Manipulations with the magnetic properties of nanostructures due to the electric field
In a previous article, we already talked about manipulating the properties of substances used in creating information storage devices. In that case, it was a switching of ferromagnetic properties. But what if you do not use a magnetic field and do not touch such concepts as magnetism at all? Will it be possible to make a productive and reliable device? It is in this direction that Randall H Victora and Ahmed Rassem Wazzan have been investigated. The main topic of this study was the control of the magnetic properties of nanostructures by means of an electric field. The goal was to consider the possibilities of creating energy-efficient high-density memory. We learn the details by reading the report of scientists. Go.
Gentlemen Victor and Wazzan have developed a technique for micromagnetic simulation of the magnetoelectric effect (ME) in the basic structures of Cr 2 O 3 (chromium sesquioxide). It was found that the microscopic magnetoelectric susceptibility is very different from the experimentally obtained values. This difference becomes more pronounced when approaching the Curie point * , affecting the operation of the device at room temperature.
To demonstrate the Curie point, we use the image from the previous article: a piece of iron heated to a temperature above the Curie point is only slightly attracted to the magnet. After cooling, its ferromagnetic properties are fully restored.
The Curie point * is a parameter that determines the temperature at which a substance loses its ferromagnetic properties. When the temperature exceeds the boundary established by the Curie point, the intensity of the thermal motion of atoms increases and destroys the magnetic order of electrons, i.e. the symmetry is broken, and the ferromagnet becomes a paramagnet (a substance that can be magnetized by an external magnetic field, such as aluminum or lithium).The use of an electric field that controls ME switching of elements has been proposed. Unlike the traditional use of an alternating magnetic field, this technique uses quantum mechanical exchange. After the establishment of temperature-dependent physical parameters, the switching characteristics were studied under various variables: temperature, acting electric field, and Cr 2 O 3 profile . It was found that the use of quantum-mechanical exchange can reduce the required electric field and improve scalability, while maintaining thermal stability * .
Thermal stability * - the ability to maintain the original composition under the influence of thermal loads.
Technology basis
Magnetoelectric Cr 2 O 3 heterostructures attracted much attention of researchers , due to the ability to switch the polarity of the exchange bias * of a ferromagnet using an electric field.
The exchange bias * is a feature of the hysteresis loops ** of magnetization reversal of magnetic materials, which is manifested in the asymmetric arrangement of the loop relative to the ordinate axis.This switching is a consequence of the close relationship between the boundary magnetization of the sample surface and antiferromagnetic ordering inside the sample, which can be changed by applying an alternating electric field and a constant magnetic field. Such processes differ from those that occur inside other multiferroics * (for example, BaTiO 3 - barium titanate).
Hysteresis ** is a property of physical systems whose instant response also depends on their current state.
Multiferroics * are substances in which two or more types of ferro-ordering are present (ferromagnetic, ferroelectric, and ferroelasticity).The theory of this technology was tested both on bulk Cr 2 O 3 and on a thin film of this substance. However, reducing the film thickness below 100 nm and lateral scaling to the size of modern CMOS devices faces a number of problems and difficulties. The thinner the film becomes, the lower the electromagnetic response becomes, and the level of necessary energy increases sharply. Not to mention the fact that the antiferromagnet Cr 2 O 3 should work at the limit of electric breakdown * .
Electrical breakdown * is a jump in the current strength in a dielectric that occurs when a voltage is applied above a critical voltage.In addition, the need to use a magnetic field in the exchange bias switching circuit, identified in studies, makes the system much less attractive for the production of memory controlled by an electric field.
The smaller the device, the stronger the magnetic field should be, even if the electric will work on the verge of breakdown.
The conclusion from the above problems is the need to implement approaches that can reduce or eliminate the need for external fields. This study does not give unambiguous answers and is not the basis of the future revolutionary structure. It considers the possibility of using exclusively an electric field to control magnetoelectric elements, while eliminating the need for a magnetic field.
Scheme and structure
Image No. 1
Image 1a shows a memory block based on Cr 2 O 3 . The device consists of ME Cr 2 O 3 with a crystalline structure of alpha-alumina and reading the tunnel magnetoresistance * unit.
Tunnel magnetoresistance * is a quantum-mechanical effect that occurs when a current flows between two layers of ferromagnets separated by a thin layer of dielectric.Excellent antiferromagnetic coupling with Cr 3+ surface spins was demonstrated in Co / Pd * combinations due to epitaxy * , as well as in Co / Pt * combinations via ion sputtering * .
Epitaxy * - the growth of one crystalline material on the surface of another at lower temperatures.The basis of the switching element is a rectangular core of ME Cr 2 O 3 , surrounded by a permanent magnet and a magnetic switch (magnetic shunt). Schematically, this is reflected in image 1b . A permanent magnet plays a critical role in providing the magnetic field necessary for Cr 2 O 3 through the exchange interaction of Cr 3+ moments. In other words, the need to use some kind of magnetic field, internal or external, is exhausted by the field arising from the exchange interaction along the edges between the permanent magnet and Cr 3+moments. A magnetic shunt is necessary in order to break the wandering field, which can negatively affect the neighboring components responsible for the applied field.
