TECHNICAL NOTE
Quloud-Mag commentary (1) Background
In the next three parts, we will explain magnetic material simulation using the product Quloud-Mag. First, in Part 1, we will explain the expectations for simulation in the development of magnetic materials and what kinds of magnetic material simulation technologies have been developed to date. In the second part, we will explain the differences between conventional magnetic material simulation and the "multiscale simulation" provided by Quloud-Mag. In the third part, we will introduce the results of actual magnetic material simulation using Quloud-Mag.
INTRODUCTION
HISTORY
History and simulation of material and device development
Let's consider predicting new materials using computer simulations. It is known that all electrons and atomic nuclei are described by the fundamental equations of physics known as quantum mechanics. More specifically, it is known that they behave according to an equation called the Schrödinger equation. If a material is composed of atomic nuclei and electrons, it should be possible to predict the physical properties of the material by solving the Schrödinger equation. This is called "first-principles" material simulation because it does not require experimental values or empirical rules. It is a method of making predictions without experimental values in accordance with quantum mechanics. By using the latest supercomputers, we can understand things at the atomic level as if we had seen them before, with high accuracy (you can see how accurate it is by looking at the calculation results described later) without using experimental values. The ability to clarify the causal relationship between atomic structure and device characteristics is an important guideline for device design.
First-principles material simulation is a powerful tool that allows prediction and analysis of physical properties without experimental values, and even provides guidelines for device design, but not all material simulations can be covered by first-principles material simulation alone. In recent years, first-principles material simulations are often based on density functional theory (also called DFT (abbreviation of Density Functional Theory)). I will introduce density functional theory on another occasion. Density functional theory is basically a theory for the ground state (absolute zero, -273°C), and if you try to deal with excited states or finite temperature states (physical properties at room temperature), you must at least perform special post-processing. Furthermore, because first-principles material simulations are highly accurate, they take a lot of time to calculate. Therefore, even with the current highest performance supercomputers, it is almost impossible to simulate on the micrometer scale (10^-6m). This naturally leads to a demand to handle larger system sizes even if it means lowering the accuracy. After all, the materials that humans handle are extremely large atomic groups of 10^23 (Avogadro's number), which is a gap of 20 orders of magnitude from the atomic calculations of only about 10-10^3 handled in first-principles material simulations. It is no exaggeration to say that the difficulty of materials science lies in the sheer breadth of scale.
The opposite of first-principles material simulation is empirical material simulation. In empirical material simulation, experimental values and empirical values are used in the simulation, not necessarily in a first-principles approach. Usually, in empirical material simulation, empirical equations (alternative to the Schrödinger equation) are known for each purpose, such as to take into account the temperature effects we want to know or to perform larger-scale simulations, and they contain some material-dependent "parameters". We must obtain the parameters in advance by some experiment or other method before performing an empirical simulation. However, once we obtain such parameters in some way, subsequent calculations can be performed on a much larger scale than first-principles simulations, and the effects of temperature can be incorporated.
PAST
Simulations for the development of new magnetic materials
In recent years, magnetic materials are one of the materials that have been the subject of heated research into new materials. Magnets are at the forefront of magnetic materials. Magnets are used in motors, and the stronger the magnet, the more energy efficient it can be. Currently, neodymium magnets are widely used as strong magnets, but dysprosium, a rare earth, is used in neodymium magnets to increase their coercive force. Research into new magnetic materials that do not use rare earths is still being actively conducted. Strong magnets are not only used in motors, but also in memory. Although it is not often seen in daily life these days, research and development of magnetic tape is still progressing steadily. Although it is not seen in daily life, magnetic tape is used for data storage in financial institutions and even for cloud data storage, and it is still an indispensable material in our highly information-oriented society. It is not only strong magnets that are attracting a lot of attention as magnetic materials. A certain type of weak magnet called soft magnetic material has also become an important material in recent years. In the 5G/6G society, information is transmitted at high speed using various electromagnetic waves. However, there are parts of precision instruments that are affected by the magnetic fields of such external environments. Such parts must be shielded from external magnetic fields in some way. That's where soft magnetic materials come in. Soft magnetic materials are a type of magnet that can easily change its magnetization direction to match an external magnetic field. This flexibility acts as a magnetic shield, responding to a specific frequency and erasing it. Furthermore, they act as an amplifier, aligning their own magnetization to a slow external magnetic field and further enhancing the external magnetic field. The search for such soft magnetic materials is also the work of current researchers.
