Outreach

Posted on by Arturo Rodríguez

How does a Scanning Tunnelling Microscope (STM) work?

How do microscopes work?

Each type of microscope uses different ways of obtaining information from the sample they are studying. Classical optical microscopes use light to probe the samples, this of course has its limitations, as light is just visible between certain wavelengths. This means that just objects slightly smaller than those wavelengths can be observed with them, setting the minimum observable distance with them at around 200 nm. Therefore, with this kind of microscopes we can study cells or other biological systems which are bigger than this distance, but we cannot obtain information of  smaller things such as atoms.

But what if we want to observe these smaller things? One possible solution for that is using particles with smaller wavelengths as probes. This typically means using more massive particles, as the wavelength decreases when the mass increases. One of the easiest ways to do that is using electrons as waves, the microscopes that do that are called electron microscopes, and the most used ones are transmission electron microscopes (TEM) and scanning electron microscopes (SEM). With this kind of microscopy, it is possible to resolve objects down to around 15nm (High resolution TEMs (HRTEM) can reach 0.05 nm under very special conditions).

But there is another big family of microscopes. This is the scanning probe microscopy (SPM) family, to which STM belongs. All the techniques inside the SPM family are characterized for approaching the tip of the microscope to the sample to obtain information from it in different ways and then scan with it to form a complete image. Every technique inside this family uses different physical properties to work, and the property that STM uses is the quantum tunnelling effect (hence the name). With STM, features smaller than 0.1nm can be resolved horizontally, and 0.01nm features regarding depth. These values are especially useful as atoms have a typical size of around 0.3 nm, which means that STMs can achieve atomic resolution.

Figure 1.- Worm studied with SEM

The quantum tunnelling effect

STMs use the quantum tunnelling effect as their principle of operation. This is a purely quantum mechanical effect that allows a particle to go through a potential energy barrier. If we make a comparison with the classical day by day world, it would be as if someone would go through a wall as a ghost, without interacting with it. This effect is related with the wave properties of the particles in the nanoscale, and the probability of it happening decreases the thicker the barrier is (the thicker the wall is for the ghost) and the bigger the particle is. What kind of particles are we talking about then? Well, some of the smallest particles that we humans know how to work with are electrons, so those will be the particles used in our STMs. And, what is a barrier for these electrons? A barrier is anything the electrons can’t go through. That can be an isolator such as plastic or wood, or in this case, the absence of anything, the vacuum.

If we apply a difference of potential in a wire, the electrons should be able to travel through it. But if we then cut the wire in the middle, the electrons will stop flowing from one side to the other. We will no longer have a current. The quantum tunnelling effect tell us that if we now put the two extremes of the wire really close (less than one atom of distance from one another), the quantum properties of the electrons will allow them to “jump” from one wire to the other quite often. The electrons will “tunnel” through the empty space and will reach the other cable, and the movement of electrons is a current, so then we will observe a current in our basic circuit even though it is not closed. As we know that the probability of tunnelling decreases when the barrier increases, if we separate our wires a little, the current will decrease, and if we put them closer it will increase. It will reach the maximum current when the wires touch, when we will observe the normal current that we had when the wire was not cut.

Figure 2.- Classical particles need enough energy to go over the barriers, quantum particles can go through the barriers instead.

So how does a STM work then?

Let’s imagine our theoretical circuit already cut in the middle. The only important things here are the wires and the gap in between them. The wires are made out of metal and the gap is made out of nothingness. Perfect. Now we want to see tiny things with this setup, so the first thing is choosing what we want to see; that’s the sample. The sample is going to be attached to one of the cut sides of the wire, which makes of it just the new end of the wire as it is also metallic. Then we take the other cut side and we sharpen it. We sharpen it the best we can until the very tip is just one atom thick; this is our tip. If we now approach the tip and the sample we will get the same thing that we got before with the two cut wires: some current going through due to the tunnelling effect when really close, but there is a difference, our tip is now one atom thick. This means that if we now move to the side we can observe the current in a different atom. We can keep moving the tip sideways keeping it at the same distance of the sample all the time (this means making sure we let the same current go through the vacuum), but sometimes the sample will have holes (so we will have to approach the tip) or mountains (so we will have to retract the tip). If we keep track of how do we have to move the tip to keep the current constant, we will get lines of the topography of the sample! If we stack several lines of the topography, this is, if we scan the surface of the sample, we will get complete three-dimensional images of the sample!

