Online Spintronics Seminar #119: Vivek Amin (IU)

Ok, I hope we're live now, leave that up, yeah, we're live. Okay, we're almost ready to go. Please give me a few seconds. Okay, so we'll start recording now. No, it's 3:30 3:30. Okay, I think we're ready, so let's get started. Welcome to esonic

online

seminar

number 9, so we welcome Professor V

amin

back after a four-year hiatus, so he gave one of the first

seminar

s in the series about four years ago. he comes back with a somewhat advanced version of the same topic it's a non-local spin orbit TS umac is an assistant professor in the physics department at Indiana University in Indianapolis they just changed their name or completed a merger or whatever their degree in electrical engineering from the University of Texas at Austin and a PhD in physics from Texas A&M.

Prior to joining Indiana University, he worked as a postdoc and research scientist with a joint professorship at Maryland and the University of Maryland College Park. Amin uses computational and analytical methods to study electronic transport in condensed matter systems with a focus on

spintronics

Neuromorphic computing of quantum materials and, as you can see, the spin orbit of Tor, so with this I'll turn it over to you, el vi, please take over. Well, I just wanted to thank Carol and Shin for inviting me again. It's good to be back after four years, like Carol said. So today I'm going to talk about the work I did with Alexi Kov and Carol Belenco at the University of Nebraska Lincoln um the title is nonlocal spin orbit torque and I'll tell you exactly what nonlocal means as the talk goes on, okay, before we start.

I want to give a cursory announcement to my theory group at IU Indianapolis um. So if you are interested, email me at vpam iu.edu. Well, let's start with what I would like you to learn from this talk and that is that orbital torques are an energy efficient control of magnetization. Dynamics, eh, but there are several. The open challenges, two of the biggest, are that there is disagreement about the important microscopic mechanisms, even after all this time, and there is still not enough energy for widespread integration, so there are still some problems that need to be addressed. despite the progress that has been made. have been done so what I will tell you today are theoretical calculations of non-local spin orbit torques in non-magnetic ferromagnetic trays, so we will move away from Bayers towards TR uh layers and the prediction of a new and novel mechanism of indirect torque which is based on two ingredients, um, the physics of the current giant magnet, resistance and spin-to-spin conversion, like spin orbit procession and spin exchange effects, okay, so here it is the roadmap for my talk.

I will begin with an introduction to spin-orbit torque and discuss both conventional and unconventional mechanisms, then move on to talk about the experimental evidence for non-local spin-orbit torques that require these new ingredients to be explained, and finally we will talk about the non-local spin orbit. Torque payers and ferromagnetics, specifically indirect torques that are driven by interlayer spin orbit dispersion, are fine to start with, as we all know. Magnetic tunnel joints are extremely versatile and there are several uses for them. They have been used as hard heads, of course, where the magnetic free layer changes its direction of magnetization depending on what the magnetization of the etched medium is and has a readout of the bit through the Giant Magneto resistor or the Magnor tunnel resistor.

You can also flip this and instead use the magnetic tunnel junction as a bit to store information instead of reading information and this is what is done in magnetoresistive random axis memories. So here's an example of what an mram and an individual bit might look like, most of the bit is actually made up of the transistor that is. is being used to access that, but the magnetic tunnel junction is essentially located here and again depending on the magnetization configuration, whether it has a parallel or antiparallel configuration, it can store a one or a zero and of course it can read this out loud. its resistance due to the resistance of the tunnel magnetator, we know that in the antiparallel configuration we have a high resistance and in the parallel configuration we have a low resistance, so we can use this to read the bit that the open challenge is writing and the state.

The fourth art is to use twist torques specifically spin transfer torques right now which will be explained in a moment and then finally we can also redesign the magnetic tunnel joint to behave like a twist torque oscillator and now what we do is we run a current through this device and using the spin transfer torque we can incite self-sustained oscillations of the magnetic free layer uh and then using the Magneto resistance we can get an oscillating resistance and we have essentially converted a DC signal into an AC signal on the nanoscale and this of course has advantages because it is a low power nanoscale oscillator, but it can also mimic the properties of the synapse and neurons.

So how do we control magnetic tunnel junctions? The conventional way has been through spin transfer torque. which we can use to control the magnetization of the free layer, so how does this work very briefly? We run out of plane current through this device and the current becomes spin polarized in the bottom ferromagnetic layer, the spins then enter the top ferromagnetic layer and start processing the process incoherently, which is known as phase lag, so because of the strong exchange interaction, these spins are then processed around magnetization, but because the spins are processed incoherently, the only thing that is common between all of these spins is their angular momentum component along along the In the magnetic order of the magnetization, the transverse component now points in all directions and therefore the spins lose the net transverse component of the magnetization, so it started with an angular momentum in this direction and ended with a net angular momentum along the magnetization and So as a result, you have angular momentum transfer, which is the spin transfer torque, and here's an animation showing exactly what I just said.

