Magneticfieldinduced antiferromagnetism in the kondo lattice by kevin stuart david beach b. Green street, urbana, il 61801, usa november 9, 2016 abstract we discuss spin models on complete graphs in the mean eld in nitevertex limit. Mean field theory calculation of magnetic exponents. Pdf unified meanfield study of ferro and antiferromagnetic. Unified meanfield study of ferro and antiferromagnetic. Consider ising model on a 2d lattice with antiferromagnetic interaction. A unified theory based on so5 symmetry of superconductivity. Green street, urbana, il 61801, usa november 9, 2016 abstract we discuss spin models on complete graphs in the mean. Coexistence of antiferromagnetism and superconductivity in. There are also examples of disordered materials such as iron phosphate glasses that become antiferromagnetic below their neel.
The origin of the ferromagnetism and other exchange interactions have been shown in chapter 3. There are materials that exhibit antiferromagnetic and ferromagnetic transition states. Using an effective meanfield theory to treat both superconductivity and antiferromagnetism at equal footing, we study the model within the landau energy functional approach and a linearized theory. Their corresponding structural and magnetic properties transition resemble that of a metalinsulator transition and as a result there is a large change in conductivity with an applied field. Nov 20, 2014 hello, i am trying to work out a mean field theory for an antiferromagnetic ising model on a square lattice.
This allows for the change in shape of the spin bands, described by the correlation factors, which decreases kinetic energy of the system. The mean field theory does not give a good description of the variation of m at low temperatures. The problems of phase separation and orderdisorder transition in binary alloys are also included in the solution. Antiferromagnetism, charge density wave, and dwave superconductivity in the extended tju model. May 23, 2016 using an effective meanfield theory to treat both superconductivity and anti ferromagnetism at equal footing, we study the model within the landau energy functional approach and a linearized theory. Coexistence of superconductivity and antiferromagnetism in. In winter 2010, professor chris hammel plans to teach a second course which will focus on experimental aspects of magnetism. How about antiferromagnets magnetic moments compensate. Critical behavior of mean eld xy and related models. We analyze the competition between antiferromagnetism and superconductivity in the twodimensional hubbard model by combining a functional renormalization group flow with a mean field theory for spontaneous symmetry breaking. Kimichika fukushima, in advances in quantum chemistry, 2015.
Mean field theories aim for quantitative power while forgoing explanatory power. Antiferromagnetic order of strongly interacting fermions in a. Magnetic phase transition in the mean field approximation. Basic elements of statistical physics statistical physics deals with systems composed of a very large number of interacting particles. Pdf coexistence of antiferromagnetism and superconductivity. Antiferromagnetism was discovered theoretically more than 80 years ago. Request pdf magnetic ordering of itinerant systems in modified mean field theory. Journal of the physical society of japan 61 1992 pp. The part of the ising hamiltonian containing spin s0 reads as follows, where we decompose the spins sj into their mean value the magnetization, and fluctu. The effective hartree field and the gain in kinetic energy due to the onsite and intersite correlation factors drive the.
A mean field temperature t mf can be associated with this energy scale, that can be between 0 and k, depending on the filling factor. A simultaneous meanfield treatment, of both phenomena, ferro and antiferromagnetism, in the framework of the braggwilliams theory, shows the importance of the interplay between the two corresponding order parameters in determining the features of the phase diagram. We show that a class of characteristic features which. Ferromagnetism along with the similar effect ferrimagnetism is the strongest type and is responsible for the common phenomenon of magnetism in magnets encountered in everyday life. A simple extension of the band theory of paramagnetism by the introduction of an exchange. Pdf a simultaneous meanfield treatment, of both phenomena, ferro and antiferromagnetism, in the framework of the braggwilliams theory, shows the. Antiferromagnetism, charge density wave, and dwave. Magnetic ordering of itinerant systems in modified mean field. Magnetic ordering of itinerant systems in modified mean field theory. When the modern theory of critical phenomena was developed, dipolarcoupled ferromagnetsin which the dipoles are atomic magnetic momentspresented material realizations on which concepts could be tested.
Antiferromagnetism plays a crucial role in giant magnetoresistance, as had been discovered in 1988 by the nobel prize winners albert fert and peter grunberg awarded in 2007 using synthetic antiferromagnets. The language and arrangement of the manuscript have not been revised. A growing theory and source of research on antiferromagnets is their contribution to superconductivity. The author of this textbook is accountable for the professional level and language correctness. Exact critical temperature by meanfield approximation adam lipowski and masuo suzuki.
A short treatment of a simple model of ferrimagnetism is also included. For conventional bcs bardeencooperschrieffer superconductors, the energy scale of the pair formation is the same as the true phasetransition temperature into a superconducting sc state. We found that the meanfield solution of the hubbard model. The theory of ferromagnetism qualitatively defines the domain size and shape, which depend on the competition between different interactions in a ferromagnetic crystal l. The mean field theory predicts exponential convergence of the magnetization to the value at zero temperature. We found that the mean field solution of the hubbard model is an excellent tool to stimulate students reflections. How to deal with mean field method in antiferromagnetism.
