**5. Summary**

 [94] studied the Fe5Co70Si10B15 amorphous alloys and reported that the as-quenched sample shows a symmetric hysteresis loop (Fig. 24a). After annealing at 420 °C, the hysteresis loop becomes pinched (Fig. 24b) and annealing under a magnetic field of 10 kOe leads to a signif‐

**Figure 24.** The magnetic induction (B) vs. magnetic field (H) hysteresis loops of amorphous alloys Fe5Co70Si10B15: (a) asquenched, (b) annealed and (c) annealed in a magnetic field. These images were published in Ohta *et al*. [94]. Copy‐

Kohmoto *et al.* [95] have reported on the loop shift of the Fe5Co70Si10B15 amorphous alloys annealed at 180 °C for different time. The shift along the field axis was found to increase with the increase of annealing time. Rivas *et al.* [96] observed the shifted M-H loops in the metallicglass Co66Si16B12Fe4Mo2 ribbons annealed at 510 °C and "pre-magnetized" under a magnetic field of 400 kA/m at room temperature. A large negative field offset was observed when the initial applied field was parallel to the pre-magnetizing field, and the field shift was positive as the initial applied field was antiparallel to the pre-magnetizing field. However, no shift of M-H hysteresis loops was observed when the magnetic field was applied perpendicular to the direction of the pre-magnetizing field. The results suggest that the shift of M-H hysteresis loops in the annealed pre-magnetized ribbons originate from the coexistence of the amorphous and crystalline phases. After annealing, the amorphous matrix contains partially crystallized particles which are much magnetically harder if compared to the amorphous matrix. When subjected to a relatively high pre-magnetizing field, the magnetic moments of the particles tend to align along the applied field direction. Due to the large magnetic anisotropy, the magnetic spins of the hard-magnetic particles remain unchanged under the ac applied magnetic field used for the reorientation of the magnetic moments in the soft matrix. Therefore, a strong unidirectional dipolar magnetic field is formed, which can exert a strong restoring force on the reorientations of magnetic moments of the soft matrix, and thus produces a shift

The term "magnetic aging" indicates the time-dependent changes in the magnetization of ferromagnetic materials. These changes are also commonly referred to as "magnetic viscosity" or "magnetic after-effects". The typical relaxation time spans several orders of magnitude; it ranges from less than a second in superparamagnetic particles to millions of years in magnetic rocks.[97] Various mechanisms that contribute to the magnetic aging have been proposed,

icant shift of the loop along the H-axis (Fig. 24c).

236 Ferroelectric Materials – Synthesis and Characterization

right 1980, Elsevier.

of M-H hysteresis loops.

**4.4. Magnetic aging**

Biasing effects in different ferroic systems show a highly complex phenomenology which depends on several variables whose significance and contribution vary from case to case. Biased P-E and S-E ferroelectric loops are mainly generated by aging and fatigue processes, which are generally caused by the arrangement of charged defects and charge carriers in a certain configuration. A common cause of these two processes can be attributed to the development of an internal bias, which induces preferential polarization and strain configu‐ rations. In aging, the presence of an internal bias gives rise to pinched and asymmetric/shifted loops, while in fatigued samples the bias results in asymmetric and shifted loops. These features are mostly reversible upon opportune thermal treatments or electrical cycling, but fatigue shows also irreversible effects consisting, for instance, of mechanical damage such as microcracks that cannot be recovered. Aging effects are homogeneous since the controlling mechanisms are active down to the unit cell scale according to the symmetry-conforming property of point defects. Fatigue features instead can be highly inhomogeneous due to the screening retardation of the locally varying depolarizing field during electric field cycles. Under certain circumstances, aging of ferroelectrics can be explained within the concept of the symmetry-conforming property of point defects, which seems to be able to satisfactorily explain also biasing effects in non-polar ferroelastic materials. According to this principle, short-range ordered defects in ferroelastics tend to arrange themselves over time following the crystal symmetry of the hosting unit cell. The time-dependent change in the symmetry of point defects induces memory effects of equilibrium configurations, determining biased stress-strain hysteresis loops. In ferroelectric/ferroelasic perovskites, a partial replacement of A- and B-site cations with acceptor and donor species, respectively, produces analogous hardening and softening effects on ferroelectric and ferroelastic hysteresis loops under electric field and mechanical stress. Biasing effects in single phase ferromagnetic systems are usually generated by spatially inhomogeneous arrangement of spins on the unit cell scale. In magnetic hetero‐ structures and composites characterized by the simultaneous existence of ferromagnetic and antiferromagnetic ordering within the material, biasing effects are due to the competitive contributions from the coexisting soft and hard magnetic phases. The exchange interaction at the interfaces between dissimilar phases, the presence of the uncompensated spins, the formation of spin glass-like phases and spin canting effects, together with pinned preferential magnetization states are the most important possible mechanisms of biased M-H hysteresis loops. The thermally activated magnetic aging and the existence of domain wall pinning/depinning and rejuvenation effects in ferromagnetic materials introduce common characteristics with aging phenomena in ferroelectric/ferroelastic systems.
