Giant Magnetoresistance - 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: Giant Magnetoresistance, Scanning Tunnelling Microscope, Operating Principles, Normal-Ferromagnetic Metal, Magnetic Susceptibility, Diamagnetic Contribution, Exchange Interaction

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
2009 EXAMINATIONS
Part II
PHYSICS - Paper 4.B ( 2 hours )
An indication of mark weighting is given by the numbers in square brackets following
each part.
Candidates should answer question 1 (40 marks) and TWO questions from questions
A2 to A4 (40 marks each).
PHYSICAL CONSTANTS
Planck’s constant h= 6.63 ×1034 J s
~= 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

2009 EXAMINATIONS

Part II

PHYSICS - Paper 4.B ( 2 hours )

  • An indication of mark weighting is given by the numbers in square brackets following each part.
  • Candidates should answer question 1 (40 marks) and TWO questions from questions A2 to A4 (40 marks each).

PHYSICAL CONSTANTS

Planck’s constant h = 6. 63 × 10 −^34 J s ℏ = 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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Module 421 - Advanced Solid State & Nanophysics (The time allocated is 120 minutes. Candidates should answer question 1 and TWO questions from questions 2 to 4.)

Compulsory question:

  1. (a) Describe the operating principles of a scanning tunnelling microscope. [14] (b) Describe the origin of giant magnetoresistance in normal-ferromagnetic metal multi-layers. State the main application of this phenomenon in electronics. [14] (c) The magnetic susceptibility of CaO doped with 0.01% Fe has two contributions: (i) a paramagnetic contribution from Fe2+^ ions; (ii) a diamagnetic contribution from the Ca2+O^2 −^ matrix. Compare the relative magnitudes of the two contributions at high and low temperatures and estimate the temperature at which the total magnetic sus- ceptibility is zero. [12]

Answer one of the following two questions:

  1. (a) Describe the origin of the exchange interaction. Write down the Heisenberg Hamiltonian for spins in a ferromagnetic solid explaining the meaning of all terms involved. Explain whether the exchange constant J has to be positive or negative for a solid to be ferromagnetic. Sketch typical spin arrangements characteristic for (i) ferromagnetic and (ii) antiferromagnetic ordering. [14] (b) Use the mean-field self-consistent theory approach to show that the self- consistency equation for the polarisation < Sz > of interacting spins with N nearest neighbors in a solid, at a temperature T , is given by

< Sz >=

tanh

JN < Sz > 2 kT Use this equation to derive the critical temperature for ferromagnetic ordering (the Curie temperature, TC ). [16] (c) Use the self-consistency equation given in (b) to derive the temperature de- pendence of the magnetisation in the vicinity of the ferromagnetic transition (|T − TC | ≪ TC ). Sketch the magnetisation as a function of temperature. [10]