Electrons Mediate Antiferromagnetic Spin-Spin Interactions in Superconductors

JQI Fellow Jay Sau, in collaboration with physicists from Harvard and Yale, has been studying the effects of embedding magnetic spins onto the surface of a superconductor. They recently report in paper that was chosen as an "Editor's Suggestion" in Physical Review Letters, that the spins can interact differently than previously thought.

This hybrid platform could be useful for quantum simulations of complex spin systems, having the special feature that the interactions may be controllable, something quite unusual for most condensed matter systems.

The textbook quantum system known as a spin can be realized in different physical platforms. Due to advances in fabrication and imaging, magnetic impurities embedded onto a substrate have emerged as an exciting prospect for studying spin physics. Quantum ‘spin’ is related to a particle’s intrinsic angular momentum. What’s neat is that while the concept is fairly abstract, numerous effects in nature, such as magnetism, map onto mathematical spin models.

A single spin is useful, but most practical applications and studies of complex phenomena require controlling many interacting spins. By themselves, spins will interact with each other, with the interaction strength vanishing as spins are separated. In experiments, physicists will often use techniques, such as lasers and/or magnetic fields, to control and modify the interplay between spins. While possible in atomic systems, controlling interactions between quantum spins has not been straightforward or even possible in most solid state systems.

In principle, the best way to enhance communication between spins in materials is to use the moving electrons as intermediaries. Mobile electrons are easy to come by in conductors, but from a quantum physics perspective, these materials are dirty and noisy. Here, electrons flow around, scattering from the countless numbers of vibrating atoms, creating disruptions and masking quantum effects. One way physicists get around this obstacle is to place the spins on a superconducting substrate, which happens to be a quiet, pristine quantum environment.

Why are superconductors are a clean quantum host for spins? To answer this, consider the band structure of this system.

Band structure describes the behavior of electrons in solids. Inside isolated atoms, electrons possess only certain discrete energies separated by forbidden regions. In a solid, atoms are arranged in a repeating pattern, called a lattice. Due to the atoms’ close proximity, their accompanying electrons are effectively shared. The equivalent energy level diagram for the collective arrangement of atoms in a solid consists not of discrete levels, but of bunches or bands of levels representing nearly a continuum of energy values. In a solid, electrons normally occupy the lowest lying energy levels. In conducting solids the next higher energy level (above the highest filled level) is close enough in energy that transitions are allowed, facilitating flow of electrons in the form of a current.

Where do superconductors, in which electrical current flows freely without dissipation, fit into this energy level scheme? This effect is not the result of perfectly closing a gap--in fact the emergence of zero resistivity is a phase transition. As some materials are cooled the electrons can begin to interact, even over large distances, through vibrations in the crystal called phonons. This is called “Cooper pairing.” The pairs, though relatively weak, require some amount of energy to break, which translates into a gap in the band structure forming between the lowest energy superconducting state and the higher energy, non-superconducting states. In some sense, the superconducting state is a quantum environment that is isolated from the noise of the normal conducting state.

In this research, physicists consider what happens to the spin-spin interactions when the spins are embedded onto a superconductor. Generally, when the spins are separated by an amount greater than what’s called the coherence length, they are known to weakly interact antiferromagnetically (spin orientation alternating). It turns out that when the spins are closer together, their interactions are more complex than previously thought, and have the potential to be tunable. The research team corrects existing textbook theory that says that the spin-spin interactions oscillate between ferromagnetic (all spins having the same orientation) and antiferromagnetic. This type of interaction (called RKKY) is valid for regular conductors, but is not when the substrate is a superconductor.

What’s happening here is that, similar to semiconductors, the magnetic spin impurities are affecting the band structure. The spins induce what are called Shiba states, which are allowed electron energy levels in the superconducting gap. This means that there is a way for superconducting electron pairs to break-up and occupy higher, non-superconducting energy states. For this work, the key point is that when two closely-spaced spins are anti-aligned then their electron Shiba states mix together to strengthen their effective antiferromagnetic spin interaction. An exciting feature of this result is that the amount of mixing, and thus effective interaction strength, can be tuned by shifting around the relative energy of Shiba states within the gapped region. The team finds that when Shiba states are in the middle of the superconducting gap, the antiferromagnetic interaction between spins dominates.

Author and theorist Jay Sau explains the promise of this platform, “What this spin-superconductor system provides is the ability connect many quantum systems together with a definitive interaction. Here you can potentially put lots of impurity atoms in a small region of superconductor and they will all interact antiferromagnetically. This is the ideal situation for forming exotic spin states.”

Arrays of spins with controllable interactions are hard to come by in the laboratory and, when combined with the ability to image single spin impurities via scanning tunneling microscopy (STM), this hybrid platform may open new possibilities for studying complex interacting quantum phenomena.

From Sau’s perspective, “We are at the stage where our understanding of quantum many-body things is so bad that we don’t necessarily even want to target simulating a specific material. If we just start to get more examples of complicated quantum systems that we understand, then we have already made progress.”

This article was written by E. Edwards/JQI

Source: http://jqi.umd.edu/