**1. Introduction**

Ferroic materials such as ferroelectrics, ferroelastics and ferromagnetics exhibit two or more possible equivalent stable states with uniform orientation of the spontaneous polarization, spontaneous strain and spontaneous magnetization in absence of an external electric field, mechanical stress and magnetic field, respectively. These thermodynamic equilibria corre‐ spond to minima in the free energy as a function of the order parameter (P – polarization, S – strain and M – magnetization). Under the action of external fields, these equilibrium states can

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be switched from one to another, giving rise to symmetrical polarization-electric field (P-E), strain-stress (S-σ) and magnetization-magnetic field (M-H) hysteresis loops. It is often the case where two or more order parameters are coupled within the same phase and a change in one parameter produces a variation in another, as it occurs in multiferroic systems. The free energy profile can be influenced by many factors, such as compositional and structural inhomogene‐ ity, defects, internal fields, thermal and loading history. These can induce preferential states of the order parameters, leading to the appearance of deformed and asymmetric hysteresis loops. The understanding of these biasing effects and the study of their possible advantages/ disadvantages for specific applications, with the relative elaboration of strategies to induce/ avoid them, is of crucial importance to maximizing the performance of functional devices based on ferroic systems.

The present chapter aims to provide an overview of different biasing effects which can occur in different types of ferroic materials, with particular focus on the phenomenology and on the underlying microscopic mechanisms of the anomalies observed in hysteresis loops. The chapter is organized in three main parts. The first part describes the distortions of P-E and S-E hysteresis loops in ferroelectric/ferroelastic materials. The two main phenomena, which cause biased hysteresis loops, namely aging and fatigue, are comprehensively reviewed by describing the most important features in bulk systems and the inherent microscopic mecha‐ nisms. Attention is also given to imprint phenomena in thin films, with description of the most important models developed to explain the shifting of the polarization hysteresis loops. The second part is focused on biasing effects in ferroelectric/ferroelastic materials under mechan‐ ical stress, with detailed description of the influence of composition, poling state and temper‐ ature on the stress-strain curves of perovskite systems. Additionally, biased stress-strain loops in shape memory alloys are also briefly reviewed, highlighting the different mechanical behavior of the martensite and austenite phases. This section is concluded with a summary on Bauschinger effect observed in ferroelastic materials during cyclic mechanical loading. The third and last part describes the biasing processes occurring in ferromagnetic materials, with the main focus on the asymmetric M-H loops caused by the exchange bias effect, and by the coexistence of different magnetic phases in inhomogeneous magnetic systems.
