Single-domain magnetite particles produced by magnetotactic bacteria (MTB) and aligned in chains, called magnetosomes, are potentially important recorders of paleomagnetic, paleoenvironmental and paleolife signals. Rock magnetic properties related to the anisotropy of magnetosome chains have been widely used to identify fossilized magnetosomes (magnetofossils) preserved in geological materials. However, ambiguities exist when linking magnetic properties to the chain structure because of the complexity of chain integrity and magnetostatic interactions among magnetofossils that results from chain collapse during post-depositional diagenesis. In this paper, magnetic properties of three sets of samples containing extracted magnetosomes of the culturedMagnetospirillum magneticumstrain AMB-1 were analyzed to determine how chain integrity and particle concentration influence magnetic properties. Intact MTB and well-dispersed magnetosome chains are characterized by strong magnetic anisotropy and weak magnetostatic interactions, but progressive chain breakup and particle clumping significantly increase the degree of magnetostatic interaction. This results in a change of the magnetic signature toward properties typical of interacting, single-domain particles, i.e., a decrease of the ratio of anhysteretic remanent magnetization to the saturation isothermal remanent magnetization, decreasing in the crossing point of the Wohlfarth-Cisowski test and in the delta ratio between losses of field and zero-field cooled remanent magnetization across the Verwey transition, as well as vertical broadening of the first-order reversal curve distribution. We propose a new diagram that summarizes the Verwey transition properties, with diagnostic limits for intact and collapsed chains of magnetosomes. This diagram can be used, in conjunction with other parameters, to identify unoxidized magnetofossils in sediments and rocks.
 Intact magnetosome chains often acquire a significantly enhanced low-temperature saturation IRM (SIRM) when cooling the sample across the Verwey transition in a strong field (FC) compared to cooling in zero field (ZFC), which results in an apparent bifurcation of zero-field-warming SIRM curves between FC and ZFC below the Verwey transition [Moskowitz et al., 1993]. The δ-ratio (δ = δFC/δZFC) quantifies the difference between the remanence losses of FC (δFC) and ZFC (δZFC) curves upon warming through the Verwey transition [Moskowitz et al., 1993], where the δ-ratio exceeds 2 for intact magnetosome chains [Moskowitz et al., 1993, 2008; Pan et al., 2005b; Li et al., 2009, 2010a, 2010b].
 Identification and quantification of magnetofossils in sediments and rocks is, nevertheless, not straightforward because chain fragmentation, and collapse and aggregation of magnetosomes during post-depositional processes may alter the original bulk magnetic signature, and magnetofossils often occur in mixtures with abiogenic magnetic minerals [e.g.,Kopp and Kirschvink, 2008]. Therefore, it is essential to evaluate the effects of magnetosome chain disruption on the bulk magnetic properties. Moskowitz et al. [1988, 1993] found that the lysed (broken) magnetosome chains, compared with intact MTB cells, have relatively reduced values of coercivity, remanence coercivity, remanence ratio and ARM/IRM. Kobayashi et al.  demonstrated that these values gradually decrease with increasing chain collapse. Recently, Li et al. [2010a] showed that lysed chains are characterized by lower δ-ratio and largerδZFC values, as well as an increased vertical spread of the FORC distribution. These experimental studies suggest that the chain structure of magnetosomes plays an important role in contributing to the unique magnetic properties of magnetosomes (magnetofossils). However, knowledge about magnetic anisotropy and magnetostatic interactions of magnetosomes remains sparse, and systematic studies of the bulk magnetic properties of magnetosomes with different degrees of chain integrity and particle concentration are needed.
 In this study, we carried out detailed rock magnetic measurements (i.e., hysteresis loops, IRM acquisition curves, DC and AC demagnetization curves, ARM induction curves, FORCs, and low-temperature thermal demagnetization curves) on three sets of magnetosome-bearing samples with systematic variations in chain integrity and particle concentration. Magnetosomes were obtained from cultures ofMagnetospirillum magneticumAMB-1. Our aim is to investigate the effects of chain dependent magnetic anisotropy and magnetostatic interactions on the bulk magnetic properties of magnetosomes. This is important for magnetofossil identification in natural samples.
