1. Lecture 19 Magnetism and Matter Learning Objective: to examine some aspects of magnetic properties of materials Transformers Motors Generators (for examples) - nearly always have iron cores Permanent Magnets Magnetic Recording Tapes Computer Disks (for examples) - all depend directly on the magnetic properties of materials

2. v L Angular Momentum L = m e vr Orbital Motion

3. Magnetism and Spin AtomMagnetic Dipole Moment (/10 -24 A m 2 ) H9.27 He0 Li9.27 O13.9 Ne0 Na9.27

4. Paramagnetism Atoms of a paramagnetic material have permanent magnetic dipole moments. In an external field B 0, the dipoles tend to align with B 0 - Results in an additional magnetic field B m. Material with N atoms,  maximum =  N. Randomization of the dipoles orientations by thermal collisions significantly reduces the total dipole moment (  total ) These dipoles are randomly oriented - Magnetic fields average to zero. Compare with 2B2B Example: T = 300 K, B = 1.5 T,  =  B

5. The increase of the strength of the B-field by the paramagnetic material is described by the relative permeability constant  m. Ampere’s law in materials becomes: I free refers to the external currents Magnetic moment per unit volume (magnetisation) M: magnetic susceptibility Material (STP)  m Air1.000304 Oxygen1.00133 Liquid Oxygen (-190 o C)1.00327 Nickel Monoxide1.000675

6. Potassium chronium sulphate - a paramagnetic salt Pierre Curie discovered experimentally that the magnetization M of a paramagnetic specimen obeyed: M cannot increase without limit, as Curies’s law implies, but must approach a value

7. rCrC Diamagnetism No intrinsic magnetic dipoles Dipole moments induced by an external magnetic field Induced B-field opposes the external field (Lenz’s law) B < B 0 No intrinsic magnetic dipoles {Compare with a paramagnetic material B > B 0 } Permeabilities of Some Diamagnetic Materials Material (STP)  m Bismuth 1 – 1.9  10 -5 Beryllium 1 – 1.3  10 -5 Methane 1 – 3.1  10 -5 Glass 1 – 1.5  10 -5

8. Ferromagnetism Materials with atoms having unpaired electron spins (iron, cobalt, nickel, gadolinium, and dysprosium). Electron spins become coupled  10 10 atoms combine to form a domain (l  10 -7 m)  large electromagnetic moment. When the domains are randomly arranged, the specimen as a whole is unmagnetised. Domains which are magnetized in the direction of an external magnetic field grow at the expense of those which are not aligned to the magnetic field. B ext  m becomes very large  10 3 – 10 5

9. Magnetization Curve for a Ferromagnetic Material All magnetic moments in the material are aligned parallel to the external field

10. Ferromagnetism: Magnetization Curves and Hysteresis Loops Magnetization is different when the external magnetic field is increasing from when it is decreasing - hysteresis loop Explanation - reorientations of domain directions are not totally reversible Uses - magnetic storage of information Part of Curve Operation a to b increase of B 0, using an unmagnetized ferromagnetic field b to c B 0 reduced to zero c to d B 0 is reversed in direction, and its magnitude increased to a maximum d to e B 0 is again reduced to zero e to f B 0 is again increased to its forward maximum

11. Materials may be broadly grouped as diamagnetic, paramagnetic, or ferromagnetic. Review and Summary Paramagnetic materials are (weakly) attracted by a magnetic field, have intrinsic magnetic dipole moments that tend to line up with an external magnetic field, thus enhancing (slightly) the field. This tendency is interfered with by thermal agitation. Diamagnetic materials are (weakly) repelled by the pole of a strong magnet. The atoms of such materials do not have intrinsic magnetic dipole moments. A dipole moment may be induced, however, by an external magnetic field, its direction being opposite that of the field. Ferromagnetic materials result from a quantum interaction between neighbouring atoms locking the atomic dipoles in rigid parallelism in spite of the disordering tendency of thermal agitation. Due to strong alignment of the spin magnetic moments of the electrons (quantum mechanical effects). Hysteresis: ferromagnetic magnetization curves do not retrace themselves but instead exhibit a phenomenon called hysteresis. Some alignment of dipoles remains even when the external magnetic field is completely removed; the result is the familiar “permanent” magnet.

12. Review and Summary