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SYMPOSIUM: MAGNETIC PROPERTIES OF MATERIALS

1. INTRODUCTION

ON MAGNETIC MATERIALS

All substances can be influenced by applied magnetic fields. In terms of magnetic properties, substances are usually divided into 3 broad categories: 1) Ferromagnetic substances such as iron, steel, cobalt, and nickel are able to become highly magnetic in a relatively weak magnetic field. Such substances contain substantial internal magnetic fields in the absence of an applied magnetic field. 2) Paramagnetic substances such as liquid oxygen have a capability to be magnetized which is slightly greater than that of a vacuum and much less than that of iron. When placed in a magnetic field, paramagnetic substances are magnetized parallel to the lines of force of the field to an extent proportional to the intensity of the field (but not at extremely low temperatures or extremely high fields). When removed from an applied magnetic field, the magnetization of paramagnetic substances returns to zero. 3) Diamagnetic substances such as the alkalis and alkaline earth metals, the halogens, and the noble gases are repelled by magnets and tend to position themselves at right angles to the magnetic lines of force. Like paramagnetic substances, when removed from an applied magnetic field, the magnetization of diamagnetic substances returns to zero. Diamagnetism was discovered in 1846 by Michael Faraday (1791-1867).

ON MAGNETIC MATERIALS AND SPINTRONICS

The term "spintronics" refers to a relatively new field that aims to combine ferromagnets with semiconductors to develop electronic devices that exploit the quantum mechanical of electrons as well as their charge.

In this context, the term "spin" refers to the part of the total angular momentum of a particle (electron, atom, etc.) that is distinct from its orbital angular momentum -- in other words, spin is essentially a rotation momentum. According to quantum mechanics, spin is quantized and restricted to a particular set of values for each type of particle. (For more details concerning spin, see the notes below.)

One aim of this new field is to integrate information storage with information processing, but a broader goal is to develop new functionality that does not exist separately in a *ferromagnet or in a semiconductor. To this end, investigators are searching for "emergent behavior" in combined ferromagnetic semiconductor structures.

In general, "ferromagnetism" is a property of certain materials subjected to a magnetic field, the magnetic field causing induced magnetism which combines with the applied field to increase the local field. Ferromagnetic materials are strongly attracted to a magnetic pole and have high effective magnetic permeabilities that are greatly dependent on the applied magnetizing field. Iron, cobalt, nickel, and certain alloys are typical examples of ferromagnetic materials. During the past five decades, several ionically bound compounds have been discovered to be ferromagnetic. Some of these compounds are electrical insulators, but others have the conductivity of semiconductors. Above its Curie point (Curie temperature), the spontaneous magnetization of a ferromagnetic material vanishes and the material becomes "paramagnetic", i.e., it remains only weakly magnetic. This evidently occurs because the thermal energy becomes sufficient to overcome the internal aligning forces of the material.

Of importance in magnetoelectronics is the phenomenon of "giant magnetoresistance" (GMR). GMR is a quantum mechanical effect observed in magnetic thin-film structures composed of alternating ferromagnetic and nonmagnetic layers. When the magnetic moments of the ferromagnetic layers are parallel, the spin-dependent scattering of charge carriers is minimized, and the material has its lowest electrical resistance. When the ferromagnetic layers are anti-aligned, the spin-dependent scattering of charge carriers is maximized, and the material has its highest resistance. The directions of the magnetic moments are manipulated by external magnetic fields applied to the materials. These materials can now be fabricated to produce significant changes in resistance in response to relatively small magnetic fields, and to operate at room temperature.

The first report of the discovery of GMR appeared in 1988.The first commercial product using GMR (a magnetic field sensor) became available in 1994. The first products involving GMR to have major economic impact are "read" heads for magnetic hard disk drives, these devices announced by IBM in November 1997. The next major economic impact from the discovery of GMR is expected to come from nonvolatile magnetic computer memory, i.e., computer memory that remains intact when the computer is switched off. The Honeywell Corporation announced the demonstration of GMR random access memory (RAM) in January 1997.