2. Samples and Methods
2.1. Sample Preparation
M. magneticumAMB-1 (ATCC strain 700264) has been cultured anaerobically at 26°C in 10 L of modified ATCC-recommended liquid medium with addition of 60μM ferric quinate. Cells grown to the stationary phase were harvested by centrifugation. Three sets of samples with different degrees of magnetosome chain integrity were obtained by subjecting the whole cells to 3 ultrasonic treatments, i.e., in 30 ml of distilled water (set A1), NaOH (0.1 M) (set A2) and urea (8 M) (set A3) solutions. We used an ultrasonicator (VCX130, SONICS, USA) with 65 W power and 5 s pulse applied cycles followed by 5 s pauses for a total of 20 min for each treatment. Magnetosomes were collected with a bar magnet (5 mT max.) and washed five times with distilled water. Finally, each set of extracted magnetosomes was suspended in 3 mL of distilled water for subsequent dispersion experiments.
 Each set of extracted magnetosomes was equally divided into three groups (a, b and c). The (a) group (A1a to A3a) was directly frozen with liquid nitrogen and then freeze-dried without dilution. Groups (b) and (c) were dispersed by mixing with powdered calcium fluoride (CaF2) to make samples with different degrees of particle concentration and interactions. The (b) group (A1b to A3b) was produced by dilution to ∼0.15% (the similar dilution used by Kopp et al. [2006b]) in CaF2by mixing 1 mL of extracted-magnetosome suspension with 0.2 g CaF2powder, frozen with liquid nitrogen and freeze-dried. The (c) group (A1c to A3c) was prepared similar to group (b) but with a larger dilution factor by mixing with 1.0 g CaF2 powder.
 To avoid post-oxidation of magnetosomes, the following strategies were adopted during sample preparation: (1) AMB-1 cells were harvested by centrifugation at 4°C and the whole-cell sample was freeze-dried; (2) ultrasonic disruption was carried out in an ice-bath (0°C) in an argon atmosphere; (3) magnetosome extraction, sample washing, and packing was undertaken inside an anaerobic chamber (Coy Labs, USA, [O2] <300 ppm). Distilled water, NaOH and urea solutions were pretreated by bubbling with nitrogen for 1 h to remove dissolved oxygen; and (4) all samples were maintained in pure nitrogen atmosphere at T = −20°C prior to magnetic measurements.
2.2. Room Temperature Magnetic Measurements
 Static IRM acquisition and DC demagnetization curves were measured up to 300 mT in 5 mT increments on previously demagnetized samples using a Model 3900 vibrating sample magnetometer (Princeton Measurements Corporation VSM3900, sensitivity = 0.5 × 10−9 Am2). ARM acquisition, IRM and ARM AF demagnetization curves, as well as pulse-field IRM acquisition and demagnetization curves were measured with a 2G enterprises superconducting rock magnetometer system (2G-760) coupled with a Model 2G-660 automatic sample degaussing system (sensitivity = 2 × 10−12 Am2). An ARM was acquired in an 80 mT AF with a DC bias field that was stepwise increased from 0 to 0.3 mT, followed by stepwise AF demagnetization up to 100 mT. Acquisition curves of pulse-field IRM were obtained in 5 mT increments with a pulse magnetizer, followed by stepwise demagnetization with a pulsed field in the opposition direction.
 To simplify comparison of remanence results, IRM acquisition curves were normalized to the SIRM for each sample, and backfield or reversed field demagnetization curves were rescaled as 1/2(1 + IRM(−H)/SIRM). The median destructive field (MDF) corresponds to the pulsed field (MDFpf) or AF (MDFaf) at which half of the SIRM or ARM is destroyed. To characterize magnetostatic interactions, the R-value of the Wohlfarth-Cisowski test [Cisowski, 1981] was determined on the following pairs of acquisition and demagnetization curves: static-field IRM (Rsf) and pulse-field IRM (Rpf). The efficiency of weak-field ARM acquisition (ARM/SIRM versus DC bias field) was also used to estimate magnetostatic interactions [Moskowitz et al., 1993; Kobayashi et al., 2006; Kopp et al., 2006b].