In the search for various magnetic materials, attempts have been made to use first-principles material calculations and empirical material simulations. In first-principles material calculations, research has been conducted to examine how the magnetic moment and magnetic anisotropy change when the elemental composition of a magnetic material is changed. However, the disadvantage of all of these is that they basically behave in the ground state, that is, at absolute zero. This is because magnetic materials have characteristic temperatures unique to each material, called the Curie temperature and Neel temperature, above which the magnetic properties disappear. Depending on the temperature, it will change whether or not the material can behave as a magnetic material even at room temperature. In other words, the effect of finite temperature is a factor that must be considered for magnetic materials. The fact that it cannot be considered is a major disadvantage. In addition, most magnetic materials are ceramics made of solidified particles, and particle size dependence is also a major factor of interest. For example, in magnetic memory, a particle of about 10 nanometers in size functions as one bit. However, in first-principles material simulation, it is hopeless to simulate a size of 10 nanometers in terms of calculation time estimates, and current computers cannot handle such a large system in its entirety. On the other hand, empirical material simulation has the advantage of being able to calculate the nominal temperature and to simulate large system sizes of 10 nanometers or more. However, the disadvantage is that parameters must be prepared in advance, and in the end, experiments must be conducted to obtain the parameters from the experimental results, so its use in actual fields has been limited.
The parameters must be obtained in advance (e.g., through experiments)
Long calculation time, temperature effects cannot be included, and large systems cannot be handled
defect
Can take into account temperature effects and can handle many systems
Calculations can be performed without experimental data (powerful for prediction and analysis of phenomena)
Strong Points
Empirical Materials Simulation
First-principles material simulation
FIRST-PRINCIPLES
First-principles and empirical materials simulation
Let's consider predicting new materials using computer simulations. It is known that all electrons and atomic nuclei are described by the fundamental equations of physics known as quantum mechanics. More specifically, it is known that they behave according to an equation called the Schrödinger equation. If a material is composed of atomic nuclei and electrons, it should be possible to predict the physical properties of the material by solving the Schrödinger equation. This is called "first-principles" material simulation because it does not require experimental values or empirical rules. It is a method of making predictions without experimental values in accordance with quantum mechanics. By using the latest supercomputers, it is possible to understand things at the atomic level as if you had seen them before, with high accuracy (you can see how accurate it is by looking at the calculation results described later) without using experimental values. The ability to clarify the causal relationship between atomic structure and device characteristics is an important guideline for device design.
First-principles material simulation is a powerful tool that makes it possible to predict and analyze physical properties without experimental values, and even to provide guidelines for device design, but not all material simulations can be covered by first-principles material simulation alone. In recent years, first-principles material simulations are often based on density functional theory (also called DFT, short for Density Functional Theory). We will introduce density functional theory on another occasion. Density functional theory is basically a theory for the ground state (absolute zero, -273°C), and if you try to deal with excited states or finite temperature states (physical properties at room temperature), you must at least perform special post-processing. Furthermore, because first-principles material simulations are highly accurate, they take a long time to calculate. Therefore, even with the current highest performance supercomputers, it is almost impossible to simulate on the micrometer scale (10^-6m). Naturally, then, there is a demand to deal with larger system sizes even if it means lowering the accuracy. After all, the materials that humans handle in their hands are extremely large atomic groups of 10^23 (Avogadro's number), and there is a gap of 20 orders of magnitude between the calculations of atoms at most 10-10^3 handled in first-principles material simulations. It is no exaggeration to say that the difficulty of materials science lies in the breadth of this scale. The opposite of first-principles material simulation is empirical material simulation. In empirical material simulation, experimental values and empirical values are used in the simulation, not necessarily in a first-principles approach. Usually, in empirical material simulation, empirical equations (alternative to the Schrödinger equation) are known for each purpose, such as to take into account the temperature effects we want to know or to perform larger-scale simulations, and they contain some material-dependent "parameters". We must obtain the parameters in advance by some experiment or other method before performing an empirical simulation. However, once we obtain such parameters in some way, subsequent calculations can be performed on a much larger scale than first-principles simulations, and the effects of temperature can be incorporated.
MULTISCALE
Multi-scale simulation: Combination of first-principles and empirical materials simulation
We have explained about first-principles material calculation and empirical material simulation. Each simulation has its own advantages and disadvantages. Recently, multiscale simulation, which aims to connect these different hierarchical simulations, has started to attract attention. As written above, empirical material simulation requires parameter information prior to simulation. Until now, parameters have often been extracted from experimental values. Instead of this experiment, multiscale simulation is an attempt to extract parameters from first-principles material simulation. Although there have been plans to perform multiscale simulation in the past, it has been difficult to realize it due to the weak power of computers, and for other reasons, such as the lack of a methodology for how to extract parameters from first-principles material simulation. Now that there is a growing momentum to accelerate the development of new materials through material simulation, multiscale simulation technology is suddenly becoming hot.
