allowed them to be fully aligned with the laboratory field. Ideally, the only mechanism that would then lower the alignment efficiency in the magnetite-only experiments would be grain rotations as the magnetite settled onto the highly uneven surface of the ADP crystals. However, despite the ultrasonification step, it is possible that some of the magnetite grains adhered to one another via magnetostatic interactions, thereby creating magnetite aggregates with elevated masses and lowered net magnetizations, which in turn would lower their alignment efficiency. We do not believe that such magnetostatic interactions occur in natural speleothems. First-order reversal distributions on speleothems show a strong component of non-interacting single-domain magnetite during their normal growth periods46.

The relationship between alignment efficiency and the amount of detrital material in a speleothem can be seen in natural samples as well. A study by Zhu et al.22 compared the magnetic fabrics of two speleothems from two different cave systems along the Yangtze River. One speleothem had a columnar calcite fabric with an overall alignment efficiency near 3.4%. The easy axis of remanence anisotropy was very close to the NRM direction, suggesting that the ambient magnetic field strongly controls the anisotropy. The other speleothem had a microcrystalline fabric with annual banding and an average alignment efficiency near 0.86%. Its easy axis was unrelated to both the calcite growth direction and the NRM direction. The microcrystalline speleothem had a much higher concentration of impurities (6942-12880 ppm) than the columnar speleothem (1178-1352 ppm). This suggests that without (or with minor) flocculation, there is near-perfect alignment of the easy axis with the field direction. Even with very minor impurities, the alignment efficiency is still below 10%, consistent with the idea that a secondary mechanism, such as syn-depositional rotation, is involved in lowering the efficiency. Since more impurities were associated with lower alignment efficiencies, the microcrystalline fabric likely had more flocculation, leading to a lack of relationship between remanence anisotropy and field direction. These overall trends are consistent with the trends found in this study.

As speleothems grow, they experience a range of growing conditions. Often such changes in growth conditions are manifest as fine-scale laminations, observable through the carbonate fabric, organic matter concentration, and/or trace elements/isotopes47,48. Formation of these laminae can be triggered by fluctuating drip rates, infiltration rates, and soil erosion conditions1,49,50. These variable background conditions can affect the water column thickness and detrital input to a speleothem, changing the field intensity recording properties of the speleothem as it grows.

As of our current understanding, paleodirectional records in speleothems are far more robust than their paleointensity records. One way to work toward a better understanding of speleothem paleointensity records would be to report proxies for the amount of detrital material (e.g., high-field susceptibility, 232\(\text {Th}\), Al concentration, etc.) alongside paleointensity estimates. This approach would help build an empirical understanding of how flocculation affects remanence. Additional modeling could also be used to expand on how surface textures affect DRM processes for steeply dipping surfaces.

Methods

Artificial speleothems of ammonium dihydrogen phosphate (ADP) were precipitated from solution, forming the tetragonal mineral biphosphammite. Some carbonate minerals were considered for the matrix, but ultimately rejected. Calcite grows very slowly, making it difficult to use. Attempts to use the carbonate mineral witherite (\(BaCO_3\)) resulted in an extremely fragile and powdery matrix. The ADP matrix had a fast growth rate and resulted in a rough surface texture similar to that of stalagmites.

Alfa Aesar’s commercial ammonium dihydrogen phosphate (\(NH_4H_2PO_4\), A15283) was dissolved in deionized (DI) water to create a supersaturated (0.5 g/mL) base solution. Commercially available Wright magnetite powder (112978) was used for the magnetic detrital component of the speleothem. It has a mean grain diameter of 0.44 \(\mu m\), a mean axial ratio of 1.33, and an average coercivity of 8-11vmT43,51, which falls neatly within the coercivity range found for natural speleothems. Kaolinite powder from Sigma Aldrich was used as the non-magentic detrital component of the artificial speleothems. Kaolinite is ubiquitous in sedimentary systems and flocculates in low saline environments without the addition of organic materials52. The mass and volumetric ratios of magnetite and kaolinite in each growth type are listed in Table 1.

Each speleothem was precipitated in a sample box (18 mm x 18 mm x 15 mm) over the course of three days. Crystals were grown within a set of Helmholtz coils to enable particles to settle in controlled Earth-like magnetic fields (15, 30, 50, 70 \(\mu T\)). The applied field for all samples had a declination of \(0^\circ\) and an inclination of \(60^\circ\). First, 1 mL of solution was pipetted into each sample box, forming a fine-grained crust of biphosphammite along the bottom of the box. Then, the magnetite and kaolinite were mixed into the bulk solution. Over the course of growing, the bulk solution was ultrasonicated and \(\frac{1}{2}\) mL aliquots of the magnetite-kaolinite mixture were added \(\sim 5\) times with an interval of about 2 hours between each addition. An approximately 0.5 cm thick sample is precipitated over the course of a day. Finally, before the solution completely evaporated, DI water was used to rinse out excess mixture and stop further precipitation and the crystal was kept in the Helmholtz coils to dry completely, resulting in the texture seen in Fig. 2c.

Table 1 Composition of each set of samples.
Full size table

Magnetic analysis of the specimens was done at the Institute for Rock Magnetism (IRM) at the University of Minnesota. Full vector magnetization was measured on the 2G Enterprises SQUID U-channel (noise floor \(\sim 1\times 10^{-11} \, Am^2\)). Alternating field (AF) demagnetization between 0 and 150 mT was used to demagnetize the natural remanent magnetization (NRM). An isothermal remanent magnetization (IRM) was applied using the 2G Core Pulse Magnetizer. A 200 mT field was applied at a declination of \(0^\circ\) and an inclination of \(0^\circ\), and the resultant magnetization was measured on the 2G Enterprises SQUID U-channel. Data analysis was done using the PmagPy library53.