Home | About | Table of Contents | Advanced Search | Copyright | Feedback | Privacy

2.6.6 Magnetic properties of materials

Many magnetic properties of materials are expressed in terms of the magnetic field strength H, magnetic flux density B and the magnetic polarization J. The SI units of H and B are, respectively, ampere per metre (A m⁻¹) and tesla (T).

The relation between the quantities expressed in SI units is:

              B= μ₀ H + J

in which µ₀ is 4π × 10⁻⁷ H m⁻¹, the magnetic constant (permeability of free space). The absolute permeability, μ( = B/H) and the volume susceptibility κ (= J/μ₀H), are thus related by the equation:

            μ = μ₀(1 + κ)

The mass susceptibility χ is equal to κ/ρ, where ρ is the density. The relative permeability μ_r = μ/μ₀ is the permeability of the material relative to that of a vacuum and is the value given in the tables.

In ferromagnetic materials as H is increased steadily from zero the permeability changes and is at first relatively small, its value being defined as the initial permeability, then reaches a maximum value, and finally decreases towards μ₀ as the polarization tends towards a limiting value (B − μ₀H). The flux density remaining when H is reduced to zero is the remanent flux density and the negative H needed to reduce B to zero is the coercive force. The remanent flux density and coercive force for a cycle which proceeds to saturation are called the remanence, B_r, and the coercivity, H_cB. In an open magnetic circuit the variation of J with H is usually measured and the coercivity is then denoted by H_cJ.

When a ferromagnetic material is taken through a cycle of magnetization there is a loss of energy as heat due to the combined effects of hysteresis, induced eddy currents and domain wall motion. The hysteresis loss per unit volume, Q_h = H dB, has been shown empirically to vary as B^1.6_max over a limited range of peak flux density of up to about 1 T for high saturation materials, and 0.5 T for low saturation materials. This relationship, known as the Steinmetz law, is nevertheless only approximate. Some indication of the second loss, namely the eddy current power loss, may be calculated from standard formulae once certain relevant physical parameters are known. In their present forms, however, these formulae are only approximate. The total power losses that will be dissipated in laminar material when an alternating flux is developed in it has a direct bearing on the efficiency that can be realized in equipment such as transformers and electric motors and should therefore be known accurately. Accordingly the power losses of representative forms of typical materials are measured and some of these are given in Table (3) in terms of power loss per unit mass.

Many magnetic properties of ferromagnetic materials depend greatly on previous history, state of strain, temperature, size, perfection and orientation of crystals, and the effect of small traces of impurity may be enormous.

When heated, ferromagnetic materials become paramagnetic at a temperature known as the (ferromagnetic) Curie point.

Ferrimagnetic materials (ferrites) have all of the above characteristics of ferromagnetic materials. However, due to their high resistivity, soft (low coercivity) ferrites are widely used in high frequency applications, in which case the following parameters are also of interest:

Apart from changes in their magnetic permeability, some materials have other responses to changes in magnetic field strength. All conducting materials exhibit the Hall effect, of which there are two forms. In the transverse Hall effect a voltage is developed in a direction at right angles to a current passing through the material when a magnetic field is applied in a mutually perpendicular direction. The relationship between the current flowing through the material I_x, the output voltage, V_y, the thickness of the material, t_z, and the applied magnetic field strength, H_z, is given by:

             V_y = (K_H I_x μ₀ H_z) /t_z

where K_H is the transverse Hall coefficient of the material. It has been found that some semiconducting materials have sufficiently high Hall coefficients to produce convenient, small size and low cost magnetic sensors. Indium arsenide having a Hall coefficient of 0.75 Vm/TA is a widely used material.

The same conditions that produce the transverse Hall effect also give rise to a voltage in the direction of the current and this is sometimes called the longitudinal Hall effect but more usually magnetoresistance. Until recently only small changes in resistance have been observed (up to 2% for the widely used Ni₈₀Fe₂₀ material at room temperature) but the so-called giant magnetoresistance (GMR) has been observed in multilayers of Fe/Cr (50% change in resistance) and Co/Cu (120% change in resistance). However, strong magnetic field strengths (≈ 800 kA/m) and a temperature of 4.2 K are required to observe GMR in a multilayer. In all cases the magnetoresistance of a material is a complex function of the applied magnetic field strength, temperature, material type and thickness.

