By Denny D. Tang

When you are a semiconductor engineer or a magnetics physicist constructing magnetic reminiscence, get the knowledge you wish with this, the 1st e-book on magnetic reminiscence. From magnetics to the engineering layout of reminiscence, this functional booklet explains key magnetic homes and the way they're concerning reminiscence functionality, characterization equipment of magnetic motion pictures, and tunneling magnetoresistance impact units. It additionally covers reminiscence telephone ideas, array structure, circuit versions, and read-write engineering matters. you are going to comprehend the smooth fail nature of magnetic reminiscence, that is very diverse from that of semiconductor reminiscence, in addition to ways to take care of the problem. you are going to additionally get precious problem-solving insights from real-world reminiscence case experiences. this is often an important e-book for semiconductor engineers who have to comprehend magnetics, and for magnetics physicists who paintings with MRAM. it's also a worthy reference for graduate scholars operating in electronic/magnetic machine learn.

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Bhadra and K. P. Roche, Phys. Rev. Lett. 66, 2152 (1991). S. S. P. Parkin, Phys. Rev. Lett. 67, 3598 (1991). R. Coehoorn, Phys. Rev. B 44, 9331 (1991). M. T. Johnson, S. T. Purcell, N. W. E. McGee, R. Coehoorn, J. aan de Stegge and W. Hoving, Phys. Rev. Lett. 68, 2688 (1992). J. Unguris, R. J. Celotta and D. T. Pierce, Phys. Rev. Lett. 79, 2734 (1997). P. A. Gru¨nberg, Sensors & Actuators A 91, 153 (2001). M. A. Ruderman and C. Kittel, Phys. Rev. 96, 99 (1954). C. Kittel, Quantum Theory of Solids (New York: Wiley, 1963), p.

We can assume that the interactions between all moments are identical and the displacements between the moments are independent of one another; then, all of the aij are equal. Let g substitute for aij. Therefore, the exchange interaction field can be written as follows: H ¼ gM: ð2:62Þ This is the original formulation of the Weiss Law. If we consider the case of the absence of an applied magnetic field, the field affected by the spontaneous magnetization is shown in Eq. 62). Substituting Eq. 62) into the Langevin equation, the spontaneous magnetization can be expressed as follows: M gmM kB T À : ð2:63Þ ¼ coth M0 kB T gmM At a temperature corresponding to the Curie temperature the spontaneous magnetization tends to zero and thus the ferromagnetic state becomes to a paramagnetic state.

For a given geometry, the relation between MS and HD is usually expressed as ð3:5Þ HD ¼ NM S ðin SI unitsÞ; where N is called the demagnetizing factor and is dimensionless. For cgs units, MS in Eq. 5) is replaced by 4pMS. It can be proven that N ¼ Nx þ Ny þ Nz ; ð3:6Þ in an (x, y, z)-coordinate system. In the case of an elliptic-shaped film, the demagnetizing field is uniform for a uniformly distributed magnetization [1, 2]. The demagnetization factor is a function of both the direction of magnetization and the shape of the film.