Of course, all the details about how to keep the wires so close without touching, how to move the tip sideways, how to read the currents, etc. are complex issues that require high level engineering to be solved, but those are not the things that explain how a STM works. Many other things have to be done to properly obtain images out of these microscopes, for example, due to the close distance between tip and sample, it is necessary to have damping systems in order to decouple the microscope from any kind of vibration that could crash the tip into the sample.

Figure 3.- Monoatomic Iridium step edges and terraces observed via STM. Size of the image is 300x300nm.
Figure 4.- Closer look to the Iridium surface showing individual Iridium atoms arranged in a hexagonal structure. Some defects can be seen in the sample.

References:

Figure 1: Philippe Crassous / FEI Company (www.fei.com)

Figure 2: https://cosmosmagazine.com/science/physics/quantum-tunnelling-is-instantaneous-researchers-find/

Posted on by Paolo Sgarro

The relation between magnets, symmetry and future computer technologies

Introduction, computers and information storage
I would like to anticipate that the present post is going through several different topics, and chances are that the reader might not be familiar with any of them. I hope anyway to be able to provide several inputs, so that maybe some of them might trigger the curiosity of the reader. The objective of this post is to make a connection between technology, and therefore objects which belong to our everyday experience; and some of the fundamental and fascinating concepts of physics, which enable the technology to work.
In the first part, I will talk about objects who possess some computing functions, focusing on information storage. In the second part, after a short explanation on magnetism, it is shown how information storage is made possible by the physical phenomenon known as symmetry breaking. In the end, I will talk about how broken symmetry systems can be also useful for novel computing technologies.
As we use any computing device, when we input any command, what is actually happening,, is an electrical charge flow. The device we are using consists of: a processor, that performs a modification on the information; and a memory, where the information, in form of a ‘0’ (zero) or ‘1’ (one) is stored. At any clock cycle, some information, is taken from the memory, the processor performs a mathematical operation on these information (sum, multiplication, etc…) and the result is stored in the memory. Any computer program, any app installed on the phone, no matter how complicated it might seem, is a sequence of these operations.
Although several ways can be employed to store temporarily an information coming from a computation stage, to later use it for the next one, our daily usage of electronic devices requires also that, once the power is turned off, the data is not deleted. This is the case for non-volatile memories, whose story begins when IBM sold the first Hard Disk Drive (HDD), in 1956.
In hard disk, the information (‘0’ or ‘1’), is stored in some materials, known as ferromagnets (called also magnets in a colloquial way). Magnetic materials have played an important role in information storage, even before HDD, for example in Vynil music recording. Today new memory concepts are being explored, like MRAM, that still makes use of magnetic materials.

Magnetism, ferromagnetic materials and symmetry breaking
The first thing coming to our mind when it comes to magnetism is the property of some materials, like iron, of attracting or repulsing each other. These materials are called ferromagnetic and are defined by the property of keeping their magnetization even though no magnetic field is applied. This definition opens, at least, the question of what magnetic field and magnetization are.
I’ll introduce magnetism with a high school example. Let’s consider two metallic wires through which an electrical current flows. Let’s imagine to control separately the two currents, being able to decide the intensity and direction of the flow.
The first thing we do is to apply the same current in the same direction and make the two wires approach each other. We will see that, as the two wires approach, they tend to repel each other. The more the distance decreases, the more the force exerted between the two intensifies. If the amount of current flowing increases, the force increases as well. If the direction of the current flowing in one of the two wires is changed, the force will have opposite sign, and the two wires will attract each other.
In physical terms we will say that a magnetic field is associated to the current flowing through the first wire, which results in a force exerted to the electrical charges in the second wire. Of course, the explanation works also the other way round, as the current in the second wire generates a magnetic field as well.
This phenomenon closely resembles the attraction and repulsion of magnetic materials, and in fact the root is the same. Magnetic field, in fact, is associated to the flow of an electrical current and, at the atomic level, magnetic materials are composed of microscopic spires of current, called magnetic moments. In ferromagnetic materials, as an external magnetic field is applied, the magnetic moments will tend to align to it and, if the magnetic field is turned off, they will (tend to) keep the same direction (cfr. Figure 1). The build-up of the magnetic field generated by these spires is known as magnetization. This is the property exploited in information storage, where the data is encoded in the magnetization direction of a permanent magnet.