Reviewing the field of spintronics in the May issue of Physics Today, Peter Gruenberg (Juelich Research Center, DE) points out that the study of layered magnetic structures is one of the hot areas in current magnetism research, the interest due largely to growing applications in magnetic sensors and magnetic storage media such as computer disks and random access memories. Gruenberg suggests that magnetic random-access memories (MRAMs) based on structures of magnetic metallic films interspersed with nonmagnetic metallic or insulating interlayers could be the next generation in magnetic-storage technology, replacing the semiconductor-based dynamic random-access memories (DRAMs) that are the current standard. The advantages of MRAMs include retention of information when the computer is switched off, high storage density, and low energy consumption. Gruenberg states: "The field of layered magnetic structures is broad and still expanding, with many different phenomena of interest. It remains a fascinating field, rich with opportunities both in basic research and in potential applications."

ON THE THEORY OF MAGNETIC MATERIALS

In theoretical physics, in general, the term "field" refers to a mathematical representation of the spatiotemporal distribution of a force or forces experienced by a test object at each point in a region, the field essentially serving as the mediating entity between any objects in that field. The field may result from an application from outside the system, or from components of the system, or both.

In general, in this context, the term "mean field" refers to the average field produced at a point in space in a system of distributed field sources, and a "mean-field theory" is any theory based on a mean field approach. The essential idea of a mean field approach is that by considering only the average field at any point the field equations that describe the system often become tractable.

The major experimental observations concerning magnetism were clearly delineated by Pierre Curie (1859-1906) in a 100-page paper in 1895, a paper which reported his work on the effects of temperature on magnetic materials, the subject of his doctoral dissertation. In this monumental paper, Curie clarified the knowledge of his time and indicated directions for future research. Already in 1895, it had long been recognized that substances with magnetic properties can be divided into 3 categories -- diamagnetic, paramagnetic, or ferromagnetic --according to their behavior in magnetic fields. According to the current view: a) In "diamagnetism", the magnetization of a substance is in the opposite direction to that of the applied field. Diamagnetism results from changes induced in the orbits of electrons in the atoms of a substance by the applied field. All substances are to some extent diamagnetic, but it is a weak form of magnetism and it may be masked by stronger forms of magnetism. b) In "paramagnetism", the atoms or molecules of the substance are capable of being aligned in the direction of the applied field. Paramagnetism occurs in all atoms or molecules with unpaired electrons. c) In ferromagnetic substances, within a certain temperature range, there are intrinsic net atomic magnetic moments, which line up in such a way that magnetization persists after the removal of the applied magnetic field. Below a certain temperature (Curie point; Curie temperature), an increasing magnetic field applied to a ferromagnetic substance will cause increasing magnetization to a high value. Above the Curie point, ferromagnetic materials become paramagnetic.

In this context, the term "molecular field" refers to the molecular field theory of Pierre Weiss (1865-1940), a theory first proposed in 1907 to explain the behavior of ferromagnetic materials. A Weiss molecular field is an effective magnetic field which acts on atomic magnetic moments within a domain, the field tending to align the moments, and the field in turn generated by these magnetic moments. The Weiss molecular field theory is a mean-field theory.

In 1928, Werner Heisenberg (1901-1976) demonstrated that from the perspective of quantum mechanics, the cause of ferromagnetism lies in the *quantum-mechanical exchange interaction between electrons, the interaction imposed by the Pauli exclusion principle. This was really an explanation rather than a contradiction of the Weiss mean-field theory, an amplification in terms of quantum considerations. Many physicists, however, felt uncomfortable with the new quantum-mechanical approach to magnetic materials: the classical theory gave a more immediate feeling of understanding, with a closer relationship to directly observable phenomena. In addition, the mathematical difficulties of quantum mechanics as applied to such systems resulted in many problems remaining unsolved. For these reasons, the classical approach to the magnetic properties of materials persisted for another generation.

ON THE ISING MODEL

In theoretical physics, one approach that has proved to be of great general utility is to begin with an attempt to identify and understand the simplest model exhibiting the same essential features as the physical problem in question. In condensed-matter physics, such a model is the so-called "Ising model", an approach that has been applied to ferromagnetism, and also to a number of other systems. In general, the Ising model consists of an array of entities in one, two, or three dimensions, with each entity capable of being in one of two possible states, with each entity interacting only with its nearest neighbors, with a condition that when two neighboring entities are in the same state the total energy of the pair is reduced compared to when the same two neighboring entities are in opposite states. These are the elements of the model, with other conditions imposed depending on how the model is used. Various versions of the model have been of great utility in studies of cooperative phenomena in condensed-matter systems, and the model itself has an interesting human story attached to it.

