The cooling-rate effect on microwave archeointensity estimates
Departamento de Geofísica, Instituto de Astronomia, Geofísica e Ciências Atmosféricas, Universidade de São Paulo, São Paulo, Brazil
Geomagnetism Laboratory, Department of Earth, Ocean and Ecological Sciences, University of Liverpool, Liverpool, UK
Corresponding author: W. Poletti, Departamento de Geofísica, Instituto de Astronomia, Geofísica e Ciências Atmosféricas, Rua do Matao, 1226 Cidade Universitaria, Universidade de Sao Paulo, São Paulo 05508-090, Brazil. (firstname.lastname@example.org)
 New microwave (MW) paleointensity data on historical bricks from Northeast Brazil presented a bias toward higher fields when compared to previous cooling-rate corrected double-heating paleointensity estimates; the same relates to the previously reported values for pottery from Southwestern Pacific islands. A simple theoretical approach suggests that the MW bias in both collections is due to a cooling-rate effect on MW estimates. We then experimentally corrected the MW cooling-rate effect on Brazilian fragments, increasing the degree of consistency between the previous and new results (reducing discrepancies from 25% to 8%). Results indicate similar experimental behavior between microwave and thermal procedures despite the different ways in which the energy is transferred into the spin system. Finally, they allow cooling times of less than 90 s to be empirically estimated in most of these MW experiments highlighting the need for systematic cooling-rate corrections to be applied in similar MW paleointensity studies in the future.
 The strength of the past Earth's magnetic field can be inferred from the fossil magnetism of igneous rocks and archeological baked clay materials. Several variants of the classical double-heating paleointensity method have been developed since the pioneering work of Thellier and Thellier . Some of the most popular today are: (a) the modifications of the classical Thellier-Thellier (TT) protocol, proposed by Coe , Aitken et al. , and Yu et al. ; (b) the Triaxe (TR) method [Le Goff and Gallet, 2004; Gallet and Le Goff, 2006]; and (c) the Microwave (MW) method [Walton et al., 1992, 1993; Shaw et al., 1996]. In all of these methods, the natural remanent magnetization (NRM) is stepwise replaced by partial thermoremanent magnetizations (pTRM).
 Modern TT protocols apply additional heating steps for monitoring thermomagnetic alteration [Coe et al., 1978], magnetic anisotropy [e.g., Rogers et al., 1979; Veitch et al., 1984], and multidomain (MD) effects [e.g., McClelland et al., 1996; Riisager and Riisager, 2001]. This method and their corrections can be easily implemented in any paleomagnetic laboratory but it is very time consuming (~1.5 h per temperature step). The TR method is conducted in a three-axis (Triaxe) vibrating sample magnetometer, coupled to a small furnace [Le Goff and Gallet, 2004]. Measurements are made continuously while the sample is heated and the system allows the application of a laboratory magnetic field (up to 200 μT) along the direction of the original remanence, thus minimizing anisotropy effects. Several studies have demonstrated the equivalence between TR and TT paleointensity methods [Le Goff and Gallet, 2004; Gallet and Le Goff, 2006; Genevey et al., 2009; Hartmann et al., 2010, 2011]. The Triaxe provides fast paleointensity estimates (~2.5 h per sample) and seems to be unaffected by cooling-rate effects on archeological baked clay materials [Le Goff and Gallet, 2004], but the sensitivity of the vibrating sample system limits its application to strongly magnetized samples (> 10−2 A/m).
 In the MW method, magnetic minerals are directly excited by high-frequency microwaves [Walton et al., 1992, 1993]. In general, the progressive increase in microwave power successively affects magnetic carriers with increasing unblocking temperatures. The MW method also produces rapid paleointensity estimates (~1.5 h per sample), and most importantly, it can significantly reduce magnetic alteration as the bulk sample is heated to lower temperatures and for less time than in conventional thermal experiments [e.g., Shaw et al., 1996, 1999; Hill and Shaw, 1999, 2000; Hill et al., 2002a, 2002b; Casas et al., 2005; Ertepinar et al., 2012].
