Comparison of Micromagnetic Modeling and Experiment Considering Grain Size Distribution at 1–20 kHz

Wenbin Meng^a,b · Changgeng Zhang^a,b · Yongjian Li^a,b · Hao Zhang^a,b
Journal of Magnetism and Magnetic Materials (2025)
DOI: 10.1016/j.jmmm.2025.173350

---

Abstract

The miniaturization and lightweight design of electrical equipment result in the widespread application of nanocrystalline alloys in high-frequency power electronic transformers and high-frequency switching power supplies. To elucidate the intrinsic correlation between mesoscopic magnetization behavior and macroscopic magnetic properties of nanocrystalline alloy, magnetic property measurement and micromagnetic modeling are performed on the 1K107B nanocrystalline alloy. The actual grain morphology characteristics are obtained through transmission electron microscopy (TEM) observation, and the three-dimensional micromagnetic simulation model with the same grain size statistical distribution is constructed. The broadband magnetic property test data are combined with mesoscopic theory to determine the key parameters for micromagnetic simulations. Comparative analysis between the traditional model with uniform grain size and the improved model constructed in this paper shows that, for predicting loss density and coercivity, the average deviation between the improved model and experimental data is less than 10%, demonstrating higher prediction accuracy. These results indicate that micromagnetic models considering actual grain size distributions can more accurately reflect the magnetization mechanisms in nanocrystalline alloy.

---

Keywords

Nanocrystalline alloy · Magnetic properties test · Micromagnetic simulation · Grain size distribution · Magnetic moment rotation

---

1. Introduction

With the increasing demand for high power density and high-efficiency power converters, high-frequency magnetic components such as transformers and inductors often dominate the size of converters and lead to significant losses, making them a primary target for optimization. As a biphasic composite soft magnetic material, nanocrystalline alloy features a microstructure in which nanoscale α-Fe(Si) grains are uniformly distributed within an amorphous matrix, each grain randomly oriented [1]. Due to this unique microstructure, it exhibits low anisotropy constant and magnetostrictive coefficient while also possessing excellent comprehensive magnetic properties—high saturation induction, high initial permeability, low coercivity, and low core losses—making it widely used in electromagnetic shielding, wireless charging, and high-frequency transformers [2–4].

The magnetization characteristics of nanocrystalline alloy can be explored from macroscopic and mesoscopic perspectives.

• Macroscopic level: Based on Ampère’s circuital law and Faraday’s induction law, one can measure permeability, remanence, coercivity, and core loss [5,6].
• Mesoscopic level: The dynamic behavior of magnetic domains under external excitation is observable via the magneto-optical Kerr effect. Without applied stress, random anisotropy yields irregular domain patterns; applied stress during annealing induces uniaxial anisotropy and stripe-like domains [8]. High-speed imaging shows that, as excitation frequency increases, materials with strong anisotropy exhibit regular domain changes, whereas those with weak anisotropy do not [9].

Experimental methods alone struggle to reveal the underlying mesoscopic magnetization mechanisms [10]. Micromagnetic simulation compensates by visualizing domain processes. Simulations solve the Landau–Lifshitz–Gilbert (LLG) equation (often under small-angle linearization) for magnetization dynamics [11–13]. Prior models include:

• Random anisotropy simulations relating grain size to coercivity [14].
• Nd₂Fe₁₄B composite magnets showing grain/phase distribution effects [15].
• Shape-anisotropy studies via demagnetization factors [16].
• 3D models using uniform spherical grains to study volume fraction and loss [17–19].

However, these idealized models neglect actual grain size distributions, which critically influence macroscopic properties.

In this work, we integrate TEM-based grain size statistics with broadband magnetic measurements of 1K107B nanocrystalline alloy. From ring-specimen tests, we derive key micromagnetic parameters—saturation magnetization (M_s), crystalline anisotropy constant (K_1), and exchange stiffness (A). We then construct a 3D micromagnetic model incorporating the measured grain size distribution and compare it to a uniform-grain model. The improved model reduces prediction error (loss density, coercivity) to below 10% and introduces the average magnetic-moment rotational angular velocity to characterize dynamic magnetization under 1–20 kHz excitation.

---

References omitted for brevity.