The following points are made by Brian Hayes (American Scientist 2000 88:384):

1) The Ising model was invented in 1920 by Wilhelm Lenz, who proposed it as a simplified version of a ferromagnet (Physik. Z. 1920 21:613). In 1925, a student of Lenz, Ernst Ising, chose the model as the subject of his doctoral dissertation at the University of Hamburg (DE), and the model has subsequently borne Ising's name.

2) Lenz and Ising formulated the original model in terms of "spins", although the concept of rotation is never used. In the original model, a spin is merely one of two states, characterized by an arrow pointing either up or down but in no other direction. The spins are arranged in a grid or lattice pattern. Spins at neighboring sites prefer to point the same way: the energy is lower when adjacent spins are parallel, and the energy is higher when adjacent spins are antiparallel. Except for these nearest neighbor preferences, the spins do not interact at all. Thermal fluctuations tend to randomize the spins. Finally, an external magnetic field may impose a bias on the spin directions.

3) Hayes points out that the Ising model is indeed a crude picture of a ferromagnet: a) the Ising spins correspond to spinning electrons in iron atoms; b) the lattice represents the crystal structure; c) the nearest neighbor interaction mimics the overlap of quantum mechanical wave functions in adjacent iron atoms. The one element in the model that has no obvious counterpart in real systems is the requirement that spins take on only two possible orientations.

4) Ising's doctoral dissertation examined whether the 1-dimensional version of the model exhibited a Curie point. The results were negative: the 1-dimensional Ising model exhibits no phase transition at any temperature above absolute zero. Ising apparently believed this negative result would hold in higher dimensions as well, but in this conjecture he was wrong.

5) Ising's published results (Z. fur Physik 1925 31:253) were essentially ignored until 1936, when Rudolf Peierls (1907-1995) showed that a 2-dimensional Ising model might exhibit a temperature-dependent phase transition . An exact calculation of such a system, a mathematical tour de force, was made by Lars Onsager (1903-1976) in 1944. Exact calculations for 3-dimensional Ising models have remained intractable, but approximations and computer simulations involving the model have proved extremely useful, and the value of the model has grown rather than diminished through the years. An important approximation method is known as "the renormalization group": the simplest version of this algorithm gathers sets of spins into blocks, replaces each block with a single new spin, and finally adjusts the couplings between spins to compensate for the coarsening of the lattice.

6) Concerning Ernst Ising, there is no record of Ising ever publishing anything else in physics. After receiving his doctorate, Ising taught physics in German public high schools, but as a Jew he was dismissed from his teaching post when Hitler came to power in 1933. Ising then taught at a Jewish boarding school in Potsdam (DE), until that school was destroyed in the Kristallnacht pogrom of 1938. Ising and his wife fled Germany, but they escaped only as far as Luxembourg before the war overtook them. They managed to survive the occupation, and they finally reached the US in 1947. Ising taught physics and mathematics in Minot, North Dakota (US), and then taught for almost 30 years more at Bradley University in Peoria, Illinois (US). In 1998, Ernst Ising died at the age of 98.

MAGNETIC LEVITATION OF ORDINARY OBJECTS

In this context, "lifting" is distinguished from "levitation", with levitation referring to stable floating in an applied magnetic field.

The following points are made by Andrey Geim (PhysicsToday September 1998):

1) All materials can be lifted by magnetic fields that are currently standard. Due to the readjustment of electron orbits in a magnetic field, all objects exhibit diamagnetism, which determines the lowest possible limit of their magnetic response. Fields of approximately 10 *tesla are sufficient to lift practically any substance.

2) Magnetic fields strong enough to lift diamagnetic materials became available during the mid 20th century, and superconductors were first levitated in 1947. It took 50 years to rediscover the levitation of conventional room-temperature diamagnetic materials. In 1991, Beaugnon and Tournier magnetically lifted water and a number of organic substances. Other researchers soon levitated liquid hydrogen, helium, and frog eggs. The author's research group at the University of Nijmegen (NL) has levitated practically everything at hand, "from pieces of cheese and pizza to living creatures including frogs and a mouse." (The article includes a photograph of a levitated live frog in the bore of a 20 T magnet, the frog reported to exhibit no adverse effects from exposure to the magnetic field.) The magnetic fields used in these experiments have been available for decades.