Since the properties may vary considerably from specimen to specimen due to chemical composition and state of heat treatment, the values given are only to be regarded as typical of the materials mentioned. A range of values is indicated by a dash.

Symbols used in tables:

   B   = magnetic flux density
   B_r  = remanence
   H   = magnetic field strength
   H_cB = induction coercive force, coercivity
   H_cJ = magnetization coervice force, coercivity
   J    = magnetic polarization
   J_s   = (B − μ₀H)_s = saturation polarization
   Q_h  = hysteresis loss per unit volume per cycle
   μ_r   = relative magnetic permeability
   μ_i   = initial relative magnetic permeability

(1) Magnetic susceptibilities of paramagnetic and diamagnetic materials

Values are mass susceptibility per kilogram, χ, at 20°C.

	× 10−8			× 10−8			× 10−8
Common elements
Hydrogen   .  .  .  .  .	−2.49		Aluminium  .  .  .  .  .	+0.82		Germanium  .  .  .  .  .	−0.15
Oxygen.  .  .  .  .  .  .	+133.6		Copper      .  .  .  .  .	−0.107		Silicon   .  .  .  .  .  .  .	−0.16
Helium    .  .  .  .  .  .	−0.59		Silver      .  .  .  .  .  .	−0.25		Arsenic    .  .  .  .  .  .	−0.39
Neon   .  .  .  .  .  .  .	−0.41		Gold       .  .  .  .  .  .	−0.19		Indium  .  .  .  .  .  .  .	−0.14
Argon .  .  .  .  .  .  .	−0.60		Platinum  .  .  .  .  .  .	+ 1.22		Antimony .  .  .  .  .  .	−1.09
Krypton    .  .  .  .  .	−0.41		Mercury  .  .  .  .  .  .	−0.21		Tellurium  .  .  .  .  .  .	−0.39
Xenon    .  .  .  .  .  .	−0.40		Bismuth   .  .  .  .  .  .	−1.70		Gallium  .  .  .  .  .  .  .	−0.30
Nitrogen   .  .  .  .  .	−0.54		Sulphur   .  .  .  .  .  .	−0.62		Phosphorus .  .  .  .  .	−1.13
Sodium     .  .  .  .  .	+0.75		Lead   .  .  .  .  .  .  .	−0.15
Potassium .  .  .  .  .	+0.65		Uranium .  .  .  .  .  .	+2.19
Common compounds						Common materials
H2O     .  .  .  .  .  .	−0.90		NiSO47H2O   .  .  .	+20.1		Araldite  .  .  .  .  .  .	−0.63
NO      .  .  .  .  .  .	+59.3		NiSO4K2SO47H2O	+13.9		P.V.C    .  .  .  .  .  .	−0.75
CO2     .  .  .  .  .  .	−0.59		CuSO45H2O  .  .  .	+ 7.7		Perspex .  .  .  .  .  .	−0.5
NH3     .  .  .  .  .  .	−1.38		MnSO44H2O .  .  .	+81.2		Polyethylene   .  .  .	+0.2
HCl      .  .  .  .  .  .	−0.75		FeSO4(NH4)2   .  .
H2SO4    .  .  .  .  .	−0.50		SO46H2O   .  .  .	+40.6
NaCl    .  .  .  .  .  .	−0.64
NiCl2   .  .  .  .  .  .
(anhydrous)  .  .	+78.5
(in solution)  .  .	+43.0

    Notes:
    (1) To obtain values in CGS units per gramme, the SI values given should be multiplied by 10³ /4π.
    (2) For a more complete list of elements, see L. F. Bates, Modern Magnetism (CUP).

(2) Feebly magnetic steels and cast irons

    * In general, the relative magnetic permeability decreases at higher values of magnetic field strength.
    ^†  Low permeability reference materials available from National Physical Laboratory, Teddington, Middlesex, TW11 0LW, UK.
    ^‡ C. B. Post and W. S. Eberley, ‘Stability of austenite in stainless steels’, Trans. Am. Soc. Metals, 1947, 39, p. 868.

