The spins in typical magnetic materials form 3D ordered arrays as they are cooled, like a liquid solidifying. Some magnets, however, form 1D chains or 2D sheets that do not freeze into a static ordered arrangement but stay instead in a dynamic liquid-like state. These states can give rise to unusual quantum phenomena, some of which possess properties thought to be key to next-generation quantum technologies.
One such quantum phenomenon is the “Haldane phase", which formed the basis of the 2016 Nobel Prize in Physics and is the prototypical example of “topological matter". The Haldane phase can occur in infinite chains of magnetic spins that can point in any direction in space, known as Heisenberg spins. It occurs only when the spins align antiparallel to their nearest neighbour in an antiferromagnetic arrangement (AFM) and each spin is made from an even number of unpaired electrons (integer-spin, S).
While the Haldane phase is predicted to occur for all integer-spins, it has only been detected in S = 1 chains and remains elusive for all larger even numbers, where S ≥ 2. This is because the larger the spin, the more stringent the requirements on the other magnetic interactions in the material. The higher spin phases are more sensitive to magnetic anisotropy, meaning an S ≥ 2 AFM spin chain must be closer to the ideal Heisenberg model. Furthermore, the so-called Haldane gap, the characteristic energy gap in the excitation spectrum of a Haldane phase, is predicted to shrink five-fold as the spin increases from S = 1 to S = 2, making it significantly harder to see when it is present.
Motivated by these challenges, Jem Pitcairn from the University of Nottingham and his collaborators made a new compound CrCl2(pyrimidine) and investigated its magnetic properties. They found it was formed from infinite CrCl2 chains bridged by organic pyrimidine molecule into 2D sheets. “Our magnetic measurements and neutron diffraction experiments confirmed an S = 2 spin state on the Cr ion and an antiferromagnetic alignment of spins in the CrCl2 chains, so we decided to investigate how close this material was to the Haldane phase," explains Jem.
They used inelastic neutron scattering on the LET instrument at ISIS to measure the magnetic interaction energies through the chloride bridge and pyrimidine linker, shown as J1 and J2, respectively in the figure below. Jem describes their results: “We found the interactions are much stronger through the CrCl2 chain than through the organic connector, making this a host material for S = 2 AFM spin chains and showing that organic linker bridged CrCl2 materials are a good family to search for this Haldane phase."
(a) A schematic representation of the S = 2 antiferromagnetic spins along the CrCl2
chains and their interaction through the pyrimidine bridge. (b) The experimental INS data collected at LET and the fit to these data with linear spin wave theory.
They also found that CrCl2(pyrimidine) undergoes normal 3D magnetic ordering, but the ability to make analogous compounds with tuneable properties by swapping the organic molecule suggest it could be used to tune the magnetic interactions towards ideal conditions for the Haldane phase.
This work was carried out in collaboration with the University of Birmingham, the Institut Laue Langevin and ISIS Neutron and Muon Source.
Jem adds; “This result is really promising. The stringent requirements on the magnetism make a flexible chemical design route like this one especially valuable for the pursuit of this unrealised topological phase."
The full paper can be found online at DOI: 10.1021/jacs.2c10916