Physics of Magnetism

12 CHAPTER 3. PARAMAGNETISM OF FREE IONS M finding an atom in a state with energy is given by The magnetization of the system ca ...

SECTION 3.2. THE CURIE LAW 13 Substitution of this result into Eq. (3.1.5) leads to Since sinh one obtains After carrying out th ...

14 CHAPTER 3. PARAMAGNETISM OF FREE IONS in Chapter 8). For one has J = 9/2 and g = 8/11 (see Table 2.2.1). Furthermore, we make ...

SECTION 3.2. THE CURIE LAW 15 The magnetic susceptibility is defined as Using Eq. (3.2.2), we derive for the magnetic susceptibi ...

16 CHAPTER 3. PARAMAGNETISM OF FREE IONS The magnetic splitting of the ground-state multiplet level (J = L – S = 5 –5/2 = 5/2) a ...

SECTION 3.2. THE CURIE LAW 17 sublevels are no longer equally spaced, or to a splitting where the level with m = – J is not the ...

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4 The Magnetically Ordered State 4.1. THE HEISENBERG EXCHANGE INTERACTION AND THE WEISS FIELD It follows from the results descri ...

20 CHAPTER 4. THE MAGNETICALLY ORDERED STATE In most cases, it is sufficient to consider only the exchange interaction between s ...

SECTION 4.1. THE HEISENBERG EXCHANGE INTERACTION AND THE WEISS FIELD 21 ferromagnetic 3d elements like Ni, Co, and Fe (parallel ...

22 CHAPTER 4. THE MAGNETICALLY ORDERED STATE This does not lend credence to the notion that short Fe–Fe distances favor antiferr ...

SECTION 4.2. FERROMAGNETISM 23 all the steps from Eq. (3.1.4) to Eq. (3.2.2). This means that Eq. (3.2.2) should actually be wri ...

24 CHAPTER 4. THE MAGNETICALLY ORDERED STATE Combining this expression with Eq. (4.2.7) leads to Upon substitution of (Eq. 4.2.5 ...

SECTION 4.2. FERROMAGNETISM 25 exclusively on the form of the Brillouin function It is independent of parameters that vary from ...

26 CHAPTER 4. THE MAGNETICALLY ORDERED STATE 4.3. ANTIFERROMAGNETISM A simple antiferromagnet can be visualized as consisting of ...

SECTION 4.3. ANTIFERROMAGNETISM 27 The temperature dependence of each of the two sublattice moments can be obtained by means of ...

28 CHAPTER 4. THE MAGNETICALLY ORDERED STATE It follows from Eq. (4.3.12) that the susceptibility of an antiferromagnetic materi ...

SECTION 4.3. ANTIFERROMAGNETISM 29 where Since the field is applied parallel to the A sublattice and antiparallel to the B subl ...

30 CHAPTER 4. THE MAGNETICALLY ORDERED STATE We will now consider the susceptibility of an antiferromagnetic single crystal with ...

SECTION 4.3. ANTIFERROMAGNETISM 31 and hence the susceptibility by In a polycrystalline sample, one has crystallites with all or ...