(3) Soft (low coercivity) materials

Material (approx. % composition , balance iron)	B/T for H/(A m−1) =		Relative permeability μr		Js T	HcB A m−1	Br T	Curie point °C	Resistivity 10−8 Ωm	Specific total loss for J = 1.5 T,   f = 50Hz W/kg	Specific apparent power for J = 1.5 T,   f = 50Hz VA/kg
	1000	5000	Initial μi 1000	Maximum μr 1000
Ferromagnetic elements
Iron, high purity (single
crystals in preferred direction)  .  .	2.01	2.01	—	1500	2.16	12	—	770	10	—	—
Armco iron      .  .  .  .  .  .  .  .  .  .  .	1.55	1.72	0.25	7	2.16	80	1.3	770	11	—	—
Cast iron (annealed)     .  .  .  .  .  .  .	0.60	0.86	—	—	1.70	400	—	—
Swedish iron (annealed)     .  .  .  .  .	1.52	1.72	—	—	2.16	70	—	770	—	—	—
Nickel      .  .  .  .  .  .  .  .  .  .  .  .  .  .	0.45	0.55	—	—	0.615	400	—	358	9	—	—
Cobalt      .  .  .  .  .  .  .  .  .  .  .  .  .  .	0.21	0.70	—	—	1.76	950	—	1115	9	—	—
Steels (solid)
Carbon steel (annealed) 1% C  .  .  .	0.75	1.54	—	—	2.00	600	—	—	—	—	—
Constructional steels:
0.3% C, 1% Ni	1.32	1.68	—	—	2.10	250	—	—	—	—	—
0.4% C, 3% Ni, 1.5% Cr  .  .  .  .	0.75	1.67	—	—	2.05	500	—	—	—	—	—
Mild steel, 0.1% C    .  .  .  .  .  .  .	1.46	1.74	—	—	2.15	150	—	—	10
Steels (sheet)†
Grain oriented silicon steels with
preferred magnetic properties in
direction of rolling of the parent strip
(d.c. magnetization):
Unisil-H, 103-27-P5, (27MOH) 2.9% Si	1.93	2.00	—	93	2.00	6	—	745	45	1.00 (J = 1.7T)	1.38 (J = 1.7T)
Unisil,089-27-N5,(27M4)              097-30-N5, (30M5) 3.1%Si            111-35-N5, (35M6)	1.86	1.96	—	75	2.00	7	—	745	48	0.84	1.16
	1.86	1.96	—	59	2.00	7	—	745	48	0.89	1.32
	1.84	1.94	—	58	2.00	7	—	745	48	1.00	1.39
Non-oriented silicon steels:
SURA   300-35-A5, (CK-37)    2.9% Si	1.46	1.65	—	8	2.00	40	—	745	48	2.95	28
400-50-A5, (CK-40)    2.4% Si	1.48	1.69	—	7	2.03	40	—	748	44	3.60	19
800-65-A5, (DK-70)    1.6% Si	1.53	1.73	—	5	2.08	70	—	758	34	6.50	14
Non-oriented, non-silicon steel:
Newcor 1000-65-D5  .  .  .  .  .  .  .	1.59	1.75	—	8	2.15	50	—	770	12	7.00	9.6
Amorphous iron–boron alloys
(metallic glass)
Metglas‡   2605 S-3 .  .  .  .  .  .  .	—	—	—	—	1.58	8	0.7	405	125	0.15 (J = 1.7T)	0.20 (J = 1.0T)
Metglas†   2605 SC  .  .  .  .  .  .  .	—	—	—	—	1.61	5	1.1	370	125

