Magnetic Materials Basic Magnetic Quantities Magnetic Induction or

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 0= permeability of free space B = 4 10 -7 T m A-1 = 4 10 -7 H m-1

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

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 B 0 H: magnetic field intensity or field strength Units: A m-1

In free space 16. 1 Inside a solid 16. 3 16. 2 = permeability of solid, H m-1 relative permeability of solid, dimensionless

16. 4 : magnetic susceptibility of the solid Dimensionless Types of magnetic solid diamagnetic (universal) -10 -5 superconductor -1 paramagnetic +10 -3 ferromagnetic +103 -105

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= 9. 273 x 10 -24 A m 2 Net moment of two electrons of opposite spins = 0

Unpaired electrons give rise to paramagnetism in alkali metals Net magnetic moment atom 1 B crystal Fe 3 d 64 s 2 4 B 2. 2 B Co 3 d 74 s 2 3 B 1. 7 B Ni 3 d 84 s 2 2 B 0. 6 B Na 3 s 1

Example 16. 1 The saturation magnetization of bcc Fe is 1750 k. A m-1. Determine the magnetic moment per Fe atom in the crystal. a=2. 87 Å V = a 3 = 2. 873 x 10 -30 Magnetic moment per atom = 1750 x 1000 x 2. 873 x 10 -30 x 1/2 = 2. 068 x 10 -23 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. ferromagnetic Antiferromagnetic Ferrimagnetic

Fe, Co, Ni, Gd ferromagnetic Eexchange interaction= Eunmagnetized-Emagnetized Element Ti Cr Mn Fe Co Ni 1. 12 1. 18 1. 47 1. 63 1. 82 1. 98 1. 5 -2. 0 Heusler Alloys: Cu 2 Mn. Sn, Cu 2 Mn. Al Ferromagnetic alloys made of non-ferromagnetic elements

Thermal energy can randomize the spin Ferromagnetic Tcurie Paramagnetic heat Fe 1043 K Co 1400 K Gd 298 K Cu 2 Mn. Al 710 K Ni 631 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

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

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)

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

The hysteresis Loop Fig. 16. 4 Br residual induction Hc coercive field Area = hysteresis loss

Soft magnetic materials For application requiring high frequency reversal of direction of magnetization Eg. Tape head High initial permeability Low hysteresis loss Problem 16. 11 Low eddy current losses

Soft magnetic materials For low hysteresis loss ( frequency) Easily moving domain walls Low impurity, low non magnetic inclusions, low dislocation density low second phase precipitate 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. Hysteresis Saturation Resistivity Perm. Loss (Jm-3) Induction (T) (10 -6 m) Com. Fe 250 500 2. 2 0. 1 Fe-4%Si 500 100 2. 0 0. 6 Fe-Si oriented 1500 90 2. 0 0. 6 Permalloy 2700 120 1. 6 0. 55 Supermalloy 100, 000 21 0. 8 0. 65 Ni-Zn Ferrite 200 -1000 35 0. 4 1 Mn-Zn Ferrite 40 0. 3 1 (45%Ni) (79%Ni, 5%Mo) 2000

Magnetic anisotropy Fig. 16. 5 Iron single crystal <100> easy direction <111> hard direction 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 Si enhances resistivity: low eddy current losses resistivity More than 4 wt% Si will make it too brittle TDBTT Bs Wt% Si

Metallic Glass Fe + 15 -25%(Si, B, C) T Tm Stable liquid High solute L+ High resistivity glass log t Amorphous Isotropic Low eddy current loss No hard direction No grain boundary Easy domain wall movement Low eddy current loss

50 Hz Fe-4 wt% Si K Hz Permalloy, Supermalloy MHz Ferrites

Hard magnetic materials For permanent magnets Motors, headphones High Br, high Hc Br Hc = energy product Mechanically hard c Magnetically hard Martensitic high carbon steels (Br Hc=3. 58 k. Jm 3) Alnico alloys: directionally solidified annealed in a magnetic field (Br Hc=5. 85 k. Jm 3) 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: Ba. O 6 Fe 2 O 3 (Br Hc=48 -144 k. Jm 3) Co-Rare Earths (Sm, Pr) (Br Hc=200 k. Jm 3) Nd 2 Fe 14 B (Br Hc=400 k. Jm 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 (1613 -1680)