The Kronmüller formula is used to qualitatively explain the coercivity of permanent magnets. Such simple expressions are useful for understanding the elements that influence the coercivity. This study attempts to derive Kronmüller formula within the framework of the Ginzburg-Landau theory. The results revealed that the coercivity of the magnetic material was defined by the slope of the free energy landscape. The reduction parameter α for the magnetic anisotropy field H_k in the Kronmüller formula depends on the functional form representing the free energy landscape that changes with the magnetization process of the material, and it is shown that α < 1 under the condition of absolute zero temperature T = 0. Furthermore, it was revealed that α depends on the entropy of the system and that it may show a larger reduction rate at a finite temperature T ≠ 0. Thus, it is important to acquire the free energy landscape and clarify the order parameter dependence of entropy in the magnetization process of the magnetic material.

  We used a lead field normalization and measurement covariance matrix R into a weighted minimum-variance spatial filter (WMV). An inverse estimation, with an extended source, arranged at the surface of a realistic ventricular model was carried by WMV, weight-normalized minimum-norm (WMN), and minimum-variance spatial filter (MV) with and without noise. The performances of these spatial filters were evaluated using the estimation error and ratios of all positions with an estimation error below 2 cm. Moreover, the proper regularization parameter was determined from the estimation error. The results of the statistical analysis, while handling varied source positions, show that WMV has the best performance for magnetocardiography (MCG) extended source inverse estimation because it leads to less estimation error and is capable of stable inverse estimation, even at high noise levels. In other words, the combined lead field normalization, with the measurement covariance matrix R used in WMV, is a good choice for our MCG system.