复习题. 2 Calculate the intensity of magnetic field in the air gap of the magnetic circuit shown in the figure. Use the values N=200,

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Isabella Casey
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1 复习题 1 Calculate the magnetic moment of a sphere of radius R made from a magnetic material with magnetic susceptibility, when it is magnetized by an external magnetic field H. How is the value of the moment changed in the limit of? Calculate the intensity of magnetic field in the air gap of the magnetic circuit shown in the figure. Use the values N=00, i=5a,s 1= m, S = m,l 1=1m,l = 0.01m, =500 3 Give the statement of Hund s rule and its physical explanations. 4 Try to prove = 0 for S electron 5 What is the meaning of g factor. Derive expression of Landéfactor g by L-S coupling model. g ( +1) + S( S +1) L( L +1) = 1+ ( +1) 6 How to get the information related to g factor in solid experimentally. Why does the value from gyromagnetic effect, g, differ from g measured by FMR? 7 Describe the basic feature of 5 kinds of magnetism in solids. Magnitude of, its T and H dependences 8 Explain why doesn t superpose to the vector summation between l and s. 9 What is the electron confijuration Cr, Mn, Co, Ni, Cu, Zn atoms according to Hund s rule (Fe atoms), and the values of their S, L, and g. 10 Give the values of, L, S and g factor of Mn +++, Fe ++, Co ++ and Ni ++, Cr + and calculate and H. 11 Derive d due to electron orbit by classical method. 1 State the basic principle of Landau diamagnetism and De Haas-Van Alphan effect. 13 Knowing that copper has atomic number 9, atomic mass 63.54, density 8.94 g cm -3, and average orbital radius 0.5Å, calculate its relative diamagnetic susceptibility. Use the following values: Avogadro s number N= mol -1, electric charge of electron e= C, and electron mass m= kg. 14 The ground state wave fuction for hydrogen atom is 3 1/ / a h ( a0 ) e, a0 = = mc = 0 r 8 Based on statistical interpretation of wave function, (a) prove ground state: <r > = 3a 0 (b) cm

2 calculate Mol diamagnetic susceptibility d 15. Why do conduction electrons show paramegetism sometimes and diamagnetism sometimes? 16. The atomic electron configuration of isolated Cu atom is 3d 10 4s 1 and that of Pd is 4d 10 5s 0. How is the basic magnetism of Cu and Pd metals? Why? 17. Calculate the relative paramagnetic susceptibility for an idea gas, in which each molecule has a magnetic moment with =1, g= at 1 atmosphere pressure and 0ºC. The 1 mol idea gas takes a volume of.41 at the above-mentioned temperature and pressure. Avogadro s number is mol Which groups of atoms in periodic table have non-zero magnetic moment in isolated state? 19. Derive M=M 0B ( ), in which = g B/k BT for normal paramagnetism. 0. Derive M B( ) = = cth + cth in M = M 0 B ( ) M Derive B ( ) =, 3 when << 1; And derive B ( ) L( ), when and B ( ) 1, when >> 1. And derive M Ng th, when S B 1. Derive Curie law and Pauli susceptibility at 0 K. 3. State and explain the weak magnetism for different portion in periodic table. 4. Plot schematically different -T of different weak magnetism. Explain briefly. 5. Try to explain why alkaline metals are all paramagnetic and no one is ferromagnetic. And why alkaline earth metals are all paramagnetic while their outer electrons are all s? 6. Explain why only Cr, Mn, Fe, Co, Ni are mag. ordering in TM, while more elements of mag. order in RE. 7. Knowing that nickel has the Curie point f =68.3K, =1/, and saturation moment M s =0.6 B, calculate the molecular field at 0K according to the Weiss theory. 8. Describe the derivation of Ms-T, -T in Weise theory. Explain the origin of paraprocess susceptibility. 9. Derive the Tc by using Weise theory and state the meaning of Tc and p. 30. Derive the Stoner s criterion of itinerant FM. 31. Compare the two criteria of FM of localized model and itinerant model. Give a comment on the two models of FM.

3 3. Give magnetic moment of magnetic transition metal Fe, Co, Ni by the pictures of band structure in itinerant FM model. 33. Give the examples for stating the difference of -T in Transition metal. 34. Give three different methods to determine T c of strong magnetic materials and the way to determine saturation magnetization précis 35. What are p s and p eff, and p c? How to determine the p s and p eff, and p c experimentally? 36. Give the schematic plots of six kinds of temperature dependence of magnetic susceptibility of various magnetism in solid. Explain briefly for each. 37. Spins of RE and TM are AFM coupled. Explain the alignment of atomic moments in LRE-TM and HRE-TM alloys. 38. Explain the N and P type Ms T relation. How to explain M-T curve with compensation point and compensation composition? 39. For a antiparallel aligned AFM, derive the expressions for and //. Prove > //. 40. Explain the interfacial exchange coupling in FM/AFM bilayer 41. Describe various kinds of spin structures of ferrimagnetism. 4. Derive and plot the -T of two sublattice ferrimanetism:1/ =T/C + 1/ 0 + /(T- ). 43. How do you understand the ground state electron spin configuration of H, Fe, Cr at low temperature and the conduction electrons in rare earth metal 44. What is the difference between exchange integral and molecular field M? How is their temperature variations? How to control Tc.? 45. Give pictures of the illastration of the interaction in magnetic oxides CoO and FeO, NiO by using superexchange energy expression E ex = isi S j, i = d [ ] ( E ) ( E ) 46. How do you understand the two features of exchange interaction? 47. Is there exchange interaction in all many electron systems? Give a general formulation. 48. Give pictures of 4 kinds of exchange interaction, their features and applications. 49. How do you consider the exchange interaction in TM? 50. How to determine M s, M 0 experimentally? 51. Give three different methods to determine T c and T N of magnetic ordered materials 5. How to determine the p s and p eff, and p c experimentally? Calculate p c for Fe and Co. 53. How do you understand spin wave exitation? s t