 Hysteresis loops were measured with the VSM between ±500 mT, and hysteresis parameters, including saturation magnetization (Ms), saturation remanence (Mrs), and coercivity (Bc) were determined after the high-field slope corrections fit to a linear or nonlinear functions [Jackson and Solheid, 2010]. Remanence coercivity (Bcr) was determined from DC demagnetization curves of SIRM. FORCs [Pike et al., 1999; Roberts et al., 2000] were measured according to the protocol described by Egli et al. . For each sample, 300 FORCs were measured with a positive saturation field of 500 mT and a field increment (δH) of 0.63 mT. FORC diagrams were calculated using the FORCinel version 1.21 software with a smoothing factor (SF) of 5 [Harrison and Feinberg, 2008]. According to the Preisach  interpretation of the FORC diagram, the horizontal (Bc) and vertical (Bb) axes indicate the microcoercivity and interaction field distributions for SD particles, respectively [Pike et al., 1999; Roberts et al., 2000]. Two FORC parameters, median coercivity (Bc,FORC) and half-width interaction field (Bb,1/2), are defined as the median Bc which is given by the marginal coercivity distribution and as the interaction field value where the broadest Bb distribution reduces to half of its maximum, respectively [Egli, 2006b; Egli et al., 2010; Winklhofer and Zimanyi, 2006].
2.3. Low-Temperature Magnetic Measurements
 Low-temperature magnetic measurements were performed with a Quantum Design Magnetic Property Measurement System (MPMS XP-5, sensitivity = 5.0 × 10−10 Am2). ZFC and FC curves were obtained by cooling samples from 300 K to 10 K in zero field and in a 2.5-T field, respectively, followed by imparting a SIRM in a 2.5-T field (hereafter termed as SIRM10K_2.5T), and then measuring the remanence in zero field during warming to 300 K. The Verwey transition signature of magnetosome chains is characterized by the δ-ratio (δFC/δZFC), in which δFC and δZFC are calculated as δ = (M80K − M150K)/M80K, where M80K and M150K are the remanences measured at 80 K and 150 K, respectively [Moskowitz et al., 1993].
2.4. Electron Microscopy
 Intact cells or extracted magnetosomes of AMB-1 were deposited onto carbon-coated copper grids and studied by using a JEOL JEM-2010 transmission electron microscope (TEM) at a 200 kV accelerating voltage. For scanning electron microscope (SEM) observations, powder samples of extracted magnetosomes were mounted on an aluminum SEM stub using copper tape, and are then coated with gold (∼5 nm in thickness). SEM analyses were performed on the Zeiss Supra 55 SEM microscope. The microscope was operated at 5 kV with a working distance of 7.5 mm. Two detectors were used: in-Lens detector for secondary electron imaging (nano-topography of the sample) and an Angle selective Backscattered (AsB) detector for low-angle backscattered electrons, which provide a contrast that is more sensitive to crystal orientation. The spatial arrangements of extracted magnetosomes and their dispersion states within CaF2 matrix were examined in situ.
3.1. Electron Microscopic Examinations
 TEM and SEM observations indicate that the sequential cell treatments for sample preparation produced an increasing degree of chain breakup and particle aggregation (Figure 1). The first-step treatment destroyed visible cell structures and caused some degree of chain aggregation (chain pairs), with most particles remaining in chains and associated with cell debris (Figures 1b and 1e). After the second-step treatment, magnetosome chains are still recognized, but are mostly packed to form large aggregates (Figure 1c). The third-step treatment led to magnetosome clumping (Figure 1d).
 SEM observations indicate that the CaF2particles have plate-like shapes with typical sizes of ∼10 μm in plane length (Figure 1i). The extracted magnetosomes are attached to CaF2 and are well dispersed in the diluted samples (Figures 1f–1j). Nevertheless, the main features of spatial arrangements of extracted magnetosomes still remain, i.e., isolated chains of magnetosomes occur predominantly in set A1 (e.g., Figures 1f, 1i, and 1j), short chains and individual particles coexist in set A2 (e.g., Figure 1g), and individual particles dominate set A3 (e.g., Figure 1h).
