homework1

Homework for Solid’s Magnetism

1, Pauli spin susceptibility. The spin susceptibility of a conduction electron gas at absolute zero temperature (T~0) may be discussed by another method. Let

n +=n (1+η)/2; n -=n (1-η)/2

be the concentration of spin-up and spin-down electrons.

(1) show that in a external magetic field B 0, the total energy of the spin-up band in a free electron gas is

),1(2

1-)(105/30ημηε++=+B n E B Where F n εε10

30=, in terms of Fermi energy F ε in zero magnetic field (B 0=0). Also find a similar expression for E ?.

(2) Minimize -++=E E E total with respect to η and solve the equilibrium value of η in the

approximation 1<<η. Go on to show the magnetization is F B

B n M εμ3/302=. 2，Diamagnetic susceptibility of atom hydrogen. The wave function of the hydrogen atom in its

ground state (1s) is 0/2/130)(a r e a --=πψ, where cm 10529.0/8220-?==me a . The charge density is 2

),,(ψρe z y x -=. According to the statistical interpretation of the wave function, show

that for this state 2023a r >=<, and calculate the molar diamagnetic susceptibility of atom hydrogen.

3，Heat capacity of magnons. Use the approximation magnon dispersion relation 2ak =ωto the leading term in the heat capacity of a three-dimensional ferromagnet at low temperature. (k is the wavevector). (Integral: 772.1)333.1(4343)!23(11

2/512/501/2/32/3==?==-∑∑?∑∞=-∞=-∞

∞=-ππn n n x n x n n dx e x e dx x

) 4，给定三个外观相同的物体：（1）永久磁体；（2）顺磁材料；（3）未磁化的铁磁材料。不用任何外加磁场，可以鉴别它们吗？若可能，请描述方法；若不行，请给出理由。

5，（1）什么是Heisenberg 哈密顿量？（2）它表征铁磁体的什么相互作用？（3）为什么平均场理论不能适用于铁磁体的低温态？

6，碱金属Na ，贵金属Cu ，过渡金属Cr 、Fe 和V ，各属哪类磁性物质？并说明相应类磁性的主要特点。