Figure 1 

If watched closely, the property of ferromagnetic materials that makes them useful is their order. In fact, in nature, sometimes, systems tend to spontaneously get ordered.
Ferromagnetism, in a material, occurs below a temperature known as Curie temperature. Let’s imagine to take a sample of Cobalt, above his Tc (around 1388°, but below its melting point, 1495°) and to cool it down. Cobalt is known to have an easy direction for the magnetization, therefore, as Tc is crossed, the magnetic moments will pass from a highly disordered (or symmetric) state, where each of them is randomly oriented, to a state where there is a favorite magnetization direction (broken symmetry). This is called spontaneous symmetry breaking and is a very broad natural phenomenon.

Figure 2

In physics, symmetry is the property of invariance upon a certain modification. For example, rotational symmetry is the property of anything that does not change upon rotation, and so on. In nature, it might happen that a system has the possibility to lower its energy by breaking some of its symmetry, hence choosing a well-defined state in place of the symmetric one. For example, a ball on top of a perfectly symmetric hill can lower its gravitational energy by choosing the direction of fall, thus breaking the rotational symmetry of the system “hill+ball” (cfr. Figure 2). Interestingly, it will be the slightest breath of wind to determine the direction of fall, and thus the final state of the system. Another analogous case is the Euler strut. As an increasing vertical force is applied to it, at some critical point, the strout bends, breaking again rotational symmetry (cfr. Figure 3).

Figure 3

Examples can go way further: any crystalline material (metals, e.g.) breaks translational symmetry; superfluids (if you don’t know what they are, look for them on YouTube and have fun) break a symmetry called “gauge”; moreover, according to astrophysicists, directly after the Big Bang, a symmetry breaking phenomenon has originated the growth of the universe.

Novel computing concepts
Now we are done with the first goal of the post, which was to connect a technology that is present in our daily use to one of the most fundamental and ubiquitous concepts of physics.
In the last part, I would like to run the path in the opposite direction, and connect broken symmetry systems some novel concepts of computing. Recently, the exponential improvement of computer performances has started to slow down and, at the same time, new concepts for computing have been proposed. Interestingly, broken symmetry systems play a role for many of them.
The first concept I am talking about is in-memory computing (IMC). As I described in the first section, in standard computers, the storage and the processing units are separated. The communication between them is known as a bottleneck, being the part that mostly slows down the operations. To overcome this, it has been suggested to change the architecture, and to have computation and storage units, that receive several inputs, perform operations between them and store the data. IMC is based on broken symmetry systems, like ferromagnets, but also ferroelectric (aligned electric dipoles), and phase change materials (change from amorphous to crystalline, breaking translational symmetry), and on building units to efficiently control the material order parameter (i.e. magnetization, polarization etc.).
The second interesting concept regards neuromorphic computing. The idea is to build a network of elements (neurons) connected by a variable weight (synapse). This network can perform algorithms specifically designed for artificial intelligence. The role of broken symmetry systems, here, is to have a continuous variation of the order parameter (e.g. rotation of magnetization or polarization) to be associated to the weight of the synapse.
With these two extremely quick mentions, I am concluding this post. I hope that, after reading it, there is some more curiosity on the topics treated, and some more awareness on the connection between science and technology.

Posted on by spear

ESR12 makes headlines…!

An interview with Arturo Rodríguez (ESR12, UHAM) was recently published in the local newspaper of La Rioja, Arturo’s hometown. In the article, our ESR describes working with STM and life as a PhD student at University of Hamburg.

English translation below!

“I couldn’t resist writing my initials with twenty-nine atoms”

Arturo Rodríguez · In Hamburg, with the most powerful microscopes in the world

JAVIER ALBO

SANTO DOMINGO. The young man from Santo Domingo de la Calzada, Arturo Rodríguez Sota, is the beneficiary of an ITN Marie Curie scholarship in the European Union funded SPEAR (Spin-orbit materials, Emergent phenomena and related technologies training). He is studying for a PhD in Physics in Hamburg, for whose University he works.

What is your mission? My project is based on looking for skyrmions in the vicinity of superconductors, which are two very specific things that don’t get along very well. If I were to find them, it would be a great advance for the creation of quantum computers and other very promising technologies related to them, in addition to opening the door to exciting new physics, such as, perhaps, Majorana fermions. In a more general way, one could say that I work with scanning tunneling microscopes (STM) to study matter at the nanoscale. They are the most powerful microscopes in the world and allow us to observe individual atoms. They get their name from the principle on which they are based, a quantum effect called the Tunneling Effect, which allows electrons to overcome potential barriers as if they were ghosts walking through walls. The information obtained from this type of experiment enables the development of nanotechnology on which our phones and computers are based. Our group specializes in the study of the magnetic properties of these systems, for which we use a special microscope type (SP-STM), which, in addition to all of the above, it allows us to observe the magnetic moment or spin of the atoms.

