Exotic properties of electron moments & nucleus
Hello friends! I am the Anu, an electron, which is the fundamental particle of the smallest building block of matter, an atom. My species were discovered in 1897 A.D. by Sir J. J. Thomson (1856-1940). He was working with the cathode tube and observed a glow, which he initially named cathode rays. With further experiments in the magnetic and electric fields, Sir Thomson found that these rays consist of particles called ‘corpuscles.’ He named these particles ‘electrons’, and that is us, which was predicted by George Johnstone Stoney (1826-1911) in 1891 as the fundamental unit of electric charge. This was a little about my discovery. My discovery further established Dalton’s prediction of an atom that consists of varied masses and properties of constituents. He presented a plum pudding model, in which he assumed the electron is distributed as the plum in the pudding of the positively charged sphere known as the nucleus. Rutherford, in 1909, further improved this by imparting the alpha particle on the thin gold foil. He observed that most of the alpha particles passed the foil, and few of them were deflected at large angles and backscattered as well, and this experimentally proves that most of the space in the atom is empty and a heavy positive center is present in the atom with the electron revolving around it.
As quantum physics budded in the early 20th century, Bohr incorporated the quantization concept in the electron orbital motion of Rutherford’s model. He successfully explained the discrete atomic spectra of hydrogen. This was not the final version of the atomic reality. Modern quantum physics describes the electron orbit around the nucleus, not just in spherical orbitals but also in other probabilistic configurations. Each orbital has a discrete angular moment in terms of the reduced Planck’s constant (ħ). For example, s orbital has l = 0 and p has l = 1, and so on. Along with the electron’s different localized and delocalized orbital configurations, it has an intrinsic magnetic moment known as the spin moment. The quantization spin moment was experimentally observed during the Stern-Gerlach experiment. The electron orbits around the nucleus and has its own spin angular magnetic moment. We do not straightforwardly exist around the nucleus as predicted by Bohr. Various factors impact our state and behaviors, and the various phenomenon occurs because of us. There is a quantum mechanical concept of the wave function, as presented by Schrödinger, that predicts my state and the various phenomena that happen because of that. However, there is still much to explore with further advancements in experimental abilities and computational progression. L’Huillier has finally observed my real-time movement experimentally, for which she was awarded the Nobel Prize in Physics and became a Nobel laureate in 2023.
As I have told you, I have two distinct moments out of a few present, and these spin moments are not independent and depend on their interaction with localization and delocalized orbital configuration. This interaction between the spin and orbital motion is known as the spin-orbit interaction or spin-orbital coupling (SOC). This coupling has been observed significantly in the platinum and rare-earth elements, because of which they have many modern applications. However, the coupling is there except for the s-orbital elements where l=0 which causes the diminishing of the SOC. The general formula for the spin-orbit interaction energy is as follows:
where ‘ESO‘ is the spin-orbit interaction energy, ‘A’ is the spin-orbit coupling constant, ‘l’ is the orbital angular moment quantum number, which defines the shape of the electron orbital, and ‘s’ is the spin magnetic moment of the electron. Here, the interaction is present between the l and s, therefore known as “spin-orbit coupling”.
Initially, the SOC was predicted in the energy band splitting in the atomic spectra of some heavy elements in the absence of the external magnetic field. In the 20th century, understanding the reason behind using quantum mechanics by reducing the Dirac equation in the nonrelativistic form by Schiff presented, and Man, this property is not just energy splitting. Still, this degeneracy uplifting has a pool of natural phenomena as their root in it. Considering the Hartree-Fock description of the atom, where each of us electron moves independently of the other within an average field created by all the other electrons, the many-body problem of quantum mechanics is simplified. This was done by Schiff in 1955 for the single electron, and it was stated as follows:
where, α is the spin-orbit coupling constant, V potential due to the nucleus. However, the generalization of the SOC is not straightforward with the previous approach. Things were potential in the atom’s nucleus that have to be considered with the other electron interactions, and this incorporates spin-spin interaction with the dipole interaction because of the spin moments as well. These corrections were added by Blume and Watson in 1962. This gives a solution to the constant value of the experimental spin-orbit coupling.
As the above equation says, spin-orbit coupling is a combination of the spin magnetic moment and orbital magnetic moment contribution with a reduction in it with the spin-spin interaction and dipole moment between the spin-spin magnetic moments, which was presented by Elliott in 1953. Further rearrangements were done by Horie in 1953, and a new definition of the spin-orbit constant has evolved. The Horie rearrangement includes the outer screening electron contributions to the ξ’, i.e., spin-orbit interaction constant. This was the theoretical explanation of the spin-orbit interaction energy. Now, it is time to explain further the fundamental properties of the magnetic materials that originated in the SOC.
As the localization of the orbital in the atom happens, our spin tries to fix it in specific directions. These give rise to anisotropy in magnetic materials, which is known as Magnetocrystalline anisotropy. Along with the change in the size and shape of the magnetic materials, magnetostriction is a result of SOC. Anisotropy magnetoresistance also has cause lies in the SOC. This was stabilized a lot earlier. Now and in the late 20th century, advanced behaviors like the Dzyloshinskii-Moriya interaction (DMI), spin-Hall effect, Rashba effect, and spin-orbit torque result from the SOC.
Firstly, I will talk about an exciting phenomenon, DMI; when high SOC and the inversion symmetry break the magnetic compounds, this gives rise to the asymmetrical exchange, and that is known as DMI. As an electron, it is stimulating because it stabilizes the skyrmions, and my spin property can give rise to new computing and storage, which overcome the Joule heating. I will also discuss the spin Hall effect, which results in the spin-polarized current with spintronics applications. Spin Hall effect was initially observed in GaAs by Wolf in 2001. The Rashbha effect is also a result of the high SOC and is an important effect in tweaking the electronic band structure for the spintronic spin polarization applications. Nowadays, the scientific community is trying to build magnetoresistive random access memory (MRAM) using the spin-orbit torque resulting from the high SOC in the material, which promises low-power memory.
This SOC is significant, and the scientific community is working on harnessing this phenomenon to build future memory and sensors. This was the story of my home atom’s understanding, along with the introduction of orbital angular and spin magnetic moments and SOC prediction and the theoretical study with potential applications. I hope you enjoyed the physical phenomenon of our electrons, and I will see you soon for the next spintronic story.