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A highly coveted objective of modern materials science is to optimize multiple coupled functionalities in the same single phase material and control the cross-response via multiple external fields. One important example of such multi-functionality are multiferroic materials where two or more ferroic properties are intrinsically coupled. They include, among others, the magneto-electric and magneto-structural materials, which are well understood at the nano- and continuum length (and time) scales. The next emerging frontier is to connect these two limiting scales by probing the mesoscale physics of these materials.This book not only attempts to provide this connection but also presents the state-of-the art of the present understanding and potential applications of many related complex multifunctional materials. The main emphasis is on the multiscale bridging of their properties with the aim to discover novel properties and applications in the context of materials by design. This interdisciplinary book serves both graduate students and expert researchers alike.

This book brings together an emerging consensus on our understanding of the complex functional materials including ferroics, perovskites, multiferroics, CMR and high-temperature superconductors. The common theme is the existence of many competing ground states and frustration as a collusion of spin, charge, orbital and lattice degrees of freedom in the presence of disorder and (both dipolar and elastic) long-range forces. An important consequence of the complex unit cell and the competing interactions is that the emergent materials properties are very sensitive to external fields thus rendering these materials with highly desirable, technologically important applications enabled by cross-response.