So as the spins come in they start to process around the magnetization and you have a loss of the transverse spin component which then results in angular momentum transfer or spin transfer torque. Now there are several problems with this, the first is that it is energy inefficient, since you are passing a current through an oxide layer, so you are losing omics energy. Heating, uh, the other problem is that repeated writing will damage the oxide layer. So eventually your bit may not work and a possible solution is to separate the reading and the correct path and this is where the spin orbit torque comes into play because now what we do.

Instead, what we are going to do is run a current in the rail and, through various effects involving spin orbit coupling, such as the spin Hall effect, we can make the spin current in the rail or the in-plane charging current become an out-of-plane current. spin current which can then flow into the upper ferromagnetic layer and a stress torque, so this is just one way, of course, in which a spin orbit pair can occur, but if we think about things in terms of angular momentum deposits, it's easy to see why the spin orbit pair holds the promise that yes, if we look at the spin transfer pair, the toric spin transform is actually a transfer of angular momentum between the carrier spins and the magnetic order which is mediated by the exchange interaction, so we have these two reservoirs of angular momentum and the The angular momentum of the carrier spins is fixed by the polarization of the ferromagnet;

However, if we add spin-orbit coupling to the mix, then the carrier spins are coupled to the orbital momenta via spin-orbit coupling and the orbital momenta are coupled to the atomic lattice via the Spin Potential. Kum, so through this extended coupling we can transfer all the angular momentum we want, in principle, from the atomic lattice to the magnetic order. This is because we are tapping into a virtually unlimited reserve of angular momentum for which the SP orbit torque is promising. Of course, the dark side of all this is that we have to have a conversion efficiency that is quite strong, so right now we don't necessarily have a spin orbit torque advantage over spin transfer torque.

Well, what are the traditional ones? Spin Orbit Torque Mechanisms, the two mechanisms most are familiar with are the spin Hall effect and the Rasha Edelstein effect, so very briefly, the spin Hall torque works as follows : We pass an inflammatory current through the non-magnet and through this Hall effect SP, we get an out-of-plane current which then flows into the ferromagnetic player and exerts a spin transfer torque. The spin couple damps the magnetization towards a special direction s which is given by the out-of-plane direction that crosses the electric field and that direction is always in-plane. in a Bayer and therefore whenever we use Hall torque to damp magnetization, at most we can damp in-plane magnetization, unless we have external magnetic fields.

We also have a mechanism of the precipitated Edelstein effect and in this case the same thing. The internal electric field will create a spin buildup at the interface and the interfacial spin buildup induced by the current also pointing along that special direction will exert an exchange torque on the magnetization. Okay, so these were the two prototypical spin orbit torques and there. There were early attempts to try to unravel these mechanisms. These attempts involved theoretical analyzes based on symmetry and experiments that changed the thickness of a spacer layer that was added in the middle between the ferromagnet and the heavy metal to try to see if as the thickness of the spacer layer reached zero. , maybe we can capture an interfacial contribution, so I would like to tell you that what happened after that was that we unraveled all the mechanisms, we found out what the dominant mechanisms were and then everyone lived happily ever after, but in reality things were in the opposite direction, so instead of getting simpler, they actually got more complicated, so in the next few slides I'll talk about the advances in the spin orbiter since then, the image of the spin orbit pair beyond the conventional turn. and R Edelstein mechanisms, so really what started this whole Avalanche was looking at the expanded role of interfaces, in particular looking at spin memory loss and revisions to magnetoelectronic circuit theory.

Basically what this means is that when we think about the angular momentum flowing into the ferromagnet we don't have perfect transmission of angular momentum, we can have some loss at the interface and that is due to spin orbit coupling, so we have a transfer of angular momentum back to the atomic lattice and, as a result, we have to revise the circuit. Theoretical models that we originally used to explain how spin transport worked at interfaces were electronic circuit theories, so in this scheme we don't worry so much about indices. Basically, each of these little boxes is a contour diagram of the different elements of the Matrix that pair accumulations, spin accumulations and charge accumulations at the interface of the spin currents that eventually flow through the interface and without spin orbit coupling, many of these terms are zero, so the theory is very simple when you turn on spin orbit coupling, break enough symmetries and everything.

Suddenly, all of these different coupling mechanisms turn on, so at the end of the day it becomes very complicated to figure out what accumulations are causing what currents and, as a result, what torques, so this was again something of a first snowball for Avalanche. and a lot of theory and experiments were done around this, but then things got even more complicated when it was realized that in addition to transferring angular momentum to the atomic lattice at the interface, the opposite could happen, so in other In other words, the interface could actually generate a spin current much like the spin Hall effect does in bulk nonmagnetic material and this is really not that surprising if we think about the fact that, according to theeruption of the Edelstein effect, we have a spin orbit field that polarizes the carrier. spin at the interface, if we then move away from the interface along a mean-free path and then consider the scattering of electrons out of the spin orbit field, we can obtain filtering and procession effects that can then result in spin currents outside of the plane, so the net effect is that when we stop thinking of the interface as a purely two-dimensional object and think about scattering away from that interface, we get three-dimensional out-of-plane spin currents where the spin directions of those spin currents do not have to be the same as what the Adelstein eruption effect predicts, in addition to this, there are different dependencies on the disorder and material parameters for the spin currents generated by the interface than the eruption sign effect, which complicates further things and we can actually split the spin currents generated by the interface into two different classes. a spin orbit filtering effect that has the same symmetry as the precipitated Balin effect and a uh spin orbit procession effect that actually has a spin current polarization that spins relative to the eruption B Stein effect, okay, so continue again as the situation becomes more complicated.