What is it like working in your team? My group is very good, both scientifically and personally. I work surrounded by wonderful people like my supervisor, Dr. Kirsten von Bergmann, or those who have already become good friends as well as promising scientists Jonas Spethmann and Vishesh Saxena. Working with them is a combination of learning, enjoying and improving. We do science together and science is not knowing, to finally end up knowing. Working with them I have learned that the most beautiful thing someone can say is “I don’t know”, and then immediately search for the answer with all their heart. I’m happy.

What has surprised you the most to see or do on the other end of the microscope? Simply the fact of being able to see individual atoms already seems to me a feat worth mentioning. They only measure a fraction of a nanometer! One of the most beautiful things I have found were some atoms that naturally bunch together in groups of three due to an asymmetry. They look like little hearts! I usually say that I have discovered “the smallest hearts in the world”. Besides that, these microscopes not only allow you to see, but also to ‘touch’ and move individual atoms. As soon as I had the chance to work with them, I wasn’t able to resist writing my initials with only 29 atoms. It is something that will stay with me for the rest of my life.

Caption: Arturo, with the microscope he uses and his initials written with atoms.

Posted on by Maha Khademi

Neuromorphic Computing: A Brief Explanation

Have you ever thought about why we can not perform brain tasks on our computers? Well of course I don’t mean a simple cat/dog recognition, or calculus (Computers have been specifically designed to do a very limited number of brain functions extremely well – even better than humans), but something bigger like analyzing new and unfamiliar situations.

To answer this question, let’s first see how conventional computers work:

Simply explained, there are two main units: a processing unit to process and analyze the data and a memory unit to store them. These two blocks are separated from each other and every time that a task must be done, the data should go back and forth between these two units. This architecture is known as Von Neumann architecture [1].

Fig1: Von Neumann architecture: in a conventional computing system, when an operation f is performed on data D, D has to be moved into a processing unit, leading to significant costs in latency and energy [2].

As you’ve already found out, there are two issues with this architecture that makes it almost impossible to do heavy tasks with:

  1. Energy consumption, as the blocks are “separated” and lots of Joule heating can happen in between.
  2. Not fast enough, due to the time required for the data to go back and forth.

This is also known as the Von Neumann bottleneck [3]. In other words, the architecture causes a limitation on the throughput, and this intensive data exchange is a problem. To find an alternative for it, it’s best to take a look at our brain and try to build something to emulate it, because not only is it the fastest computer available, but it is super energy efficient.

The brain is made up of a very dense network of interconnected neurons, which are responsible for all the data processing happening there. Each neuron has three parts: Soma (some call it neuron as well) which is the cell body and is responsible for the chemical processing of the neuron, Synapse which is like the memory unit and determines the strength of the connections to other neurons, and Axon which is like the wire connecting one neuron to the other.

Fig2: Neural networks in biology and computing [4].

Neurons communicate with voltage signals (spikes) generated by the ions and the chemicals inside our brains. There have been many models presented on how they work, but here will be discussed the simplest (and probably the most useful) one: The leaky integrate and fire model [5].

Fig3: leaky integrate and fire model, Incoming pulses excite the biological neuron; if the excitation reaches a threshold, the neuron fires an outcoming spike, and if not, it relaxes back to the resting potential [6].

As it was said earlier, neurons communicate with spikes which can change the potential of the soma. If a spike from a previous neuron arrives at a neuron after it, the potential of the soma increases. However, this is temporary, meaning that if no other spikes arrive afterward, the potential of the soma will reach the relaxed level again (leakage). On the other hand, if a train of spikes arrives at the neuron, they can accumulate (integrate) and if the potential reaches a threshold potential, the neuron itself will generate a spike (fire). After firing, the potential will again reach the relaxed level.  

Apparently, the connections between all the neurons are not the same, and the differences are in the synapses. The form and combination of the synapses change in time depending on how active or inactive those two neurons were. The more they communicate, the stronger and better their connection, and this is called “synaptic plasticity”. (This is why learning something new is so hard because the connections between the neurons need time and practice to get better!). For more investigation into the fascinating world of the brain, this book is recommended: Neuronal Dynamics: From Single Neurons to Networks and Models of Cognition [7].

