Magnetic Properties

Magnetic field

ØMagnetic field is a force which is generated due to energy change in a volume of space.

ØA magnetic field is produced by an electrical charge in motion e.g. current flowing in a conductor, orbital movement and spin of electrons.

ØThe magnetic field can be described by imaginary lines as shown in the figure below for a magnet and a current loop.

Magnetic field Strength

ØIf a magnetic field, H, is generated by a cylindrical coil

(solenoid) of n turns and length l,  H = nI/l (A/m)

ØMagnetic flux density, B: It is the magnitude of the field strength within a substance subjected to a field H B = H (Tesla or Weber/m²)

Ø, called the permeability, is the measure of the degree to which a material can be magnetized.

ØIn vacuum B = _oH. _o is the permeability of vacuum and is a universal constant. _o = 4 x 10^-7(H/m). _r = /_o is the relative permeability.   

Magnetic moments

Ø Being a moving charge, electrons produce a small magnetic field having a magnetic moment along the axis of rotation.           

ØThe spin of electrons also produces a magnetic moment along the spin axis.

ØMagnetism in a material arises due to alignment of magnetic moments.

Magnetic Dipole and Monopole

ØAnalogous to electric dipole, a magnetic dipole can be defined as two monopoles of opposite and equal strength separated by a certain distance.

ØA magnetic monopole, however, is not observed in nature.

ØIf there are N monopoles each located at a point given by a vector ā, then the magnetic dipole moment can be defined as a vector, ū   N u mai _i

i1

ØTwo monopoles of strength +m and –m separated by distance l, will give a dipole ū = mā₁ – mā₂ = m(ā₁ – ā₂) = mĪ

ØA bar magnet can be thought of consisting of two opposite and equal poles at its two ends.

Magnetization

Ø With the application of a magnetic field magnetic moments in a material tend to align and thus increase the magnitude of the field strength.                              

ØThis increase is given by the parameter called magnetization, M, such that B = _oH  + _oM.

M = _mH.

_m is called magnetic susceptibility.

_m = _r – 1

Magnetism

Ø Depending on the existence and alignment of magnetic moments with or without application of magnetic field, three types of magnetism can be defined.

Diamagnetism

Ø Diamagnetism is a weak form of magnetism which arises only when an external field is applied.

ØIt arises due to change in the orbital motion of electrons on application of a magnetic field.

ØThere is no magnetic dipoles in the absence of a magnetic field and when a magnetic field is applied the dipole moments are aligned opposite to field direction.

ØThe magnetic susceptibility, _m (_r – 1) is negative i.e. B in a diamagnetic material is less than that of vacuum.

                                   H =0                          ^H

Diamagnetic materials:

Al₂O₃, Cu, Au, Si, Zn

Paramagnetism

Ø In a paramagnetic material the cancellation of magnetic moments between electron pairs is incomplete and hence magnetic moments exist without any external magnetic field.

ØHowever, the magnetic moments are randomly aligned and hence no net magnetization without any external field.

ØWhen a magnetic field is applied all the dipole moments are aligned in the direction of the field.

ØThe magnetic susceptibility is small but positive. i.e. B in a paramagnetic material is slightly greater than that of vacuum.

Paramagnetic materials: Al, Cr, Mo, Ti, Zr

Ferromagnetism

Ø Certain materials posses permanent magnetic moments in the absence of an external magnetic field. This is known as ferromagnetism.

ØPermanent magnetic moments in ferromagnetic materials arise due to uncancelled electron spins by virtue of their electron structure.

ØThe coupling interactions of electron spins of adjacent atoms cause alignment of moments with one another.

ØThe origin of this coupling is attributed to the electron structure. Ferromagnetic materials like Fe (26 – [Ar] 4s²3d⁶) have incompletely filled d orbitals and hence unpaired electron spins.

Antiferromagnetism

Ø If the coupling of electron spins results in anti parallel alignment then spins will cancel each other and no net magnetic moment will arise.

ØThis is known as antiferromagnetism. MnO is one such example.

ØIn MnO, O^2- ions have no net magnetic moments and the spin moments of Mn²⁺ ions are aligned anti parallel to each other in adjacent atoms.