3.2. FORC Diagrams
 Coercivity and interaction distribution trends can be recognized in the FORC diagrams in Figure 2. The whole-cell sample has a FORC distribution with a clear so-called central ridge feature [Egli et al., 2010], which indicates no or negligible inter-cell or inter-chain interactions [Pike et al., 1999; Roberts et al., 2000]. The FORC diagram for sample A1a has a typical “tear drop” shape of interacting SD particles, as described by Pike et al.  and Egli [2006b]. FORC diagrams for samples A2a and A3a (also without dilution) exhibit strong magnetostatic interactions between individual particles, in which the contours intersect the Bb axis and significantly expand in the vertical direction (Table 1). As expected, dilution produces FORC diagrams with a smaller vertical spread, and thus a less amount of magnetostatic interactions. Overall, the vertical spread of FORC diagram increases with increasing particle concentration (from right to left in Figure 2), and with increasingly strong ultrasonic treatment (from top to bottom). The central ridge of FORC diagram, which is characteristic of non-interacting and weakly interacting uniaxial SD particles [Egli et al., 2010], becomes sharper with dilution (from left to right) and with decreasingly ultrasonic treatment (from bottom to top). The position of the peak of the FORC distribution is not significantly affected by dilution, but shifts to lower Bc values with increasingly strong treatment (Table 1).
Table 1. Room Temperature Magnetic Parameters for the Studied Series of AMB-1 Magnetosome Samplesa
Notation: R, from the Wohlfarth-Cisowski test, is determined by the following pairs of acquisition and demagnetization curves: DC field IRM (Rsf) and pulsed-field IRM (Rpf); MDF, median destructive field, corresponds to the pulsed-field (MDFpf) or alternating field (MDFaf), at which half of a total remanence is destroyed; χARM/SIRM (Bapplied=0.1 mT), χARM (χARM=ARM0.1 mT/79.5775 A/m) normalized to SIRM; Bcr, coercivity of remanence, is determined by DC demagnetization curve of SIRM; Bc, Mrs and Ms indicate coercivity, remanent magnetization and saturation magnetization, respectively, which are determined from room temperature hysteresis loops; Bc,FORC and Bb,1/2 are defined as the median coercivity of the marginal coercivity distribution and as the interaction field value where the broadest Bb distribution reduces to half of its maximum, respectively.
The Bc in parentheses indicates the coercivity value where the broadest Bb distribution is obtained.
 ARM acquisition curves normalized by SIRM are shown in Figure 3. As expected, ARM is lowered by increasing magnetostatic interactions from chain aggregates to disordered magnetosome clumps (i.e., AMB > A1a > A2a > A3a). Progressive sample dilution also decreases magnetostatic interactions (e.g., A1a < A1b < A1c). ARM acquisition curves for the extracted magnetosome samples are intermediate between the limiting cases of non-interacting SD particles and chains (e.g., AMB-1 cells) and highly interacting SD particles from Chiton teeth [Cisowski, 1981], respectively.
3.4. Remanent Magnetization Curves
 Results of the Wohlfarth-Cisowski test [Cisowski, 1981], where the shape of acquisition and demagnetization curves, normalized to SIRM, are compared and shown in Figure 4. In an ideal case of non-interacting SD particles, the IRM acquisition and demagnetization curves are symmetric with respect to each other and cross atR = 0.5. Crossing values R<0.5 are indicative of magnetostatic interactions in SD particles or of non-SD behavior [e.g.,Moskowitz et al., 1988, 1993]. In the case of the present study, this consideration is irrelevant because all of the particles under investigation are SD. The R-parameters for the whole-cell sample AMB-1 are close to 0.5 (e.g.,Rsf = 0.48 and Rpf = 0.49; Figure 4a and Table 1), which confirms that isolated magnetosome chains behave like non-interacting SD particles, as also shown by FORC measurements. Magnetization curves for AMB-1 are symmetric, with no low- or high-coercivity tails: this is typical of MTB magnetite due to the narrow distribution of anisotropies and grain sizes [e.g.,Moskowitz et al., 1993].