Complicatedly, in the late 20's it was realized that symmetry allows there to be spin currents in pheromone magnets where the spin direction does not align with the magnetization, and so what that means is when those spin currents they flow toward the boundaries of the layers where the inversion occurs. If the symmetry is broken, they can exert a spin orbit torque and that means that in theory a ferromagnet can exert a torque on itself if there is a broken symmetry between the top and bottom shells. Otherwise, those two contributions the torque will cancel out as the top layer here usually has a different interface in the bottom layer connected to the heavy metal, this means you have a possibility of having anomalous or self torque in the ferromagnetic layer and there are still several questions debated such as what are the exact mechanisms and what determines the efficiency, does it have any loss due to spin orbit coupling in the ferromagnetic layer and how can we distinguish these bulk mechanisms from interface generated spin currents which actually have the same symmetries and give the same types of spin currents, the last piece to be added to this puzzle is orbital Hall twerks, so the prediction of the orbital Hall effect actually dates back to 2008, but it was necessary until the late 2010s and early 2020 so that we began to investigate the potential of the orbital hall effect that an orbital spin pair exerts and in this case the procedure is that the orbital hall effect creates an orbital current that then becomes a spin accumulation that more late is considered to typically occur in the ferromagnet in the ferromagnet, so it has a different procedure than what happens with the spindle torque, okay, so those are the zoo of mechanisms that we believe exist in some form at Bayers, So what then is the motivation for studying TR layers?

The B layers are already very complicated, well, what we know about the TR layers is that they break additional symmetries that the B layers do not have, so, for example, with a non-magnetic Bayer ferromagnet, we know that we have a symmetry in the mirror plane that forces the spin orbit torque to disappear when the magnetization points along this special. Inlane direction here along the y direction um, this means that you can never change ferromagnetic materials with perpendicular magnetic isotropy deterministically because you will change the pheromone magnet to this inlane direction and then you won't be able to do anything else to be able to do this, you have You have to break the symmetry of the mirror plane so that the torque no longer disappears in this direction with a B layer, you have to do it with a magnetic field applied with the tril layer, you have already broken the symmetry from the ferromagnetic background. layer as long as the direction of magnetization is in a given appropriate direction, for example here, if the magnetization of the upper pherome magnetic layer points out of plane and the magnetization of the lower layers points in plane, then it can have orbit torques rotation. which can change the top ferromagnetic layer, so switching to systems where we can change the plan magnetizations, which is thought to give us better switching efficiency, is certainly one of the motivations for switching to orbit torques of spin and TR layers, another motivation is that If you remember from the introduction, we have so many different devices that already use toggle layers, whether they are read heads or mram bits, so we look at these devices and think about them in terms of a current in the plane and what the turns are.

The orbital twerks that result from them could also be useful for interacting with the types of devices we've already created in the past. Well, in this talk I will focus on the ferromagnetic TR layers, not the P layers, and I am specifically going to discuss a mechanism or a set of mechanisms that we call non-local spin orbit torques and these have a different character than the mechanisms I talked about above and generally we can divide them into two different types, so let's call those direct ones in which a spin current from one ferromagnetic layer is generated in that layer and then flows to the other layer and exerts a pair.

This is a fairly conventional process and has been studied and is an indirect mechanism involving interlayer dispersion of the indirect mechanism. It is essentially the novel mechanism here, so how do we understand the indirect mechanism? The indirect mechanism contains two main ingredients, the first ingredient is current and simple Giant Magneto resistance and the second ingredient is spin to spin conversion, the reason why we need these two. The ingredients are because normally when we think of spin orbit torque, we think of an out-of-plane spin current that is generated and then exerts a torque or spin buildup that is generated directly at an interface Of course it all ends up turning into a spin buildup when you exert a torque, but when it comes to TR layers, the TR layers can now communicate with each other through the Giant Magneto resistance of the current flame, as I'll talk about in this second , and that provides a way of communication between the two layers. which we didn't consider earlier, so that's one ingredient, the other ingredient that we don't normally think about is spin to spin conversion, so we usually think about charge to spin conversion, we have an electric field and then that generates a spin current, but now that we have magnetic pherom layers that already have spin polarized currents, maybe the spin to spin conversion is also important, okay, so let's look at the first ingredient, which is the resistance of the Giant Magnet current and flat, um, so these are the famous experiments that resulted in the Nobel.

