Spinning state "solid" in an artificial cellular lattice

In certain scientific circles there is a discussion about the magnetic correlation at low temperatures in a two-dimensional artificial magnetic cellular lattice. Theorists claim that such a system is capable of demonstrating the formation of a solid state with zero spin entropy * . However, in practice, such properties have not yet been discovered. This study makes a confident step towards understanding the above phenomena. What exactly did the researchers know, we will understand thanks to their report. Go.

Entropy * - in simple terms, this is a state of a system whose elements are not ordered, i.e. are chaotic.

This study aims to study the magnetic correlation in the permalloy artificial cellular lattice * . The dimensions of the elements were of the order of 12 nm (length) at 5 nm (width) at 10 nm (thickness). Neutron scattering * and temperature-dependent micromagnetic modeling became an important indicator in the process of deducing the results of the study.

Permalloy * - an alloy of iron and nickel with magnetically soft properties. Such materials have the properties of a ferri- or ferromagnet, and their coercive force (magnetic field strength necessary for the complete demagnetization of the material) is no more than 4 kA / m.

Neutron scattering * - there are two main types: elastic and non-elastic scattering. Elastic allows us to study the structure of solids, liquids and gases, since only scattering is considered when the atoms do not become excited. With non-elastic neutron scattering, it is possible to obtain data on the bonds in the substance through the occurring excitation processes in the atoms. Neutron scattering is excellent for analyzing magnetic materials, since neutrons have magnetic properties and act as elementary magnets.

Numerical simulation of the reflectometry data * of polarized neutrons explains the temperature-dependent evolution of the spin correlation in this system.

Neutron reflectometry * - a neutron beam falls on a flat sample that scatters particles. Observations of these particles are made at a certain angle. The obtained angular spectrum allows us to determine the magnetic properties of the elements of the test sample.

As the temperature decreases to ≈7 K, the system tends to develop a new spin solid state, manifested by an alternating distribution of magnetic eddy currents * of opposite chiralities * .

Eddy currents * - electric current arising in conductors when the magnetic field acting on them varies with time.

Chirality * - asymmetry (lack of symmetry) of the right and left side of an object.

The test results are complemented by temperature-dependent micromagnetic simulations, which confirm the predominance of the spin solid state over the ordered state of a magnetic charge in an artificial cellular lattice. These data provide an opportunity to investigate the correlation of a new spin solid state in a two-dimensional artificial cellular lattice.

System Basics and Research

A two-dimensional cellular lattice is an ideal basis for testing many properties of magnetic materials, as well as their interaction within a single system. The researchers paid special attention to such unusual things as different states of matter: spin ice * , spin liquids * and spin solid, formed by the distribution of magnetic eddy currents of opposite chiralities.

Spin ice * is a substance in which the magnetic moments of atoms are ordered in the same way as protons in ordinary ice.

Spin liquid * is the state of systems where the word “liquid” is used to emphasize the fact that spins are disordered, which differs from the ferromagnetic spin state, as well as the state of water (liquid) is different from the state of ice (crystal structure). The main difference of the spin liquid is the preservation of this state even at the lowest temperatures.

An important aspect is the fact that the complex variety of magnetic phases under the control of entropy, which appear to be predicted in an artificial cellular lattice as a function of temperature reduction, cannot be realized in the exchange material.

Recent theoretical studies state that the honeycomb lattice at high temperatures exhibits the properties of a paramagnetic * , corresponding to gas with a magnetic charge of ± 1 and ± 3.

Paramagnetic * - a substance that is able to magnetize under the influence of an external magnetic field, has a positive magnetic susceptibility, but it is well below unity.

When the temperature decreases, the system goes from the state of spin ice, when the magnetic moments are arranged according to the principle “2 inwards and 1 outwards” or “1 inwards and 2 outwards”. That is, 2 magnetic moments (or 1 in the second variant) are directed inside the cell of the cellular lattice, and 1 moment (or 2 in the second variant) is directed outwards.

A further decrease in temperature leads to the formation of a new ordering mode, which is characterized by a topological “charge order” with a magnetic charge of ± 1. ( Image number 3 ).

In this case, it is expected that the amount of heat will correspond to the strength of the dipole interaction * (≈D).

Dipole interaction * - the interaction of two magnetic dipoles (the limit of either a closed loop of electric current or a pair of pluses, since the source sizes are reduced to zero, maintaining a constant magnetic moment).

