Ferromagnetic domain walls

Figure 3.30 Magnetic domains in a ferromagnetic crystal (schematic). The magnetic dipoles, represented by arrows, are aligned parallel in each domain. The domain walls constitute (approximately) planar defects in the structure.

Ferromagnetic and ferroelectric materials are only two examples of a wider group that contains domains built up from switchable units. Such solids, which are called ferroic materials, exhibit domain boundaries in the normal state. These include ferroelastic crystals whose domain structure can be switched by the application of mechanical stress. In all such materials, domain walls act as planar defects running throughout the solid. 

Ac-susceptibility measurements on (Ga,Mn)As with x = 0.042 have been performed in alternating B from 0.1-4 mT. In the temperature dependence of susceptibility, there is a sharp peak at about 48 K at 0.1 mT, which suggests a ferromagnetic phase transition. The temperature and magnetic field dependence is rather complicated and an increase of B involves additional peaks (the number of which up to 4), which may be due to domain formation and domain wall movement (Sadowski et al. 2000). There is also a report about ac-susceptibility measurements on (Ga,Mn)As with x = 0.07, which shows that there is no difference between the field-cooled and zero-field cooled ac-susceptibilities measured with B = 10 mT (Van Esch et al. 1997). 

Ferromagnetic (In,Mn)As/GaSb heterostructures with rectangular hysteresis show also peculiar light-irradiation effects. In particular, the coercive force is drastically reduced by the illumination, which suggests a reduction of the domain wall pining energy (Oiwa et al. 2001). 

Domain Wall Superconductivity in Ferromagnetic Superconductors and Hybrid S/F Structures... 

Summary. On the basis of phenomenological Ginzburg-Landau approach we investigate the problem of order parameter nucleation in a ferromagnetic superconductor and hybrid superconductor - ferromagnetic (S/F) systems with a domain structure in an applied external magnetic field H. We study the interplay between the superconductivity localized at the domain walls and between the domain walls and show that such interplay determines a peculiar nonlinear temperature dependence of the upper critical field. For hybrid S/F systems we also study the possible oscillatory behavior of the critical temperature TC(H) similar to the Little-Parks effect. 

The profile Bz(x, y) is determined by the ratio of two length scales thickness of a ferromagnetic film D and distance between the domain walls w (hereafter we consider the width of the domain wall to be much less than ). Provided the ferromagnetic film is rather thick (D w), the magnetic... 

Ferromagnetic domains are regions in which unbalanced electron spins are aligned. Parts of three domains are indicated. The dashed lines are 180° and 90° domain walls. From W. F. Hosford, Physical Metallurgy (Boca Raton, FL CRC Press, 2005), p. 445, figure 26.4. 

More generally, the dynamic behavior of domain walls in random media under the influence of a periodic external field gives rise to hysteresis cycles of different shape depending on various external parameters. According to a recent theory of Nattermann et al. [54] on disordered ferroic (ferromagnetic or fe) materials, the polarization, P, is expected to display a number of different features as a function of T, frequency, / = iv/2tt, and probing ac field amplitude, E0. They are described by a series of dynamical phase transitions, whose order parameter Q = uj/2h) Pdt reflects the shape of the P vs. E loop. When increasing the ac... 

Figure 7. Illustration of partial domain wall formation in an AF layer when the AF is sandwiched between two FM layers. (A) When the AF thickness (tAF) is very small compared to So, no partial DW is formed and the two FM are direct coupled and the AF follows the rotation of the ferromagnets. (B) When tAF is sufficiently large, a partial DW forms with a critical angle starting from 90° up to which the AF moments can be twisted and (C) when tjp > So, a 180° DW is established.

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