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

许多关于前中生代地质学的主要假说严重依赖于古地磁数据。岩石中的剩磁记录了古老的磁场，并提供了有关板块构造和地球发电机历史的信息。为了使剩磁发挥作用，它必须在岩石受到温度升高、压力和化学环境变化的影响时保持稳定。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，许多最有前途的磁性记录器并不适合良好的古地磁记录器的标准模型。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。相互作用的影响因磁矩的热弛豫而变得复杂，在磁矩中，磁化强度跳过了稳定状态之间的能垒。相互作用的磁铁模型面临的最大挑战是找到这些能量障碍。这个建议的目的是利用数值代数几何中的一些强大的方法来计算粒子相互作用和热涨落的磁效应。相互作用磁体的平衡方程可表示为多项式方程组。我们将利用同伦延拓的方法来寻找这类系统的所有稳定态和过渡态。磁化强度与时间的关系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.亚玄武岩和前寒武纪屏蔽体中钛磁铁矿包裹体的剩磁获取和退磁理论。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组成的网络。颗粒相互作用和颗粒生长对古强度测量精度的影响将被确定。沉积体系的等温磁滞测量模型，包括可能具有显著相互作用的单磁区和超顺磁性颗粒。其中包括重新磁化的碳酸盐，具有趋磁细菌化石的沉积物，以及含有云母或磁黄铁矿的沉积物。这样的系统可以携带有关古代环境和人类影响的重要信息。一种涉及振荡磁场的测量模型，包括无滞后剩磁(ARM)和交变磁场剩磁退磁。这些测量是古地磁分析中常用的工具。

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.