 It is well known that the differences between cooling times in nature and in the laboratory can influence paleointensity estimations, potentially leading to overestimates of more than 10% for single domain (SD) grains [e.g., Fox and Aitken, 1980; Dodson and McClelland-Brown, 1980; Halgedahl et al., 1980; Yu, 2011; Biggin et al., 2013]. This influence can be described by a cooling-rate factor used to correct paleointensity estimates, which is expressed by:
where ΔTRM represents the fraction of the TRM fraction underestimated or overestimated in paleointensity experiments, k is a constant which depends on the material properties, and CTnatural and CTlaboratory are the cooling times in nature and laboratory, respectively [Dodson and McClelland-Brown, 1980; Halgedahl et al., 1980]. Experimentally, the TT cooling-rate correction is routinely applied to archeological materials where the original (or natural) cooling times can be reproduced (or approximated) in the laboratory. It can be carried out by comparing the pTRM acquired in typical laboratory cooling times and the pTRM acquired in slow cooling times, which are as close as possible to that of the original cooling time [e.g., Chauvin et al., 2000; Genevey and Gallet, 2002; Genevey et al., 2009; Hartmann et al., 2010, 2011; Ertepinar et al., 2012]. In the TR method, paleointensity experiments using different cooling times (25, 6, and 2°C/min) gave similar intensity results suggesting that a cooling-rate correction is unnecessary on archeological baked clay materials [Le Goff and Gallet, 2004; Gallet and Le Goff, 2006]. These findings are corroborated by the good agreement within 5% between TR paleointensity estimations and cooling-rate (and anisotropy) corrected TT estimations on the same archeological materials [Le Goff and Gallet, 2004; Gallet and Le Goff, 2006; Genevey et al., 2009; Hartmann et al., 2010, 2011]. For the MW method, the majority of studies have been carried out on subaerial lavas where the vortex state or interacting nature of the ferrimagnetic grains implies that the cooling-rate correction is probably not critical [see Biggin et al., 2013]. However, for archeological baked clay materials and chilled geological materials (e.g., volcanic glasses), the application of a cooling-rate correction may be important because these materials tend to have finer magnetic grain sizes. In addition, as the MW method has rapid cooling times, this effect could be especially important. Although some authors have applied different kinds of MW cooling-rate corrections [Shaw et al., 1999; Ertepinar et al., 2012], their effectiveness has not yet been fully investigated.
 In this paper, we test MW cooling-rate corrections in two sets of archeological fragments. The first set corresponds to new experimental results using the MW method from archeological brick fragments from Northeast Brazil previously studied using the TT and TR methods [Hartmann et al., 2010]. The second set comprises archeological pottery from Southwest Pacific islands for which both MW and TT paleointensity estimates were obtained [Stark et al., 2010]. We strengthen these two important paleointensity results by reconciling microwave paleointensity data with classical double-heating methods to add a sizable new data set. A comparison of the different paleointensity methods is made, and based on these results, we propose an experimental correction for the cooling-rate effect on MW estimations taking into account the laboratory and original cooling times.
2 Materials and Methods
 We have analyzed archeological brick fragments from Northeast Brazil with ages ranging from 1574 to 1910 A.D. [Hartmann et al., 2010, supplementary Table S1]. Previous analyses indicate that the main magnetic carrier is (titano)magnetite with different Ti contents and domain states, as revealed by hysteresis loops, heating and cooling cycles of low-field susceptibility showing a strong decrease at 580°C [Hartmann et al., 2010]. Unblocking temperatures varied between 200°C and 475°C for most samples except for fragment MAE2-01 for which the maximum unblocking temperature reaches 550°C. For some fragments, hematite and also a high-coercivity, low-unblocking temperature magnetic phase are present [McIntosh et al., 2007, 2011], which is probably associated to a substituted hematite phase [Hartmann et al., 2010, 2011].