4 54. Why spin wave excitation predominates over single spin flip? 55. How to demonstrate the existence of spin waves? How to excite spin waves? 56. Give some examples of the effect of band structures on magnetism in solids and explain. 57. The expression for magnetocrystalline energy for cubic, hexagonal systems and that of uniaxial and unidirectional anisotropy. How to determine the easy and hard directionfrom the expression of anisotropy energy? 58. What are the easy axes of Fe and Co crystals? Demonstrate the order of easiness of the three principal axes, [100], [110] and [111] for Fe. 59. Knowing the values for M s =1.79T and K 1= m -3, calculate the anisotropy field in the c-axis for cobalt. Ignore terms higher than K 60. Describe the methods for measuring the anisotropy constants. 61. Describe the methods for enhancing the anisotropy constants. 6. What is directional order? Describe the origin of induced anisotropy in alloys.. How to obtain high induced anisotropy by field annealing? 63. What is the meaning of 100 and 111? How to determine it precisely? The expression for isotropic magnetoelastic energy and the meaning 64. What is shape anisotropy? Give out the shapes which could be magnetizied uniformly under the uniform magnetic field. Which shape of the sample could neglect the demagnetizing field? 65. The expression for shape anisotropy of an ellipsoid and the meaning. 66. Describe the condition for the occurrence of uniform demagnetizing field and for nonuniform demagnetizing field. How to calculate the nonuniform demagnetizing field. 67. Describe the theoretical model for illustration of magnetic anisotropy. 68. What is the basic structure of Bloch wall and Neel wall? What is the condition of occurrence of Bloch wall and Neel wall? 69. What is the regulation of the rotation of magnetization in domain wall? Are there sharp boundaries at both sides of the domain wall? Why? 70. Why does the DW has higher energy than the domain? Where in a 180ºdomain wall in Co has highest energy? Where in a 180º(100)-domain wall in Fe has highest energy, how about a 90º wall.? 71. Describe briefly the experimental methods for observing the domain structure. 7. What is the dependence of domain width on the dimension of crystal and grain? 73. Why the domain structure inside the crystal and grain is regular and wide while that at the surfaces and the grain boundaries are small, irregular and complicated? 74. Give a comment on the calculation of the critical size of the single domain state of a spherical

5 particle with simple methods 75. Why multi-domain structure exists in bulk materials while very fine particles become to single domains? How to estimate the critical size of single domain particle? 76. In a multi-domain materials where the energy is higher? 77. When the size of FM granules in diamagnetic metallic matrix decreases from bulk particles to atomic size, how do you expect the variation of their magnetic property? 78. Give a comment on the calculation of the critical size of the single domain state of a spherical particle with simple methods 79. Three kinds of magnetization processes and their general appearance in magnetization curve and hysteresis loop. How about the reversible and irreversible processes? 80. How does the DW energy change with position due to the variation of stress? 81. How does the DW energy change with position due to non-magnetic inclusions? 8. Give a general formulation of quasi-static DWD and reversible susceptibility due to DWD, and also of H 0 of irreversible DWD. How is the angular dependence of r and H 0? 83. Give a general formulation of magnetization process of quasi-static DR and of H 0 of irreversible DR. 84. If E K = K U1Sin and K U1 >0, calculate the M-H curve due to DR when H is along the hard axis. How is it when E K = K U1Sin + K USin 4? 85. If E K = K U1Sin and K U1 >0, calculate the M-H hysteresis loop due to DR when H is along the easy axis. How are the H C and M R? How do they change when H makes an angle with easy axis? 86. What is the feature of nonuniform irreversible rotation? 87. Explain why H n< K/M s and H n may be even negative. How to distinguish the two situations of H o>h n and H o<h n? 88. How to identify whether a magnetic sample is paramagnetic, superparamagnetic or ferromagnetic? Make a plan for measurements. 89. When you observe a rectangular hysteresis loop how do you prove whether it is due to DR or DWD? 90. In AFM/FM bilayers, there is a unidirectional anisotropy and shift of hysteresis loop of FM layer-exchange bias. When the FM is demagnetized an interfacial DW structure occurs. Why? 91. Give a plot to show the dependence of H c on the size of ferromagnetic particles. Explain briefly. 9. What is superparamagnetism? How to determine the magnetic moment of the superparamagnetic particles? When a particle is near the critical size how is the behavior of H c, M R?

6 93. Why superparamagnetism is a limit of the density of areal bits for magnetic storage? How to decrease the critical size for superparamagnetism?

Lecture 5. Chapters 3 & 4. Induced magnetization: that which is induced in the presence of an applied magnetic field. diamagnetic.

Lecture 5. Chapters 3 & 4. Induced magnetization: that which is induced in the presence of an applied magnetic field. diamagnetic. Lecture 5 Induced magnetization: that which is induced in the presence of an applied magnetic field diamagnetic paramagnetic Remanent magnetization: that which remains in the absence of an external field