 O2 Mn2+

Ferrimagnetism

Ø Certain ionic solids having a general formula MFe₂O₄, where

M is any metal, show permanent magnetism, termed ferrimagnetism, due to partial  cancellation of spin moments.

ØIn Fe₃O₄, Fe ions can exist in both 2+ and 3+ states as    Fe²⁺O^2– (Fe³⁺⁾₂(O^2-)₃ in 1:2 ratio. The antiparallel coupling between Fe³⁺ (Half in A sites and half in B) moments cancels each other. Fe²⁺ moments are aligned in same direction and result in a net magnetic moment. 

Octahedral Tetrahedral Fe3+ Fe2+

Domains

ØFerromagnetic materials exhibit small-volume regions in which magnetic moments are aligned in the same directions. These regions are called domains.

ØAdjacent domains are separated by domain boundaries. The direction of magnetization changes across the boundaries.

ØThe magnitude of magnetization in the material is vector sum of magnetization of all the domains.

Magnetization and Saturation

ØWhen a magnetic field is applied to a ferromagnetic material, domains tend to align in the direction of the field by domain boundary movement and hence, the flux density or magnetization increases.

ØAs the field strength increases domains which are favorably oriented to field direction grow at the expense of the unfavorably oriented ones. All the domains are aligned to the field direction at high field strengths and the material reaches the saturation magnetization, M_s.

The initial slope of the B-H curve at H =0 is called initial permeability, _i, which is a material property.

Hysteresis

ØIf the field is reduced from saturation by magnetic reversal, a hysteresis develops.

ØAs the field is reversed the favorably oriented domains tend to align in the new direction. When H reaches zero some of the domains still remain aligned in the previous direction giving rise to a residual magnetization called remanence, M_r.

H_c, the reverse filed strength at which magnetization is zero, is called Coercivity

Hard and Soft magnets

ØBased on their hysteresis characteristics ferro and ferrimagnetic materials can be classified as hard and soft magnets.

Ø Soft magnets have a narrow hysteresis curve and high initial permeability and hence easy to magnetize and demagnetize. It is just opposite for the Hard magnets.

Hard and Soft magnets

ØThe magnetic hardness is expresses by a term called energy product which is the area of the largest rectangle that can be drawn in the second quadrant (red-hatched).

ØConventional hard magnetic materials like steel, Cunife(CuNi-Fe) alloys, Alnico (Al-Ni-Co) alloy have BH_max values in the range of 2 – 80 kJ/m³. High-energy hard magnetic materials like Nd₂Fe₁₄B, SmCo₅ exhibit BH_max  80 kJ/m³. ØHard magnets are used in all permanent magnets in applications such as power drills, motors, speakers.

ØSoft magnets like Fe, Fe-Si are useful when rapid magnetization and demagnetization is required as in transformer cores.

ØImpurity and other defects should be low for this purpose as they may hinder the domain wall movement through which domains align.

Magnetic anisotropy

ØThe magnetic properties of a crystalline material are not isotropic i.e. properties are not the same in all crystallographic direction.

ØThere always happens to be a preferred direction in which magnetization is easier. For example, [0001] direction is the preferred magnetization direction in Co. For Fe it is [100] as shown in the diagrams below.

Effect of Temperature

ØThe atomic vibration increases with increasing temperature and this leads to misalignment of magnetic moments. Above a certain temperature all the moments are misaligned and the magnetism is lost. This temperature is known as Curie temperature, Tc.

ØFerro and ferrimagnetic materials turn paramagnetic above curie point. For Fe Tc = 768 C, Co – 1120 C, Ni – 335 C.

                      Below T_c                       Above T_c                                      Temperature                  _Tc

Superconductivity

ØSuperconductivity is disappearance of electrical resistance below a certain temperature.

ØThe temperature below which superconductivity is attained is known as the critical temperature, T_C.

ØThe superconducting behavior is represented in a graphical form in the figure below.

Bardeen-Cooper-Schreiffer (BCS) Theory

Ø  John Bardeen, Leon Cooper and John Schreiffer – BCS theory, Noble prize for Physics in 1972 .

ØThe temperature dependence of metals arises out of scattering of electrons due to atomic vibrations which increase with temperature. 

