# 磁化強度

${\displaystyle \mathbf {M} \ {\stackrel {def}{=}}\ n\mathbf {m} }$

## 馬克士威方程組

### 磁感應強度、磁場強度和磁化強度之間的關係

${\displaystyle \mathbf {H} \ {\stackrel {def}{=}}\ {\frac {1}{\mu _{0}}}\mathbf {B} -\mathbf {M} }$

${\displaystyle \mathbf {M} =\chi _{m}\mathbf {H} }$

### 磁化電流

${\displaystyle \mathbf {J} _{b}\ {\stackrel {def}{=}}\ \nabla \times \mathbf {M} }$
${\displaystyle \mathbf {K} _{b}\ {\stackrel {def}{=}}\ \mathbf {M} \times {\hat {n}}}$

${\displaystyle \mathbf {J} =\mathbf {J} _{f}+\mathbf {J} _{b}+\mathbf {J} _{P}}$

${\displaystyle \mathbf {J} _{P}={\frac {\partial \mathbf {P} }{\partial t}}}$

### 靜磁學

${\displaystyle \mathbf {\nabla \cdot H} =-\nabla \cdot \mathbf {M} }$
${\displaystyle \mathbf {\nabla \times H} =0}$

${\displaystyle \mathbf {\nabla \cdot E} ={\frac {\rho }{\epsilon _{0}}}}$
${\displaystyle \mathbf {\nabla \times E} =0}$

## 磁性物質

### 抗磁性

${\displaystyle \chi =-\ {\frac {\mu _{0}NZe^{2}}{6m}}\langle r^{2}\rangle }$

### 順磁性

${\displaystyle \chi =C/T}$

### 鐵磁性

${\displaystyle \chi =C/(T-T_{c})}$

${\displaystyle \Delta M(T)/M_{0}=\beta T^{3/2}}$

### 反鐵磁性

${\displaystyle \chi ={\frac {2C}{T+T_{N}}}}$

${\displaystyle \chi ={\frac {2C}{T+\theta }}}$

• 假設外磁場垂直於自旋，則垂直磁化率近似為常數 ${\displaystyle \chi _{\perp }\approx C/T_{N}}$
• 假設外磁場平行於自旋，則在絕對溫度0K時，平行磁化率為零；在從0K到奈爾溫度 ${\displaystyle T_{N}}$ 之間，平行磁化率會從 ${\displaystyle \chi _{\parallel }(0)=0}$ 平滑地單調遞增至 ${\displaystyle \chi _{\parallel }(T_{N})=C/T_{N}}$

## 註釋

1. ^ 更確切地說，當 ${\displaystyle \mu B/K_{B}T\gg 1}$ 時，居里定律成立；其中，${\displaystyle \mu }$ 是磁矩，${\displaystyle K_{B}}$波茲曼常數

## 參考文獻

1. ^ HP Meyers. Introductory solid state physics 2. CRC Press. 1997: 362; Figure 11.1. ISBN 0748406603.
2. ^ Catherine Westbrook, Carolyn Kaut, Carolyn Kaut-Roth. MRI (Magnetic Resonance Imaging) in practice 2. Wiley-Blackwell. 1998: 217. ISBN 0632042052.
3. Chen, Chih-Wen, Magnetism and metallurgy of soft magnetic materials, Courier Dover Publications: pp. 1, 7–8, 12, 1977, ISBN 9780486649979
4. Kittel, Charles. Introduction to Solid State Physics 6th. John Wiley & Sons. 1986: pp. 299–302, 323–324, 330–335, 340–344, 351–352. ISBN 0-471-87474-4.
5. ^ Chikazumi, Sōshin; Chad Graham. Physics of ferromagnetism 2nd. Oxford University Press. 2009: 140-142. ISBN 9780199564811.