 A total of 155 specimens (112 for paleointensity measurements and 43 for cooling-rate correction) from 26 brick fragments corresponding to 10 sites were analyzed using the MW method. An automated microwave system working at a frequency of 14 GHz and coupled to a superconducting quantum interference device magnetometer (Tristan's model DRM-300 rock magnetometer) was used for the experiments [Shaw and Share, 2007]. For each fragment, one cylindrical specimen (5 mm diameter × 3 mm long) was first demagnetized with the microwave system, providing an appropriate demagnetization range to perform the paleointensity measurements. Subsequently, a minimum of two sister specimens were selected for MW paleointensity measurements using the Coe  protocol, i.e., the first step in zero field and the second step in an applied laboratory field. Stepwise magnetization measurements were carried out between 5 and 40 W with microwave application time intervals varying between 2.5 and 5 s. Each microwave application at a given power for a given time produces a “power-integral” corresponding to a remanence fraction (equivalent to peak temperature in a thermal experiment). Laboratory fields were applied following previous paleointensity results (25–40 μT) [Hartmann et al., 2010]. Magnetic mineralogical alteration was monitored through additional steps of microwave partial remanence (pTMRM) checks [Coe et al., 1978] after every two steps. Multidomain bias was determined by applying the pTMRM tail checks [Riisager and Riisager, 2001], also after every two steps. In addition, domain state bias was evaluated by applying parallel and antiparallel laboratory fields for at least one specimen per fragment. Following insights from modeling and experiments, if parallel and antiparallel estimates yield the same intensity within error, MD bias is likely to be small [Biggin, 2006, 2010]. Anisotropy of remanence effects were minimized by applying the magnetic field either parallel or antiparallel to the NRM [Rogers et al., 1979; Le Goff and Gallet, 2004]. Strict selection criteria for paleointensity estimates at specimen and at fragment level follow Hartmann et al. [2010, 2011] (see Table S2 in the supporting information).
 The MW cooling-rate experimental correction used here on the Brazilian brick fragments was based on that developed by Shaw et al. , involving two different steps for at least two specimens per fragment. First, a laboratory TRM was imparted in the specimens using a slow cooling time of 25 h from 480°C to room temperature in an applied laboratory field of 35 μT. Then, we attempted to recover the imparted laboratory field in these specimens using the MW method following exactly the same routine described before for virgin specimens. As a result, up to two cooling-rate correction factors (fMW) per fragment were determined by computing the ratios between the laboratory field (35 μT) and the respective paleointensities recovered by the MW method:
where PI _ CR represents the MW paleointensity estimation. The corrected paleointensity (PIC) was given by:
which is the product between the MW paleointensity measured in virgin specimens (PI) and the cooling-rate correction factor (fMW). Finally, an intensity value at fragment level (PIF) was computed from the paleointensity average,
where m represents the number of MW paleointensity results. It is worth noting that we have systematically corrected the parallel or antiparallel-induced paleointensity estimates by its respective parallel or antiparallel cooling-rate correction factor.
3 Results and Discussion
 From the 155 analyzed specimens (26 fragments), a total of 74 (47 for MW paleointensity and 27 for cooling-rate correction factors) yielded reliable results (see Table S1). The main reasons to reject results were the following: (a) their low magnetization (< 15 μA/m) due to the small sizes of the specimens, (b) their low percentage of demagnetization (f < 0.4), and (c) magnetic alteration during the experiments evidenced by loss of Arai plot linearity and/or pTRM check failure. Magnetic mineralogical alteration was mainly detected after very unstable microwave absorption, which can be attested by the growth of melt spots in the specimens after stepwise measurements. The pTMRM tail checks were employed to detect non-ideal MD-like effects and these produced maximum discrepancies of ~5% in those experiments where the laboratory field was aligned antiparallel to the NRM. In parallel experiments, where their usefulness is known to be more limited [Biggin and Thomas, 2003; Biggin, 2006], the maximum discrepancies were ~1.5%. At fragment level, intensity averages cooling-rate corrected are within 2% when compared with the global average (product between cooling-rate factors average and PI results average, both determined with parallel and antiparallel laboratory fields). All told, these results suggest negligible potential for bias of our palaeointensity results from MD-like effects.
