4.2.7 Continuum approximation 4.Teaching method Teaching:Group Discussion:Autodidacticism under the guidance of the teacher 5.Comments Carefully prepare lessons,prepare students and make preparations before class:In the teaching process,we pay attention to cultivating students'creative thinking,take students as the main body and enhance students'sense of participation:Corresponding exercises and supplementary exercises after class. Problems (4.1)Show that two magnetic dipoles ul and u2 separated by r have a dipolar energy equal to 3 E= 40 (4.2)Calculate the magnitude of the magnetic field 1 A and 10 A from a proton in a direction (a)parallel and (b)perpendicular to the proton spin direction. (4.3)Estimate the ratio of the exchange and dipolar coupling of two adjacent Fe atoms in metallic Fe. (The exchange constant in Fe can be c setting it equal to kTc where TC is the Curie temperature.For Fe,TC =1043 K. (4.4)Provide a rough estimate of the size of the exchange constant in a magnetic oxide which is coupled by superexchange using the measured value of the electronic bandwidth (determined by inelastic neutron scattering)of 0.05 eV.Take the Coulomb energy to be ordering temperature (4.5)Consider the case of two interacting spin-1/2 electrons.The good quantum numbers are S=0 and 1 so that there is a triplet state and a singlet state which will be separated by an energy gap A.We define the sign of A so that when A >0 the singlet state (S=0)is the lower state and A 0 the triplet state is the lower state.These situations are shown in Fig.4.6(a)and (b) Show that the susceptibility in this model is given by 2Ng43 X=kT6+eak可 which is known as the Bleaney-Bowers equation.It is plotted in Fig.4.6(c).4.2.7 Continuum approximation 4. Teaching method Teaching; Group Discussion; Autodidacticism under the guidance of the teacher 5. Comments Carefully prepare lessons, prepare students and make preparations before class; In the teaching process, we pay attention to cultivating students' creative thinking, take students as the main body and enhance students' sense of participation; Corresponding exercises and supplementary exercises after class. Problems： (4.1) Show that two magnetic dipoles u1 and u2 separated by r have a dipolar energy equal to (4.2) Calculate the magnitude of the magnetic field 1 A and 10 A from a proton in a direction (a) parallel and (b) perpendicular to the proton spin direction. (4.3) Estimate the ratio of the exchange and dipolar coupling of two adjacent Fe atoms in metallic Fe. (The exchange constant in Fe can be crudely estimated by setting it equal to kBTc where TC is the Curie temperature. For Fe, TC =1043 K.) (4.4) Provide a rough estimate of the size of the exchange constant in a magnetic oxide which is coupled by superexchange using the measured value of the electronic bandwidth (determined by inelastic neutron scattering) of 0.05 eV. Take the Coulomb energy to be ~1 eV, Hence estimate the antiferromagnetic ordering temperature. (4.5) Consider the case of two interacting spin-1/2 electrons. The good quantum numbers are S = 0 and 1 so that there is a triplet state and a singlet state which will be separated by an energy gap A. We define the sign of A so that when A > 0 the singlet state (S = 0) is the lower state and when A < 0 the triplet state is the lower state. These situations are shown in Fig. 4.6(a) and (b). Show that the susceptibility in this model is given by which is known as the Bleaney-Bowers equation. It is plotted in Fig. 4.6(c)