Disordered magnetic systems

While some disordered magnetic systems do display spin-glass behavior, those that are not geometrically frustrated can behave in a fundamentally different way. In... 

In this section we discuss some disordered magnetic systems that do not fit well under any of the subject headings of the other sections in this review. am-DyAg (sect. 8.3.1) is the only amorphous f-moment material studied with [iSR to date, as the pyrochlores (sect. 8.3.2) are the only perfectly fhistrated f-magnets studied with p,SR. Quasicrystals (sect. 8.3.3) must stand somewhat separately because they have atomic structure that is neither amorphous nor merely disordered-crystalline. For a discussion of spin-glass-like behavior in Ce, Yb, and U strongly correlated electron materials, see sect. 9. 

Disordered magnetic systems fall into three main types ... 

The exponents apply not only to solid systems (e.g. order-disorder phenomena and simple magnetic systems), but also to fluid systems, regardless of the number of components. (As we have seen in section A2.5.6.4 it is necessary in multicomponent systems to choose carefully the variable to which the exponent is appropriate.)... 

For magnetic systems, NMR is a useful technique in the investigation of the behavior of the magnetic moments and the critical phenomena (order-disorder, critical fluctuations)34,35. ... 

Systems of randomly oriented magnetic nanoparticles randomly dispersed in a supporting medium or matrix and that interact via dipole-dipole forces (last subsection) are systems having several energetically equivalent supermoment orientational states, at given temperatures and applied fields. As such, it is relevant to compare their magnetic behaviors with both the observed behaviors of canonical SG systems (dilute magnetic alloys such as MnCu) and the theoretical predictions from overly simple SG models. This has lead to a productive examination of the effects of dipolar and other inter-particle interactions in synthetic nanoparticle model systems that is reviewed below. Hopefully, this will in turn motivate the development of more realistic theoretical models of disordered dipolar systems. 

For magnetic systems, the effect of weak quenched uncorrelated point-like disorder on the critical behavior is usually predicted by the Harris criterion [40] disorder changes the critical exponents only if the specific heat critical exponent ap re of the pure (undiluted) system is positive ... 

The same field-theoretical representation may be obtained starting from the quite different type of lattice model known as one of the basic models in the theory of magnetic systems. We present it here since for what follows it serves to introduce different types of disorder in the polymer system. Let us consider a simple (hyper) cubic lattice of dimension d, and to each site prescribe a m-component vector S r) with a fixed length (for convenience one usually sets 15 = m). Imposing a pair interax tion with the energy proportional to the scalar products between pairs of spins, this defines the Stanley model (also known as the 0(m) symmetric model). The Hamiltonian of this model reads [77] ... 

The free energy can be used to determine the specific heat and the temperature dependence of the specific heat can tell us something about the possible order-disorder phase transitions in magnetic systems. A is an extensive property and hence depends on the system size. It is here conveniently written as a product of the system size N) and a system-size independent parameter which can be considered as the free energy per site. 

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