At much lower temperatures, the system goes into a state of spin ordering of eddy currents with zero entropy, which can be briefly called the state of a spin solid. This is a new magnetic phase with zero entropy and magnetization.


Image number 3 (for ease of viewing posted here and further on the text)

A detailed study of the indicators of polarized neutron reflectometry and small-angle neutron scattering * revealed the formation of an additional magnetic separation from the intraplane correlations with a decrease in temperature to 7 K.

Small-angle neutron scattering * is the elastic scattering of a neutron beam on matter inhomogeneities whose dimensions exceed the radiation wavelength, which is λ = 0.1–1 nm.

Diffusion scattering is perfectly determined by the numerical simulation of the solid-state spin configuration, where the magnetic moments along with the connecting elements of the permalloy cellular lattice exhibit an alternating order of eddy currents of opposite chiralities.

The formation of the state of a spin solid was also, independently of other indicators, confirmed by temperature-dependent micromagnetic modeling, which showed the development of the temperature dependence of the spin correlation in the cellular lattice with the same dimensions of its elements.

At the moment, the basis of attempts to achieve a spin state of a solid is the method of electron beam lithography for the manufacture of samples. This method results in samples of small sizes, but with large elementary parameters. As a rule, the cellular lattice of this type indicates a high level of energy of inter-element bonds ≈104 K.

However, a new type of cellular lattice has recently been proposed, which consists of very thin (a few angstroms * ) and well-separated permalloy elements of large size (length ≈500 nm, width 20-50 nm). In this case, the inter-element energy is greatly reduced.

Angstrom * - 1 Å = 0.1 nm.

For testing, a cellular lattice with very small components was chosen, since their small size itself greatly reduces electrostatic energy from about 12 to 15 K. Therefore, this is the best option for studying the temperature dependence of magnetic phases.

The results of the experiments and their analysis

To create a cellular lattice, it was necessary to synthesize a copolymer diblock (consisting of two paired blocks) hexagonal pattern and connect the permalloy to the surface of the silicon substrate in ultra-high vacuum * .

Ultra-high vacuum * - gaseous medium with a very low gas density, when the pressure is 10 ^-9 mm Hg. and below.

Similar diblock copolymer templates were also used to create nanostructured materials.

Under suitable physical conditions, the diblock copolymer is prone to self-organization, whereas a one-component sample will create large periodic structures.

The simplicity in setting the structural properties and lattice parameters by changing the composition and / or molecular weight of the diblock copolymer makes it possible to create a multitude of nanomaterials. A striking example is the creation of nano-points, nano-rings and nanoparticle nodes.

Relatively recently, diblock patterns in conjunction with GLAD (glancing angle deposition) made it possible to create directed hierarchical structures of metallic nanoparticles.


Image number 1a

The image above ( 1a ) shows a snapshot of a cellular grid sample taken with an atomic force microscope * .

Atomic force microscope * - allows you to determine the surface topography with resolution up to atomic.

Measurements obtained by small-angle X-ray scattering with a sliding incidence (GISAS) showed high quality sample structures. GISAS provide an opportunity to consider in more detail the structural features of the system. For such measurements, a Ga K _α * source with a wavelength of 1.34 Å and an angle of incidence of 0.15 ° was used.

Zigbahn notation * - in X-ray spectroscopy is used to name the spectral lines (a feature of a part of the spectrum that manifests itself in a local decrease or increase in the signal level).

To attenuate the reflected beam, a 1 mm thick stainless steel film was used.


Image №1b

The image above ( 1b ) shows that the bond length = 12 nm, width = 5 nm, and lattice segregation = 31 nm.

The second and third peaks correspond to a two-dimensional hexagonal lattice. It is also noted that peaks of a higher order are overlapped by the background in the data, which arises due to possible sample heterogeneity. The dimensions of the lattice components vary within the 12x5 nm required for research. However, these deviations do not have a strong influence, since even the inter-element energy changes extremely little (less than 2 K with changes in size by 2 nm).

Simulation of GISAXS data confirmed the presence of a large domain (region) of a long-range structural order in the cellular lattice (paracrystal correlation length = 250 nm).

In order to investigate the correlation between magnetic moments and cellular elements, experiments with polarized neutrons, namely reflectometry, as well as GISAXS, were carried out. The combination of these procedures made it possible to investigate the magnetic correlation in the cellular lattice at a scale from 5 nm to 10 μm.