Now, it’s time to get back to the Von Neumann bottleneck. With inspiration from the brain, it can be seen that it’s better to place the memory unit in the vicinity, or even inside, the processing unit (just like the soma and the synapses which are really close), this way so much time and energy can be saved. It is also obvious that the processing units are better to be nonlinear as in the brain, and the memory unit should be able to be changed or manipulated to mimic the synaptic plasticity. We know how different parts should behave in order to have a computer to at least function like the brain, but the big question is: What hardwares should be used? What kind of devices act like a neuron, or a synapse? And even if we find them, are we able to place them close to each other to overcome the Von Neumann bottleneck?

These are the questions that Neuromorphic computing tries to answer. In other words, it is an attempt to build new hardware to be able to do computing like our brain. Some of the most promising candidates here are the spin-orbit devices as they are super-fast, energy-efficient, and more importantly, nonlinear [8][9]. I will talk about them and their major role in this field more in detail in the second part of my post soon!

Please don’t hesitate to ask questions: mahak@chalmers.se

References:

1. Von Neumann, J. Papers of John von Neumann on computers and computer theory. United States: N. p., 1986. Web.

2. Sebastian, A., Le Gallo, M., Khaddam-Aljameh, R. et al. Memory devices and applications for in-memory computing. Nat. Nanotechnol. 15, 529–544 (2020).

3. John Backus. 1978. Can programming be liberated from the von Neumann style? a functional style and its algebra of programs. Commun. ACM 21, 8 (Aug. 1978), 613–641.

4. Bains, S. The business of building brains. Nat Electron 3, 348–351 (2020).

5. Brunel, N., van Rossum, M.C.W. Lapicque’s 1907 paper: from frogs to integrate-and-fire. Biol Cybern 97, 337–339 (2007).

6. Kurenkov, A., DuttaGupta, S., Zhang, C., Fukami, S., Horio, Y., Ohno, H., Artificial Neuron and Synapse Realized in an Antiferromagnet/Ferromagnet Heterostructure Using Dynamics of Spin–Orbit Torque Switching. Adv. Mater. 2019, 31, 1900636.

7. Gerstner, W., Kistler, W., Naud, R., & Paninski, L. (2014). Neuronal Dynamics: From Single Neurons to Networks and Models of Cognition. Cambridge: Cambridge University Press.

8. Grollier, J., Querlioz, D., Camsari, K.Y. et al. Neuromorphic spintronics. Nat Electron 3, 360–370 (2020).

9. Zahedinejad, M., Fulara, H., Khymyn, R. et al. Memristive control of mutual spin Hall nano-oscillator synchronization for neuromorphic computing. Nat. Mater. 21, 81–87 (2022).

Posted on by Salvatore Teresi

Ferroelectric materials and applications

Ferroelectrics are a category of material that in absence of an external applied voltage they still show a remanent polarization. The reason can be found in their atomic structure. For example the family of perovskites are ferroelectric material due to their specific crystal arrangement. Perovskite all share this similar ABX3 structure, where usually the X is oxygen and the A and B represent two different metals.

Fig.1 Phases of KNbO3 (potassium niobate) at different temperatures. It shows some structures where is possible to have a remanent polarization due to non-centro symmetry of the Niobium atom (in green) inside the cubic structure. When the Niobium atom is exactly at the center (in this case above 708 K) the material is not anymore ferroelectric [1].

One of most famous and studied is lead zirconate (PbZrxTi1-xO3) commonly called PZT. One of the biggest issues with this material is the toxicity due to the presence of the lead. For this reason, researchers focused on finding a material with similar characteristics. So many of them came out like barium titanate (BaTiO3), know as BTO or strontium titanate (SrTiO3) known as STO. In the picture here above another example of a lead-free perovskite material: potassium niobate (KNO3).

The remanent polarization properties is given by the presence of an atom inside this cubic-like structure that is not exactly at the center but slightly shifted. This non centro-symmetric structure give rise to a non-compensated positive charge of the body atom (Ti or Nb for example). The ferroelectric properties then are just given by the presence of the non-compensated charge when all the external voltages are removed. The temperature has an important role since for every material, for a given energy the structure tend to become a symmetric body centered cubic structure, hence there is a critical temperature after which the ferroelectric materials become paraelectrics. In this state they still react non-linearly to an external applied field but they do not show a remanent effect in absence of it.