Award from the groups of Albert Fa and Peter Grinberg um and on the left and center you can see figures reproduced from those original articles uh showing the fundamental measurements of the current resistance of the flammable GI Magnet. On the right you can see one of the first theoretical calculations by Cam and Barnas using the Boltzman formalism to capture the physics of the current and planned Giant Magneto resistance and the important point here, the point they found is that the physics, the scale of length that was important for this was the mean free path and therefore, while As the ferromagnetic layers were within a free path of each other, a simple current giant magnetic resistance could be obtained, what does that look like?

Here I am showing you calculations from a recent article, this is the focus of this talk. These are semiclassical calculations or Boltzman calculations and here what we're looking at is a ferromagnetic tray and what I'm plotting are the in-plane spin currents as a function of the out-of-plane direction, um, so if you look here in this cartoon , this can give a better idea of ​​what is happening, so we have two ferromagnetic layers and when we run an in-plane current, we are going to have two in-plane spin polarized currents, one rail spin polarized current in each layer , so in this top ferromagnetic layer we are It will have a spin biased current in the rail where the spin direction is along the magnetization of that layer and the same in the bottom layer, so here I am just showing the current Lane turning PL in the top layer and predictions from Boltman calculations. is that if we look at that in-plane spin current as a function of the out-of-plane direction, the in-plane spin current decays in magnitude and that exponential decay has a mean free path decay length, so that is the important length scale for this decay and you can See this in these graphs here, so if we look at this bottom graph where the non-magnetic spacer is 12 nanometers, you can see that in the ferromagnetic layers we have in-plane spin polarized currents where the spin direction of those currents aligns with the magnetization, so Ferromagnetics, a layer A has magnetization along each layer, but as I approach the interface in the order of a half-less path, I get some operation of this current and then I have a decay into the non-magnetic material, so everything is fine, but once you start to bring these ferromagnetic layers closer together, once they are in an immune free path order, you can start to see that. there is an interaction between both layers, in fact you can get quite a strong interaction, you can even have the magnitude of the spin polarized, change the direction of the current, so once we have a small gap or layer, these two ferromagnetic layers can communicate with each other, so that's Our first ingredient for reviewing spin orbit torques in ferromagnetic trays is okay, so now what we're going to do is look at the experimental evidence for spin orbit torques. nonlocal spin before we move on to the theory ah okay I see what happened so this slide has been moved this was ingredient two um this is spin to spin conversion so if we think about what happens in a ferromagnetic material or at a non-magnetic ferromagnetic interface, we can have a situation where a charge current or a spin polarized current that is decelerating in-plane and then becomes an out-of-plane spin current where the directions of spin have been swapped, so the first example of this was predicted by lipshits on the oov in 2009, which is known as a spin swap, so this prediction actually happened.

This was predicted to occur in non-magnetic materials and essentially the physics is the same as the spin Hall effect. Later, we also realized that spin polarized current in the vicinity of an interface will undergo spin orbital dispersion and through the spin orbit procession effect that caused spin currents generated at the interface, we should also we could get a spin direction swap, so what you see in this chart here are a bunch of different diagrams showing all the different ways that in-plane spin currents can become out-of-plane spin currents in the interfaces, so this is the essential spin-to-spin conversion process that can occur at a non-magnetic ferromagnetic interface.

Well, those are the two ingredients and now we will talk about the evidence for the nonlocal spin orbit TS. Well, normally when we think about spin orbit torque measurements, we can think about them in terms of torques or we can think about them in terms of fields, so if we think about them in terms of torques, we usually see things in terms. of a damping pair and a field pair and we will expand on it later, but for now, if we consider these two pairs, we can also rewrite them in terms of fields because both the damping pair and the field pair have the same shape.

M crosses something, so what's in front of the magnetization we could call the field, so this is the damping-like field and the field-like field, which is confusing terminology, so here I plotted the fields instead of torque and nice What happens when thinking about these two ways is that if the magnetization dynamics are slow enough, then we would expect that the magnetization would actually want to target one of these fields depending on its strength instead of being a torque in which we have to calculate. the dynamics, so we can also see this by looking at the Land Li Skillbert equation, we just take this term that includes our effective field and the torque due to the spin orbit.

We write them interms of effective fields, then we have a net effective field. in which the magnetization dynamics is governed by well then things get complicated as they always do when you go from layers to tr layers due to the lower symmetry the number of unique fields increases well then how do we see this ? um, let's take a simple approach, if we look at the bottom magnetic pherome layer, we know that that layer and the middle layer, the middle spacer layer, can generate this type of spin current where the direction of the spin flow and the direction of the field electrical are orthogonal to each other, so This is the spin Hall effect, however, due to the broken symmetry in the ferromagnet compared to non-magnetic layers, we can also have other spin currents, so here is an example of another spin current allowed by symmetry.

