Magnetic Materials

Basic Magnetic Quantities Magnetic Induction or Magnetic Flux Density B Units: N C -1 m -1 s = Tesla (T) = Wb m -2

2006: UNESCO Nikola Tesla Year 150 th birth Anniversary of Nikola Tesla AC vs. DC

Ampere’s law in free space i B  0 = permeability of free space = 4  T m A -1 = 4  H m -1

Magnetic dipole moment m i Area=A m=iA Units: A m 2

Magnetization M of a solid A solid may have internal magnetic dipole moments due to electrons Magnetic dipole moment per unit volume of a solid is called magnetization Units: A m 2 /m 3 = A m -1

Ampere’s law in a solid i B0B0 H: magnetic field intensity or field strength Units: A m -1

In free space Inside a solid  = permeability of solid, H m -1 relative permeability of solid, dimensionless

 : magnetic susceptibility of the solid  Types of magnetic solid Dimensionless diamagnetic superconductor paramagnetic ferromagnetic (universal)

Origin of permanent magnetic moments in solids: 1. orbital magnetic moment of electrons 2. spin magnetic moment of electrons 3. spin magnetic moment of nucleus We will consider only spin magnetic moment of electrons

Bohr magneton  B The magnetic moment due to spin of a single electron is called the Bohr magneton  B  B = x A m 2 Net moment of two electrons of opposite spins = 0

Unpaired electrons give rise to paramagnetism in alkali metals Na 3s 1 Net magnetic moment 1  B Fe 3d 6 4s 2 4  B atomcrystal 2.2  B Co 3d 7 4s 2 3  B 1.7  B Ni 3d 8 4s 2 2  B 0.6  B

Example 16.1 The saturation magnetization of bcc Fe is 1750 kA m -1. Determine the magnetic moment per Fe atom in the crystal. a=2.87 ÅV = a 3 = x Magnetic moment per atom = 1750 x 1000 x x x 1/2 = 2.068x A m 2 = 2.2  B

Ferromagnetic, ferrimagnetic and antiferromagnetic materials Due to quantum mechanical interaction the magnetic moment of neighbouring atoms are aligned parallel or antiparallel to each other. ferromagneticAnti- ferromagnetic Ferri- magnetic

ferromagnetic Fe, Co, Ni, Gd Element TiCrMnFeCoNi E exchange interaction = E unmagnetized -E magnetized Heusler Alloys: Cu 2 MnSn, Cu 2 MnAl Ferromagnetic alloys made of non-ferromagnetic elements

Thermal energy can randomize the spin FerromagneticParamagnetic T curie heat Fe1043 KCo1400 KNi631 K Gd298 KCu 2 MnAl710 K

Ferrimagnetic materials Ferrites M 2+ : Fe 2+, Zn 2+, Ni 2+, Mg 2+, Co 2+, Ba 2+, Mn 2+, Crystal structure: Inverse spinel See last paragraph (small print) of Section 5.4

Crystal structure: Inverse spinel Ferrites O 2+ FCC packing 4 O 2+ 8 THV 4 OHV Antiferromagnetic coupling Fe 3+ M 2+ Net moment due to M 2+ ions only.

If Fe is ferromagnetic with atomic magnetic moments perfectly aligned due to positive exchange interaction then why do we have Fe which is not a magnet? Answer by Pierre Ernest Weiss (1907) Existence of domains known as Weiss domains

Domain walls are regions of high energy (0.002 Jm -2 ) due to moment misalignment. Then why do the exist? Ans: Fig. 16.3

Randomly aligned domains 1. decrease the manetostatic energy in the field outside the magnet 2. increase the domain wall energy inside the magnet A magnet will attain a domain structure which minimizes the overall energy

16.3 B never saturates M saturates The value of B at the saturation of M is called the saturation induction (~ 1 T)

Two ways for aligning of magnetic domains: 1.Growth of favorably oriented domains (initially) 2.Rotation of domains (finally) Initial permeability Saturation induction

The hysteresis Loop Fig B r residual induction H c coercive field Area = hysteresis loss

Soft magnetic materials High initial permeability Low hysteresis loss Low eddy current losses For application requiring high frequency reversal of direction of magnetization Eg. Tape head Problem 16.11

Easily moving domain walls Low impurity, low non magnetic inclusions, low dislocation density low second phase precipitate Soft magnetic materials For low hysteresis loss (  frequency) For low eddy current loss (  frequency 2 ) Material: high resistivity Design: Lamination Choose: Pure, single phase, well-annealed material of high resistivity

Table 16.1 Material Init. Rel.HysteresisSaturation Resistivity Perm.Loss (Jm -3) Induction (T) (10 -6  m) Com. Fe Fe-4%Si Fe-Si oriented Permalloy (45%Ni) Supermalloy 100, (79%Ni, 5%Mo) Ni-Zn Ferrite Mn-Zn Ferrite

Magnetic anisotropy Fig easy direction hard direction Iron single crystal Polycrystal: attempt to align easy direction in all grains Preferred orientation or texture By rolling and recrystallization By solidification By sintering ferrite powder in magnetic field

Fe-4% Si alloy for low frequency transformers Wt% Si resistivity BsBs T DBTT Si enhances resistivity: low eddy current losses More than 4 wt% Si will make it too brittle

L+  T Stable liquid log t TmTm glass Metallic Glass Fe %(Si, B, C) High solute High resistivity Low eddy current loss AmorphousIsotropicNo hard direction AmorphousNo grain boundary Easy domain wall movement Low eddy current loss

50 HzFe-4wt% Si K HzPermalloy, Supermalloy MHzFerrites

Hard magnetic materials For permanent magnets Motors, headphones High B r, high H c B r H c = energy product Martensitic high carbon steels (B r H c =3.58 kJm 3 ) Alnico alloys: directionally solidified and annealed in a magnetic field (B r H c =5.85 kJm3) Mechanically hard c Magnetically hard Large M phase as elongated particle in low M matrix

Elongated Single Domain (ESD) magnets Long particles, thickness < domain wall thickness Each particle a single domain No domain growth possible only rotation Ferrite: BaO 6 Fe 2 O 3 (Br Hc= kJm 3 ) Co-Rare Earths (Sm, Pr) (Br Hc=200 kJm 3 ) Nd 2 Fe 14 B (Br Hc=400 kJm 3 )

For true understanding comprehension of detail is imperative. Since such detail is well nigh infinite our knowledge is always superficial and imperfect. Duc Franccois de la Rochefoucald ( )