Oxford Professor uses NAG components to aid the design of new magnetic materials

Magnetic materials come in many different forms. The most familiar are ferromagnets, such as iron and nickel, which become magnetized in an external magnetic field and retain their magnetization after the field has been switched off. Ferromagnets are used in compasses, electronic recording devices, transformers, speakers, and many other everyday devices. Other, more subtle, forms of magnetism also exist and are particularly interesting because of their role in creating new states of matter with potentially useful properties, such as high temperature superconductivity or quantum information processing devices.

Magnetism arises from the existence of magnetic dipole moments, like tiny bar magnets, on some or all of the constituent atoms of the substance. The size of the magnetic moment is governed by the electronic state of the atom, which in turn depends on the local surroundings of the atom and the way the atom is bonded to its neighbours. Experiments that determine the electronic state of atoms in magnetic substances are therefore extremely valuable for understanding the origin of magnetic behaviour and for engineering materials with new or improved magnetic properties.

The original impetus for developing the software to analyze the experiments described here came from the availability of new experimental probes for studying magnetism. Neutron spectroscopy, in particular, has become a very powerful probe of the magnetic state of atoms thanks largely to advances in instrumentation at spallation neutron sources like the ISIS Facility at the Rutherford Appleton Laboratory. This technique makes it possible to obtain accurate measurements of level splittings in atoms caused by interactions with the crystalline environment. Detailed information on the many-electron states of atoms can be obtained from these level splittings and the corresponding spectral intensities.

Armed with the experimental data, Professor Andrew Boothroyd, at the University of Oxford Physics Department, needed the analytical tools to work out the state of the electrons and hence understand their magnetic behaviour. The creation of SPECTRE – the system designed to undertake the data analysis – and its subsequent evolution took place over many years as specific problems arose during the course of the research.

Having used numerical routines from NAG in previous projects, Professor Boothroyd turned to NAG to provide the mathematical code required by SPECTRE. SPECTRE uses the most up-to-date atomic models, which makes the results very accurate and quantitative. In brief, SPECTRE calculates the neutron spectra in terms of a small number of unknown parameters, and determines these parameters by least-squares fitting to the data. The core of the calculation is a series of matrix diagonalizations carried out by NAG routines designed to handle Hermitian matrices. The least-squares fitting is also performed by NAG routines. The lowest energy eigenfunctions found by the program are used to calculate other experimentally accessible physical properties such as the magnetic susceptibility and specific heat capacity.

SPECTRE will be made available to other magnetic materials groups in the hope that it will make it easier for scientists to interpret neutron spectroscopy data and thereby contribute towards the improvement of magnet materials.

Professor Andrew Boothroyd said “NAG’s reputation for accuracy, flexibility and robustness made it the first choice for the calculations in SPECTRE. I am delighted to be working with NAG to make the fruits of one person’s labour freely available to the whole scientific community.”

Mick Pont, Principal Technical Consultant at NAG commented “Software such as that developed by Professor Boothroyd is of fundamental importance in advancing human knowledge in the field of magnetism. We at NAG are very proud that our numerical components have proved useful in this endeavour. Since NAG was founded on collaborative principles we are particularly pleased that SPECTRE will be available for the use of others.”

For more information about the availability of SPECTRE please contact Professor Boothroyd.

Contact details:
Professor Andrew Boothroyd, Department of Physics, The University of Oxford