Towards Thermally Activated High-Field Micromagnetism

High-field magnetic measurements and procedures, such as hysteresis, first-order reversal curves (FORC), and alternating-field (AF) demagnetization, are foundational methods in rock and paleomagnetic studies. Interpreting these data can be challenging and often requires an understanding of the particle scale contributions to these signals. This requires a numerical approach using micromagnetic models along with the inclusion of thermal fluctuations, which result in time dependent relaxation in experimental observations. This is a challenge that requires knowledge of all stable domain states, their connectivity, and  energy barriers that partition the energy landscape that results from the field strength and orientation of each particle. This typically requires considerable user input and analysis, making this an unfeasibly time-consuming endeavor.

We are developing a method that calculates exact energy surfaces for uniformly magnetized particles and approximate energy surfaces for single vortex (SV) particles, akin, to software tools such as the Singe Domain Comprehensive Calculator (SDCC; Cych et al., 2025, doi: 10.1093/gji/ggaf149). This technique is integrated into the micromagnetic software package MERRILL and readily identifies minimum energy domain states, their connectivity, and (using the nudged elastic band method), can calculate the energy barriers between states. This automated process dramatically reduces user input and analysis at the cost of additional computational time resulting in high-field energy landscapes (HELs) which can then be used to simulate a wide range of thermally activated experiments, including hysteresis loops, FORC diagrams, anhysterestic remanent magnetization (ARM) acquisition and AF demagnetization. Additional computational resources are not, however, significant, since our method runs in a matter of minutes to hours on a modern laptop computer. This new approach will take the rock and paleomagnetic community one step closer to incorporating micromagnetic tools as a part of the standard analytical repertoire used to interpret the behavior of natural samples and reconstruct the signals they carry.