Ion sputtering * - the surface of a solid is bombarded by heavy charged particles (or neutrals), which leads to the emission of atoms.
Co - Cobalt, is a ferromagnet.
Pd - Palladium, is a paramagnet.
Pt - Platinum, is a paramagnet.
The Landau — Lifshitz — Hilbert equation (LLG)
The equation taking into account thermal fluctuations describes the results of micromagnetic simulations of the structure proposed by the researchers.
The modeling of ME Cr 2 O 3 is fraught with two unusual difficulties: the dependence of the magnetization on the electric field and the operation is close to the Curie point.
The first problem was solved by using the linear magnetoelectric effect (ME) ratio of an antiferromagnet (AF), where M = a E, when exposed to a magnetic field that destroys the symmetry of two opposite sublattices. Simply put, if there is no electric field, then the spin moments from two opposite sublattices eliminate each other, producing zero magnetization.
* a
The second problem requires a clear understanding that such internal properties as anisotropy * (Ku), damping * (Ƞ) and exchange (A ex ) are important indicators of length scale measurements based on renormalization theory * .a - instead of alpha (sorry, I could not insert the normal letter alpha into the text, so I used the letter "a")
Anisotropy * - different properties of media in various directions within the medium.
Damping * - elimination or reduction of oscillations in mechanisms. It can also be considered as mitigating the negative impact of any effect on the object.
Renormalization * is a phenomenon in quantum field theory. The values implemented as external parameters of the problem can change as a result of the equations of motion (in our case, this is a map of the evolution of the field in time and space).Researchers gave preference to a numerical solution rather than an analytical one, since it was necessary to obtain the most realistic results. For this, the predicted renormalized parameters (anisotropy, exchange, and magnetization saturation) should coincide with the predicted atomic models, which are valid even at a temperature close to the Curie point. The evaluation of damping was simplified by determining the similarity between the sublattice of the antiferromagnet Cr 2 O 3 and the ferromagnet (for example, FePt is an alloy of iron and platinum) and the scaling method, which was based on previously calculated results.
Image No. 2
The image above ( 2a ) shows the calculated values of A ex, Ku and Ƞ for a length scale of 1.5 nm.
The main distinguishing feature of the modeling of Cr 2 O 3 is the replacement of magnetization with magnetic polarization enhanced by an electric field. This requires the renormalization of the magnetoelectric effect to a state opposite to ordinary magnetization. Since such actions have not yet been described previously, the researchers had to apply a method that required full agreement between the results of large samples and experimental results. This allowed us to extract a necessary for the calculations.
The magnetostatic interactions between the cells were ignored in the calculations due to the low magnetization (<10emu / cm 3) and relatively small sizes of the tested samples.
To verify changes in the ME in the critical temperature mode, the susceptibility of the ME was overestimated using the techniques described previously. The calculations were carried out for E = 2MV / cm and H = 6 kOe. To form a general idea of ME, the calculations were carried out taking into account a uniform external magnetic field, and not inhomogeneous, as is the case in the quantum exchange interaction at the edges of the sample.
The magnetoelectric susceptibility is defined as a obs (T) = [M (T)] / E , where [M (T)] is the average net magnetization of all cells. A a obsin turn, represents the predicted magnetoelectric susceptibility required for the Landau – Lifshitz – Hilbert equation as an input parameter. The values of a iso were chosen for each temperature indicator so that the values a obs follow experimentally obtained values (A ex pt). The results of the analysis are shown in the image below ( 3 ).
Image No. 3
The graph shows a strong difference between the microscopic a iso and the observed macroscopic a obs for both sampling scales * .
Discretization * - transformation of a continuous function into a discrete one.While a obs and A ex pt follow non-monotonous behavior, a iso gradually increases with temperature. The closer the temperature is to the Curie point, the greater the difference between a iso and a obs . As they approach the Curie point, collective spin vibrations violate microscopic ME responses.
These results indicate that the strength of the magnetoelectric effect is greatly reduced when approaching the Curie point, even though the ME susceptibility at the atomic level is extremely strong. This indicates the need to improve the test sample in order to ensure its normal operation at room temperature.
Switch Characteristics
The exchange field emanating from a permanent magnet completely eliminates the need to apply a magnetic field. The degree of exchange interaction between the permanent magnet and Cr 2 O 3 cells at the edges is expressed as follows: A PM = 2x10 -7 erg / cm. If this parameter is lower, then the exchange in critical temperature mode will be unstable. The orientation of the magnetization of the permanent magnet was constant to maintain a constant exchange field at the edges of Cr 2 O 3 . It was also found that the switching frequency of a cell with a volume of 1.5 nm 3 coincides with that predicted for 3% of cells with a volume of 0.5 of the tested.
