Paramagnetism and Diamagnetism - Advanced Solid State - Exam, Exams of Solid State Physics

This is the Exam of Advanced Solid State which includes Paramagnetism and Diamagnetism, Principle of Operation, Exchange Interaction, Ginzburg-Landau Theory, Phase Transitions, Ferromagnetic Material, Giant Magnetoresistance etc. Key important points are: Paramagnetism and Diamagnetism, Principle of Operation, Exchange Interaction, Ginzburg-Landau Theory, Phase Transitions, Ferromagnetic Material, Giant Magnetoresistance, Quantum Wires

Typology: Exams

2012/2013

Uploaded on 02/20/2013

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L A N C A S T E R U N I V E R S I T Y
2008 EXAMINATIONS
Part II
PHYSICS - Paper 4.B ( 2 hours )
The time allocated is 120 minutes.
An indication of mark weighting (30 marks per section) is given by the numbers in
square brackets following each part.
Candidates should answer question 1 and TWO questions from 2 to 4.
PHYSICAL CONSTANTS
Planck’s constant h= 6.63 ×1034 J s
¯h= 1.05 ×1034 J s
Boltzmann’s constant kB= 1.38 ×1023 J K1
Mass of electron me= 9.11 ×1031 kg
Mass of proton mp= 1.67 ×1027 kg
Electronic charge e= 1.60 ×1019 C
Speed of light c= 3.00 ×108m s1
Avogadro’s number NA= 6.02 ×1023 mol1
Permittivity of the vacuum ǫ0= 8.85 ×1012 F m1
Permeability of the vacuum µ0= 4π×107H m1
Gravitational constant G= 6.67 ×1011 N m2kg2
Bohr magneton µB= 9.27 ×1024 J T1(or A m2)
Bohr radius a0= 5.29 ×1011 m
Gas constant R= 8.31 J K1mol1
Acceleration due to gravity g= 9.81 m s2
1 standard atmosphere = 1.01 ×105N m2
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L A N C A S T E R U N I V E R S I T Y

2008 EXAMINATIONS

Part II

PHYSICS - Paper 4.B ( 2 hours )

  • The time allocated is 120 minutes.
  • An indication of mark weighting (30 marks per section) is given by the numbers in square brackets following each part.
  • Candidates should answer question 1 and TWO questions from 2 to 4.

PHYSICAL CONSTANTS

Planck’s constant h = 6. 63 × 10 −^34 J s h¯ = 1. 05 × 10 −^34 J s Boltzmann’s constant kB = 1. 38 × 10 −^23 J K−^1 Mass of electron me = 9. 11 × 10 −^31 kg Mass of proton mp = 1. 67 × 10 −^27 kg Electronic charge e = 1. 60 × 10 −^19 C Speed of light c = 3. 00 × 108 m s−^1 Avogadro’s number NA = 6. 02 × 1023 mol−^1 Permittivity of the vacuum ǫ 0 = 8. 85 × 10 −^12 F m−^1 Permeability of the vacuum μ 0 = 4 π × 10 −^7 H m−^1 Gravitational constant G = 6. 67 × 10 −^11 N m^2 kg−^2 Bohr magneton μB = 9. 27 × 10 −^24 J T−^1 (or A m^2 ) Bohr radius a 0 = 5. 29 × 10 −^11 m Gas constant R = 8 .31 J K−^1 mol−^1 Acceleration due to gravity g = 9.81 m s−^2 1 standard atmosphere = 1. 01 × 105 N m−^2

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Section A: Module 421 - Advanced Solid State & Nanophysics (The time allocated for this section is 120 minutes. Candidates should answer question A1 and TWO questions from questions A2 to A4.)

Compulsory question:

A1. (a) Describe the physical origins of paramagnetism and diamagnetism. If a sub- stance is expelled from a region of high magnetic field, is it paramagnetic or diamagnetic? Explain your answer. [10] (b) Describe the principle of operation of a scanning tunnelling microscope. [10] (c) Describe qualitatively the classical and quantum Hall effects in two-dimensional electron systems, and discuss their origins. [10]

Answer two of the following three questions:

A2. (a) What is the physical origin of the exchange interaction? Write down the Heisen- berg Hamiltonian describing a magnetic solid and explain which sign of the ex- change constant in the Heisenberg Hamiltonian promotes ferromagnetic rather than antiferromagnetic ordering. [10] (b) Use the Ginzburg-Landau theory of phase transitions to describe the magneti- sation of a ferromagnetic material at temperatures close to the Curie temper- ature. Describe the influence of crystalline anisotropy on the magnetisation of ferromagnetic materials. Explain how anisotropy influences the formation of domains in ferromagnetic phase transitions. With the aid of a sketch, describe hysteresis in ferromagnets. [12] (c) Describe the difference between the band structures of ferromagnetic and normal metals. Explain the origin of giant magnetoresistance in normal- ferromagnetic metallic multi-layers and state its main application. [8]