 Magnetization curves for samples with a decreasing degree of chain integrity (i.e., AMB > A1a > A2a > A3a) have progressively decreasing R and MDF values (Table 1); the magnetization curves also become progressively more right-skewed with decreasing chain integrity (Figures 4b–4d). In contrast, sample dilution tends to increase R toward the value typical of intact cells (e.g., A1a < A1b < A1c) (Table 1). For sample sets A2 and A3, MDF, Bcr and Bc values increase with increasing dilution, while they slightly decrease for set A1 (Table 1). A possible interpretation is that magnetosome chains were fragmented during dilution, resulting in a slightly decreased anisotropy.
3.5. Hysteresis Parameters
 On a Day plot (Bcr/Bc versus Mrs/Ms) [Day et al., 1977; Dunlop, 2002], data for the whole-cell sample of AMB-1 fall in the same cluster as for intact MTB cells [Moskowitz et al., 1993; Pan et al., 2005b; Lin and Pan, 2009; Zhu et al., 2010], with Bcr/Bc and Mrs/Msvalues typical of non-interacting, uniaxial SD particles [Cisowski, 1981]. With progressive chain disruption but no dilution, the hysteresis parameters move away from the uniaxial SD region along the SD-MD mixing line (Figure 5 and Table 1). Hysteresis parameters for set A1 (black circles) seem to be less affected by dilution and are close to the uniaxial SD region. Sets A2 and A3 have lower Mrs/Ms and higher Bcr/Bc values. Dilution treatments result in the diluted A2 and A3 samples moving back slightly toward the uniaxial SD region (Figure 5).
3.6. ZFC and FC SIRM Curves
 Thermal demagnetization curves of SIRM10K_2.5Tfor all nine extracted magnetosome samples and the whole-cell sample are shown inFigure 6. Compared with their intact counterpart (AMB-1), both ZFC and FC warming curves have steep SIRM decay for the extracted magnetosomes. The value of TD10→30K, which is equal to 100 × (M10K − M30K)/M10K, increases with progressive cell disruption (e.g., AMB <A1a < A2a < A3a), and decreases with progressive sample dilution (e.g., A2a > A2b > A2c) with the exception for the A1 set (Table 2). The remanence loss between 10 and 30 K can be attributed to the combined effects of magnetostatic interactions and superparamagnetic (SPM) relaxation [Pike et al., 2000]. The latter might emerge in collapsed chains because of the decrease of uniaxial anisotropy.
Table 2. Low-Temperature Magnetic Parameters for the Studied Series of AMB-1 Magnetosome Samplesa
10 → 30 K
10 → 300 K
10 → 30 K
10 → 300 K
Notation: Tv, Verwey transition temperature, is determined from the maximum of the dM/dT of FC data; δFC and δZFC is calculated from δ=(M80K-M150K)/M80K (M80K and M150K are the remanences measured at 80 K and 150 K, respectively). TD%(X→Y K)=(MX-MY)/MX×100 (MX and MY are the remanences measured at X K and Y K, respectively).
 All samples have the same Verwey transition temperature of 102 ± 2 K, which is much lower than that of stoichiometric magnetite [Walz, 2002], but comparable to that of fresh AMB-1 cell samples (104 K) and other MTB strains that have not undergone further oxidation beyond the possibly original non-stoichiometric state [Moskowitz et al., 2008; Li et al., 2009; Li and Pan, 2012]. Compared with the whole-cell sample AMB-1, extracted magnetosome samples have much higherδZFC but lower δ-ratio values (Table 2). Eight extracted magnetosome samples with the exception of A1c have δ-ratios between 1.20 and 1.86, which is lower than 2.0, and thus fail the Moskowitz test as expected [Moskowitz et al., 1993; Weiss et al., 2004a; Li et al., 2010a]. The A1 sample set, which consists of intact chains with various dilutions, is characterized by relatively higher δ-ratios and lowerδZFC values compared with A2 and A3 sets. Within the same sample set, dilution increases the δ-ratios but reducesδZFC values (Table 2).