Image number 2

Image 2 demonstrates the indicators of measurements of different intensity of reflection with neutrons in the spin-up and spin-down state, as well as at a temperature of 300 K and 7 K.
The y axis represents the scattering vector outside the plane (formula No. 1). The difference between the z-components of the incident and outgoing wave vectors (formula 2) is displayed by the x axis.


Formula 1 and 2

Thus, the vertical and horizontal directions correspond to correlations outside the plane and inside the plane. The reflection corresponds to x = 0. There is a clear difference between scattering at high and low temperatures.

At a temperature T = 300 K, the reflection intensity is more than 2 orders of magnitude stronger than in the case of non-specular data, which is quite common for such systems.

There is also a slight scattering in non-specular regions, caused by the paramagnetic nature of the moment and the cellular structure as such.

When the sample temperature was lowered to 7 K, the non-specular signal increased greatly. As a result, the specular beam could not be distinguished on a non-specular background. If we consider that the nuclear structure does not undergo significant changes due to cooling, then this effect can be explained solely by changes in the magnetic characteristics of the system.

The wide band along the horizontal axis in the neutron reflectometry graphs at a temperature of 7 K indicates the development of magnetic correlations in the plane of the cellular lattice (Image No. 2).

For further analysis of the magnetic structure of the sample, the data obtained experimentally are compared with those obtained by calculations based on a theoretical base, which made it possible to predict the state of the magnetic phases, in particular, the paramagnetic state, as well as spin ice (ice-1), charged, ordered configurations (ice-2) and spin solid. All this is visualized in the image number 3.


Image number 3

To simulate various magnetic states, the Born distorted-wave approximation (DWBA) was used.

As can be seen from the lower plots in image No. 2, the scattering of light does not coincide with the spin-spin correlation value. The difference between ice-2 and the spin of the solid is rather small, although the figures correspond to the experimental data on the spins of the solid. As mentioned earlier, the spin state of a solid body was achieved by alternating eddy currents of different chirality.

Experiments have shown that the inter-element energy in an artificial cellular lattice is about 12 K. This indicator is extremely important for the formation of a magnetic charged ordered state, followed by a solid state when the temperature drops to 0 K. As a conclusion, the observed increase in intensity is fully consistent with the predicted computing the behavior of the sample.


Image number 4

Along the Q _y axis, models from the Q _z range = 0.025 Å ^-1 ... 0.045 Å ^-1 , shown in image No. 3, and the calculated data, shown in image No. 4, were combined. At 300 K, a visible jump is observed near Q _y = 0.02 Å ^-1 , which corresponds to the structure of the nucleus, as well as complete scattering in the state of gas or ice-1. As the temperature decreases to 7 K in the region of Q _y = 0.012 Å ^-1 , an additional intensity has been formed, which corresponds to the ice-2 state and / or the spin state of a solid body.

However, in order for the sample to demonstrate the ice-2 state, with Q _y = 0.025 Å ^-1 , a final intensity should be observed, which is not in the calculated data.

As a result, the intensity profile looks very limited, although it corresponds to the predicted profiles for the spin state of a solid and for the mixed state (solid / ice).


Image number 5

The above are the results of temperature-dependent micromagnetic modeling at temperatures of 0 K, 100 K, 200 K, and 300 K. Each of them shows qualitative differences in the curves of magnetic hysteresis.

Conclusion of researchers

An experimental study of the correlation of magnetism and a decrease in the temperature of the artificial cellular lattice showed the appearance of a spin state of a solid body. This becomes possible when the temperature falls below the interelement energy, that is, approximately 12 K. This state is unique for a two-dimensional structure. Unlike three-dimensional systems, strong fluctuations of the magnetic order limit the possibility of magnetic ordering in low-dimensional structures. It is also worth noting that the theory of spin waves is applicable to similar two-dimensional systems only at low temperatures.

I strongly recommend that you read the report of the researchers, available here.

Epilogue

This study is a tool for understanding the properties of low-dimensional magnets, the relationship of the spin state and temperature, as well as the magnetic characteristics of an artificial cellular lattice. To a greater extent, the work of researchers carries theoretical results, supported by experimentally obtained data. It turns out that the results of these experiments have no practical application? This statement is both true and not. Such studies are aimed at understanding the various properties of various materials. Having received answers to the questions posed by the researchers, it is possible to expand the range of the theoretical base, which will allow us to further describe in more detail not only the properties, but also the possible areas of application of the newly discovered characteristics of this or that system. This study can be exaggeratedly called a drop in the knowledge cup, filling it in, we can discover new technologies and improve existing ones.

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