Posted: Jun 19, 2013 
Penetrating the quantum nature of magnetism

(Nanowerk News) Scientists using inelastic neutron scattering at the Institut LaueLangevin have for the very first time given a complete description of a onedimensional ½ Heisenberg antiferromagnet as realized in nature in copper sulphate – incidentally, an everyday compound used in school science experiments as well as in herbicides and algae control in swimming pools. Their results, published in Nature Physics ("Fractional spinon excitations in the quantum Heisenberg antiferromagnetic chain"), provide a fully quantitative validation of the spin half chain Heisenberg model for a quantum spin liquid.


Schematic representation of the magnetic excitations in a spin½ (Heisenberg) antiferromagnetic chain and overview of the neutron scattering results for CuSO45D2O. a) Fully polarized (saturated) state. The creation of a magnon by inelastic scattering of a neutron can be imagined as a single spin flip. The Zeeman energy prevents any growth of the flipped section that propagates like a single entity. This magnon can classically be visualized as a spin wave, a coherent precession of the local spin expectation value around the field direction. b) Zero magnetic field state. Snapshots of large antiferromagnetically correlated regions of the ground state. The spins could be found in a locally antiferromagnetic configuration with equal probability in any direction (for example, the opposite one (shadows)). The neutron acts on the singlet ground state and excites triplet states which we may imagine as a local spin flip surrounded by two domain walls, which individually correspond to a spinon carrying spin½. The spatial extent of a spinon depends on the anisotropy: in the Ising limit, a local spin flip decomposes into two spinons; in the Heisenberg limit, it decomposes into a rapidly converging series of statescontaining two, four and higher even numbers of such spinons. c) Intensity maps of the experimental and theoretical magnon dispersion in the fully polarized phase of CuSO45D2O for µοH =5T> ΟHsat and T ~ 100 mK, above the Néel transition temperature to threedimensional antiferromagnetic ordering. The two observed branches (flat and cosineshaped) are associated with two nonequivalent Cu2C sites in CuSO45D2O (Cu1 and Cu2, respectively). The cosineshaped dispersion corresponds to the excited magnon of the saturated Heisenberg antiferromagnetic Cu1 chain and the flat branch around 0.7 meV is a transition between two local Zeeman levels of the decoupled Cu2 sites. d) Intensity colour maps of the experimental inelastic neutron scattering spectrum of the Cu1 chain spins in the zerofield phase of CuSO4 5D2O, and theoretical two and fourspinon dynamic structure factor.

Physics works by trying to explain complex things with simple models. Magnetism is a particularly tough nut to crack as it shows to be very resistant to simple description. This is primarily due to the quantum mechanical nature of magnetic phenomena and makes for the excitement of the field.

One of the simplest models in magnetism is Heisenberg’s antiferromagnetic spin ½ chain. Despite its simplicity it took almost a hundred years of theory and many experiments to come finally to grips with it. The latest stage dates back to about 2006, when modern calculations allowed a clear theoretical prediction. Nonetheless, experiments had difficulties in gauging the predictions of theory. The problem was very much related to difficulties in measuring neutron scattering intensity on an precise absolute scale.

The breakthrough was achieved by using a standard of comparison intrinsic to the sample. Copper sulfate materializes in a nearly perfect way the onedimensional spin ½ Heisenberg antiferromagnet. By applying a strong magnetic field Mechthild Enderle and her collaborators drove the magnetic system of copper sulfate into a well understood “classical” ferromagnetic state, for which the scattering intensity is known precisely, and that as such could serve as a reference. This allowed them to eliminate all extrinsic corrections and thus allowed them to demonstrate a quantitative agreement between calculation and theory. As predicted nearly one third of the excitation spectrum stems from higherorder spinon states. One of the holy grails of magnetism can be considered found.

The experiments were achieved through inelastic neutron scattering experiments performed on cold tripleaxis spectrometer IN14 at ILL.