4.1. Characterizing Magnetostatic Interactions
χARM/SIRM ratios for samples from this study are plotted versus corresponding Bb,1/2 and Rsf values in Figure 7. χARM/SIRM correlates well with Bb,1/2 and Rsf, which indicates their consistency for characterizing magnetostatic interactions. Existing models of interaction effects on ARM [Egli, 2006a] and FORC measurements [Egli, 2006b] predict the χARM/SIRM and the vertical half-width of the FORC distribution for interacting SD particles as a function of their volume concentration (i.e., the volume fraction p of the sample that is occupied by the particles). Comparison of these parameters for the same concentration values defines a black line inFigure 7a (data courtesy of Ramon Egli). Using the initial χARM/SIRM of AMB-1 reported inTable 1as the non-interacting value (i.e.,ra in Egli [2006a]), the resulting curve is consistent with our experimental data. The weakly interacting samples (i.e., A1b, A2b, A3b, A2c and A3c), i.e., those where the coercivity is larger than the interaction field, are in good agreement with the theoretical correlation of Egli [2006a, 2006b]between these parameters. Data for high interacting samples (i.e., A1a, A2a and A3a) and non-interacting samples (i.e., AMB-1 and A1c) agree less well with the theoretical curve. The data below the theoretical curve for samples of A1a, A2a and A3a can be interpreted as their more or less bimodal FORC diagrams (Figures 2b, 2e, and 2h), which may result from a non-homogeneous assemblage of interacting particles or/and a mixture of interacting particles and more or less weakly or non-interacting particles (e.g., residual magnetosome chains) [Chen et al., 2007]. For non-interacting sample, the lower limit of the vertical width of the FORC diagram is set by the resolution of the measurements ΔH (δH × (SF + 1/2) [Egli et al., 2010]. It ought to have zero vertical width if it is perfectly defined (i.e., ΔH = 0). However, it will always have a nonzero value of Bb,1/2 because of the finiteness of the field steps used in FORC measurements and the smoothing factor used when processing FORC data [Egli et al., 2010]. The data above the theoretical curve for AMB-1 and A1c are related to an experimental limitation of FORC measurements in this study, e.g., ΔH = 3.5 mT.
 ARM has been widely used for characterizing and identifying magnetic particles in geological samples, e.g., as a grain size indicator in rock magnetism [Johnson et al., 1975; King et al., 1982], and as a normalization factor in paleointensity studies [Banerjee and Mellema, 1974; Shaw, 1974; Yu, 2010], as well as to quantify magnetofossils in fresh and marine sediments [Petersen et al., 1986; Egli, 2004c; Paasche and Løvlie, 2011]. However, magnetostatic interactions reduce the χARM/SIRM and ARM/SIRM ratios of interacting SD particles to an extent that depends on their volume concentration, as observed experimentally [Sugiura, 1979], and predicted by analytical models [Egli, 2006a]. Experimental data from this study indicate that ARM is strongly affected by and highly sensitive to magnetostatic interactions (Figure 3). Even a slight increase in the vertical spread of the FORC distribution or a slight decrease of the crossover parameter Rused for the Wohlfarth-Cisowski test is associated with a strong decrease in ARM/SIRM. For example, compared with the initialχARM/SIRM value of the whole-cell AMB-1 sample, which is indicative of non-interacting value, ARM for A1b is reduced to ∼50% while accompanied by a small change inBb,1/2(e.g., 1.2 mT and 2.2 mT for AMB-1 and A1b, respectively) andR(e.g., 0.49 and 0.45 for AMB-1 and A1b, respectively) (Table 1). Most importantly, experimental data from this study also demonstrate that χARM/SIRM does not decrease below a critical threshold of 1 × 10−3m/A if magnetosome chains remain intact and well dispersed (i.e., whole-cell sample AMB-1 and extracted-magnetosome sample A1c). On the other hand, caution should be used when screening geological samples for magnetofossils using ARM measurements, because chain collapse can lower theχARM/SIRM ratio below this threshold, which is often considered diagnostic of the presence of magnetofossils [Moskowitz et al., 1993].
