Condensed-Matter Physics (1986) / Chapter Skim
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4 Magnetism
4 Magnetism
Pages 95-112
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From page 95... ...
In magnetic insulators each atom with an unfilled shell possesses an intrinsic magnetic dipole moment. In addition to their interaction with the applied field, the dipoles interact with one another through long-range dipolar forces and short-range exchange interactions, the latter arising from the interplay of electrostatics and quantum 95
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From page 96... ...
Studies of the magnetic properties of materials with localized moments occupy an unusual position in solid-state physics. This happens because these properties can be characterized using models involving only the individual atomic moments, rather than the full array of atomic electrons.
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From page 97... ...
These occurred not only in ideal systems but in various types of disordered materials as well. The period since 1970 has also been an era of rapid growth in computer simulation studies of various static and dynamic properties of magnets.
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From page 98... ...
(The value of exact solutions can hardly be overestimated.) A useful secondary feature of 1-D exact solutions is their ability to serve as testing grounds to give insight into the degree of reliability of the various approximate calculational techniques that must, of necessity, be employed in 3-D.
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From page 99... ...
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From page 100... ...
METALLIC MAGNETS Transition-Metal Ferromagnets Metallic magnets can be divided into two classes depending on whether the magnetic atoms belong to the transition-metal series or to the rare-earth and actinide series. Recent advances in the theory of transition-metal ferromagnets have led to a better understanding of the nature of their ground state and of their magnetic properties at finite temperatures.
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From page 101... ...
in iron and nickel that are seen in inelastic neutron scattering. These observations and others have led to a number of new theoretical schemes for extending the ground-state band picture to finite temperatures.
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From page 102... ...
Two approaches more directly concerned with the underlying electronic structure are the local-band theory and the alloy analogy. Each assumes a disordered magnetization configuration, approximately solves for the electronic states in the mean exchange field produced by the configuration, and demands that the configuration be reproduced self-consistently.
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From page 103... ...
In the past decade this has been strikingly evidenced in cerium metallic and semimetallic compounds and, more recently, in the actinides, with most recent work in plutonium compounds. The association of exceptionally strong anisotropy in magnetic properties with the region where the local-to-nonlocal f transition occurs suggests a strong connection between the two phenomena.
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From page 104... ...
For the heavier rare earths mixed valence involves a fluctuation between two degenerate nearly localized states, whereas for cerium the mixed-valence behavior may be associated with a 4f localization/delocalization transition. Whether this is indeed so is a question of great interest.
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From page 105... ...
On the theoretical side, we anticipate an exceptionally active effort in trying to understand the ground-state properties of lattices of mixed-valence ions on the basis of Hamiltonians that include narrow f states, broad conduction bands, hybridization, and If correlation effects. DISORDERED SYSTEMS Introduction As in other fields of condensed-matter physics, the study of disordered materials has been an area of intense activity in magnetism in recent years.
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From page 106... ...
Should this be the case, is it to a state of conventional magnetic order or to a low-temperature disordered phase not present in the ideal magnets? Disordered Ferromagnets, Antiferromagnets, and Paramagnets The title of this subsection refers to systems that undergo phase transitions to states of conventional long-range order characteristic of ideal magnets or else are sufficiently dilute that they remain in their high-temperature or paramagnetic phase at all temperatures.
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From page 107... ...
The second entailed the development of computer simulation techniques, which made possible a direct calculation of the neutron-scattering cross section by integrating the linearized equations of motion of the spins (Figure 4.4~. Studies of magnons in substitutionally disordered magnetic insulators have provided important general tests of our understanding of NEUTRON SCATTERING FROM Rb2 MnO54 M9046 F4 AT 4.0K AS COMPaRED WITH COMPUTER SIMULATIONS I ' I I 1 ' 2 1 ·^ Q=(0.5,0, 2.9)
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From page 108... ...
The percolation concentration refers to the concentration below which there is no longer an infinite cluster of mutually interacting magnetic atoms. Near the percolation point there is a direct competition between the thermal disorder due to the temperature and the substitutional disorder coming from the dilution.
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From page 109... ...
Unlike a ferromagnet, where the moments in the ground state are parallel, or an antiferromagnet, where there are interpenetrating lattices of oppositely directed moments, the spin glass has a large number of nearly degenerate ground states with widely differing noncollinear spin arrangements. The multiplicity of ground states can arise in a number of different ways.
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From page 110... ...
On the low-temperature side, the properties of the ground states are being analyzed along with the corresponding elementary excitations and their contribution to the specific heat and inelastic neutron scattering, for example. Spin-glass behavior has been established in a great many materials, seemingly rivaling in number those showing conventional magnetic order.
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From page 111... ...
Different simulation methods have now been developed for addressing different problems in magnetism. For example, the bulk, macroscopic behavior of magnetic models and the dependence on variations with temperature and magnetic field can be determined by Monte Carlo methods.
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From page 112... ...
, which is itself changing. A computer simulation method known as spin dynamics is used to update the environment of each moment constantly, and hence determine the time development of the system as a whole.
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