Chapter 12, FERROMAGNETISM, ANTIFERROMAGNETISM. AND FERRIMAGNETISM Video Solutions, The Solid State: An Introduction to the Physics of Crystals for Students of Physics, Materials Science, and Engineering

Problem 1

Magnetic ions with $S=\frac{5}{2}$ and $L=0$ are spaced $0.5 \mathrm{~nm}$ apart. Calculate the magnetic energy of one ion due to the field of its neighbour. At approximately what temperature would the moments be aligned due to this type of interaction?

Kratika Bhadauria

Numerade Educator

01:40

Problem 2

Derive the relationship between the 'internal' field of a ferromagnet and the Curie temperature. Calculate this field for iron which has a Curie temperature of $1043 \mathrm{~K}$ and an effective moment of $2.2 \mathrm{Bohr}$ magnetons per ion.

Kratika Bhadauria

Numerade Educator

02:14

Problem 3

Calculate the width of a domain wall as follows. Across a domain wall the direction of magnetization changes by $180^{\circ}$. If the wall is $N$ atoms thick write down an expression for (a) the exchange energy per unit area of wall and (b) the anisotropy energy assuming that half the wall is magnetized in the hard direction. Minimize the total energy with respect to $N$. If the exchange.constant $J=10^{-21} \mathrm{~J}$, the anisotropy energy $K=4 \times 10^4 \mathrm{~J} \mathrm{~m}^{-3}$ and the atomic spacing is $0.3 \mathrm{~nm}$, calculate the width of the wall and the energy per $\mathrm{m}^2$ of wall for $S=1$.

Satpal Satpal

Numerade Educator

01:50

Problem 4

The ferromagnet europium oxide has a Curie temperature of $70 \mathrm{~K}$. The europium ion has $J=\frac{7}{2}$ and $g=2$. Assuming the internal-field model, determine the ratio of the magnetization at $300 \mathrm{~K}$ in a field of $10^{-2} \mathrm{~T}$ to that at $0 \mathrm{~K}$.

Anand Jangid

Numerade Educator

04:41

Problem 5

The hysteresis curve in Fig. 12.7(b) has a width $H$ of $50 \mathrm{Am}^{-1}$ and an overall length in $B$ of $1 \mathrm{~T}$. Estimate the energy per cycle which is dissipated per cubic metre. If the material is used as a cubic transformer core of side $10 \mathrm{~cm}$, estimate the power dissipation at $50 \mathrm{~Hz}$

Km Neeraj

Numerade Educator

04:16

Problem 6

Show that the susceptibility of an antiferromagnet below the Néel temperature is $\mu_0$, when the field is applied perpendicularly to the axis of alignment This may be done as follows In Fig 129 draw the direction of the internal field produced by $m_{\mathrm{x}}$ (remember that it acts in the direction opposite to $m_{\mathrm{X}}$ ) This field produces a moment on $m_Y$ which acts in opposition to that due to the external field $B$ Calculate the angle for which the net moment is zero For this angle determine the component for $m_Y$ (and $m_X$ ) along $B$ and hence find the susceptibility. Assume that rotations from the axis of antiferromagnetic alignment are small

Amit Srivastava

Numerade Educator