Material (approx. % composition , balance iron)	Flux density B/T for H/(A m−1) =						Relative permeability μr		Js T	HcB A m−1	Br T	Curie point °C	Resistivity 10−8 Ωm
	1.0	10	50	100	1000	50 000	Initial μi 1000	Maximum μr 1000
Nickel iron alloys
Supermumetal§     Nilomag 771¶   70–80% Ni with small   Mumetal plus§   amounts of other     Mumetal§   elements   EPC 20¶
	0.45	0.72	0.76	0.78	—	—	200	400	0.77	0.55	0.5	350	55
	0.30	0.70	0.75	0.77	—	—	80	300	0.77	0.8	0.45	350	55
	0.18	0.60	0.72	0.75	—	—	60	240	0.77	1.0	0.45	350	55
Nilomag 641¶        65% Ni + small                            amount of other                            elements, oriented	—	—	—	—	—	—	0.4–1.0	200–400	1.4	4	1.35	590	48
Nilomag 471¶     Super Radiometal§       50% Ni + small   Radio metal 4550§   amounts of       other elements     Satmumetal§     HCR alloy§ +oriented structure
	0.03	1.02	1.25	1.4	1.62	—	2–11	50–120	1.6	4–12	0.4–1.2	530	43
	0.01	0.48	1.05	1.18	1.62	—	3–6	20–50	1.6	12–24	0.4–1.0	530	50
	0.20	1.15	1.3	1.35	—	—	65	240	1.5	2.0	0.7	550	60
	—	0.3	1.46	1.50	1.55	—	0.5–1.0	50–100	1.6	10	1.5	525	40
Radio metal 36§ 35% Ni	—	0.15	0.72	0.90	1.2	—	2	15	1.3	12	0.35	180–270	80
Hyperm 36 36% Ni		constant permeability alloy					1.75	6	—	—	—	—	—
R2799§  30% Ni, temperature	—	—	—	—	0.1	—	—	—	0.45	—	—	70	85
compensating alloy
Cobalt-iron alloys§
Permendur 24  24% Co	—	0.002	0.02	0.05	1.45	2.34	0.25	2.0	2.35	950	1.65	980	20
Permendur 49  49% Co	—	0.01	0.13	0.33	1.85	2.34	1.0	7	2.35	140	1.5	980	47
Supermendur   49% Co, 2% V	—	—	2.05	2.1	2.3	2.34	—	70	2.35	20	2.1	980	40
Hisat 50         49% Co, 0.3% Ta	—	—	1.5	1.8	2.3	2.44	—	18	2.44	40	1.8	980	10
Other alloys
Heusler alloy   61% Cu, 26% Mn, 13% Al	—	—	—	0.01	0.25	0.45	—	—	0.48	550	—	330	—
Isoperm         30% Ni, 11% Cu		constant permeability alloy					0.06	0.065	—	—	—	—	—
Perminvar       40% Ni, 25% Co		constant permeability alloy					0.30	1.5	1.55	100	—	715	19
Nickel copper  70% Ni, 30% Cu	—	—	—	—	0.07	0.15	—	—	—	—	—	10–100	—

    Manufacturers: ^† European Electrical Steels Newport, Gwent. ^‡ Allied Chemical Corpn., Morris Township, NJ, USA. ^§ Telcon Ltd, Crawley. ^¶ Henry wiggin & Co., Hereford.
    Notes:
    (1) The initial relative permeability values for the nickel iron alloy are for a magnetic field strength of 0.4 A/m.
    (2) For further information on the properties of solid steels see J. Woolman and R. A. Mottram(1964–9) Mechanical and Physical Properties of the BS En Steels, Vols. 1, 2 and 3, Pergamon.

Material	Initial relative permeability μi	Frequency range MHz	Loss factor at maximum frequency 10−6	Temperature factor 10−6 /°C	Flux density B/T for H/(A m−1) =800	Power loss density for B = 0.2T, f = 16 kHz mW/cm3	IEC hysteresis coefficient ηB	Disaccommodation factor 10−6	Curie point °C	Resistivity Ωm
Carbonyl iron powder cores
type 100	30	0.1–2	700	20	—	—	—	—	—	—
type 500	12	1–10	250	12	—	—	—	—	—	—
type 900	10	1–50	600	12	—	—	—	—	—	—
type 901	5	10–100	1500	12	—	—	—	—	—	—
Magnetic iron oxide powder cores
type 910	4	20–300	500 (at 100 MHz)	40	—	—	—	—	—	—
Iron flake cores
used for interference    suppression, relative    initial permeability    falls rapidly with    frequency	90 at 1 kHz	—	—	—	—	—	—	—	—	—
	65 at 150 kHz	—	—	—	—	—	—	—	—	—
Ferrite cores
(a) for radio, TV and
low power uses:
nickel zinc,
type F13	650	0.05–1	130	—	—	—	—	—	180	300
type F14	220	0.1–2	50	—	—	—	—	—	270	1000
type F16	125	1–10	100	—	—	—	—	—	270	1000
type F22	19	5–40	500	—	—	—	—	—	500	1000
manganese zinc,
type F10	5000	0.01–0.1	12	—	—	—	—	—	180	0.5
type F8	1500	0.05–0.5	80	—	—	—	—	—	180	1
type F11	600	0.1–1	50	—	—	—	—	—	220	5
(b) perminvar, high
frequency low power
uses
type F25	50	5–40	300	—	—	—	—	—	450	1000
type F29	12	10–200	1000	—	—	—	—	—	500	1000
(c) manganese zinc for
high power uses
type F6	1500	—	—	—	0.45	150	—	—	180	1
type F5	2000	—	—	—	0.48	75	—	—	200	1
(d) manganese zinc, high
stability, low loss,
telecommunications
uses
type P10	2000	—	12*	0–2	—	—	2.5	8	150	1
type P11	2200	—	5*	0.5–1.5	—	—	0.8	5	150	1
type P12	2200	—	3*	0.4–1.0	—	—	0.4	3	150	1

    * Loss factor at 100 kHz.
    Note: For more complete details of soft ferrite materials see E. C. Snelling, Soft Ferrites, Properties and Applications (Iliffe Books Ltd., London).

