Transforming understanding of paleomagnetic recording in igneous rocks: Insights from aging experiments on lava samples and the causes and consequences of ‘fragile’ curvature in Arai plots

The theory for recording of thermally blocked remanences predicts a quasi-linear relationship between low fields like the Earth’s in which rocks cool and acquire a magnetization. This serves as the foundation for estimating ancient magnetic field strengths. Addressing long-standing questions concerning Earth’s magnetic field require a global paleointensity dataset, but recovering the ancient field strength is complicated because the theory only pertains to uniformly magnetized particles. A key requirement of a paleointensity experiment is that a magnetization blocked at a given temperature should be unblocked by zero-field reheating to the same temperature. However, failure of this requirement occurs frequently and the causes and consequences of failure are poorly understood. Recent experiments demonstrate that the remanence in many samples typical of those used in paleointensity experiments is unstable, and exhibits an ”aging’ effect in which the unblocking temperature spectrum changes over only a few years resulting in non-ideal experimental behavior. While a fresh remanenence may conform to the requirement of equality of blocking and unblocking temperatures, aged remanences may not. Blocking temperature spectra can be unstable (fragile), which precludes reproduction of the conditions under which the original magnetization was acquired. This limits our ability to acquire accurate and precise ancient magnetic field strength estimates because differences between known and estimated fields can be significant (up to 10 μT) for individual specimens, with a low field bias. Fragility of unblocking temperature spectra appears to be related to grain size and may be related to features observed in first-order reversal curves.

tensity experiment is that a magnetization blocked at a given temperature should be un-23 blocked by zero-field reheating to the same temperature. However, failure of this require- Arai plots. Left-hand panels: distribution of (un)blocking temperatures. Blue and red are the unblocking and blocking temperature (T ub , T b ) spectra, respectively. Middle panels: NRM demagnetization (blue) and pTRM acquisition (red). The order in which the steps are taken alternates between NRM demagnetization (zero-field cooling) first and pTRM acquisition (in-field cooling) first as shown in b). Right-hand panels: plots of TRM remaining versus pTRM gained. Data for in-field followed by zero-field (IZ) steps first are indicated as blue dots; zero-field followed by in-field cooling (ZI) steps first are indicated as red dots. Heavy dashed lines are the relationship predicted by Néel theory. a-c) A case in which blocking and unblocking temperature spectra are identical (Law of Reciprocity obeyed). d-f) A case in which the unblocking temperature spectrum is shifted to lower temperatures than the blocking temperatures. g-i) A case in which the blocking temperature spectrum is wider than the unblocking temperature spectrum with both high and low temperature tails. j-l) A case in which the unblocking temperature spectrum is broader than the blocking temperature spectrum.
Thellier's laws are only strictly true for non-interacting uniaxial single domain (SD) magnetic particles whose behavior is understood using the theory of Néel (1949,1955). 117 In Figure 1d-f, we show an example of a case in which the unblocking temperature spec-118 trum (blue) is somewhat lower than the blocking temperature spectrum (red). The re- 119 sulting Arai plot sags below the theoretical line (heavy dashed line Figure 1f). 120 When the unblocking temperature spectrum is narrower than the blocking tem-121 perature spectrum (Figure 1g), the Arai plot is 'hook' shaped ( Figure 1i) and when there 122 is a large low temperature bias to the unblocking temperature spectrum with a small high 123 temperature component, the Arai plot is 'S'-shaped (Figure 1l). The ultimate cause of 124 sagging, 'hook', or S-shaped Arai plots stems from a failure to satisfy the Law of Reci-125 procity where remanence can be removed at either a lower temperature than originally 126 imparted (low-temperature pTRM tails) or at a higher temperature (high-temperature 127 pTRM tails), respectively. In this paper, we focus on possible causes and consequences 128 of the widely observed 'sagging' in Arai plots (including the hooked and S-shaped curves 129 in Figure 1i and l, respectively), while ignoring the influence of chemical alteration, non-130 linearity in TRM response, cooling rate or anisotropy effects. Law of Reciprocity is violated by all specimens, and the larger the grain size, the larger 138 the deviation from theory. The portion of pTRM lost by heating to below the blocking 139 temperature is termed a 'low-temperature pTRM tail' and that above is a 'high temper-140 ature pTRM tail'.