Bc,FORC has good linear correlation with Bc and Bcr, and poorer linear correlation with MDFpf and MDFaf. Furthermore, for the measured samples, Bc is systematically lower than the corresponding Bc,FORC values, while Bcr values nicely fall onto the s = 1 line with Bc,FORCvalues. FORC and hysteresis loop measurements on oriented samples of uncultured MYR-1 [Li et al., 2010b] at various angles with respect to the magnetosome chain direction indicate a strong linear correlation between Bc,FORC and Bcr, but poor correlation between Bc,FORC and Bc. Taken together, these studies reinforce the idea that Bc,FORC is equivalent to Bcr rather than Bc.
4.3. The δ-Plot and Identification of Magnetofossils
 Experiments in this study indicate that both intact cells of AMB-1 and extracted magnetosomes in well-dispersed chains haveδ-ratios larger than the threshold of 2.0, which supports the validity of the Moskowitz test [Moskowitz et al., 1993] for magnetofossil identification. In contrast, increasing degrees of chain disruption or particle aggregation, or both, produce lower δ-ratios and higherδZFC values, which makes the Verwey transition signature more similar to that of abiogenic assemblages of SD magnetic particles [Moskowitz et al., 1993; Carter-Stiglitz et al., 2002; Li et al., 2010a]. This trend is summarized in a plot of δZFC versus δFC/δZFC (hereafter referred to as the δ-plot), where these data can be fitted by the functionδFC/δZFC = 7.11 exp(−δZFC/0.057) + 6583.22exp(−δZFC/0.0063) + 1.21 (r2 = 0.999) (Figure 9).
 Detailed rock magnetic analyses of cultured MTB (i.e., AMB-1) that were subjected to a varying physical and chemical treatments that produce increasing cell and magnetosome disruption were made to assess changes in the magnetic signature of magnetosomes associated with chain disruption. With progressive chain breakup or/and particle clumping, the magnetic parametersBc, Bcr, MDF, Bc,FORC, χARM/SIRM and δ-ratio decrease, whileBb,1/2 and δZFC values increase. This indicates that rock magnetic measurements are sensitive to both magnetic anisotropy and magnetostatic interactions, which are useful for qualitatively and quantitatively detecting magnetofossils in geological samples. For samples with predominantly SD magnetic particles and relatively narrow grain size distributions (e.g., MTB magnetite), the χARM/SIRM or ARM/SIRM ratios appear to be more sensitive to the degree of magnetostatic interactions. By comparison, results from this study reinforce the idea that Bc,FORC is equivalent to Bcr rather than Bc. The δ-plot (δZFC versus δFC/δZFC), which summarizes Verwey transition properties, correlates well with the spatial and geometric arrangements of magnetosomes, and could provide a new method to diagnose unoxidized magnetofossils. We propose that comprehensive analyses (e.g., χARM/SIRM, FORC, δ-plot, FMR and TEM) are needed to effectively detect magnetofossils in bulk natural samples.
 This work was supported by the CAS/SAFEA International Partnership Program for Creative Research Teams (KZCX2-YW-T10) and NSFC grants (41004024, 410250113, and 40974036). J.H.L. is grateful for support from the China Postdoctoral Science Foundation (CPSC grant 201104144). Y.X.P. and Q.S.L. acknowledge support from the CAS ‘100’ Talents Program. We are grateful to Ramon Egli and Andrew P. Roberts, and other two anonymous reviewers for their constructive comments that significantly improved the original manuscript. We thank Richard J. Harrison for useful discussions concerning FORC data processing. We also thank Haitao Chen for kind assistance with FORC re-measurements. TEM observations were performed at the Technical Institute of Physics and Chemistry, Chinese Academy of Sciences (Beijing). SEM observations were performed at the Institut de Minéralogie et de Physique des Milieux Condensés (IMPMC, CNRS-UPMC, Paris).