Fig.2 Behaviour of a dielectric, a paraelectric and a ferroelectric material under an applied external electric field [2].

The polarization bistability for a zero external applied field is the key feature that makes ferroelectrics good candidates for memory applications. In recent year, many studies focused on integrating the ferroelectric materials in order to create new memories, more competitive from an energy computation point of view or overall faster writing and reading speed as FE-Fet [3], FE-RAM [4] or MESO [5] and FESO [6]. If for the first two the ferroelectric properties are aimed to improve the properties of already existing devices, like transistors or non-volatile random access memories; for the MESO and FESO case the aim is more ambitious. The idea is to develop a new logic based on spin controlled by ferrolectric non-volatility.

Recently, others materials showed to have ferroelectricity properties like Germanium telluride (GeTe), Indium arsenide (InAs) and many others. These materials show a simpler combination of only two atoms and that are not insulating like perovskites (sually they are metalic or semiconducting).

The bigger advantage is the possibility to pattern them in order to produce nanodevices, given by an higher durability when subjected to nanofabrication steps like etching. This one tend to destroy the crystal structure and hence the properties of the insulating perovskites . As a consequence, these new materials bring the ferroelectric-based devices a step closer to mass production and adoption.

If we take into account the case of germanium telluride, the ferroelectricity comes from the unusual bonds between germanium and tellurium layers. They tend to form a stronger bond with a neighbour layer with respect to the other forming a bilayer structure that is not symmetric (see pictures below). Similarly under an applied electric field the structure reorganize, causing the polarization to change sign (if the field is strong enough). It can be also seen as the germanium in the center of the cell moving along the larger diagonal of the deformed cubic cell (also called rhombohedral cell, left picture).

Fig. 3  Left: Cell structure of Germanium telluride (yellow Germanium, blue tellurium). Right: Switching mechanism: a) stable configuration of layer of Germanium (yellow dots) bonded to Tellurium ones (in red). b) when an electric field is applied, an unstable state appear where Germanium is bond to both top and bottom Tellurium atoms. c) Final state in which the Germanium atoms will be bond to the Tellurium atoms in the upper level with respect to the initial state [7]

So in a similar way to perovskites germanium telluride is know to show a remanent polarization at room temperature that can be controlled by an external applied electric field.

I hope you enjoyed this small talk on ferroelectrics, I will write in future a part 2 to explain the relation between ferroelectricity and spin-logic based devices. For further information you can email me at: salvatore.teresi@cea.fr

References

[1] P. Hirel et al., Phys. Rev. B 92 (2016) 214101.

[2] http://faculty-science.blogspot.com/2010/11/ferroelectricity.html

[3] Stefan Ferdinand Müller (2016). Development of HfO2-Based Ferroelectric Memories for Future CMOS Technology Nodes. ISBN 9783739248943.

[4] Dudley A. Buck, “Ferroelectrics for Digital Information Storage and Switching.” Report R-212, MIT, June 1952.

[5] Manipatruni, S., Nikonov, D.E., Lin, CC. et al. Scalable energy-efficient magnetoelectric spin–orbit logic. Nature 565, 35–42 (2019). https://doi.org/10.1038/s41586-018-0770-2

[6] Noël, P., Trier, F., Vicente Arche, L.M. et al. Non-volatile electric control of spin–charge conversion in a SrTiO3 Rashba system. Nature 580, 483–486 (2020). [7] A. V. Kolobov, D. J. Kim, A. Giussani, P. Fons, J. Tominaga, R. Calarco, and A. Gruverman, Ferroelectric switching in epitaxial GeTe films, APL Materials 2, 066101 (2014).

[7] A. V. Kolobov, D. J. Kim, A. Giussani, P. Fons, J. Tominaga, R. Calarco, and A. Gruverman, Ferroelectric switching in epitaxial GeTe films, APL Materials 2, 066101 (2014).

Posted on by Saxena Vishesh

Antiferromagnetism

Hello readers! This first post is about antiferromagnets. I talk about the general concepts in antiferromagnetism and then later I dive into some interesting complex antiferromagnetic states at the atomic scale! I hope you have a good read! Please feel free to reach me out at my email for any further questions! (vsaxena@physnet.uni-hamburg.de)

Click here to check out the post And stay tuned for my next one! I will come back some more interesting magnetism!

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