This is a spin current that could result. from the magnetic spin Hall effect, for example, or from spin currents generated by the interface, but regardless of what mechanism creates this spin current, we now have two spin currents that could flow into the upper ferromagnetic layer and the corque exercised, which means that we have two fields. What we have to consider is that we have to have the original field parallel to the polarization of the first spin current and relative to that field we can have both a damping torque and a field torque that is given by these two higher expressions, However, this lower spin current can also exert a torque relative to this rotated field and as a result we can get a damping-like torque and a field-like torque relative to the rotated field, so again, if we go from the image of the pair to the image of the fields, we can write a special field for each of these and now we have four unique fields, we have a damping type field and a field similar to the spin Hall orientation and then we have a field similar to damping and a field similar to rotated polarization, so these There are four different things we can measure.

I'm showing what they look like in this cartoon. In this particular case, these damping type fields point in the same direction, but because these two lower fields are foreign to the magnetization of the lower layer by inverting the lower layer. magnetization we can invert this field and this field and so we can distinguish them in experiments, okay, here are the results of the work of Shin Fan's group from 2017, looking at a triple layer that was permanent alloy on the top and a perpendicular magnetized layer which had many layers, um, the bottom ferromagnetic layer, um, and here are measurements of the different fields, and if you look at the rotated fields, there's something that's quite curious: the damping of the rotated field is actually smaller than the field rotated, so why is our typical exp expectation strange?

If we have spin currents that are emitted from the bottom ferromagnetic layer, say that then flow into the top ferromagnetic layer, we expect the relationship between field and damping, like torque, to be approximately that of the relationship between the imaginary and the damping parts. actual mixing conductance if no other mechanisms are involved, so if it is just those spin currents flowing into the top layer it is the spin mixing conductances that will roughly determine the relationship between field and damping as torque ; however, we know that the spin mixing conductance at typical nonmagnetic ferromagnetic interfaces is on the order of 10%.

So in other words, having a field-like torque that is actually greater than the damping-like torque due entirely to the imaginary part of the mixing conductance is extremely different. Now it is true that this ratio does not have to be equal to this, for example for non-rotated components we could certainly have a stronger torque field due to the fact that we have a strong Oread field in the system, but in reality there is no conceivable way based on Oread fields or interfacial torques here that we actually have a field-type torque. greater than damping as torque for the rotated case, so this is already a puzzle, so there are other experiments that have shown similar behavior, so these are Hall harmonic measurements on a platinum cobalt peroid pan .

And what you're seeing here are graphs of exactly those four. Fields extracted from Hall harmonic measurements as a function of platinum thickness. Now these results are not as surprising, let's say, as the others, but you can still see that there is a fairly strong relationship between the field-like field and the Damping-like field for small thicknesses of platinum in the paper, this was attributed to the thickness of magnetization, uh, tilt due to small thicknesses of platinum, um, but in any case, we still see a strong relationship between these two, which is peculiar, okay, so let's get back to these. fields and this will now move on to the theoretical part of the talk.

An alternative way of writing these fields we could simply add them together and when we do we can see that what is in front of the magnetization is for the damping. The pair as the field and the pair as the field are actually quite different, so if we put this back into our original expressions we get something that is actually much simpler, instead what we find is that the damping as the torque is wet relative to its own direction and the field as the torque. The torque is processed relative to a different direction, so one way to understand the reduced symmetries of the TR layers is that the damping type torque gets its own field and the field type torque gets a different field and a key point here is that if we consider spin currents that are emitted from one layer that then goes to a different layer and exerts a torque without any other special effect in mind and if we only consider the standard circuit theory that governs the interface, then we actually expect that these fields are aligned and I will explain this in more detail later, but what experiments have clearly shown us is that they are not right, so now let's talk about the nonlocal spin orbit torsion theory and TR shells , as we have talked about symmetry before.

Bayers determines the shape of the pair, so due to the symmetry of the mirror plane, we are guaranteed pairs that have this shape, so we have a damping pair, a field pair, and we also have higher order pairs if the we expand in terms of vector spherical harmonics um, but for the moment we will only consider these two torques, so what happens when we switch to tr layers? Well, TR layers we have lower symmetry, which means we don't necessarily have the torque description that we had before, so One of the interesting things is that if you do the symmetry analysis, you find that you can still write the spin orbit torque in a TR layer in terms of damping type torque and field type, it's just that the damping type torque has its own feel and the field like torque also has its own field.

This is exactly what we saw when we were manipulating the fields of experimental results. This is just symmetry telling us that this is absolutely one way we can write these torques, but actually more symmetry analysis can be done. give us detailed expressions of what these special fields should look like in terms of the magnetization of the other layer, so I know there's a lot going on here, so to summarize for the TR layers, we have torques on the magnetization which are damping like torque relative to a field, one field as torque relative to a different field and it is the bottom ferromagnetic layer that controls the direction of these special fields, so if we now want to analyze all the different torques in a TR layer, we have many different options and as we talked about before, there are a lot of different mechanisms that cause spin orbit torques, so we'll use this terminology which is very rough to define what we mean by local and non-local torques, so we're looking a local torque.

