ABSTRACT
The idea of classical Boolean computing with single electron spins was described in Chapter 15. It is an interesting notion, but it is also somewhat academic since the operating temperature is likely to be a few Kelvin. There is however a room-temperature version of single spin logic where a single spin is replaced with a single-domain shape anisotropic ferromagnet, as shown in Fig. 17.1. The domain contains many spins, but, because of strong exchange interaction between the spins, they all point in the same direction. If a magnetic field or some other entity makes the spins reorient by rotating, all the spins will rotate in unison so that the entire ensemble of spins acts like one giant classical spin [1]. This has an important ramification. Magnets of certain shapes (e.g., the elliptical disk shown in Fig. 17.1) have only two stable magnetization orientations. In this case, the orientations are along the major axis of the ellipse (“up” and “down”), which can be used to encode logic bits “0” and “1” just as a single electron spin’s two stable orientations in a magnetic field can be used to encode binary bits. Therefore, the single domain nanomagnet can act as a binary switch since it has two stable states. The difference with single electron spin in a magnetic field is that there the two stable states were energetically non-degenerate, but here they are degenerate and no magnetic field is needed to maintain the bistability. The bistability is entirely due to the anisotropic shape of the nanomagnet. One can switch the magnet from one stable state to the other (which is
equivalent to switching the stored bit from 0 to 1, or vice versa) in a variety of ways. Let us briefly compare the magnetic switch with a transistor switch at this point. A transistor (e.g., a MISFET) also has two stable conductance states (“on” and “off”) and switching between them is accomplished by driving charges in and out of the transistor’s channel. Each charge acts as a single degree of freedom and if N charges are involved in the switching action, then the minimum energy that will be dissipated in the switching process can be shown to be NkT ln(1/p) where p is the probability of static error (i.e the probability that a bit will switch spontaneously, resulting in error). However, in the case of the magnet switch, even if there are N spins, since they all rotate in concert, they act like a single degree of freedom. Hence the minimum energy that will be dissipated in switching a magnet is kT ln(1/p) [2]. Therefore, the magnet has an intrinsic energy advantage over the transistor –
to
FIGURE 17.1
(a) An elliptical nanomagnet small enough to contain a single domain. In the nanomagnet, exchange interaction between the spins makes all of them point in the same direction as shown. Because of the elliptical shape of the magnet, which makes it shape-anisotropic, the spins tend to point along the major axis of the ellipse. The two directions – “up” and “down” along the major axis – are stable orientations for the magnetization vector of the magnet and they can be used to encode the logic bits 0 and 1. (b) When the magnetization of the magnet rotates under some external perturbation, all the spins rotate together in unison. That makes the entire single-domain nanomagnet behave like one giant classical spin.