3) In contrast to diamagnetic substances, paramagnetic substances cannot levitate. Only diamagnetic substances can flaunt *Earnshaw's theorem, which states that no stationary object made of charges, magnets, and masses can be held in space by any fixed combination of electric, magnetic, and gravitational forces. Diamagnetism involves electron motion around nuclei, and thus is not a fixed configuration as required by the theorem.

4) A diamagnetic substance can levitate only close to an inflection point of the vertical component of the magnetic field. This is a purely geometric condition independent of the field strength.

5) The author suggests an example of the exploitation of the diamagnetic force: the direction of growth of germinating seeds, which ordinarily depends on gravity, can in the absence of gravity (e.g., in a space ship) be determined by a small permanent magnet (O.A. Kuznetsov and K.H. Hasenstein, Planta 1996 198:87).

Notes:

tesla: International System unit of magnetic flux density. 1 tesla = 1 weber per square centimeter.

Earnshaw's theorem: The classic statement of this theorem is that a charge cannot be held in stable equilibrium in an electric field under the influence of electric forces alone. The theorem as given in the text by Geim is a recent reformulation by Michael Berry (M.V. Berry and A.K. Geim, Eur. J. Phys. 1997 18:307)

NOTES AND TERMINOLOGY

spin: In quantum mechanics, electrons, protons, and neutrons have an intrinsic angular momentum known as "spin", and a *magnetic moment parallel or antiparallel to that angular momentum. When electrons are combined together to form an atom or ion, there is a resultant angular momentum which is a combination of the intrinsic spin of the electrons and the angular momentum due to their motion about the nucleus, and this is the "spin" of the atom or ion. Atoms or ions with non-zero spin are magnetic atoms or ions. The idea of electron spin was first proposed by Goudsmit and Uhlenbeck in 1925 to explain the splitting of atomic spectroscopic emission lines in the presence of a magnetic field. Elementary particle spin involves a virtual rotation about the axis of the particle, which means only two spin states are possible, one clockwise and one counterclockwise.

ferromagnetic: A ferromagnet is a material (such as iron) in which there may be a permanent *magnetic moment, and in which the spins of the atoms are aligned parallel to each other.

magnetic moments: (magnetic dipole moment) The intrinsic spins of the electrons in an atom, together with the motion of the electrons around the nucleus, give rise to a magnetic field around the atom, and the magnitude of this field is related to the magnetic dipole moment of the atom or ion.

spin-dependent scattering: In this context, the term" scattering" refers to the change in direction of a particle because of a collision with another particle or system.

superconductivity: Superconductivity is a property of many metals, alloys, and chemical compounds at temperatures near absolute zero, at which temperatures their electrical resistivity vanishes and they become strongly diamagnetic. Diamagnetic substances such as the alkalis and alkaline earth metals, the halogens, and the noble gases are repelled by magnets and tend to position themselves at right angles to the magnetic lines of force.

superconducting pairs: (Cooper pairs) In the late 1950s, John Bardeen (1908-1991), Leon N. Cooper, and John R. Schrieffer demonstrated that superconductivity involves the formation of bound pairs of electrons, called "Cooper pairs". Their theory (BCS theory) argued that the electron pairs were "glued together" by small deformations (phonons) in the crystal lattice, the deformations accompanying the motions of electrons. But although phonons had been implicated in superconductivity many years before BCS theory, it was not until the 1960s that it became possible to definitively identify phonons as the "glue" (the interaction energy quanta) in conventional superconductivity.

quantum-mechanical exchange interaction: In general, an "exchange interaction" is an interaction resulting from the continued exchange of particles in a manner that bonds their hosts together (e.g., covalent bonding). Within each domain in ferromagnetic materials, the individual atomic magnetic moments are spontaneously aligned by exchange forces.

In this context, the "Pauli exclusion principal" is the rule that no two electrons in a system can possess the same set of quantum numbers.

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