What are the properties of bismuth antimonide

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In certain magnetic materials, the electron spins show an unusual topological order.

Topological effects are becoming more and more important in solid state physics. Two electronic quantum states cannot be continuously converted into one another if they are not topologically equivalent. (A tire, for example, is topologically equivalent to a mug with a handle, but not to a sphere.) This stabilizes unusual conditions. With the quantum Hall effect, the topology of the non-conductive electron states inside the sample differs from the one-dimensional, electrically conductive states at the edge of the sample. To do this, the electrons must be exposed to a magnetic field. It doesn't need to be an external field, as is the case with the quantum Hall effect. It can also be the magnetic field that relativistic electrons feel in an electric field. This magnetic field underlies the spin-orbit coupling and leads to novel topological effects that are currently being intensively investigated. Two research groups have now discovered novel arrangements of electron spins in crystals.

Fig .: Graphic representation of the structure of the vortex filaments on the surface of manganese silicon. Sebastian Mühlbauer and his colleagues made this visible for the first time with neutrons. (Image: TUM)

The spin-orbit coupling causes the electron spins to spin. In manganese silicide (MnSi) this means that the spins are arranged in a screw pattern below 29.5 K. The spin direction completes a full turn if you move 19 nm along the screw axis. Since the distances between the atoms are only about 0.5 nm, the magnetic and atomic structures are independent of each other. If you bring an MnSi crystal into an external magnetic field, it partially aligns the spins and the screw structure is deformed. But at around 0.1 Tesla there is a discontinuous transition to an “A phase”. The result is a new magnetic structure that had previously puzzled scientists. Christian Pfleiderer from the Technical University of Munich and his colleagues have now clarified this structure - with surprising results.

The researchers examined the magnetic structure of two crystalline MnSi samples using neutron radiation. In doing so, they repeatedly found a six-fold diffraction pattern for the A phase, regardless of how the magnetic field was aligned with the crystal. The resulting magnetic structure was therefore independent of the crystal structure and had a hexagonal symmetry. Magnetic objects, which were initially unknown, were arranged in a honeycomb pattern in planes that were perpendicular to the magnetic field. A closer examination showed that these were so-called skyrmions, topological suggestions that go back to studies by the British physicist Tony Skyrme in the 1960s. In the magnetic skyrmions, the spin directions were so knotted that they could only be untied with great expenditure of energy. This made the skyrmions (meta-) stable objects that behaved like atoms and arranged in a regular pattern.

Topological excitations, which were caused by the spin-orbit coupling and which were similar to the skyrmions, also occurred in crystalline bismuth antimonide (Bi1-xSbx) on. This is what Zahid Hasan from Princeton University and his colleagues report. But the basic electronic state of the crystal that carried these stimuli already had a remarkable structure. It was a topological band gap isolator whose electrons were entangled with one another in a complicated way. Entangled states are usually very prone to failure, but in bismuth antimonide the collective entanglement is topologically stabilized: like a knot or a skyrmion, it cannot simply dissolve.

According to the theory, electronic states should appear on the surface of such a topological band gap insulator, which fill the band gap and make the surface a special metal. The electron spins in this metallic surface were ordered into structures that resembled the skyrmions in the A phase of manganese silicide. Hasan and his colleagues were able to show this with spin- and angle-resolved photoemission spectroscopy. However, the topological excitations of the spins in the surface did not occur directly in the spatial space but in the two-dimensional momentum space of the surface electrons. The various, topologically stabilized excitations give the investigated materials not only unusual electrical and spin-magnetic properties. They could also be used to stabilize complex entangled states such as those needed in quantum information processing.

RAINER SHARP

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