Molecular field origin for magnetic ordering of magnetic materials
Authors: Qi Wei-Hua  , Li Zhuang-Zhi  , Ma Li  , Tang Gui-De  , Wu Guang-Heng  , Hu Feng-Xia  ,   Hebei Advanced Thin Film Laboratory, College of Physics and Information Engineering, Hebei Normal University, Shijiazhuang 050024, China;,   State Key Laboratory of Magnetism, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
Published: December 2020

In 1907, Weiss proposed that there is a molecular field to explain the magnetic ordering of magnetic materials. However, it has not been clarified where the molecular field comes from so far. In recent decades, the magnetic ordering of metals and alloys were explained by using the direct exchange interaction of between electrons on neighboring atoms, while magnetic ordering of oxides were explained by using the super exchange interaction and double exchange interaction models. The intrinsic relation between those exchange interactions has not been well explained. This resulted in the fact that there are many puzzles for magnetic ordering of the magnetic materials. For example, what role the Cr cations play in spinel ferrite CrFe2O4; why the calculated molecular magnetic moment (3.85B) for La0.85Sr0.15MnO3 by using double exchange interaction model is lower than its experimental value (4.20B); whether there is a relation between the average atom magnetic moment and their electrical resistivity for each of Fe, Co and Ni metals. These several puzzles have been explained recently by our group through using an O 2p itinerant electron model for magnetic oxides and a new itinerant electron model for magnetic metals. In this paper, a model for the molecular field origin is proposed. There are three states for the electrons rotating with high speed at the outer orbits of two adjacent ions of magnetic oxides or metals and alloys. 1) There is a probability with which form the electron pairs with opposite spin directions and a certain life time, named Weiss electron pairs (WEP); the static magnetic attraction energy between two electrons of WEP is the elementary origin of Weiss molecular field. 2) There is a probability with which two electrons with the same spin direction exchange mutually. 3) If there are two electrons at the outer orbit of an ion, then for its adjacent ion whose orbit has only one electron, the excess electron will itinerates between the ions. Furthermore, the energy equation of WEP, equilibrium distance, re0, and maximum distance, rem, between electrons of WEP are derived. The probability with which WEP forms in each of several perovskite manganites is investigated. For perovskite manganites La0.8Ca0.2MnO3, La0.75Ca0.25MnO3, La0.70Sr0.30MnO3, the crystal cell constants increase linearly with temperature when the temperature is much lower than the Curie temperature, TC, while they show a rapid increase nonlinearly near TC. We then calculate the difference in MnO bond length at TC between the linear and the nonlinear variation, △dobs. Obviously, when the distance between the two electrons of WEP, re, is larger than the rem, WEP and the magnetic ordering energy both disappear. Assuming △dobs=rem-re0, the probabilities with which WEP appears in La0.8Ca0.2MnO3, La0.75Ca.25MnO3, La0.70Sr0.30MnO3, are calculated to be 0.07%, 0.31% and 3.13%, respectively. These results indicate that the WEP model for the magnetic ordering energy is qualitatively reasonable.