Competition of two terms in exchange Hamiltonian for magnetic substances

Abstract

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, A2ex=-2A1ii ·sj-2A2ii·sj，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 21+A22(A11〉+A2‖2 〉), and t he energy (relative to exchange interaction) eigenvalue E =-Nz（A1-A2）-2NzA 22A1+A2=-Nz（A2-A1）-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.