1.1  Motivation

The exponential growth of the semiconductor industry has successfully proceeded for about four decades supported by continued improvement of complementary metal-oxide-semiconductor (CMOS) technology. For the next several years, there will be no apparent substitutes for the CMOS technology and its future development is already charted by the International Technology Roadmap for Semiconductors (ITRS) [1]. However, fundamental physical and economic limitations [2, 3, 4] such as leakage, high power densities, process variability, and soaring costs will bring the scaling of CMOS devices to an end. Therefore, besides exploring and introducing new materials, device structures, and design technologies, investigating possible alternative technologies to replace or at least to supplement CMOS is important to proceed with the performance enhancement of logic devices and circuits [5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]. Right now there are many different devices under investigation with widely varying performance parameters e.g. energy, speed, area, et cetera. Spintronic devices [16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29] especially magnetoresistive devices [30, 31] with a tunnel barrier junction structure [32], are strong candidates due to their non-volatility and compatibility with CMOS technology [33, 34, 35, 36, 37, 38, 39, 40].

Despite the advantages of high speed and unlimited endurance, the first generation of magnetic tunnel junctions (MTJs) [41, 42, 43], which utilized Oersted fields for the magnetization switching, was unfavorable in terms of scalability and energy consumption. By using the spin-transfer torque [44, 45] switching technique [46, 47], the second generation of the MTJ (STT-MTJ) [48, ?, 49] eliminates the need for current lines adjacent to memory cells, which were required previously for generating a switching field. Thus, by using the same interconnects for reading and writing operations, the STT-MTJ is more scalable and yields smaller switching energies [22, 23]. Magnetoresistive random-access memory (MRAM) with STT-MTJs as memory elements combines the speed of static RAMs (SRAMs), the density of dynamic RAMs (DRAMs), the non-volatility of flash memory, and has all the characteristics of a universal memory [39]. STT-MTJ technology is also attractive for building logic configurations which combine non-volatile memories and logic circuits (so-called logic-in-memory architecture [50]) to overcome scaling obstacles of CMOS logics [37, 51, 52, 53, 54, 55, 56, 57, 58, 59]. Furthermore, STT-operated spintronic devices realize memristive behavior  [60, 61, 62, 63, 64, 65, 66, 67].

The memristor (memory-resistor) is the fourth fundamental circuit element predicted from a symmetry argument of circuit theory in 1971 [68]. However, its first physical realization, in titanium dioxide (TiO                      2   ), was announced about four decades later [69]. It can be thought as a passive programmable resistor. It holds a resistance state that depends on the history of the applied voltage/current even when the power is off. Memristive devices and systems [70, 71, 72] are capable of storing and processing information and offer unique properties which cannot be achieved in conventional electronic circuits by combining resistors, capacitors, and inductors. The most obvious application of memristive devices is non-volatile memory. Their great potential has attracted significant attention for developing alternative logic architectures [73, 74, 75, 76, 77, 78, 79, 80, 81, 82]. In addition, memristive devices can be used as artificial synapses for neuromorphic applications [83, 84, 85, 86, 87, 88, 89, 90]. As a basic element added to the circuit theory [91], memristors are also potentially suited for a wide range of tasks including analogue-to-digital and digital-to-analogue converters [92], electronic filters [93], temperature [94, 95] and power [96] sensors, oscillators [97], signal processing [98], differential [99] and programmable [100] analog circuits, and control systems [101, 102].