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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
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Part II
PHYSICS - Paper 4.B ( 2 hours )
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]