1. Magnetic Properties

2. Magnetic fieldMagnetic field is a force which is generated due to energychange in a volume of space.A magnetic field is produced by an electrical charge inmotion e.g. current flowing in a conductor, orbital movementand spin of electrons.The magnetic field can be described by imaginary lines asshown in the figure below for a magnet and a current loop.CurrentMagnetic lines of force 3. Magnetic field StrengthIf a magnetic field, H, is generated by a cylindrical coil(solenoid) of n turns and length l, H = nI/l (A/m)Magnetic flux density, B: It is the magnitude of the fieldstrength within a substance subjected to a field HB = H (Tesla or Weber/m2), called the permeability, is the measure of the degree towhich a material can be magnetized.In vacuum B = oH. o is the permeability of vacuum and is auniversal constant. o = 4 x 10-7(H/m). r = /o is the relativepermeability. 4. Magnetic moments Being a moving charge, electrons produce a small magneticfield having a magnetic moment along the axis of rotation.The spin of electrons also produces a magnetic momentalong the spin axis.Magnetism in a material arises due to alignment of magneticmoments. 5. Magnetic Dipole and MonopoleAnalogous to electric dipole, a magnetic dipole can bedefined as two monopoles of opposite and equal strengthseparated by a certain distance.A magnetic monopole, however, is not observed in nature.If there are N monopoles each located at a point given by avector , then the magnetic dipole moment can be defined asa vector, Two monopoles of strength +m and m separated bydistance l, will give a dipole = m1 m2 = m(1 2) = mA bar magnet can be thought of consisting of two oppositeand equal poles at its two ends.iNiiamu 1 6. Magnetization With the application of a magnetic field magnetic momentsin a material tend to align and thus increase the magnitude ofthe field strength.This increase is given by the parameter called magnetization,M, such that B = oH + oM.M = mH.m is called magnetic susceptibility.m = r 1 7. Magnetism Depending on the existence and alignment of magneticmoments with or without application of magnetic field, threetypes of magnetism can be defined.MagnetismParamagnetismDiamagnetism Ferromagnetism 8. Diamagnetism Diamagnetism is a weak form of magnetism which arisesonly when an external field is applied.It arises due to change in the orbital motion of electrons onapplication of a magnetic field.There is no magnetic dipoles in the absence of a magneticfield and when a magnetic field is applied the dipole momentsare aligned opposite to field direction.The magnetic susceptibility, m (r 1) is negative i.e. B in adiamagnetic material is less than that of vacuum.HH =0Diamagnetic materials:Al2O3, Cu, Au, Si, Zn 9. Paramagnetism In a paramagnetic material the cancellation of magneticmoments between electron pairs is incomplete and hencemagnetic moments exist without any external magnetic field.However, the magnetic moments are randomly aligned andhence no net magnetization without any external field.When a magnetic field is applied all the dipole moments arealigned in the direction of the field.The magnetic susceptibility is small but positive. i.e. B in aparamagnetic material is slightly greater than that of vacuum.HParamagnetic materials:Al, Cr, Mo, Ti, ZrH = 0 10. Ferromagnetism Certain materials posses permanent magnetic moments inthe absence of an external magnetic field. This is known asferromagnetism.Permanent magnetic moments in ferromagnetic materialsarise due to uncancelled electron spins by virtue of theirelectron structure.The coupling interactions of electron spins of adjacent atomscause alignment of moments with one another.The origin of this coupling is attributed to the electronstructure. Ferromagnetic materials like Fe (26 [Ar] 4s23d6)have incompletely filled d orbitals and hence unpaired electronspins. 11. Antiferromagnetism If the coupling of electron spins results in anti parallelalignment then spins will cancel each other and no netmagnetic moment will arise.This is known as antiferromagnetism. MnO is one suchexample.In MnO, O2- ions have no net magnetic moments and thespin moments of Mn2+ ions are aligned anti parallel to eachother in adjacent atoms.O2-Mn2+ 12. Ferrimagnetism Certain ionic solids having a general formula MFe2O4, whereM is any metal, show permanent magnetism, termedferrimagnetism, due to partial cancellation of spin moments.In Fe3O4, Fe ions can exist in both 2+ and 3+ states asFe2+O2 (Fe3+)2(O2-)3 in 1:2 ratio. The antiparallel couplingbetween Fe3+ (Half in A sites and half in B) moments cancelseach other. Fe2+ moments are aligned in same direction andresult in a net magnetic moment.Octahedral TetrahedralFe3+Fe2+ 13. DomainsFerromagnetic materials exhibit small-volume regions inwhich magnetic moments are aligned in the