Ferromagnetism — Question 1

Question 1

Domain populations can cancel while every domain remains magnetized

A specimen consists of domains with magnetization either $+M_s\hat x$ or $-M_s\hat x$. The fraction pointing +x is f. Neglect domain-wall volume and assume the magnitude Ms is fixed.

1. Find the sample-average magnetization and infer f when M=0.30Ms.

2. Find the change in f required to reach M=0.70Ms and the corresponding change of total moment for volume V.

Question 1 - Solution

Domain populations can cancel while every domain remains magnetized

(a) Method and calculation

$$M=fM_s-(1-f)M_s=(2f-1)M_s.$$$$\boxed{f=\tfrac12(1+M/M_s)=0.65}.$$

(b) Interpretation and further calculation

$$f_f=\tfrac12(1+0.70)=0.85\Rightarrow\boxed{\Delta f=0.20}.$$$$\boxed{\Delta m=V\Delta M=0.40M_sV}.$$

Physical check

An unmagnetized bulk state with f=1/2 can still contain fully magnetized domains; zero average is not zero local order.