ABSTRACT
Magnetostatic dipole-dipole interactions play an important role in determining properties of nanomagnetic systems along with the exchange coupling and magnetocrystalline anisotropy, which were discussed in Chapter 2. že integral-di¥erential equations of micromagnetics lead to complexity. žese equations are nonlinear because the magnetization is a vector of constant magnitude. že nature of the dipole-dipole interactions favors patterns that are divergence free in volume and induce magnetic charges on the surfaces that create demagnetizing ¢elds opposed to applied ¢elds. že emerging ¢eld of spintronics with spinpolarized currents in semiconductors proceeds with the magnetic moment of the electron as just the tail of the dog. Much of the work on giant magnetoresistance (see Chapters 4 and 5), tunneling magnetoresistance (see Chapters 10-12), and magnetic random access memories (see Chapter 35) is performed by using intelligent ways to avoid the complexities of dipole-dipole interactions. že movement to ultrathin ¢lms was motivated by reducing the role of dipole-dipole interactions in directing the process of magnetization, while at the same time eliminating the variation of magnetization in the z-direction, perpendicular to
the plane of the ultrathin ¢lm. Ewing understood the importance of the dipole-dipole interaction in ferromagnetism as early as in 1890. Ewing gave the name to “hysteresis” [1].* In 1935, Landau gave the ¢rst 3D model of a structure that minimized the e¥ects of the dipole-dipole interaction (see Figure 3.1). In the 1970s, a beautiful new technology was created using magnetic bubbles† for which understanding of the dipole-dipole interactions was critical. žis chapter is intended as an ode to complexity in anticipation that emerging technologies may yet bene¢t if the current view of dipole-dipole interactions is not far from sight. že concept of splay saving is a recurrent theme in this ode. žat concept underlies the recent work of Riccardo Hertel’s group on the propagation of domain walls along a nanotube of permalloy [2].