We will refer to it as a torque in the aeromagnetic layer that is due to microscopic mechanisms coming from adjacent layers, for example the torque in this top layer is due to mechanisms in the top layer and in the adjacent layer, something like the spin Hall effect. the effect of the sign of Ral or anomalous torques or things like that, but we are also going to consider non-local torques and all we mean by non-local Tor is that the interaction between the two ferromagnetic layers is important, in terms of local torques. These have been well studied even though there is still no complete agreement on what the dominant microscopic mechanisms are, so the question then becomes whether non-local spin-orbit torques play an important role in all three layers. .

Okay, so how are we going to investigate something? Theoretically so, since there are so many different jobs allowed in our system, one thing we can do is partially remove spin orbit coupling in the layer where we are calculating torque, for example, if we focus on spin. orbit pair in the upper ferromagnetic layer, but we turn off the spin orbit coupling, which we can do in our theoretical calculations in the upper magnetic pherom layer and in the non-magnetic spacer, then there is no possibility of an orbit pair of spin or a local spin orbit. The torque of the mechanisms of these two upper layers since the turning torque can only be caused by the lower ferromagnetic layer, so in this sense we have isolated our torques only for those for which the coupling between the two ferromagnetic layers is Importantly, as we alluded to Before there are two mechanisms, the known mechanism that we will call direct torque is that the spin current is created directly in the lower ferromagnetic layer or at its interface, flows to the upper ferromagnetic layer and exerts a torque, the alternative or indirect mechanism.

The torque will come from a strong dispersion between layers. Okay, so let's start with nonlocal direct torques, which are the mechanism typically studied. So how does this work? So we have a current in the plane and in the bottom magnetic pherome layer, which is the only place where spin orbit coupling is on, we could have a charge to spin conversion, which will give us currents like this , for example, as the spin Hall effect, so that it can then flow into the upper layer and exert a spin transfer torque and the spin transfer torque. in this particular case it's going to point this way along the direction of this finite polarization when the magnetization points along the minus x direction, so when the magnetization points along the y direction, the magnetization is in the same direction as the bias, so we get no torque, so if we plot all the different torques as a function of the direction of magnetization, we get a diagram that looks like this, where the torque disappears along this special field.

This is the special field from the symmetry analysis that we showed earlier and in this same In a simple picture, this special field is nothing more than the polarization of that spin C, so if we want corrections for this, we can see more complicated corrections by Consider the theory of magnetoelectronic circuits in a self-consistent way and we can find that this special field does not have to point exactly along the direction of the polarization but will nevertheless point in some direction as long as these two magnetizations are orthogonal to each other and , therefore we will reach some point where the magnetizations disappear and the key point here is that in experiments, if you want to determine where the special field is, you must rotate the magnetization direction and find the magnetization direction for which the magnetization disappears.

Pair of light damping that will give you your special field for damping. light torque, okay, so what else can we expect from non-local direct torques? It turns out that there are a couple of constraints on these torques that are quite important, so again, if we have a spin current that is generated in the lower ferromagnetic layer or at the interface between them once it flows into the upper ferromagnetic layer. If we now consider corrections to the magneto electronic circuit theory, we will have a scenario in which the original spin orientation will be transmitted approximately with a force of the real part of the spin. mixing conductance, but that spin current will also rotate at the interface around the magnetization and that is captured by the imaginary part of the spin mixing conductance, so the torque we are going to get approximately is a proportional damping torque to the real part. of the mixing conductance and a torque-like field proportional to the imaginary part of the mixing conductance and then the absorbed spin current will exert a torque, but the important point here is that once the magnetization pointsalong any direction of the spin current being emitted by the bottom layer, both the damping light and the field as torque must disappear and what this means is that the special fields that we defined above, the field for the torque damping and the field for the field as a pair, they have to point in the same direction if we turn off the spin Orit coupling on this top layer, so we can't get the overall result we saw before.

If we only consider that a spin current is emitted from the bottom ferromagnetic layer, we can only obtain damping as and field. as torques with the same special field, then, since the experiments saw something that was different, they saw special fields that were essentially not parallel to each other. We investigated this using avidici calculations and semiclassical calculations, so the abicial calculations were performed by Kill and his students Giovani and Alxi Kov from the University of Moraska Lincoln use density functional theory in the formal formalism of non-equilibrium green functions , so in the NF formalism you can essentially compute the special greens function, the minor greens function which can then be used to compute the nonequilibrium. spin accumulation, spin current and spin torsion, and this is done in a ferromagnetic TR layer where the two ferromagnetic layers are treated to semi-inflate the wires and the scattering region um uh is treated um in the middle between the two um is uses an Anderson disorder to Super Cell averaging and the quol package were used for the ASA lmto implementation.