(4) Permanent magnet (magnetically hard) materials
     (a) Typical alloys in the Al–Ni–Co series (cast material):

Material	Approx. composition (balance iron) %	Remanence Br T	(BH)max kJ m −3		Coercivity			Curie point °C	Maximum operating temperature °C	Resistivity μΩ m
				HcB kA m −1		HcJ kA m −1
Alni isotropic Alnico 1	Ni 25, Al 13, Cu 4	0.56	10.0	46		49		760	550	0.63
Alnico isotropic Alnico 2	Ni 19, Al 10, Co 12, Cu 6	0.73	13.5	45		48		800	550	0.65
Alcomax III anisotropic Alnico 5	Ni 13.5, Al 8, Co 24, Cu 3	1.30	43	52		53		850	550	0.55
Alcomax III semi-columnar Alnico 5 DG		1.32	49	56		57		860	550	0.55
Columax columnar Alnico 5–7		1.35	60	59		60		860	550	0.55
Hycomax II      anisotropic	Ni 14.5, Al 7, Co 29,	0.85	32	95		97		850	550	0.50
	Cu 4.5, Ti 5
Hycomax III anisotropic Alnico 8	Ni 14, Al 7.3, Co 34, Cu 3, Ti 5.25	0.90	44	127		129		850	550	0.50
Alnico 9 columnar		1.05	80	124		126		850	550	0.50

Note: The isotropic and anisotropic alloys can also be prepared by sintering, in which case the magnetic properties can be up to 20% less than those for cast material.

(b) Rare-earth alloys:

Material		Type		Remanence Br T	(BH)max KJ m−3	Coercivity		Curie point °C	Maximum operating temperature °C	Resistivity μΩ m
						HcB kA m −1	HcJ kA m −1
Supermagloy, sintered
—pressed axially		Sm Co5		0.90	160	680	1500	725	150	0.70
—pressed isostatically				0.95	176	720	1500	725	150	0.70
—anisotropic		Sm2Co17		1.05	210	760	700–2000	800	250	0.70
—bonded		Sm Co5 + binder		0.58	56	380	760	*	60*	10
Neodure Sintered Neorem anisotropic			Nd Fe B	1.15–1.35	220–350	880–960	890–1700	300–320	150	1.50
Magnequench, isotropic				0.61	64	424	1200	*	60*	180
Bemag 5N NIN 403	bonded,		Nd Fe B + binder
	injection moulded,			0.40	32	300	600	*	150	—
	anisotropic

    * Limited by the properties of the bonding material.

(c) Ferrites:

Material		Approx. composition (balance iron) %		Remanence Br T	(BH)max kJ m−3	Coercivity		Curie point °C	Maximum operating temperature °C	Resistivity μΩ m
						HcB kA m−1	HcJ kA m−1
Feroba 1  sintered isotropic MMG D1		BaO + 5.9 (Fe2O3)         SrO + 5.9 (Fe2O3)		0.22	8	135	220	450	350	104
Ferroba 2	sintered anisotropic
Ferroxdure 300				0.39	28	176	184	450	350	104
Feroba 3
Ferroxdure 380				0.37	26	240	230	450	350	104
Ferroxdure 500				0.40	30	295	320	450	350	104
Flexam P5 MMG 01	bonded isotropic			0.14	3.2	85	175	*	120*	106
Flexor 45  bonded anisotropic FXD SP106				0.25	11.2	175	240	*	120*	106

* Limited by the properties of the bonding material.

Further information on the properties of permanent magnet materials and details of manufacturers are given in M. McCaig and A. G. Clegg (1987) Permanent Magnets in Theory and Practice, 2nd edn, Pentech Press, London.

A.E.Drake.

Home | About | Table of Contents | Advanced Search | Copyright | Feedback | Privacy | ^ Top of Page ^

This site is hosted and maintained by the National Physical Laboratory © 2008.