Journal of Physics: Conference Series OPEN ACCESS Concentration of magnetic transitions in dilute magnetic materials To cite this article: V I Beloon et al 04 J. Phys.: Conf. Ser. 490 065 Recent citations - The comination of the random interaction fields method and the Bethe Peierls method for studying two-sulattice magnets V. Beloon et al - Approaches to numerical solution of D Ising model K S Soldatov et al View the article online for updates and enhancements. This content was downloaded from IP address 48.5.3.83 on 0/0/08 at 9:5
nd International Conference on Mathematical Modeling in Physical Sciences 03 IOP Pulishing Journal of Physics: Conference Series 490 (04) 065 doi:0.088/74-6596/490//065 Concentration of magnetic transitions in dilute magnetic materials V I Beloon, V Yu Kapitan and O I Dyacheno Department of theoretical and experimental physics, The School of Natural Sciences, Far Eastern Federal University, 8, Suhanova str., 690950, Vladivosto, Russian Federation E-mail: dyacheno.oi@dvfu.ru Astract. In this paper the two-sulattice crystalline ferromagnet in the approximation of the Ising model was investigated. In each su-lattice density of magnetic atoms can vary from 0 to. The exchange interactions within each sulattice and etween the spins of different sulattices are considered as given. The case of direct exchange was investigated and the conditions for the occurrence of ferromagnetism, antiferromagnetism and ferrimagnetism, depending on the concentration of magnetic atoms in each sulattice were estalished.. Introduction A large numer of magnetic materials oth in our country and aroad are currently nown, ut the experimental and theoretical researches continue in this area, as this prolem is quite urgent. The theory of phase transitions has een an active field of research for many decades already. Despite several remarale achievements on oth the conceptual and the applied sides, there still remain open questions galore. As a contriution to the conceptual side, a recent and promising proposal is the random interaction field method to phase transitions [], connecting the partition function of random fields with the law of interaction and providing an opportunity to evaluate not only the Curie point ut also the critical concentration of "ferromagnetic" atoms necessary for the appearance of ferromagnetism.. Model of the two-sulattice magnet If there are two su-lattices, in accordance with the results of [], we write the partition function of the random field at an atom of the first sulattice as follows: { H M H M H } 0 0 W( H ) exp, () π B B where B p ( M p ) + ϕ ϕ, l l H p ϕ, H p ϕ, 0 0 l l Content from this wor may e used under the terms of the Creative Commons Attriution 3.0 licence. Any further distriution of this wor must maintain attriution to the author(s) and the title of the wor, journal citation and DOI. Pulished under licence y IOP Pulishing Ltd
nd International Conference on Mathematical Modeling in Physical Sciences 03 IOP Pulishing Journal of Physics: Conference Series 490 (04) 065 doi:0.088/74-6596/490//065 α α β M, β M, index numers the atoms of the first type, l numers the atoms of the second type, ϕ is the exchange "field" created y the atom with the numer on the selected atom placed at the origin, α is the relative numer of particles oriented "up", β is the relative numer of particles oriented "down" p is the concentration of ferromagnetic particles. Respectively where ( ) W H { H M H M H } 0 0 exp, B π B B p ( M p ) + ϕ ϕ, l l H p ϕ, H p ϕ. 0 l 0 l In the simplest case ϕ, ϕ, ϕ, ϕ are constants, ϕ ϕ and summation should e carried out over nearest neighors. Sustantial simplification of the equation can e achieved y replacing the partition function of the rectangle function []. Then B m ( + + 0 0) B B M th H M H M H dh, (3) B m ( + + 0 0) B B M th H M H M H dh. (4) m m m mb We introduce the notation: H x, H h, H h, 0 0 0 0. Analogous for m, where m and m are magnetic moments of the particles of the first and second sulattices. Then the expression for the magnetization can e expressed as M th ( x M h M h ) dx. + + (5) 0 0 () At high temperatures Analogous, th th M h M + h M h + M h M. (6) ( ) ( ) 3 0 0 0 0 3 ch th th M h M + h M h + M h M. (7) ( ) ( ) 3 0 0 0 0 3 ch The conditions under which different types of magnetic ordering are oserved, can e determined y solving the system of equations (6, 7) for any values h, h, h, h. In general, the solution is 0 0 0 0 rather complicated, ut it is possile to consider some simple options. If h 0 then 0 According to (8) and (6) th M h M. (8) 0