The initial state of magnetization was balanced within 0.25 ns, after which a sharp change (“switching”) of the electric field was made. It was noted that the reverse of the electric field led to the reversal of the maximum polarization - M max = a iso E. It follows from this that the switching is actually initiated by changing M max in the model of the LLH equation.
The results of switching tests are displayed on image No. 4.
Image No. 4
It should be noted, despite the fact that the reverse of the electric field leads to a reversal of antiferromagnetism (i.e., the orientation of uncompensated surface spins Cr 2 O 3), the total magnetization remains in association with the unidirectional exchange field of a permanent magnet to minimize the necessary energy.
As a result, in order to demonstrate the switching of antiferromagnetic ordering, | M max | ⟨cos (θ)⟩ had to be used in all switching schedules instead of ⟨M max cos (θ)⟩. Where θ denotes the orientation angle of the cell spin with the axis of perpendicular anisotropy ( represented by the letter z in image 1a ), and ⟨⟩ denotes the average value for all cells. Figure 4a shows switching at different temperatures. The calculations were performed with the initial data: E = 2 MV / cm and Cr
2 O 3 22.5x22.5x60 nm. Several simulations were performed for each temperature, and the error display is represented by a standard error of 2r.
A slowdown of the switching process began to be observed with a decrease in polarization at higher temperatures, which is associated with terminal fluctuations * .
Terminal fluctuation * - deviations from the average value of random variables caused by the thermal motion of particles.Image 4b shows us the effect of the electric field on the antiferromagnetic switching process. The set of graphs shown was obtained at a temperature of 296 K and thermal stability of 46 k B T at room temperature.
Interestingly, the switching was achieved with an electric field of only 0.5 MV / cm and without changing the peak value ⟨cos (θ)⟩. This can be seen in the inset in image 4b .
The researchers also noted that the switching speed increases with a weaker electric field. This is due to the faster, due to the exchange field of the permanent magnet, propagation of switching from the edges of Cr 2 O 3 to the center.
In order to understand how small the tested memory elements can be, several simulations were carried out with two options for the dimensions of Cr 2 O 3 : 15x15 nm and 30x30 nm. In this case, the electric field was 2 MV / cm, and the temperature was 296 K. The thickness was kept at 60 nm for all the tested samples.
The results showed that in the absence of the exchange field of a permanent magnet, the required applied (uniform) field will be 14 kOe with the maximum allowable electric field strength. This indicator indicates the impracticality of using small-sized elements based on Cr 2 O 3 using a magnetic field.
Chart 4cshows the switching curves for all three options for dimensions Cr 2 O 3 . It is logical that switching occurs much faster in samples of a smaller area. This is explained by the fact that the exchange field of a permanent magnet spreads faster through a sample of a smaller area, which accelerates the process of minimizing energy exchange.
Researchers Conclusions
A magnetoelectric effect was introduced into the LLG equation to evaluate its properties in Cr 2 O 3 , as well as for its possible use in switching elements based on an electric field.
Using the renormalization approach, it was possible to simplify micromagnetic calculations by using atomic Cr 3+ spins in hexagonal lattice sites in bulk Cr 2 O 3 cells in a cubic lattice.
Experiments were also conducted to determine the relationship between temperature and the switching process.
As a result, a sample was presented demonstrating the absence of the need for a magnetic field. Switching rates were increased by reducing the acting electric field and the Cr 2 O 3 region .
The apparatus of Cr 2 O 3 with dimensions 22,5h22,5h60 nm when an electric field 0.5MV / cm is capable of reliably and efficiently produce the switching below the Curie point and thermal stability at 46 k B T .
To get acquainted with the details and details of the study, I recommend reading the report of scientists
. Unfortunately, open access to the full text of the report is currently closed. However, I managed to download it before that. Those who wish to get acquainted with it canDownload the report in PDF format from the link
Epilogue
The scientists who conducted this study did not plan to make a breakthrough. They needed to understand the ultimate properties of physical phenomena in conjunction with the use of certain chemical compounds. The research results provide the basis for new research in this area, which, subsequently, can lead to the commercialization of their prototypes. The process of studying the possibility of using an exclusively electric field and the rejection of a magnetic one is complicated by incredibly complex experiments. In order to only understand all the processes that occur in the process of one test, you need a lot of knowledge, patience and effort. What can we say about the implementation of projects based on these studies. However, any study that has discovered or clarified even the most insignificant physical or chemical process and / or phenomenon is already gaining local importance. In other words, exaggerated, if humanity did not open the wheel, then there would be no cars. If you are a researcher, never downplay the importance of your work. Who knows, maybe after years your developments will give an impetus to a new, previously uninvited technology.
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