At a critical point, the magnetization is continuous as the parameters are tuned closer to the critical point. A property possessed by some metals, alloys, and salts of transition elements in which the atomic magnetic moments, at sufficiently low temperatures, form an ordered array which alternates or spirals so as to give no net total moment in zero applied magnetic field. Antiferromagnetism and quantum criticality in insulators 2. We theoretically investigate the coexistence of antiferromagnetism and superconductivity in the ironbased superconductors by using the meanfield theory for two and threeorbital models. The clue to antiferromagnetism is the behavior of susceptibility above a critical temperature, called the neel temperature tn. Is there a mean field method to deal with the antiferromagnetic ising model. Within our approaches, we find possible coexistence of superconductivity and antiferromagnetism for both electronic and coldatomic models.
The antiferromagnetic ground state of the halffilled hubbard model with the doubly degenerate orbital has been studied by using the slaveboson meanfield. Magnetic ordering of itinerant systems in modified mean. The experimental results show however a much more rapid dependence of. Ferromagnetism article about ferromagnetism by the free. Mean field theory, also called selfconsistent field theory, is closely related to the issue of renormalization. Antiferromagnetism and dwave superconductivity are the most important competing groundstate phases of cuprate superconductors. Ppt ferromagnetism powerpoint presentation free to. Then the strong correlation effects are accounted for through a selfenergy calculation due to magnetic fluctuations magnetic fluctuations are called magnons in. Dipolar antiferromagnetism and quantum criticality in. Can we understand ferromagnetism in terms of electron currents in the framework of. We found that the meanfield solution of the hubbard model is an excellent tool to stimulate students reflections towards the treatment of realistic magnetic interactions. The equations of the dynamical mean field theory are solved with a suitably extended version of wilsons numerical renormalization group. To do this we construct a hubbard model on a lattice of selfconsistently embedded multisite clusters by means of a dynamical mean field theory in which intracluster dynamics is treated essentially exactly.
Antiferromagnetism we analyze the itinerant model for antiferromagnetism, which was developed previously by. Theory of antiferromagnetism, ii progress of theoretical. A dynamical meanfield theory approach to superconductivity. The theoretical curve is scaled to give correct values at either end. Does this imply that the mean behavior of spinspin interaction is always zero. Information obtained by a wide variety of experimental methods is provided. In physics, several different types of magnetism are distinguished.
Dynamical mean field theory of the antiferromagnetic metal. Read an effective mean field theory for the coexistence of antiferromagnetism and superconductivity. Tugrul hakioglu may, 2005 this thesis is mainly an e. There, it was first clearly shown that mean field theory approaches failed to predict the correct behavior at the critical point which was found to fall under a universality class that includes many other systems, such as liquidgas transitions, and had to be replaced by renormalization group theory. Kotliar serin physics laboratory, rutgers university, piscataway, new jersey 08855. The approximation that is made in the mean field theory mft is that fluctuations can be neglected. Critical behavior of mean eld xy and related models kay kirkpatrick and tayyab nawaz department of mathematics, university of illinois at urbanachampaign 1409 w. The present paper is based on our graduate lectures in condensedmatter physics. The model is based on the meanfield theory in the hartreefock formalism to describe the lowenergy pseudogap physics. Electronic academic textbook for faculty of science on p. Antiferromagnetism an overview sciencedirect topics.
Ferromagnetism is the basic mechanism by which certain materials such as iron form permanent magnets, or are attracted to magnets. Introduction of the molecular field allows the theory of magnetization susceptibility behavior of ferromagnets, antiferromagnets, and ferrimagnets to be developed easily chikazumi 1964, barbara et al. Being threedimensional 3d systems, they were at the upper marginal dimension for the applicability of meanfield mf theory. At a critical point, the magnetization is continuous as the parameters are tuned closer to the critical point, it gets smaller, becoming zero at the critical point.
Within our approaches, we find possible coexistence of superconductivity and anti ferromagnetism for both electronic and coldatomic models. This course is designed to be of interest to both theorists and experimentalists. Kardar,statistical physics of particlescambridge, 2007 a superb modern text, with many insightful presentations of key concepts. Ferromagnetic phenomena comments and corrections please. To the meanfield theory of a twosublattice antiferromagnet core. The calculation of critical exponents is nontrivial, even for simple models such as the ising model. Chapter 6 antiferromagnetism and other magnetic ordeer. Chapter 7 mean field theory of phase transitions 7. Mean field theory of antiferromagnetic ising model square. The effective hartree field and the gain in kinetic energy due to the onsite and intersite correlation factors drive the antiferromagnetism. Antiferromagnetism and metal insulator transition in the. The equations of the dynamical meanfield theory are solved with a suitably extended version of wilsons numerical renormalization group. Mar 10, 2014 the present paper is based on our graduate lectures in condensedmatter physics. Initially, the large n expansion was developed for the kondo.
The various thermodynamic functions and their singular behaviour can now be obtained from the corresponding partition. Applications to ironbased superconductors and cold bosefermi atomic mixtures, physics letters a on deepdyve, the largest online rental service for scholarly research with thousands of academic publications available at your fingertips. Magnetic phase transition in the mean field approximation mean field approximation recall. Here, we will introduce an approximate technique known as mean field theory. The meanfield theory is treated in detail, and thus the book is a useful text for students mastering this general method. For example, the molecular field in iron at room temperature is 6.
We use the green function technique and cpa decoupling. Describing antiferromagnetism in density functional theory dft had been an unsolved problem since the 1930s until recently. Tcd february 2007 2 1 molecular field theory of antiferromagnetism 2 equal and oppositelydirected magnetic sublattices. An effective mean field theory for the coexistence of anti. We present the results of numerical studies of superconductivity and antiferromagnetism in a strongly correlated electron system.