Competition of two terms in exchange energy.pdf

Competition of two terms in exchange energy (A ? A1 t A2) for magnetic materials Yongzhong Wang*, Zhidong Zhang Institute of Metal Research, Academia Sinica, Wenhua Road 72, Shenyang 110016, People’s Republic of China Received 6 June 2002; accepted 13 July 2002 by Z. Gan Abstract For magnetic materials with exchange interaction, A ? A1 t A2 (A1 . 0, A2 , 0), the dominant term in the exchange energies of magnetic materials (A1 for ferromagnetism, or A2 for antiferromagnetism) favors to an order of the spins, whereas the minor term with different sign (A2 for ferromagnetism or A1 for antiferromagnetism) tends to disturb such order, and the effect of the minor term could be included as an effective temperature (Teff). The magnetism of a matter depends on the competition between the dominant term and the minor term in the exchange energies. When A1 ? lA2l; A ? 0; the materials are in the spin glass state; when A1 . lA2l, there is the coexistence of FM and SG; when lA2l . A1, there is the coexistence of AFM and SG. The phase diagram has been derived based on the ratio of A1/lA2l for the ferromagnetism, antiferromagnetism and spin glass. q 2002 Elsevier Science Ltd. All rights reserved. PACS: 75.10 Keywords: D. Exchange energy; A. Ferromagnetism; A. Antiferromagnetism; A. Spin glass The exchange interaction energy between two electrons in a magnetic matter can be described as [1]: A ? ee cpaer1Tcpber2T e 2 r 2 e2 rb1 2 e2 ra2 ! caer2Tcber1Tdt1dt2; the first term and the last two terms in this formula could be represented as A1(.0) and A2(,0), respectively, so we have A ? A1 t A2. It is also valid for the magnetic alloy or compounds with mixture exchange interactions between electrons or atomic moments. The dominant term in the exchange energies A ? A1 t A2 of magnetic materials is favorable for an ordering of the spins (for example, A1 for ferromagnetism, or A2 for antiferromagnet), whereas the minor term (A2 for ferromagnetism or A1 for antiferromag- netism) is favorabl