Well, here are the results of the avantium calculations that cannot be explained by the non-local direct torques we talked about before, so what you are seeing here is a calculation. of damping type and Torx field as a function of the magnetization direction of the upper magnetization, so this magnetization of the upper magnetization is rotated in-plane while the lower magnetization points out of plane and the torques are calculated of the damping type and the field, and just as We had discussed before that the special fields point in the directions where the damping light or the field as torques disappear and what can be seen in the results is that the damping as torques disappears and in different places in the field life works, so if we look at This as a phase, they are out of phase by almost pi over two, which means that their special fields are essentially 90 degrees apart, so this is in complete contrast to the picture of the direct spin current where we have an exotic spin current coming from below. of the magnetic layer and exerts a torque, we know that this cannot happen in our system because we have disabled the spin orbit in these two upper layers, so the result we are seeing and the experimental results of the rotated torque have must be due to something more than just sin current generation from the bottom magnetic pherom layer okay so to try to understand what was going on under the hood I did semiclassical calculations and in the semiclassical calculations these are bolt turning calculations , we try the bolt transit again. using the Boltman equation and at interfaces, we assume quantum and scattering, so by combining these things we can capture the effects of mean free path and spin diffusion, but we can also capture quantum coherent scattering at interfaces, for This is a very simple model in the sense that the firm surface is essentially the same for all layers.

This is essentially the same approach used by Valy and Fern in 1993 and by Pen and Styes in later work. The difference here is that we have added twist. orbit coupling um and we are doing this cusing numerically as was done in the work here and this is what the formalism looks like in the linearized Boltman equation we have a term for the electric field we have a spin procession term that can capture the phase def uh and then we have a collision integral for which we can program different effects, for example, we could program the spin hall effect in the biased scattering of ferromagnetic lead and things like this, okay, so I'll show these results again just for remind them. that the magnetic layers can detect each other through the spin polarized currents inlan um and these are the results that the SP bolt equation shows us, we can also see that as we increase the thickness of the spin current that is found in a particular ferromagnetic layer, say for a magnetic layer a is more or less constant, while the spin current of the other layer can be quite strong, so the spin polarized current of ferromagnetic layer B can be ferromagnetic layer INF quite strong, but as the thicknesses increase, it disintegrates exponentially again, the disintegration is as if it were the mean free pa.

Well, this is what we have proposed for the non-local indirect pair, so this is the mechanism that we believe allows the special. fields don't point in the same directions and give you the rotated torque that we're seeing in the experiment, so the idea is this, if we start with our magnetization, let's say along the top layer of the minus from the plane of the lower layer we know that when we have an in-plane current we are going to have an in-plane spin polarized current in the upper layer, that spin polarized current in the rail will leak into the lower ferromagnetic layer by the same physics which causes the giant current and Simple Giant Magnet Resistance and this is where we have the second ingredient, so if we have spin to spin conversion at this interface, which we know we can have through spin exchange effects or spin procession effects. spin orbit, then we can convert this totally in-plane spin current into a totally out-of-plane one. of flat spin current and there is a conversion factor that we can calculate that tells us what the conversion strength is now if we move the magnetization, say to the Y direction, now we will get a polarized spin current and that is still going to filter in the bottom layer, however, will now undergo a spin conversion and the response that changes this spin current to the out-of-plane spin current may be different to this, so these are two different tensor elements in the tensor from answer um and So because of this, we can have an out-of-plane spin current here and here, but they can be different from each other.

Now, if we ask what the resulting torque is at the top interface as we change the direction of magnetization, we have a non-zero torque. here and a non-zero pair here this is just an example Le and this would imply that the field that governs the field as a pair is actually pointing somewhere in the middle, the point is that it doesn't point in the direction we don't have to point along the um direction from the direct spinning current mechanism. Okay, do we have a way to test the validity of this um? So with the Boltzman equation, what we did was the following, so we looked at exactly the same situation that we would rotate. magnetization and calculate the damping and field as torques and we saw what essentially resemble the results of the avid calculations.

In fact, the agreement is embarrassingly good, but the only reason is because we can modify the parameters in the semi-classical calculations. and of course we can adjust them to the payment calculations. We also don't have many parameters in semiclassical calculations. For bulk materials we mainly use the mean free path and properties of those materials. In this case we use um the uh um. Material properties for cobalt and a copper spacer layer, except we were able to change the mean free path to understand that effect, so here we see the same results as in the fertile calculation where we can get a phase difference of 90 degrees between damping. light and the field as torque which indicates a direct mechanism and to test whether or not this mechanism is governed by the leakage of currents before we can increase the thickness and by doing so what we find is that the field as torque which is a sign The dependence similar to the line depth becomes more cosine-like, like the damping torque, as we increase the thickness, so what this strongly suggests is that once we are several free paths away, the SPAC or we cut out the thick mean free pths, we have the The physics that is governed by the imaginary real parts of the mixing ducts and the special fields are aligned, whereas when the materials are close together they are not aligned, so we can see that here by simply plotting the phase difference as a function of thickness and It can be seen that we start with a strong phase difference suggesting an indirect mechanism and then as we increase the thickness we transfer to the direct mechanism.

