To prove the number of magnons per unit volume in a three-dimensional ferromagnet is given by N m V = 2 π ( 2 m * k T h 2 ) 3 / 2 ∫ 0 ∞ x e x − 1 d x

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Answer 1

Question

Chapter 7.5, Problem 64P

(a)

To determine

To prove the number of magnons per unit volume in a three-dimensional ferromagnet is given by

NmV=2π( 2 m * kT h 2 )3/2∫0∞xex−1dx

(b)

To determine

To find the fractional reduction in magnetization and write it in form of (T T 0 )3/2 and estimate value of T0 for iron.

(c)

To determine

The value of heat capacity due to magnetic excitations in ferromagnet. Estimate the value for iron and compare it with magnon and phonon contributions.

(d)

To determine

To show the total number of magnons diverges in case of two dimensional arrays at low temperature.

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Sketch the harmonic on graphing paper.

Exercise 1: (a) Using the explicit formulae derived in the lectures for the (2j+1) × (2j + 1) repre- sentation matrices Dm'm, (J/h), derive the 3 × 3 matrices corresponding to the case j = 1. (b) Verify that they satisfy the so(3) Lie algebra commutation relation: [D(Î₁/ħ), D(Î₂/h)]m'm₁ = iƊm'm² (Ĵ3/h). (c) Prove the identity 3 Dm'm,(Î²) = Σ (D(Î¡)D(Î¡))m'¡m; · i=1

Sketch the harmonic.

Answer 2

Question

Chapter 7.5, Problem 64P

(a)

To determine

To prove the number of magnons per unit volume in a three-dimensional ferromagnet is given by

NmV=2π( 2 m * kT h 2 )3/2∫0∞xex−1dx

(b)

To determine

To find the fractional reduction in magnetization and write it in form of (T T 0 )3/2 and estimate value of T0 for iron.

(c)

To determine

The value of heat capacity due to magnetic excitations in ferromagnet. Estimate the value for iron and compare it with magnon and phonon contributions.

(d)

To determine

To show the total number of magnons diverges in case of two dimensional arrays at low temperature.

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 3

Question

Chapter 7.5, Problem 64P

(a)

To determine

To prove the number of magnons per unit volume in a three-dimensional ferromagnet is given by

NmV=2π( 2 m * kT h 2 )3/2∫0∞xex−1dx

(b)

To determine

To find the fractional reduction in magnetization and write it in form of (T T 0 )3/2 and estimate value of T0 for iron.

(c)

To determine

The value of heat capacity due to magnetic excitations in ferromagnet. Estimate the value for iron and compare it with magnon and phonon contributions.

(d)

To determine

To show the total number of magnons diverges in case of two dimensional arrays at low temperature.

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 4

Question

Chapter 7.5, Problem 64P

(a)

To determine

To prove the number of magnons per unit volume in a three-dimensional ferromagnet is given by

NmV=2π( 2 m * kT h 2 )3/2∫0∞xex−1dx

(b)

To determine

To find the fractional reduction in magnetization and write it in form of (T T 0 )3/2 and estimate value of T0 for iron.

(c)

To determine

The value of heat capacity due to magnetic excitations in ferromagnet. Estimate the value for iron and compare it with magnon and phonon contributions.

(d)

To determine

To show the total number of magnons diverges in case of two dimensional arrays at low temperature.

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 5

Chapter 7.5, Problem 64P

(a)

To determine

To prove the number of magnons per unit volume in a three-dimensional ferromagnet is given by

NmV=2π( 2 m * kT h 2 )3/2∫0∞xex−1dx

(b)

To determine

To find the fractional reduction in magnetization and write it in form of (T T 0 )3/2 and estimate value of T0 for iron.

(c)

To determine

The value of heat capacity due to magnetic excitations in ferromagnet. Estimate the value for iron and compare it with magnon and phonon contributions.

(d)

To determine

To show the total number of magnons diverges in case of two dimensional arrays at low temperature.

Answer 6

Chapter 7.5, Problem 64P

(a)

To determine

To prove the number of magnons per unit volume in a three-dimensional ferromagnet is given by

NmV=2π( 2 m * kT h 2 )3/2∫0∞xex−1dx

Answer 7

Chapter 7.5, Problem 64P

(a)

To determine

To prove the number of magnons per unit volume in a three-dimensional ferromagnet is given by

NmV=2π( 2 m * kT h 2 )3/2∫0∞xex−1dx

Answer 8

(b)

To determine

To find the fractional reduction in magnetization and write it in form of (T T 0 )3/2 and estimate value of T0 for iron.

Answer 9

(b)

To determine

To find the fractional reduction in magnetization and write it in form of (T T 0 )3/2 and estimate value of T0 for iron.

Answer 10

(c)

To determine

The value of heat capacity due to magnetic excitations in ferromagnet. Estimate the value for iron and compare it with magnon and phonon contributions.

Answer 11

(c)

To determine

The value of heat capacity due to magnetic excitations in ferromagnet. Estimate the value for iron and compare it with magnon and phonon contributions.

Answer 12

(d)

To determine

To show the total number of magnons diverges in case of two dimensional arrays at low temperature.

Answer 13

(d)

To determine

To show the total number of magnons diverges in case of two dimensional arrays at low temperature.

Answer 14

Expert Solution & Answer

Answer 15

Expert Solution & Answer

Answer 16

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Answer 17

Ch. 7.1 - Prob. 1P Ch. 7.1 - Prob. 3P Ch. 7.1 - Prob. 4P Ch. 7.1 - Show that when a system is in thermal and...Ch. 7.1 - Prob. 7P Ch. 7.2 - Prob. 8P Ch. 7.2 - Prob. 9P Ch. 7.2 - Prob. 11P Ch. 7.2 - Prob. 12P Ch. 7.2 - Prob. 13P

To prove the number of magnons per unit volume in a three-dimensional ferromagnet is given by N m V = 2 π ( 2 m * k T h 2 ) 3 / 2 ∫ 0 ∞ x e x − 1 d x

Solution Summary: The author explains how to prove the number of magnons per unit volume in a three-dimensional ferromagnet.

To prove the number of magnons per unit volume in a three-dimensional ferromagnet is given by

NmV=2π( 2 m * kT h 2 )3/2∫0∞xex−1dx

To find the fractional reduction in magnetization and write it in form of (T T 0 )3/2 and estimate value of T0 for iron.

The value of heat capacity due to magnetic excitations in ferromagnet. Estimate the value for iron and compare it with magnon and phonon contributions.

To show the total number of magnons diverges in case of two dimensional arrays at low temperature.

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Chapter 7 Solutions

To prove the number of magnons per unit volume in a three-dimensional ferromagnet is given by N m V = 2 π ( 2 m * k T h 2 ) 3 / 2 ∫ 0 ∞ x e x − 1 d x

Solution Summary: The author explains how to prove the number of magnons per unit volume in a three-dimensional ferromagnet.

To prove the number of magnons per unit volume in a three-dimensional ferromagnet is given by NmV=2π( 2 m * kT h 2 )3/2∫0∞xex−1dx

To find the fractional reduction in magnetization and write it in form of (T T 0 )3/2 and estimate value of T0 for iron.

The value of heat capacity due to magnetic excitations in ferromagnet. Estimate the value for iron and compare it with magnon and phonon contributions.

To show the total number of magnons diverges in case of two dimensional arrays at low temperature.

Want to see the full answer?

Chapter 7 Solutions

To prove the number of magnons per unit volume in a three-dimensional ferromagnet is given by

NmV=2π( 2 m * kT h 2 )3/2∫0∞xex−1dx