ØCooper pair – Below T_C two electrons can pair through the lattice phonon which causes a slight increase in the positive charge around an electron and since thermal energy to scatter is low, this pair can move through the lattice.

Motion of Cooper pair through the lattice

BCS Theory contd..

Ø  Thus the charge carrier in a superconductor is a pair of electrons instead of a single electron.

ØBCS theory applies well to conventional superconductors like Al (T_C = 1.18 K), Nb₃Ge (T_C = 23 K).

ØHigh temp. superconductors – Recently a number of ceramic superconductors such as YBa₂Cu₃O₇ have been discovered whose T_C is much higher.

Superconductivity and Magnetism

The Meissner effect                            

ØA material in its superconducting state will expell all of an applied magnetic field (Fig. b). This is Meisnner effect.

ØA magnet placed over a superconductor will thus float, a phenomenon known as magnetic levitation.

                              (a)      T>T_C                                             (b)     T<T_C

Messner effect. (a) Above T_C , normal conducting state, magnetic flux penetrates. (b) below T_C, superconducting, the magnetic field is expelled.

Types of Superconductors

ØIf the field is increased, some of the superconducting materials come back to normal conducting state above a critical magnetic field H_C (Fig. c) – These are Type I superconductors. Ex. Al , Pb

ØIn another class of materials the field begins to intrude above a critical value of the applied field (H_C1) and at a higher field (H_C2) it turns into a normal conductor (Fig. d). The transition is gradual here unlike Type I. These are called Type II superconductors.

Ex. Nb₃Sn, YBa₂Cu₃O₇

Applications

Superconductors are used in

qMaglev trains which can reach very high velocity

qMRI scan machines (Medical science, Brain imaging)

qHigh efficiency electric generators

qEnergy storage

qSuperconducting Quantum Interference Device (SQUID)

qThe Large Hadron Collider (LHC) for generating high velocity particles travelling at speed of light

Key Words

Magnetism; Magnetic properties; Diamagnetism;

Paramagnetism; Ferromagnetism; Ferrimagnetism; Antiferromagnetism; Hysteresis; Soft and Hard magnets; Curie point; Superconductivity; BCS theory; Meissner effect.

References

http://www.ndted.org/EducationResources/HighSchool/Magneti sm/magnetismintro.htm

http://www.ee.ucla.edu/~jjudy/classes/magnetics/

http://media.wiley.com/product_data/excerpt/22/07803103/0780

310322.pdf

http://phy.ntnu.edu.tw/~changmc/Teach/SS/SS_note/chap11.pdf http://teachers.web.cern.ch/teachers/archiv/HST2001/accelerat ors/superconductivity/superconductivity.htm http://katzgraber.org/teaching/SS07/files/burgener.pdf http://chabanoiscedric.tripod.com/NSCHSS.PDF

Quiz

1.   What is a magnetic field?

2.   What is the source of a magnetic field?

3.   What is magnetic flux?

4.   What is permeability?

5.   What is relative permeability?

6.   What is the origin of magnetic moments in materials?

7.   What are the different kinds of magnetism?

8.   How is electron configuration related to magnetism?9. What is ferrimagnetism? How is it different from ferromagnetism?

10.    Explain the origin of ferrimagnetism taking the example of

Fe3O4

11.    What is antiferromagnetism?

12.    What is a magnetic domain?

13.    What is magnetic susceptibility?

Quiz

14.   Why do ferromagnets reach saturation on application of a magnetic field of sufficient strength?

15.   Why does a residual magnetism remains even at H = 0 during magnetic reversal in ferromagnets?

16.   What is Coercevity?

17.   What is meant by hard and soft magnets?

18.   Which parameter decides the magnetic hardness?

19.   Give examples of soft and hard magnets.

20.   What is initial permeability? How is it related to magnetization?

21.   Why should soft magnets for transformer core application be free of defects and impurities?

22.   Why the magnetism is lost when ferromagnets are heated above a certain temperature?

23.   What is magnetic anisotropy? What are hard and soft axis of magnetization?

Quiz

24.   What is superconductivity?

25.   What is BCS theory of superconductivity?

26.   What is High-temperature superconductor?

27.   What is Meissner effect?

28.   What is Type I and Type II superconductors?