magnetism in condensed matter

[...]... axis inclined to the vertical The weight of the top, acting downwards, exerts a (horizontal) torque on the top If it were not spinning it would just fall over But because it is spinning, it has angular momentum parallel to its spinning axis, and the torque causes the axis of the spinning top to move parallel to the torque, in a horizontal plane The spinning top precesses Example 1.1 Consider the case in. .. can be related by When xintrinsic oc, but xexperimental -> 1/N See Section 6.7 for more on magnetic domains One last word of warning at this stage: a ferromagnetic... electron in a magnetic field of flux density 0.3 T? What is the difference in energy of the electron if its spin points parallel or antiparallel to the magnetic field? Convert this energy into a frequency (1.2) Using the definition of spin operators in eqn 1.43, prove eqn 1.53 and the commutation relations, eqns 1.54 and 1.55 (1.3) Using the definition of the raising and lowering operators in eqns 1.57,... spin pointing parallel or antiparallel to the z axis respectively (The 'bra and ket' notation, i.e writing states in the form \t/r) is reviewed in Appendix C.) Hence The eigenstates corresponding to the spin pointing parallel or antiparallel to the x- and y-axes are This two-component representation of the spin wave functions is known as a spinor representation and the states are referred to as spinors... useful geometric construction that can aid thinking about spin is shown in Fig 1.8 The spin vector S poinls in three-dimensional space Because the quantum states are normalized, S lies on the unit sphere Draw a line from the end of the vector S to the south pole of the sphere and observe the point, q, at which this line intersects the horizontal plane (shown shaded in Fig 1.8) Treat this horizontal plane... Contents 3.2.2 3.2.3 3.2.4 Electron spin resonance Mossbauer spectroscopy Muon-spin rotation 4 Interactions 4.1 4.2 Magnetic dipolar interaction Exchange interaction 4.2.1 Origin of exchange 4.2.2 Direct exchange 4.2.3 Indirect exchange in ionic solids: superexchange 4.2.4 Indirect exchange in metals 4.2.5 Double exchange 4.2.6 Anisotropic exchange interaction 4.2.7 Continuum approximation 5 Order and magnetic... throughout this book, these quantities are measured in units of h The way in which the spin and orbital parts of the angular momentum combine will be considered in detail in the following sections In this section we will just assume that each atom has a magnetic moment of magnitude u Although an increase of magnetic field will tend to line up the spins, an increase of temperature will randomize them We... operator: so that Combining two spin-1\2 particles results in a joint entity with spin quantum number s = 0 or 1 The eigenvalue of (Stot)2 is s(s + 1) which is therefore The type of interaction in eqn 1.67 will turn out to be very important in this book The hyperfine interaction (see Chapter 2) and the Heisenberg exchange interaction (see Chapter 4) both take this form 14 Introduction either 0 or 2 for... are linear combinations of these basis states and are listed in Table 1.1 The calculation of these eigenstates is treated in Exercise 1.9 Notice that ms is equal to the sum of the z components of the individual spins Also, because the eigenstates are a mixture of states in the original basis, it is not possible in general to know both the z components of the original spins and the total spin of the resultant... matrices the raising and lowering operators are The raising and lowering operators get their name from their effect on spin states You can show directly that and using eqns 1.43, 1.63, 1.64 and 1.65 this then yields in agreement with eqn 1.53 1.3.4 So a raising operator will raise the z component of the spin angular momentum by A a lowering operator will lower the z component of the spin angular momentum . MASTER SERIES IN CONDENSED MATTER PHYSICS OXFORD MASTER SERIES IN CONDENSED MATTER PHYSICS The Oxford Master Series in Condensed Matter Physics is designed for final year undergraduate . properties of solids S. J. Blundell: Magnetism in condensed matter J. F. Annett: Superconductivity R. A. L. Jones: Soft condensed matter Magnetism in Condensed Matter STEPHEN BLUNDELL Department . in Publication Data Blundell, Stephen. Magnetism in condensed matter / Stephen Blundell. (Oxford master series in condensed matter physics) Includes bibliographical references and index. 1.