On the demagnetizing energy and demagnetizing factor of a multidomain ferromagnetic cube

Abstract

The equations E d = ½NJ² + const for demagnetizing energy and H d = −NJ for average internal demagnetizing field (J is magnetization; N is demagnetizing factor, assumed constant) are central to multidomain (MD) theories of thermoremanence (TRM) and hysteresis. Theoretical calculations reported here, based on Rhodes and Rowlands' (1954) equations for E d of an MD cube, test the variation of N with the number n of domains and with domain wall displacement x. For n even, E d (x) − E d (0) is nearly proportional to x² or J², so that N is practically constant (to ≈ 20% if n = 2, ≈ 10% if n = 4 and ≈ 5% if n = 8) for 0 ≤ J ≤ J s . This result reaffirms the validity of traditional MD rock magnetic theories. However, if n is small, N is significantly less than 4 π/3 (the single‐domain or n → ∞ value); N ≈ 2 for n = 2 and (4π/3 − N) decreases as 1/n, so that N → 4π/3 when n = 8 or 10. Grains with n odd possess a spontaneous remanence even in the absence of wall pinning that is substantial (J r ≈ 0.1 J s ) for n = 3 but decreases rapidly for larger n. This spontaneous remanence is a possible source of so‐called pseudo‐single‐domain enhancement of TRM in small MD grains.