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Chapter 20: Problem 15

Briefly explain why the magnitude of the saturation magnetization decreases with increasing temperature for ferromagnetic materials, and why ferromagnetic behavior ceases above the Curie temperature.

Short Answer

Expert verified
In ferromagnetic materials, the magnetic moments of atoms are aligned within small regions called magnetic domains. As the temperature increases, the thermal energy causes fluctuations in the alignment of magnetic moments, leading to weaker exchange interactions within the domains. Consequently, the saturation magnetization, or maximum magnetization under an external field, decreases with increasing temperature. At the Curie temperature, the exchange interactions become too weak to maintain magnetic order, causing the material to exhibit paramagnetic behavior and lose its ferromagnetic characteristics.

Step by step solution

01

Understanding magnetic domains in ferromagnetic materials

Ferromagnetic materials consist of small regions called magnetic domains. Within each domain, the magnetic moments of the atoms are aligned in the same direction due to strong exchange interactions. In the absence of an external magnetic field, the material exhibits no net magnetization, as the magnetic moments of different domains are randomly oriented and cancel each other out.
02

Temperature dependence of magnetic domains

As the temperature of a ferromagnetic material increases, the thermal energy of the atoms also increases. This added thermal energy causes fluctuations in the alignment of the magnetic moments within the domains, leading to a weaker exchange interaction between neighboring atoms. As a result, the magnetic moment alignment within each domain becomes less parallel.
03

Saturation magnetization and temperature

Saturation magnetization is the maximum magnetization that a material can achieve when fully aligned by an external magnetic field. It is determined by the degree of alignment within the magnetic domains. As the temperature increases, the disorder in the alignment also increases, thus reducing the material's ability to achieve full alignment under an external field. This results in a decrease in the magnitude of saturation magnetization with increasing temperature.
04

The Curie temperature

The Curie temperature is the temperature at which the exchange interactions in a ferromagnetic material become too weak to maintain any magnetic order, and the material becomes paramagnetic. Paramagnetic materials have no net magnetization in the absence of an external magnetic field; their magnetic moments are randomly oriented and do not interact with each other to form domains.
05

Ferromagnetic behavior ceasing above the Curie temperature

Above the Curie temperature, the ferromagnetic material loses its characteristic magnetic order and exhibits paramagnetic behavior. This is because the thermal energy becomes too high for the exchange interactions to maintain the alignment of magnetic moments within the domains, and the material loses its ability to exhibit net magnetization without an external magnetic field. Thus, the ferromagnetic behavior ceases above the Curie temperature.

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Most popular questions from this chapter

A coil of wire \(0.20 \mathrm{~m}\) long and having 200 turns carries a current of \(10 \mathrm{~A}\). (a) What is the magnitude of the magnetic field strength \(H\) ? (b) Compute the flux density \(B\) if the coil is in a vacuum. (c) Compute the flux density inside a bar of The susceptibility for titanium is found in Table \(20.2\). (d) Compute the magnitude of the magnetization \(M\).

The chemical formula for manganese ferrite may be written as \(\left(\mathrm{MnFe}_{2} \mathrm{O}_{4}\right)_{8}\) because there are eight formula units per unit cell. If this material has a saturation magnetization of \(5.6 \times 10^{5} \mathrm{~A} / \mathrm{m}\) and a density of \(5.00 \mathrm{~g} / \mathrm{cm}^{3}\) estimate the number of Bohr magnetons associated with each \(\mathrm{Mn}^{2+}\) ion.

A coil of wire \(0.1 \mathrm{~m}\) long and having 15 turns carries a current of \(1.0 \mathrm{~A}\). (a) Compute the flux density if the coil is within a vacuum. (b) A bar of an iron-silicon alloy, the \(B-H\) behavior for which is shown in Figure \(20.29\), is positioned within the coil. What is the flux density within this bar? (c) Suppose that a bar of molybdenum is now situated within the coil. What current must be used to produce the same \(B\) field in the Mo as was produced in the iron-

The formula for yttrium iron garnet \(\left(\mathrm{Y}_{3} \mathrm{Fe}_{5} \mathrm{O}_{12}\right)\) may be written in the form \(\mathrm{Y}_{3}^{c} \mathrm{Fe}_{2}^{a} \mathrm{Fe}_{3}^{d} \mathrm{O}_{12}\), where the superscripts \(a, c\), and \(d\) represent different sites on which the \(\mathrm{Y}^{3+}\) and \(\mathrm{Fe}^{3+}\) ions are located. The spin magnetic moments for the \(\mathrm{Y}^{3+}\) and \(\mathrm{Fe}^{3+}\) ions positioned in the \(a\) and \(c\) sites are oriented parallel to one another and antiparallel to the \(\mathrm{Fe}^{3+}\) ions in \(d\) sites. Compute the number of Bohr magnetons associated with each \(\mathrm{Y}^{3+}\) ion, given the following information: (1) each unit cell consists of eight formula \(\left(\mathrm{Y}_{3} \mathrm{Fe}_{5} \mathrm{O}_{12}\right)\) units; (2) the unit cell is cubic with an edge length of \(1.2376 \mathrm{~nm} ;\) (3) the saturation magnetization for this material is. \(1.0 \times 10^{4} \mathrm{~A} / \mathrm{m}\); and (4) there are five Bohr magnetons associated with each \(\mathrm{Fe}^{3+}\) ion

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