磁性物质交换Hamiltonian中两项的竞争

对于一个N电子体系, 正确的交换Hamilton应该由两项组成，为H_ex=-2A1ii·s_j-2A₂ii·sj，而不是以往的铁磁学理论使用的H_ex=-2Aii ·s_j （其中A为A₁与A₂的代数和， A₁>0, A₂<0）, 以往的理论使用了一个不合理的交换Hamiltonian量.-2A₁ii·s_j与-2A₂ii< /sub>·s_j在数学上是同类项，但是在物理上不是 同类项，它们有不同的本征态和本征值.根据量子力学中的态叠加原理，这个电子系统的本 征态矢为X〉=1A²₁+A²₂(A₁ 1〉+A₂‖2〉),其中Dirac符号1〉表示系统所有电子 的自旋平行排列时的态（简称平行自旋态）矢量，2〉表示系统所有电子或最近邻电子的自 旋反平行排列时的态（简称反平行自旋态）矢量，H_ex的本征值（即系统的 交换能） 为E=-Nz（A₁-A₂）-2NzA₂²A₁ +A₂=-Nz（A₂-A₁）-2NzA²₁A< sub>1+A₂,其中z为最近邻电子数.当A₂=0时，X〉=1〉，E =-A₁, 系统具有Wei ss 铁磁性；当A₁ =0 时，X〉=2〉，E =-A₂，系统具有Neel 反铁磁性；当A₁ =A₂（即A=0）时，X〉=12 (1〉+2〉)，E=-A₁，系统处于自旋玻璃（spin glass）态；当A₁>A ₂时，X〉=1A²₁+A²₂［(A₁-A₂)1〉+A₂(1〉+2〉)］,平行自旋态与自旋 玻璃态共存；当A₁2时，X〉=1A²₁+A2₂［(A₂-A₁)2〉+A₁( 1〉+2〉)］，反平行自旋态与自旋玻 璃态共存.与原来理论中的Weiss铁磁态或Neel反铁磁态相比，平行自旋态与自旋玻璃态共存 或反平行自旋态与自旋玻璃态共存使系统的交换能降低.自旋玻璃态中电子自旋之间取向的 随机性或无序性是由交换Hamiltonian中-2A₁iis_j与-2A₂ii·s_j之间的竞争引起的，不是热运 动引起的. 关键词： 交换哈密顿量 铁磁态 反铁磁态 自旋玻璃态

Competition of two terms in exchange Hamiltonian for magnetic substances

The unjustifiable or mistake in the previous magnetism theories has been pointed out in this paper. For a N-electron system with Heisenberg exchange integral A ₁+A₂ （A₁>0, A₂<0）, the correct exc hange Hamiltonian should be H_ex=-2A₁ii ·s_j-2A₂ii·s_j，not H _ex=-2Aii·s _j as in the previous magnetism theories, where A=A₁+A ₂. The role of the mi nor term in the exchange Hamilton was considered. Based on the principle of supe rposition of state, the eigenstate of the system with Heisenberg exchange integr al A=A₁+A₂ （A₁>0, A₂<0）X〉=1A ²₁+A²₂(A₁1〉+A₂‖2 〉), and t he energy (relative to exchange interaction) eigenvalue E =-Nz（A₁-A< sub>2）-2NzA ₂²A₁+A₂=-Nz（A₂-A_{1）-2NzA²1A1+A2,were attained，wh ere z is t he number of the nearest neighbours electrons, 1〉 means the state of the syste m when the spins of all electrons in the system arrange parallelly (the parallel spins state, for simply)，2〉 means the state when the spins of all electrons o r the nearest neighbor electrons in the system arrange antiparallelly (the antip arallel spins state, for simply). When A1 =A2≠0 ，X〉=12( 1〉+2〉)， and E=- NzA1, the system is in the spin glass（SG）state，the probabilities o f paralle l and antiparallel arrange for every pair of spins of electron of nearest neighb ours in the system are equal. When A1≠A２，the probabilit ies are not equal, and there coexist the parallel spins state and SG or the antiparallel spins sta te and SG， X〉=1A²1+A²2［(A1-A2)1〉+A2(1〉+2〉)］,orX〉=1A²1+A²2［(A2-A1 )2〉+A1(1〉+2〉)］. When the parallel spins st ate and SG or the antiparallel spins state and SG coexist, the energy of the sys tem is lower than that when only FM or AFM exists as in previous theory. Weiss f erromagnetic state or Neel anti ferromagnetic state is just a special state when A1=0 or A2=0.}