232 12.Magnetic Properties of Materials field strength to a value Hc,called the coercive field.Solids having a large combination of M,and He are called hard magnetic materi- als(in contrast to soft magnetic materials,for which the area inside the loop of Figure 12.7 is very small).A complete cycle through pos- itive and negative H-values as shown in Figure 12.7 is called a hys- teresis loop.It should be noted that a second type of hysteresis curve is often used in which B(instead of M)is plotted versus H. No saturation value for B can be observed;see Eq.(12.3).Removal of the residual induction requires a field that is called coercivity,but the terms coercive field and coercivity are often used interchange- ably.The area within a hysteresis loop (B times H or M times uoH) is proportional to the energy per unit volume,which is dissipated once a full field cycle has been completed;see also Section 11.9. The saturation magnetization is temperature-dependent. Above the Curie temperature,Tc,ferromagnetics become para- magnetic.Table 12.2 lists Curie temperatures for some elements. In ferromagnetic materials,such as iron,cobalt,and nickel, the spins of unfilled d-bands spontaneously align parallel to each other below Te,that is,they align within small domains(1-100 um in size)without the presence of an external magnetic field; Figure 12.8(a).The individual domains are magnetized to satu- ration.The spin direction in each domain is,however,different, so that the individual magnetic moments for virgin ferromag- netic materials as a whole cancel each other and the net mag- netization is zero.An external magnetic field causes those do- mains whose spins are parallel or nearly parallel to the external field to grow at the expense of the unfavorably aligned domains; Figure 12.8(b).When the entire crystal finally contains only one single domain,having spins aligned parallel to the external field direction then the material is said to have reached technical sat- uration magnetization,Ms [Figure 12.8(c)].An increase in tem- perature progressively destroys the spontaneous alignment,thus reducing the saturation magnetization,Figure 12.8(d). We have not yet answered the question of whether or not the flip from one spin direction into the other occurs in one step, that is,between two adjacent atoms or over an extended range of atoms instead.Indeed,a gradual rotation over several hun- TABLE 12.2.Curie temperature,Te for some ferromagnetic materials Metal Te(K) Fe 1043 Co 1404 Ni 631 Gd 289field strength to a value Hc, called the coercive field. Solids having a large combination of Mr and Hc are called hard magnetic materi￾als (in contrast to soft magnetic materials, for which the area inside the loop of Figure 12.7 is very small). A complete cycle through pos￾itive and negative H-values as shown in Figure 12.7 is called a hys￾teresis loop. It should be noted that a second type of hysteresis curve is often used in which B (instead of M) is plotted versus H. No saturation value for B can be observed; see Eq. (12.3). Removal of the residual induction requires a field that is called coercivity, but the terms coercive field and coercivity are often used interchange￾ably. The area within a hysteresis loop (B times H or M times 0H) is proportional to the energy per unit volume, which is dissipated once a full field cycle has been completed; see also Section 11.9. The saturation magnetization is temperature-dependent. Above the Curie temperature, Tc, ferromagnetics become para￾magnetic. Table 12.2 lists Curie temperatures for some elements. In ferromagnetic materials, such as iron, cobalt, and nickel, the spins of unfilled d-bands spontaneously align parallel to each other below Tc, that is, they align within small domains (1–100 m in size) without the presence of an external magnetic field; Figure 12.8(a). The individual domains are magnetized to satu￾ration. The spin direction in each domain is, however, different, so that the individual magnetic moments for virgin ferromag￾netic materials as a whole cancel each other and the net mag￾netization is zero. An external magnetic field causes those do￾mains whose spins are parallel or nearly parallel to the external field to grow at the expense of the unfavorably aligned domains; Figure 12.8(b). When the entire crystal finally contains only one single domain, having spins aligned parallel to the external field direction then the material is said to have reached technical sat￾uration magnetization, Ms [Figure 12.8(c)]. An increase in tem￾perature progressively destroys the spontaneous alignment, thus reducing the saturation magnetization, Figure 12.8(d). We have not yet answered the question of whether or not the flip from one spin direction into the other occurs in one step, that is, between two adjacent atoms or over an extended range of atoms instead. Indeed, a gradual rotation over several hun- 232 12 • Magnetic Properties of Materials TABLE 12.2. Curie temperature, Tc, for some ferromagnetic materials Metal Tc (K) Fe 1043 Co 1404 Ni 631 Gd 289