nd International Conference on Mathematical Modeling in Physical Sciences 03 IOP Pulishing Journal of Physics: Conference Series 490 (04) 065 doi:0.088/74-6596/490//065 th th h + h h 0 0 0 M. (9) 3 th th h h h + 0 0 0 3 ch Thus, the condition of a non-zero magnetisation M : th th h + h h. 0 0 0 > (0) In the case of a direct exchange at T 0 the values th and th cannot e greater than one, so from the definition of H, H, B and B, the condition of appearance of the concentration of the 0 0 phase transition can e determined as: pz pzpz + >. () pz pz pz If H 0, then this relation simplifies 0 pzpz. pz pz > () And finally, in the case of equivalent sulattices p p, z z and condition for the occurrence of antiferromagnetic ordering is determined as: p >. (3) z At h 0 two separate sulattices are considered for each of which there is a different transition 0 condition. Fulfillment of conditions (0) and () is sustantially depends on the concentration of "ferromagnetic" atoms in sulattices so there are critical concentrations of such atoms elow which ones ordering cannot occur. The aove-mentioned fundamental relationships determine the possiility of a corresponding ordering. To determine the Curie point T, use the relation (0): c m p z m p z th th c m m c m pz + pz pz >. m p z c c m p z c c c (4) 3. Monte Carlo simulations of two-sulattice magnets In model of two-sulattice ultrathin magnetic film with competing ferromagnetic-antiferromagnetic direct exchange interactions was otained spin-glass properties. It was shown that the Ising model on a D lattice with z 8 nearest neighors taes place divergence etween the ZFC and FC magnetization curves, Fig.. A wea antiferromagnetic interaction etween ferromagnetically ordered sulattices and approximately the same values of the magnetic moments in the sites could lead to very complex magnetic properties. Theoretical magnetic phase diagram for the plain structures with random dilution was uilt. 3
nd International Conference on Mathematical Modeling in Physical Sciences 03 IOP Pulishing Journal of Physics: Conference Series 490 (04) 065 doi:0.088/74-6596/490//065 Technological features of multicomponent compounds containing ferromagnetic atoms mae them attractive for a wide variety of modern electronic devices, such as materials for storage devices. Therefore, in recent years, these materials are the suject of intense experimental and theoretical research []. Figure : Temperature dependence of the average FC and ZFC magnetization, the external magnetic field H0.4, p c0.9. Figure : Theoretical magnetic phase diagram for a two-sulattice magnet The presence of the divergence etween the ZFC and FC magnetization curves are usually associated with the appearance of the spin-glass phase. If to use point of divergence etween the ZFC and FC curves - T f and the temperature of occurrence of the ferromagnetic ordering in the sulattices - T c, it is possile to construct a theoretical magnetic phase diagram of a two-sulattice D Ising magnet for a given exchange integrals: J AA, J BB, J AB -0.5, Fig.. The presence of divergence in ZFC and FC temperature dependence could e caused y the ordering in the sulattices, accompanied y compensation of magnetization and an increase in frustrations in the system as a whole. The wea antiferromagnetic direct interaction etween ferromagnetically ordered sulattices was shown to complex ehavior of the average magnetization of the system of spins. Was calculated the theoretical magnetic phase diagram for the two-sulattice magnet. 4. Conclusions Thus, the random interaction field method is a tool for the study of phase transitions and critical phenomena. It allows exploring the complex model systems, the study of which y other methods is facing great difficulties. A specific example is a two-sulattice magnetic material, which is composed of oth magnetic and non-magnetic atoms are considered the results of the study of the critical properties, determined the critical concentration of "ferromagnetic" of atoms necessary for the existence of ferro-, ferri-and antiferromagnetism. Acnowledgments This wor was supported y Ministry of education and science of Russian Federation within the contracts.8649.03, 07.54..403 and 4.740..089. References [] Beloon V I, Nefedev K V 00 SSP 44 63 [] Htoutou K, Ainane A, Saer M and Miguel J J 005 Physica A 358 84 4