 Figure 1 shows four typical examples of accepted Arai and orthogonal diagrams from two different fragments. Fragment SE2-19 presents very stable thermal demagnetization behavior (Figure 1a). The MW experiment shows a similar result (Figure 1b), but the NRM fraction used to compute the MW intensity (f = 0.52) is smaller than that of the TT value (f = 0.71) with a Δf of 0.19. This behavior results from the less efficient demagnetization/remagnetization in microwave experiments and is observed in all specimens, with Δf values varying from 0.05 to 0.20. For fragment MAS-03, we compared MW results for two specimens, a virgin one (Figure 1c) and a sister specimen into which an artificial TRM was imparted in the laboratory (Figure 1d). Both specimens presented similar fitting parameters (f, g, and q) in Arai diagrams. The specimen MAS-03-c01 provided a paleointensity of 44.9 ± 0.4 μT (Figure 1d), which is significantly different from the field imparted in the laboratory (35 μT) using the conventional oven, demonstrating a potential influence of the MW experimental cooling time on the paleointensity estimate and, consequently, the need for a cooling-rate correction.
 We have corrected the cooling-rate effect in two ways: theoretically and experimentally (Figure 2). Figures 2a and 2b show TT-MW data for Southwest Pacific islands and Northeast Brazil, after extrapolating equation (1) for cooling times between 5 and 90 s that represent the range of cooling times after microwave applications. For both collections, this simple theoretical MW cooling-rate correction produces a better agreement between TT and MW data (Table S3). Results of the MW cooling-rate experimental correction for Brazilian fragments are shown in Figure 2c against TT and TR data. Before cooling-rate correction, MW results produced values systematically higher (up to 25%) than those obtained with TT and TR methods (Figure 2c). But after cooling-rate correction, the difference between TT and TR with MW methods was reduced from 25% to a maximum of 8%, and in some fragments, these differences were eliminated entirely (Figure 2c). At fragment level, intensity estimates were highly consistent with standard deviations less than 8% of the mean (Table S1).
 Finally, we compared the MW cooling-rate experimental correction proposed here with that obtained for TT estimations on Brazilian fragments by Hartmann et al. . First, six TT cooling-rate correction factors (CTnatural = 25 h; CTlaboratory = 30 min) were extrapolated to the shorter cooling time of MW treatment using equation (1). These functions are represented as straight solid lines in Figure 3 which are plotted alongside the corresponding MW cooling-rate experimental correction factors for each fragment (dashed lines in Figure 3). The intersection between straight and dashed lines for each fragment provides an estimate of the laboratory cooling time for MW experiments. For most fragments, the MW cooling times are between 5 and 90 s though two fragments (MAS-03 and IMS-04) have shown cooling times of less than 1 s (~10−1 s and ~10−2 s, respectively). These differences are likely to be indicative of differing amounts of absorption from the magnetic and electric components of the microwave field [Walton and Boehnel, 2008; Suttie et al., 2010]. Nevertheless, the comparisons suggest that for this fragment set, (a) TT and MW cooling-rate corrections have similar experimental behavior, despite the different ways of transferring energy into the spin system (lattice vibrations and electromagnetic), and (b) the different cooling times between natural and laboratory conditions is a significant source of bias in the MW estimates.
 The TT-TR-MW experiments and corrections reported here indicate that all three methods can reliably be employed to obtain the past Earth's magnetic field intensity in baked clay materials. Together, they confirm the previous archeointensity results for Northeast Brazil presented by Hartmann et al.  and improve the estimates presented by Stark et al. . Several studies have demonstrated that a cooling-rate correction is needed for the TT method but is not necessary for the TR method. By comparing TT and TR with MW methods, we show that the cooling-rate effect could significantly affect MW paleointensity estimates in baked clay materials by up to 25%. However, this effect can be accounted for by applying a simple experimental correction, which relies on paleointensity measurements for sister specimens with an imparted TRM. After applying the cooling-rate correction, multimethod paleointensity estimates agreed to within ±8%. This study has thus demonstrated, for these fragments, the need to perform cooling-rate corrections during MW paleointensity acquisitions and suggests that this influence, underrated in previous studies, should be investigated for other materials too.
 This work was supported by a USP International Mobility scholarship to W. Poletti. G.A. Hartmann acknowledges grant #2010/10754-4, São Paulo Research Foundation (FAPESP). M. Hill acknowledges NERC (grant NE/I013873/1). A. Biggin performed this research while funded by a NERC Advanced Fellowship (grant NE/F015208/1). R. Trindade is funded by a CNPq PQ grant. We thank Mark J. Dekkers and anonymous reviewer for their comments that improved this paper.
 The Editor thanks an anonymous reviewer and Mark Dekkers for their assistance evaluating this manuscript.