Well, in conclusion we used both compost and semi-class calculations to reveal non-local spin-orbit torques in the TR layers and the semi-classical calculations suggested that there was a novel mechanism behind one of those non-local torques which we call current generation. indirect spin. The importance of this is that this is a spin orbit torque analogous to the resistance of the current giant flat Magnet and these types of effects had really been ignored in the spin orbit torque until now, it is distinguishable experimentally because it does not we are engaging with which IC mechanism of the microscope is causing the spin-to-spin conversion, for example, we are simply looking at the direction of the special. fields to tell us if we have an indirect mechanism or not, um, and this could also affect the out-of-plane switching efficiency, although this is a field-like pair that cannot cause out-of-plane switching, this could still affect the commutation. efficiency and in addition to this, this can also affect the interpretation of the experiments, so for more information visit this article here which is on archive and which covers all the semiclassical and symmetry analysis of Avantia, so thank you for your attention.

Thank you very much FC for this instructive talk, let's thank the speaker who uses the action buttons, so that the talk is open to questions. If you have any questions, raise your hand on Zoom and I'll call you, if you have any questions, please. um Shen, please go ahead, I'll be back. I just want to ask the first question. I think it says the second to last slide, where you showed the dependence on the thickness of the spaces. um, there's a clear change for the F type torque, but your damping touch. It also reduces significantly as the thickness of the copper increases.

Is there any simple physical explanation for that? Yeah, that actually essentially has to do with the spin resistance of the layers, so you're still going to have uh type dependence torque at a higher thickness. and that's essentially what it's capturing, I see okay and that's what I thought was just the result of the D diff diffusion models but this is not the case, we still have diffusion, we have essentially capturing both the mean path and the length of spin diffusion too, but in this case I should correct myself. We've turned off spin diffusion because we normally think that the spin diffusion length is quite long compared to the spacer layer, so here we really are.

I only see the thickness dependence, but now you don't need to have spin diffusion in your model to see the thickness dependence. I see that I see well, like copper doesn't really have a lot of diffusion, yeah, and the other thing is that even though we've used the material parameters for copper to test the torque properties as we change the gap or the layer thickness, we've created a dummy no-means path of about three netr, so that's Otherwise we're looking at something here, otherwise it's a free pad of 40 neter, so you'd have to do this very thick to see something.

Yes, we will have to make a dummy copper to do this experiment. Well, no, but it's kind of the opposite because Well, okay, if you want to see this kind of dependency, then yes, you'll need something with a lower need. I thought well, yes, thank you, thank you. Any other questions please Eric please go ahead yeah thanks for the nice chat Viv I was wondering. If there are any, I guess, all of this is calculated as Static or they are using this field based on this field approach, or they are dynamical calculations, there are no micromagnetic simulations if that's what you're asking, or any dynamics for the magnetization, then. the Val is fixed uh and then the torques are calculated in both the abonal calculations and the semi classical calculations.

I guess I was more interested in relation to interlayer exchange coupling and then spin pumping than I was before. was renamed to Interlayer Exchange Dynamic Coupling, so I was wondering if how they relate and in those situations you can have interesting, like fire level effects, like critical expansion vectors and things like that that modulate this, do you expectthose effects? to impact these non-local spin orbit torques, yes, it's a good question, so if you think about what we're seeing here, the main communication between the two ferromagnetic layers is of the order of the mean free path, so we expect There's some sort of dispersion that occurs, so if you want to see coherent effects, you need to be in a ballistic regime that's essentially smaller than the mean free path, so I imagine we wouldn't see anything like coherent effects here, in terms of the effect on spin pumping, that's also hard to say.

I mean, with spin spin you typically don't have the electric field in the right plane, so ultimately you're creating a processing magnetization and then looking at the spin out of plane. current, but here you need the inlane spin inlane charge currents to be filtered into the other layers and then inserted and then converted. Great, thanks, okay, thanks. Other questions, please, let me ask a quick question, so in this particular case, direct generation. The mechanism comes from the pheromatic magnet and can generate an unconventional component from a simple spin polarized current for example, but if we consider a somewhat more general case where the out-of-plane component is generated in some other way for example from the low crystallographic symmetry of the interface, in that case I would also expect a similar component to appear due to these non-local processes if the generating interface is separated from the receiving layer, yes, so essentially we are asking if, instead, the bottom magnetic pherome layer has something with a lower crystal symmetry that is known to give you similar types of currents, so you would also expect the same spin-to-spin conversion that would then give you this type of non-local. indirect torque and I think that by symmetry the answer is yes, you have to see something along those lines, but I certainly didn't calculate any of that, but it seems that this indirect mechanism is a step beyond symmetry considerations, I mean, no See why there would be no indirect generation in that case, um, if the thickness is below the middle path three because it always has the correct interfacial conversion, so the symmetry of that interfacial conversion is less and in which case it should generate um um , it feels like a torque.

Well, that's right, you can still have an indirect mechanism, but you can't necessarily have the same polarizations for the ejected currents that you could have in the lower symmetry system, but you're right, in principle you could have an indirect mechanism. MH mechanism, yeah, okay, any other questions, please raise your hand if it doesn't seem like it, so let's close this session and thank Beac again for this interesting talk. I'll stop recording. and stre

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g and U, if you are in the zoom session, feel free to stay and continue the discussion informally.