Magnetization
- Introduction
Nanoscale magnets made up of magnetic structures at nanometer length scales, which are atom-by-atom arrays of atomic spins assembled on nonmagnetic substrates, have been subject to extensive research in the last few years (Wiesendanger, 2018, p.3). The study conducted on the nanoscale magnets has been critical in exploring the atomic- and nanoscale magnetism that exists in the transition region between macroscopic materials and few interacting spins. The interest in nanoscale magnets arose from the need for faster, smaller, and smarter electronics increasing research in the behavior of materials at more minor scales (Ames Laboratory, 2015). Researchers have developed mechanisms and technologies to modify the physical properties of magnetic materials on the nanometer length scale, including the use of antidots, among others (Wiedwald et al., 2016, p.733). In this literature review, we explore the technologies utilized in nanoscale magnets, including the three-dimensional printing of these magnets. We also explore the different types of energies studied concerning nanoscale magnets in the reviewed literature and some of the equations essential in the production of magnets at the nanoscale.
The scanning tunneling microscope (STM) was critical in paving the way into the research of nanoscale magnets with its tip’s ability to move individual atoms on a surface (Wiesendanger, 2018, p.3). STM can also measure the magnetic properties of single atomic particles, making it possible to explore the magnetic moment of the atoms and magnetic anisotropy at a nanoscale. The creation of antidots on the surface of a thin film relies on similarly sensitive equipment that can measure and create holes accurately at a nanometer length scale. Other fields of interest in the researches into nanoscale magnets include bottom-up chains, exchange interaction in pairs and two-dimensional arrays, magnetic memories, and logic gates (Wiesendanger, 2018, p.4). The applications of these properties vary widely, but most experts believe that nanoscale magnets will play a critical role in future computing technologies. Researchers have noted that magnetism on this scale depends on the type of atoms and the interaction of the atomic spin with the conduction electrons of the substrate material (Wiesendanger, 2018, p.4). The choice of magnetic and substrate atoms, therefore, plays a critical role in determining the magnetic properties of the nanoscale magnet. This literature review will explore different materials commonly utilized in this process and their features.
Determining magnetization states in nanoscale magnets requires specialized techniques, which resolves these states in Ferro- and Ferri-magnetic particles (Fabian & Shcherbakov, 2018, p.315). These methods are critical in determining the strength and energy in the nanoscale magnets through the evaluation of different properties of the magnetic particles. Micro-magnetic modeling is a numerical method to calculate the energy barriers in particles at meta-stable states (Fabian & Shcherbakov, 2018, p.315). This method represents one of the innovative techniques used in the measurement and evaluation of micro-magnetic properties of particle systems. These measurements are critical in the manufacture of electronic devices such as random access memories created from these nanoscale magnets. Other methods for evaluating the magnetic properties of individual atoms include scanning tunneling spectroscopy (STS) (Wiesendanger, 2018, p.4). STS encompasses several different approaches, such as spin-resolved STS (SPSTS) and inelastic STS (ISTS). SPSTS evaluates the magnetic properties of an individual atom by considering its magnetization as a function of an externally applied magnetic field. At the same time, ISTS measures the excitation of the atom’s magnetization (Wiesendanger, 2018, p.4). In the next section, we explore the specific nanoscale magnets and their properties.
- Literature Review
2.1. Ferromagnetism
Ferromagnetism, the mechanism by which ferromagnetic materials form magnets. It is a critical factor in the conversion of bulk silicon into the nanostructured version of the compound. This transformation results in new properties for the nanostructured composite compared to the substrate (Granitzer & Rumpf, 2014, p.1). The physical and electric properties of the composite structure formed depend on different factors, such as the modification of the silicon surface. New spintronics focus on the magnetic properties of atomically thin two-dimensional materials that are the primary area of focus for future magnetic storage devices (Yu et al., 2010, p.1). Nanoscale magnets utilize the electric charge as well as the spin of the electron. Magnetic materials are embedded into the porous nanoscale silicon structures creating a composite structure that incorporates the magnetic properties of both the semiconductor and the magnetic fillings (Granitzer & Rumpf, 2014, p.1). The behavior of these materials on the nanoscale, when exposed to magnetic and electric fields, provides new observations that may be applicable in the manufacture of memory devices.
