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Lecture 36 - EEE 352Lecture 36 Ferromagnetism Permanent...

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Ancient ferromagnetic core memory. Ferromagnetism * Permanent retention of the magnetization * Hysterisis loops * Source of the magnetization * Domains Louis Néel Nobel prize in physics, 1970 “for fundamental work and discoveries concerning antiferromagnetism and ferrimagnetism which have led to important applications in solid state physics” EEE 352—Lecture 36
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Ferromagnetism A substance is called ferromagnetic if it has a permanent M . Usually, χ m is LARGE (>>1) . H B,M Curie temperature T c Fe 1043 K Co 1400 Ni 631 Gd 289 coercivity, or coercive force, H c saturation magnetization
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Now, last *me, we found that the magne*za*on is given as M = 3 N β 2 2 k B T B = χ m H B = μ 0 H + 3 N β 2 2 k B T μ 0 B μ = μ 0 1 3 N β 2 2 k B T μ 0 > μ 0 If our magnetization is big, this term can be driven through zero. Thus, we cannot use our simple approximation.
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As we found last time, the spin-up electrons are raised in energy, while the spin-down electrons are lowered in energy. The ratio of spin-up electrons, which has a higher population, to the spin-down electrons is The proper fraction of polarization is now given by N N = exp 2 β B k B T N N N + N = e 2 β B / k B T 1 e 2 β B / k B T + 1 = e β B / k B T e β B / k B T e β B / k B T + e β B / k B T = tanh β B k B T β = e 2 m 0 = 9.27 × 10 24 Am 2
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Ferromagnetism As in Ferroelectrics, we assume an internal field, in this case an internal magnetic field intensity H I = λ M , λ is the Weiss constant . As previously, the magnetization is The spin magnetic dipole β has been replaced by the more general value In the absence of an external field, H = 0, and
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Ferromagnetism As T 0, tanh 1, and so that x 0 M(T) / M( 0 ) 1 T < T c T > T c x 0 ( T )
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Ferromagnetism At the Curie temperature the slope of both curves are equal as x 0 0, so we can say and The WEISS POSTULATE is that the material is composed of a large number of small DOMAINS, which are randomly oriented in the material (originally). A magnetic field ORIENTS these domains, which remain in that state. Using a large, reversed field FLIPS the domains to the other direction. Fe 770 C Co 1131 Ni 358 Gd 16
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Ferromagnetism In the absence of a field (the original state), the domains are randomly distributed. The average magnetization is 0.
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