Book contents
- Frontmatter
- Contents
- Preface
- 1 Tensor properties of crystals: equilibrium properties
- 2 Tensor properties of crystals: transport properties
- 3 Review of group theory
- 4 Linear relations treated group theoretically
- 5 The magnetic point groups and time reversal
- 6 Matter tensors of rank 0, 1 and 2
- 7 Matter tensors of rank 3
- 8 Special magnetic properties
- 9 Matter tensors of ranks 4 and 5
- 10 Matter tensors of rank 6
- Appendices
- A Review of tensors
- B Stress, strain and elasticity
- C Finite deformation
- D The great orthogonality theorem
- E The Symmetry-Coordinate Transformation tables for the 32 point groups and two infinite groups
- F Proof of the Fundamental Theorem
- G Theorems concerning magnetic groups
- References
- Index
8 - Special magnetic properties
Published online by Cambridge University Press: 18 December 2009
- Frontmatter
- Contents
- Preface
- 1 Tensor properties of crystals: equilibrium properties
- 2 Tensor properties of crystals: transport properties
- 3 Review of group theory
- 4 Linear relations treated group theoretically
- 5 The magnetic point groups and time reversal
- 6 Matter tensors of rank 0, 1 and 2
- 7 Matter tensors of rank 3
- 8 Special magnetic properties
- 9 Matter tensors of ranks 4 and 5
- 10 Matter tensors of rank 6
- Appendices
- A Review of tensors
- B Stress, strain and elasticity
- C Finite deformation
- D The great orthogonality theorem
- E The Symmetry-Coordinate Transformation tables for the 32 point groups and two infinite groups
- F Proof of the Fundamental Theorem
- G Theorems concerning magnetic groups
- References
- Index
Summary
In Chapter 5, it was shown that time reversal or magnetic symmetry becomes important only when we deal with ‘special magnetic properties’, defined by the following two criteria:
The matter tensor K is a c-tensor, due to the fact that eitherXorY is a c-tensor, and
the property in question is not a transport property (involving an increase in entropy).
Such properties are given an asterisk in Table 1–1. In dealing with these properties we must take cognizance of the magnetic symmetry of the crystals in which they are observed, that is, of the 90 magnetic classes, as distinct from the 32 conventional crystal classes which sufficed for the study of all other properties.
Since the principal special magnetic properties of interest do not involve tensors of rank higher than 3 (see Table 1–1), and such ranks have already been covered for the conventional properties in Chapters 6 and 7, a diversion to special magnetic properties at this point seems appropriate. We then resume the main thrust of the book with Chapter 9, that is, continuing to consider higher tensor ranks.
As shown in Chapter 5, if K represents a special magnetic property, it must be identically zero for non-magnetic (i.e. diamagnetic or paramagnetic) crystals, as well as for antiferromagnetic crystals belonging to type-II groups. Therefore, the special magnetic properties which we consider in this chapter only exist for crystals that possess magnetic symmetry, namely, those of types I and III (see Section 5–1).
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- Crystal Properties via Group Theory , pp. 132 - 144Publisher: Cambridge University PressPrint publication year: 1995