Most researchers have identified ferromagnetic materials as the most suitable candidates for most spintronic applications (Puszkarski et al., 2016, p.1). These materials possess anisotropic magnetic properties that interest electronic device manufacturers. One of these materials is gallium manganese arsenide (GaMn)As. (GaMn)As thin films’ magnetic anisotropy determines the direction of the magnetization (Puszkarski et al., 2016, p.1). Electronic engineers intend to manipulate these magnetic properties to aid in the manufacture of magnetic memory devices (Toledo et al., 2020, p.1). Researchers are also expanding the research of nanoscale ferromagnetism from the traditional two dimensions into the third dimension, increasing the possible applications of these materials in electronic devices. The use of single material systems limits the applications of two-dimensional ferromagnetic materials due to the restrictions in their magnetic properties (Yu et al., 2010, p.1). Research into the construction of van der Waals (vdW) heterostructures that incorporate the advantages of the traditional structures may improve the properties of the composite materials. Ferromagnetism, therefore, forms the core of nanoscale magnetism, and research into additional dimensions in atomically thin films may uncover other applications for this property in electronic devices.
2.1.1. Micro-magnetic Energies
Every magnetic field contains energy in the form of moving charge carriers. This energy is known as magnetic energy. The amount of magnetic energy present in a magnetic field varies with the ferromagnetic material. Modern magnetic random access memories (MRAM) utilize magnetic switching to realize the writing of a data bit driven by spin-torque effects or external magnetic fields (Song et al., 2019, p.1). These techniques are inefficient in energy consumption and require large electric currents to achieve this objective. One solution to this problem is the application of voltage pulses on insulating multiferroic heterostructure in magnetic switching rather than using large currents. In nanoscale magnets, the magnetic energies are affected by the spatial confinement of charge carriers in spherical quantum dots (QDs), which creates bands of energy levels in confinement, just like in electrons (Çakır et al., 2017, p.250). This confinement significantly affects the optical and electronic properties of the quantum dots. Magnetic energies in the nanoscale lengths, therefore, vary depending on the anisotropic properties of the materials.
The effective magnetic field in micromagnetics is composed of five domain energy terms, including anisotropy, exchange, external field, magneto-elastic, and magneto-static (Ferona & Camley, 2017, p.1). The study of the effects of this effective magnetic field’s impact on a magnetic domain in two and three dimensions has revealed significant insights that have advanced magnetic storage and memory devices in the recent past. Researchers in the field of micro-magnetism use the Landau-Lifshitz-Gilbert (LLG) equation to determine the behavior of magnetic domains under the effect of an effective magnetic field (Ferona & Camley, 2017). This equation can be used alone or in conjunction with Maxwell’s equation to evaluate this effect in both uniform and non-uniform effective magnetic fields. Spintronic devices utilize both the spin degrees of freedom and charge of electrons since they deal with atomically thin materials where researchers can accurately measure these energies (Pradipto et al., 2019, p.1). These micro-magnetic energies determine most of the properties of nanoscale magnets. Understanding their properties and interactions is critical in developing their applications in electrical devices.
2.1.1.1. Exchange Energy
Exchange energy describes the energy expended when two electrons with the same spin-exchange positions in the same energy subshell. Different mathematical and analytical methods are used to evaluate the interactions between electrons and QDs in the same energy subshell, including the Hamiltonian process (Elsaid et al., 2017, p.1). The electrons take advantage of tunnel current between quantum states in particles at the nanoscale. Since the process expends energy, it results in the reduction of energy in the subshell. QDs contain discrete energy levels and other properties similar to regular atoms due to their confinement in all three dimensions of space (Çakır et al., 2017, p.250). These quantum dots, therefore, display the same exchange of electrons within these energy bands resulting in the dissipation of exchange energy in nanoscale magnetic devices.
2.1.1.2. Magnetostatic Energy
Magnetostatic energy refers to the energy stored in a static magnetic field. Researchers developed micro-magnetic techniques that can resolve magnetization dynamics and states at the nanometer length (Tanaka et al., 2017). As a result of these innovations, static magnetic fields at the nanoscale can be evaluated, and their magneto-static energy calculated accurately. The analysis of this energy is critical in the design of magnetic, electronic devices since the energy consumption depends on the sum of all energies consumed or dissipated. The reduction of the widths of the gate oxide in devices that rely on field-effect also requires specific knowledge of the magneto-static energy (Melo et al., 2016, p.1). The basic principles in nano-magnetic logic also rely on magneto-static coupling energies between neighboring electrons. The study of this energy is, therefore, crucial in the study of micro-magnetism.
