CMG COLLABORATIVE RESEARCH: Magnetic Viscosity and Thermoremanent Magnetization in Interacting Single-domain Ferromagnets

关于前中生代地质的许多主要假设都严重依赖于古地磁资料。岩石中的剩磁记录了古代的磁场，并提供了板块构造和地球动力学历史的信息。为了使剩余物有用，它必须在岩石经受温度升高、压力和化学环境变化时保持稳定。随着年龄的增长，合适的岩石变得越来越稀少。在中生代以前的岩石中，由于磁性矿物通过磁场相互作用，许多最有希望的磁记录并不符合古磁记录的标准模型。如果这些相互作用没有得到适当的解释，古地磁测量可能会产生误导。磁矩的热松弛使相互作用的影响变得复杂，磁矩的磁化强度会跳过稳定态之间的能垒。相互作用磁体模型面临的最大挑战是找到这些能量障碍。本提案的目的是利用数值代数几何中的一些强大方法来计算粒子相互作用和热波动的磁效应。相互作用磁体的平衡方程可以表示为多项式方程组。我们将利用同伦延拓的方法求出这类系统的所有稳定态和过渡态。磁化强度的时间依赖性可以表示为一组动力学方程。这一理论将有三个主要应用：1。陆基玄武岩和前寒武纪盾中钛磁铁矿包裹体的剩余物获取和退磁理论。这些钛磁铁矿通常是由钛铁矿片层隔开的强相互作用的磁铁矿颗粒网络。将确定颗粒相互作用和晶粒生长对古强度测量精度的影响。沉积体系的等温滞后测量模型，涉及可能具有重要相互作用的单畴和超顺磁粒子。这些沉积物包括再磁化的碳酸盐，趋磁细菌化石沉积物，以及含有灰长岩或磁黄铁矿的沉积物。这些系统可以携带有关古代环境和人类影响的重要信息。一个涉及振荡场的测量模型，包括剩磁的非滞后磁化（ARM）和剩磁的交变退磁。这些测量是古地磁分析的常用工具。

Many major hypotheses about the geology of pre-Mesozoic eras rely critically on paleomagnetic data. Magnetic remanence in rocks records the ancient magnetic field and provides information on plate tectonics and the history of the geodynamo. For the remanence to be useful, it must remain stable as the rocks are subjected to temperature increases, pressure, and changes in the chemical environment. Suitable rocks become increasingly rare as their age increases. In pre-Mesozoic rocks, many of the most promising magnetic recorders do not fit the standard model for good paleomagnetic recorders because the magnetic minerals interact with each other through magnetic fields. If these interactions are not properly accounted for, paleomagnetic measurements can be misleading. The effect of interactions is complicated by thermal relaxation of the magnetic moments in which the magnetization jumps over energy barriers between stable states. The greatest challenge facing models of interacting magnets is to find these energy barriers. The object of this proposal is to harness some powerful methods from numerical algebraic geometry to calculate the magnetic effects of particle interactions and thermal fluctuations. The equilibrium equations for interacting magnets can be expressed as systems of polynomial equations. Methods will be developed to find all the stable states and transition states for such systems using homotopy continuation. The time dependence of the magnetization can then be expressed as a set of kinetic equations. There will be three main applications of this theory:1. A theory of remanence acquisition and demagnetization for titanomagnetite inclusions in sub-aerial basalts and Precambrian shields. These titanomagnetites are often networks of strongly interacting magnetite grains separated by ilmenite lamellae. The effect of particle interactions and grain growth on the accuracy of paleointensity measurements will be determined.2. A model of isothermal hysteresis measurements of sedimentary systems involving single-domain and superparamagnetic particles that may have significant interactions. These include remagnetized carbonates, sediments with fossil magnetotactic bacteria, and sediments with greigite or pyrrhotite. Such systems can carry important information on ancient environments and human impacts.3. A model of measurements involving oscillating fields, including anhysteretic remanent magnetization (ARM) and alternating field demagnetization of remanence. These measurements are common tools in paleomagnetic analysis.