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As predicted by the phenomenological models like those shown in Figure 1

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For smaller particle sizes (e.g., 1 µm) with larger high temperature tails, the curve is S-146 shaped, similar to those shown in Figure 1l. 147 If a particle is large enough to be non-uniformly magnetized, e.g., in the flower or 148 vortex magnetic states (Williams & Dunlop, 1989;Schabes & Bertram, 1988), or the MD 149 state, its magnetic behavior cannot be described by the analytical theory of Néel (1949).

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Just below the Curie temperature, magnetic particles are close to saturation, but as par- can be understood as follows. After cooling to room temperature, a particle will have 154 some net moment because domain walls will be distributed to produce incomplete can-155 cellation, in equilibrium with the external field. As the temperature ramps up again, the 156 walls shift within the particle as they seek to minimize the magnetostatic energy. If the 157 particle is cooled back to room temperature, there could be a net magnetization loss, giv-158 ing rise to the observed low temperature tails. The domain walls may not be destroyed 159 until the temperature is near T c and some fraction of remanence could persist, giving 160 rise to high temperature tails.

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The data of Dunlop andÖzdemir (2001) were plotted with the X-axis normalized 162 to the total pTRM acquired and not the initial TRM as is traditional in Arai plots. That   ing low temperature pTRM tails (Dunlop &Özdemir, 2001 from specimens that share a common field during cooling, e.g., sister specimens from the 199 same lava flows. imens were then given another laboratory TRM and 'aged' in the same field for two years.

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For many specimens, the Arai plot curvature increased and the resulting intensity es-219 timates were biased to low values relative to the laboratory field.  Table 2  The behavior of the specimens in the original IZZI experiments is shown in Fig-230 ure 5a-d; the 'fresh' TRMs are shown in Figure 5e-h, and curvature values are summa-231 rized in Figure 6 and Table 2. We use here a value of | k| ≤ 0.164 as 'straight' (S) and   Figure 6 and Table 2.     Table 1 for references). Specimens from samples with low curvature (S) either remained straight (SS) or became significantly curved (SC) after being given a fresh TRM. Specimens from samples with high curvature (C) either became straight (CS) or remained curved (CC) after being given a fresh TRM. All CC specimens have significantly less curved Arai plots than in the original experiments, so they have 'fragile' curvature.
To address these issues, we subjected sister specimens from the samples investigated 266 by Santos and Tauxe (2019) (see Table 1) to extensive hysteresis experiments and an 'ag-267 ing' experiment, similar to that described by Shaar and Tauxe (2015), but with some 268 modifications. We describe in the following sections the experimental details, summa-269 rize the results, and consider the questions raised above concerning the temporal stabil-270 ity of fragile curvature and its effects on our ability to estimate ancient field strength.    Figure 7d, h, l, p).

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In many of our samples, the negative lobe in Zone 1 (e.g., Figure 7h, l) has two parts.

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There are several ways of characterizing and quantifying aspects of FORC diagrams.  Table 2.

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Another way to characterize FORC behavior is to consider the relationship between Zone 1 Zone 2 Zone 3 C e n tr a l ri d g e al., 2001), both the nucleation peak field (NPF) and annihilation peak field (APF) de-306 pend strongly on grain size with smaller particles having larger nucleation and annihi-307 lation fields, and the APF is larger (in the absolute sense) than the NPF because mag-308 netic structures such as a vortex are annihilated in higher fields than they nucleated (Yu  Table 2.  Table 2. Representative FORC diagrams are shown in Figure 7. We also list the values of 332 various hysteresis parameters considered in this investigation in Table 2. along the B i axis is not nearly as large as for the CC sample (see Figure 7m and Table 2).

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Interestingly, the negative lobe in Zone 1 of the iFORC diagram (Figure 7h) has two 366 "wings". We term these features NPN+ in Table 2. One explanation for the N+ feature Best-fit line with bootstrap uncertainty bounds were calculated without including data for specimen hw226a. d) Transience to Remanence ratio (T/R in Table 2) plotted against bulk domain stability (BDS). All values are listed in Table 2).
There is a quasi-linear relationship between the width parameter (Carvallo et al.,  Results for all IZZI experiments on aged specimens are shown in Figure S1. All but 420 two of the 36 aged specimens in the SS category have | k| ≤ 0.164 and are 'straight' based 421 on that criterion. The two exceptions are specimens from mc109e (mc109e-SB3) and hw226a 422 (hw226a-SB5), which appear to have altered during the experiment as indicated by a re-423 manence vector that bypasses the origin and grows into the direction of the laboratory 424 field (e.g., Figure 12a). These specimens are not discussed further.