same directions.These regions are called domains.Adjacent domains are separated by domain boundaries. Thedirection of magnetization changes across the boundaries.The magnitude of magnetization in the material is vector sumof magnetization of all the domains.DomainsDomainwall 14. Magnetization and SaturationWhen a magnetic field is applied to a ferromagnetic material,domains tend to align in the direction of the field by domainboundary movement and hence, the flux density or magnetizationincreases.As the field strength increases domains which are favorablyoriented to field direction grow at the expense of the unfavorablyoriented ones. All the domains are aligned to the field direction athigh field strengths and the material reaches the saturationmagnetization, Ms.The initial slope of the B-Hcurve at H =0 is called initialpermeability, i, which is amaterial property. 15. HysteresisIf the field is reduced from saturation by magnetic reversal, ahysteresis develops.As the field is reversed the favorably oriented domains tend toalign in the new direction. When H reaches zero some of thedomains still remain aligned in the previous direction giving riseto a residual magnetization called remanence, Mr.Hc, the reverse filed strength atwhich magnetization is zero, iscalled Coercivity 16. Hard and Soft magnetsBased on their hysteresis characteristics ferro andferrimagnetic materials can be classified as hard and softmagnets. Soft magnets have a narrow hysteresis curve and high initialpermeability and hence easy to magnetize and demagnetize. Itis just opposite for the Hard magnets. 17. Hard and Soft magnetsThe magnetic hardness is expresses by a term called energyproduct which is the area of the largest rectangle that can bedrawn in the second quadrant (red-hatched).Conventional hard magnetic materials like steel, Cunife(Cu-Ni-Fe) alloys, Alnico (Al-Ni-Co) alloy have BHmax values in therange of 2 80 kJ/m3. High-energy hard magnetic materialslike Nd2Fe14B, SmCo5 exhibit BHmax 80 kJ/m3.Hard magnets are used in all permanent magnets inapplications such as power drills, motors, speakers.Soft magnets like Fe, Fe-Si are useful when rapidmagnetization and demagnetization is required as intransformer cores.Impurity and other defects should be low for this purpose asthey may hinder the domain wall movement through whichdomains align. 18. Magnetic anisotropyThe magnetic properties of a crystalline material are notisotropic i.e. properties are not the same in all crystallographicdirection.There always happens to be a preferred direction in whichmagnetization is easier. For example, [0001] direction is thepreferred magnetization direction in Co. For Fe it is [100] asshown in the diagrams below. 19. Effect of TemperatureThe atomic vibration increases with increasing temperatureand this leads to misalignment of magnetic moments. Above acertain temperature all the moments are misaligned and themagnetism is lost. This temperature is known as Curietemperature, Tc.Ferro and ferrimagnetic materials turn paramagnetic abovecurie point. For Fe Tc = 768 C, Co 1120 C, Ni 335 C.TcMoSaturationmagnetizationTemperature0Below Tc Above Tc 20. SuperconductivitySuperconductivity is disappearance of electrical resistancebelow a certain temperature.The temperature below which superconductivity is attained isknown as the critical temperature, TC.The superconducting behavior is represented in a graphicalform in the figure below. 21. Bardeen-Cooper-Schreiffer (BCS) Theory John Bardeen, Leon Cooper and John Schreiffer BCStheory, Noble prize for Physics in 1972 .The temperature dependence of metals arises out ofscattering of electrons due to atomic vibrations which increasewith temperature.Cooper pair Below TC two electrons can pair through thelattice phonon which causes a slight increase in the positivecharge around an electron and since thermal energy to scatteris low, this pair can move through the lattice.Motion of Cooper pairthrough the lattice 22. BCS Theory contd.. Thus the charge carrier in a superconductor is a pair ofelectrons instead of a single electron.BCS theory applies well to conventional superconductors likeAl (TC = 1.18 K), Nb3Ge (TC = 23 K).High temp. superconductors Recently a number of ceramicsuperconductors such as YBa2Cu3O7 have been discoveredwhose TC is much higher.Material TC (K)Aluminum 1.18Nb-Ti alloy 10.2Nb3Al 18.9Nb3Ge 23.0YBa2Cu3O7 92Tl2Ba2Ca2Cu3O10 125 23. Superconductivity and MagnetismA material in its superconducting state will expell all of anapplied magnetic field (Fig. b). This is Meisnner effect.A magnet placed over a superconductor will thus float, aphenomenon known as magnetic levitation.The Meissner effect(a) (b)Messner effect. (a) Above TC , normal conducting state, magnetic fluxpenetrates. (b) below TC, superconducting, the magnetic field isexpelled.T>TC T