Based on experimental observations of modulated magnetic patterns in a Co 0:5 Ni 0:205 Ga 0:295 alloy, we propose a model to describe a (purely) magnetic tweed and a magnetoelastic tweed. The former arises above the Curie (or Néel) temperature due to magnetic disorder. The latter results from compositional fluctuations coupling to strain and then to magnetism through the magnetoelastic interaction above the structural transition temperature. We discuss the origin of purely magnetic and magnetoelastic precursor modulations and their experimental thermodynamic signatures. DOI: 10.1103/PhysRevLett.92.197203 PACS numbers: 75.80.+q, 62.20.Dc, 64.70.Kb, 75.30.Kz The thermodynamics of phase transitions is strongly influenced by the presence of quenched disorder [1]. In particular, statistical compositional disorder plays a fundamental role in the precursor strain modulations observed in alloys undergoing a first-order displacive transition [2]. Such strain modulations are crosshatched and give rise to the so-called (structural) tweed pattern [3] observed well above the transition temperature T M [4]. Recent advances in high resolution imaging of magnetic domain patterns, such as magnetic force microscopy [5] and Lorentz transmission electron microscopy (LTEM) [6], have revealed fascinating modulated magnetic patterns both above and below the Curie temperature in certain magnetic alloys. In contrast to the structural tweed, the magnetic modulations that occur as precursors to the magnetic transition give rise to a stripelike pattern.In this Letter we present TEM observations in Co 2 NiGa alloys showing both strain and magnetic modulations and provide a model that explains these observations. We focus on the magnetic modulations and demonstrate that the tweed concept is not just structural but applicable to a much broader class of materials. We show that, independently of specific details of the pattern or the physical variable involved in modulation, the origin of tweed lies in very general requirements in quite different materials undergoing phase transitions. For instance, polar (or dielectric) tweed has been observed in mixed B-site cation ferroelectrics, such as Pb Mg 1=3 Nb 2=3 3 -PbTiO 3 [7]. Extending previous ideas in the context of (purely) structural tweed [2], we suggest that the tweedlike modulations above the transition (structural, magnetic, or other) are a natural cooperative response in systems that are sensitive (in the sense of, e.g., phonon softening, ''susceptibility'' or other response functions) to local symmetry breaking perturbations (e.g., due to statistical disorder) assisted by anisotropic long-range interactions. The long-range nature of such interactions (elastic, magnetic, or other) connects the different perturbed regions while the anisotropy determines the specific modulations of the resulting pattern. We note that statistical compositional disorder is intrinsic to alloys and therefore they are the most probable candidates to exhibit such phenomena.We start by defining what we mean by...
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