2.1.1.3. Magneto-crystalline Anisotropy Energy
Magneto-crystalline anisotropy (MCA) is an emerging effect from the spin-orbit coupling (SOC) action in materials. This effect results in a preferred magnetization direction depending on the crystallographic structure of the material (Pradipto et al., 2019, p.1). As researchers explore atomically thin materials, specific effects appear due to the reduction in the dimensions of the material. Researchers attribute this effect to the localization of the electron orbital as a result of reduced dimensionality in nanoscale magnets. (Pradipto et al., 2019, p.1). The energy required to achieve this effect is referred to as the magneto-crystalline anisotropy energy. The studies into magneto-crystalline anisotropy also revealed that the effect is closely linked to SOC near the Fermi level, and fine-tuning of the MCA effect can be achieved through the manipulation of the band structure at this level (Pradipto et al., 2019, p.1). Perfectly tuned micro-magnets are energy-efficient and more reliable than the current magnetic memories.
2.1.1.4. Zeeman Energy
Zeeman energy, also referred to as external field energy, is the potential energy contained in a magnetized body in the presence of an external magnetic field. The measurement of Zeeman splitting (ZS) of a hole in nano-magnets, when exposed to external magnetic fields, is critical in examining hole spin properties under dimensional confinement (Vecchio et al., 2020, p.1). The effects of this energy on SOC are similar to the MCA effects except that the orbital current, in this case, becomes linear (Hernandoa et al., 2019, p.1). Zeeman energy is, therefore, a critical property of nano-magnets in the examination of the features of electrons in QDs.
2.2. Hysteresis Loop
The hysteresis loop describes the four-quadrant graph from which a magnet’s coercive force and hysteresis loss can be found. The mathematical models for magnetic hysteresis loops have garnered widespread industrial interests and applications in various fields (Vasquez & Fazzito, 2019, p.1), including nanomagnetism. Hysteresis loops for magnetic nanoparticles are notably distinct from circuits for bulk materials. When the applied field in bulk materials is cycled, the magnetization reverses (Boekelheide et al., 2019, p.1). Bulk magnets also form magnetic domains, while nano-magnets do not. The hysteresis loop utilizes graphical information to represent the properties of magnets.
2.3. Landau-Lifshitz-Gilbert Equation
The Landau-Lifshitz-Gilbert (LLG) equation is a mathematical model that describes the behavior of electrons under an effective magnetic field (Ferona & Camley, 2017, p.1). The equation represents a kinetic equation that is devoid of the acceleration term or inertia (Olive et al., 2015, p.1). The equation can be used to evaluate and develop magnetic models of varying degrees and is widely used to describe the various behaviors of atomically thin magnetic circuits (Serpico et al., 2008, p.282). Magnetization dynamics can be calculated accurately using the LLG equation supplemented with other stochastic methods to cater to fluctuations in the material’s external environment. Boundary conditions and Maxwell’s equation are used to enhance the LLG equation when analyzing non-uniform magnetization configurations due to dipolar interactions at a long-range (Ferona & Camley, 2017, p.1). The magnetic construct resulting from this coupling gives numerous coupled nonlinear differential equations. These equations provide an excellent opportunity for the study of the domain-wall formation, eddy current, and spin waves (Ferona & Camley, 2017, p.1). LLG equations are, therefore, some of the most widely utilized mathematical models in the analysis of nanoscale magnets and their properties. Research into the structure of nano-magnets relies on these equations significantly, making LLG equations a crucial part of micro and nanomagnetism.
- Conclusion
Magnetism at the nanoscale has been the subject of numerous studies and research due to its applicability in electrical and quantum computing. Magnetic storage devices rely on the innovations based on the investigation into this property of ferromagnetic materials coupled with semiconductors. This literature review explored the various aspects of nanoscale magnets, including the ferromagnetic materials used and the multiple energies found at this scale. The mathematical and phenomenological models used in the analysis of these magnets, such as the hysteresis loop and LLG equations, also illuminate the efforts involved in the process. Future magnetic storage and memory devices will rely significantly on advances made in the manufacture and improvement of nanoscale magnetic products.