MPQ Researchers Expose Concealed Magnetic Order in One-Dimensional Quantum Crystals Doped with Holes

In everyday-life, the phenomenon of magnetism is experienced quite frequently. The property, which is seen in materials such as iron, is caused by the arrangement of electron spins. Even more interesting effects are expected in case that the magnetic crystals display holes, i.e., lattice sites that are not occupied with an electron.

Due to the interplay between the magnetic correlations of the electron spins and the motion of the defect, the magnetic order looks to be suppressed. Generally, solid state Physicists are unable to isolate the two processes, so they cannot provide an answer to the question, whether the magnetic order is indeed decreased, or whether it is just concealed.

Now a team of Researchers along with Dr. Christian Groß from the Quantum Many-Body Systems Division (Director Professor Immanuel Bloch) at the Max Planck Institute of Quantum Optics have shown that in 1D quantum magnets the magnetic order is conserved even when they are doped with holes – a direct exhibition of spin-charge (density) separation. The quantum crystals were prepared by strings of ultracold atoms in an optical lattice.

The observation was achieved using a unique tool which permits tracking the motion of holes and the spin excitations individually in one measurement process (Science, 4^th August 2017). In the next step, the Researchers plan to extend the technique to 2D systems. Here, the interaction between holes and magnetic correlations is definitely more complex. It could result in the detection of exotic many-body phases that might be accountable for the incidence of high-temperature superconductivity.

The Garching team begins with cooling a group of fermionic lithium-6 atoms down to very low temperatures, a millionth of a Kelvin above absolute zero. The atoms are then trapped in a single plane in a 2D optical lattice that is formed by laser beams. The plane in turn is divided into around 10 1D tubes along which the atoms can travel. In the final step, the tubes are superimposed with an optical lattice which imitates the periodic potential that electrons see in a real material. In analogy to electrons lithium atoms transport a spin-1/2 (or magnetic moment) which can point either downwards or upwards. In an earlier experiment with a similar system the Researchers have revealed that below a specific temperature the magnetic moments of adjacent atoms align in opposite directions such that antiferromagnetic correlations occur.

In the subsequent experiment, they examine the impact of holes on the degree of order of the quantum crystal.

We achieve a certain amount of hole doping by making sure that the number of atoms loaded into the optical lattice is smaller than the number of lattice sitesNow the questions arise, whether the holes are fixed or whether they can move, and how they affect the magnetic order of the system.

Timon Hilker, First Author and Doctoral candidate at the experiment

Take for instance a familiar situation: in a theatre, if a seat in the middle of a row stays empty, the crowd moves: one by one, audience members move up – in other words: the hole travels. Something similar can be seen in the artificial quantum crystal using the quantum gas microscope which images the precise position of each single atom or defect on their individual lattice sites.

However, much in contrast to the empty chair in the theatre, the holes in the quantum crystal are delocalized. Their location is determined the very moment they are being measured.

Timon Hilker, First Author and Doctoral candidate at the experiment

At first glance, the fluctuations of the atoms in the optical lattice conceal the antiferromagnetic correlations. But the team of Christian Groß is able to take an in-depth look, because they have formulated a technique to spatially split atoms with different spin orientations. For this purpose, the optical lattice is superimposed with a superlattice such that a double well is formed on each lattice site. Along with a magnetic gradient, this results in a potential which is reliant on the spin-orientation. The major challenge of this technique is to alter optical lattice and superlattice with a precision of a few nanometers, i.e., a fraction of the laser wavelength.

In our system we can detect simultaneously holes as well as both spin states. We can directly investigate the environment of each hole. We observe, that the order is generally preserved, i.e., that the spins of the left and the right neighbor atoms are anti-aligned. Because the images display every spin and every hole, we are able to, as to speak, ‘take the holes out’ in our evaluation. Such non-local measurements are experimental new territory and open new perspectives for the study of exotic phases of matter.

Dr. Christian Groß, the Project’s Leader

Currently, the Researchers aim to apply this technique to 2D quantum crystals that are doped with holes. This would be a new method to mimic 2D holes-doped systems of correlated electrons. Experiments of that kind could result in a proper understanding of the so-called high-temperature superconductivity which was detected three decades ago. The name describes the effect that in specific compounds with layers comprising copper the electrical resistance disappears already above the boiling temperature of liquid nitrogen. The interplay between defects and antiferromagnetic correlations is thought to play a significant role in this mystifying phenomenon.