TRM in low magnetic fields: a minimum field that can be recorded by large multidomain grains

Abstract

Thermally acquired remanent magnetization is important for the estimation of the past magnetic field present at the time of cooling. Rocks that cool slowly commonly contain magnetic grains of millimeter scale. This study investigated 1-mm-sized magnetic minerals of iron, iron–nickel, magnetite, and hematite and concluded that the thermoremanent magnetization (TRM) acquired by these grains did not accurately record the ambient magnetic fields less than 1 μT. Instead, the TRM of these grains fluctuated around a constant value. Consequently, the magnetic grain ability to record the ambient field accurately is reduced. Above the critical field, TRM acquisition is governed by an empirical law and is proportional to saturation magnetization (M_s). The efficiency of TRM is inversely proportional to the mineral's saturation magnetization M_s and is related to the number of domains in the magnetic grains. The absolute field for which we have an onset of TRM sensitivity is inversely proportional to the size of the magnetic grain. These results have implications for previous reports of random directions in meteorites during alternating field demagnetization, or thermal demagnetization of TRM. Extraterrestrial magnetic fields in our solar system are weaker than the geomagnetic field by several orders of magnitude. Extraterrestrial rocks commonly contain large iron-based magnetic minerals as a common part of their composition, and therefore ignoring this behavior of multidomain grains can result in erroneous paleofield estimates.

Introduction

This work builds on the discovery of a new empirical scaling law relating the acquisition of thermal remanent magnetization, TRM, and saturation magnetization, M_s (Kletetschka et al., 2004). The law holds over the range of domain states from SD (single domain) to MD (multi domain) and strongly suggests that the demagnetization energy must play an important role in TRM acquisition in all these grain sizes. Since the demagnetizing energy is proportional to (M_s)², it must compete at the blocking temperature with the energy of the external magnetic field. The importance of the demagnetizing energy was confirmed by experiments with samples with different demagnetizing factors. The empirical law suggests a generalized approach to models of TRM recognizing the importance of the demagnetizing energy with possible ramifications for paleointensity determinations.

Kletetschka et al. (2004) found a simple relationship between the efficiency of TRM (i.e., REM, the TRM to SIRM ratio) and the saturation magnetization of the material. The efficiency for equidimensional particles plots linearly with the magnetic field, B, along grain-size independent regions determined by the saturation magnetization of the material. For magnetite (grain size ranges from SD, through PSD (pseudo single domain) to MD) the efficiency is the same. The law further shows that the TRM intensity is particularly strong for minerals with low values of saturation magnetization might help to explain strong magnetization of titanohematite without need of “lamellar magnetism” (Robinson et al., 2002) following regular TRM acquisition principles (Kletetschka, 2000, Kletetschka et al., 2002).

Just below the Curie temperature the two dominant energies, independently of grain size, are the magnetostatic energy in the external field and magnetostatic energy in the demagnetizing field. The balance between the external field energy and demagnetizing energy at high temperature was a building block in models of multidomain TRM proposed by (Néel, 1949, Néel, 1955, Stacey, 1958). Indeed, it was shown in a review article by (Day, 1977) that the various multidomain models (Dunlop and Waddington, 1975, Everitt, 1962, Néel, 1955, Schmidt, 1973, Stacey, 1958), all followed this same approach with minor variations. Schmidt's model is perhaps the easiest to follow and emphasizes that at high temperature the critical energy balance is between the magnetostatic energy in the external and internal demagnetizing fields. Thus, the field, which ultimately controls the magnetization, is the effective field rather than the external field alone. The effective field is obtained in the usual way by subtracting the demagnetizing field from the external field. The demagnetizing factor is more complicated in multidomain grains than in homogenously magnetized particles (Merrill, 1977). However, given the recognition of the importance of the demagnetizing field, it is not too surprising that multidomain material follows the linear trends found by (Kletetschka et al., 2004). What is surprising is that such different grain sizes all show such similar behavior whether they are single domain, pseudo-single domain, or multidomain. This may all be pointing towards a more general approach to TRM that, at least at high temperature, depends upon the balance between magnetostatic energy in the external field and demagnetizing fields.

The single domain TRM model (Néel, 1949, Néel, 1955) is based upon thermal activation, and despite criticism (Brown, 1959) on the nature of the physics involved in determining the frequency factor, the approach has been extremely successful and has served as the foundation of magnetic theory in rock magnetism. The equilibrium magnetization (M) at temperature above the blocking temperature is given by Boltzmann statistics involving the hyperbolic tangent dependence on the ratio of the energy determining the alignment of the magnetization with H over the thermal kT_B energy.

$$M=M_{\text{s}}\text{tanh}({\mu }_{0}V{M}_{\text{s}}H/k{T}_{\text{B}})$$

where V is the volume of the particle, H the applied field, M_s the saturation magnetization, T_B the blocking temperature, and k Boltzmann's constant. However, given the recent results (Kletetschka et al., 2004), the demagnetizing energy must play an important role. This can be included in standard Néel theory by recognizing the importance of the demagnetizing energy in determining relaxation times, which follows the approach of Butler and Banerjee (1975) as well as Dunlop and Kletetschka (2001). In the Néel theory of MD grains, blocking occurs at T_B when barriers to wall motion increase according to coercivity H_c(T) so that the domain walls pin against the demagnetizing field H_d = −NM (N is the demagnetizing factor). TRM can be expressed as Dunlop and Kletetschka (2001):

$$M_{\text{tr}}=(1-N{\chi }_0)n{(n-1)}^{1/n-1}{H}_{c0}^{1/n}{N}^{-1}{H}_0^{1-1/n}$$

and we obtain the theoretical value of M_tr just from the knowledge of the susceptibility χ₀, room temperature coercivity force H_c0, index n, applied field H₀ and demagnetization factor N. This theoretical curve is shown for hematite in Fig. 1A where n = 3, H_c0 = 4 mT, and N = 0.31 (SI) see also Dunlop and Kletetschka (2001).

While the importance of demagnetizing energy is recognized, as for example in the excellent discussion by Dunlop and Ozdemir on pages 84–102 (Dunlop and Özdemir, 1997), it appears that the full significance of the demagnetizing energy and shape anisotropy has not been generally appreciated. If one calculates the balance between the magnetostatic energy in an applied weak field (∼0.1 mT) and the demagnetizing energy, one finds that the magnetostatic energy in the external field only dominates for a few tenths of a degree below the Curie point, so that the TRM can be regarded as a departure from saturation magnetization towards equilibrium driven by the demagnetizing energy. This will be the case for PSD and MD particles. Moreover, both TRM and SIRMs are departures from saturation magnetization driven by demagnetizing energy. The difference is that TRM takes place over a range temperatures beginning close to the Curie point, but SIRM is acquired at the observation temperature. For SD particles the demagnetizing energy enters through the determination of the relaxation time, as suggested above.