Section: 12 | Properties of Magnetic Materials |

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How to Cite this Reference

PROPERTIES OF MAGNETIC MATERIALS

H. P. R. Frederikse

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Glossary of Symbols

Quantity	Symbol	SI Units	emu Units
Magnetic field	H	A m^-1	Oe (oersted)
Magnetic induction	B	T (tesla)	G (gauss)
Magnetization	M	A m^-1	emu cm^-3
Spontaneous magnetization	M_s	A m^-1	emu cm^-3
Saturation magnetization	M₀	A m^-1	emu cm^-3
Magnetic flux	Φ	Wb (weber)	maxwell
Magnetic moment	m, µ	A m²	erg/G
Coercive field	H_c	A m^-1	Oe
Remanence	B_r	T	G
Saturation magnetic polarization	J_s	T	G
Magnetic susceptibility	χ
Magnetic permeability	µ	H m^–1 (henry/meter)
Magnetic permeability of free space	µ₀	H m^–1
Saturation magnetostriction	λ (∆l/l)
Curie temperature	T_C	K	K
Néel temperature	T_N	K	K

Magnetic moment µ = γħJ = g µ_B J

where

γ = gyromagnetic ratio
J = angular momentum
g = spectroscopic splitting factor (~2)
µ_Β = Bohr magneton = 9.27401⋅10^–24
J/T = 9.2741⋅10^–21 erg/G

Earth’s magnetic field H = 56 A m^–1 = 0.7 Oe
For iron: M ₀ = 1.7⋅10⁶ A m^–1; B _r = 0.8⋅10⁶ A m^–1
1 Oe = (1000/4π) A m^–1; 1 G = 10^–4 T; 1 emu cm^–3 = 10³ A m^–1
1 Maxwell = 10^–8 Wb
µ₀ = 4π·10^–7 H m^–1

Relation between Magnetic Induction and Magnetic Field

figure 1 described below

FIGURE 1. Typical curve representing the dependence of magnetic induction B on magnetic field H for a ferromagnetic material. When H is first applied, B follows curve (a) as the favorably oriented magnetic domains grow. This curve flattens as saturation is approached. When H is then reduced, B follows curve (b), but retains a finite value (the remanence B_r ) at H = 0. In order to demagnetize the material, a negative field –H_c (where H_c is called the coercive field or coercivity) must be applied. As H is further decreased and then increased to complete the cycle (curve c), a hysteresis loop is obtained. The area within this loop is a measure of the energy loss per cycle for a unit volume of the material.

figure 2 described below

FIGURE 2. Schematic curve illustrating the B vs. H dependence for hard and soft magnetic materials. Hard materials have a larger remanence and coercive field, and a correspondingly large hysteresis loss.

Reference

Ralls, K. M., Courtney, T. H., and Wulff, J., Introduction to Materials Science and Engineering, J. Wiley & Sons, New York, 1976, p. 577, 582. With permission.

Magnetic Susceptibility of the Elements

figure 3 described below

FIGURE 3. Molar susceptibility of the elements at room temperature (cgs units of 10^–6 cm³/mol). Values are not available for Z = 9, 61, and 84–89; Fe, Co, and Ni (Z = 26–28) are ferromagnetic. Data taken from the table “Magnetic Susceptibility of the Elements and Inorganic Compounds” in Section 4.

Gray, D. E., Ed., American Institute of Physics Handbook, Third Edition, McGraw-Hill, New York, 1972, p. 5-224. With permission.

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Ground State of Ions with Partly Filled d or f Shells

Z	Element	n	S	L	J	Gr. state	p_calc	p_calc^b	p_meas
Continued on next page...
22	Ti⁺³	1	1/2	2	3/2	²D_3/2	1.73^a	1.55	1.8
23	V⁺⁴	1	1/2	2	3/2	²D_3/2	1.73^a	1.55	1.8
23	V⁺³	2	1	3	2	³F₂	2.83^a	1.63	2.8
23	V⁺²	3	3/2	3	3/2	⁴F_3/2	3.87^a	0.77	3.8
24	Cr⁺³	3	3/2	3	3/2	⁴F_3/2	3.87^a	0.77	3.7
25	Mn⁺⁴	3	3/2	3	3/2	⁴F_3/2	3.87^a	0.77	4.0
24	Cr⁺²	4	2	2	0	⁵D₀	4.90^a	0	4.9
25	Mn⁺³	4	2	2	0	⁵D₀	4.90^a	0	5.0
25	Mn⁺²	5	5/2	0	5/2	⁶S_5/2	5.92^a	5.92	5.9
26	Fe⁺³	5	5/2	0	5/2	⁶S_5/2	5.92^a	5.92	5.9
26	Fe⁺²	6	2	2	4	⁵D₄	4.90^a	6.70	5.4
27	Co⁺²	7	3/2	3	9/2	⁴F_9/2	3.87^a	6.54	4.8
28	Ni⁺²	8	1	3	4	³F₄	2.83^a	5.59	3.2
29	Cu⁺²	9	1/2	2	5/2	²D_5/2	1.73^a	3.55	1.9
58	Ce⁺³	1	1/2	3	5/2	²F_5/2	2.54^c		2.4
59	Pr⁺³	2	1	5	4	³H₄	3.58^c		3.5
60	Nd⁺³	3	3/2	6	9/2	⁴I_9/2	3.62^c		3.5
61	Pm⁺³	4	2	6	4	⁵I₄	2.68^c
62	Sm⁺³	5	5/2	5	5/2	⁶H_5/2	0.84^c		1.5

^a p_calc = 2[S(S + 1)]^½.
^b p_calc = 2[J(J + 1)]^½.
^c p_calc = g[S(S + 1)]^½.

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PROPERTIES OF MAGNETIC MATERIALS

Glossary of Symbols

Relation between Magnetic Induction and Magnetic Field

Reference

Magnetic Susceptibility of the Elements

Ground State of Ions with Partly Filled d or f Shells

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