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In the SC group, results vary strongly as a function of aging position.   Pos: position of the sample with respect to aging field (see Figure  9). B T T RM : field strength in µT estimated using the total TRM. k aged : curvature of the aged Arai plot (see also Figure S1).  We plot the data from Table 3 in Figure 13a. The curvature in Arai plots for aged 448 specimens, except for the SC group, is generally more positive than for fresh specimens.   X-axis is magnetization remaining at each temperature step for the fresh TRM (TRM1); Y-axis is magnetization remaining for each aged specimen at the same temperature step (TRM2). The initial TRM is at the upper right-hand corner of the plot. e-h) TRM blocking (infield steps).
X-axis is magnetization acquired at each temperature step of the fresh pTRM (pTRM1); Y-axis is magnetization acquired for each aged specimen at the same temperature step (pTRM2). The final pTRM is at the upper right-hand side of the plot. a, e) SS group specimens. b, f) SC group specimens. c, g) CS group specimens. d, h) CC group specimens.
suggest that there should be systematic changes in the blocking and/or unblocking tem-490 perature spectra over even two years.

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The aging experiment was conducted on 12 sister specimens of each specimen that 492 was subjected to a paleointensity experiment after being given a fresh TRM. Therefore,  Figure 14.

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The top row in Figure 14 is a comparison of the magnetizations remaining in the 500 fresh (x-axis) versus aged (y-axis) specimens during thermal demagnetization. The be-501 havior is controlled by the unblocking temperature spectrum for each specimen. For SS 502 group specimens (Figure 14a), we observe no no systematic trend in demagnetization.

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For the SC group, there is an 'S' curve with an inflection point at about the median de-504 structive temperature meaning that while the blocking temperatures have shifted in all 505 specimens, some have a pronounced shift at low blocking temperatures while others shifted 506 at high temperatures. In the CS and CC groups, however, all but one specimen appear 507 to have shifted to higher unblocking temperatures (the data points fall above the dashed 508 black line as more magnetization remains at a given step). Therefore, for both the CS 509 and CC groups, there appears to be a consistent shift to high unblocking temperatures 510 across the entire temperature range after aging.

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The bottom row in Figure 14 is similar to the top row, but is a comparison of the 512 magnetizations acquired at each temperature step. Again, for the SS group and surpris-513 ingly also for the CS group, there is no consistent aging signal. In contrast, for nearly 514 all specimens in the SC and particularly the CC groups, the points plot above the line 515 for aged specimens compared to the fresh specimens. It appears that the blocking tem-516 peratures of these groups have shifted to lower temperatures as more magnetization is 517 blocked at a given temperature step in the aged specimens than in the fresh. We note 518 that the sum of all the pTRMs (the total TRM acquired during the paleointensity ex-

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The IZZI experiment was designed to detect high temperature tails, not low tempera-

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Uniaxial single domain particles have only two stable states at a given temperature step.

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At the blocking temperature the energy barrier goes from flat to a single hump (E max 530 in Figure 15a).

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We argued that fragile curvature is related to the presence of larger particles based 532 on information gleaned from FORC diagrams. index Figure 15. Energy barriers to magnetization switching from one easy axis to the other. a) Néel particle (uniaxial SD). b) Single vortex particle with multiple easy axes.
To understand the magnetic stability of particles larger than single domain, we re-542 quire the computational approach of micromagnetic modeling (Brown, 1963 to near the Curie Temperature in Earth-like fields over two years. So, we seek another 555 mechanism that could result in such a shift.

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An example of a possible energy landscape for a cuboctohedron in the single vor-557 tex size range that switches from one easy axis to another is shown in Figure 15b. In this 558 example, a particle could be blocked in one direction with energy E 1 . Thermal energy  3. Arai plots for specimens with fragile curvature tend to become more curved when 581 given a fresh TRM and allowed to 'age' in controlled laboratory fields.   x) x) x) x) cr418f cr423c (c03f (c03h