A complex material
The complexity arises from the interplay of magnetic phenomena with the position and motion of the atoms that change with temperature. Previous theoretical models and physics calculations have thus often focused either on magnetism, on vibrations, or on the structure, separately. Although these models have been successful in pinpointing the root cause of some phenomena, like the ferromagnetism which gives rise to the magnetic field around iron objects, they lack the accuracy to make predictions in real-life conditions.
2D representation of atoms vibrating and magnetic moments fluctuating in direction and size. The magnetic moments are generally represented with arrows, with their size indicating the strength of the magnetic field generated by the relative atom. At high temperatures, strong atomic vibrations and large moments fluctuations lead to a high degree of disorder in the system.To be more concrete, Fig. 1 shows how one can visualize that the atoms (blue balls) in a solid are always vibrating, and the higher the temperature the more they move. In addition, the electrons around each iron atom produce a magnetic field, also known as magnetic moment (represented as green arrows in the illustration). Similary to the movement of the atoms increasing with temperature, the magnetic moments fluctuate in direction (transverse spin fluctuations, TSF) and magnitude (longitudinal spin fluctuations, LSF) more and more with increasing temperature, up to a point where they can be thought as being completely disordered. This is the temperature when a magnet would lose its ability to attract other magnetic materials. Furthermore, the presence of defects in real materials, which govern the mechanical strength of metals, introduces one more degree of disorder. Putting together all these phenomena in a unified theoretical framework is a very challenging task.
This is the research focus of the Theory of Disordered Materials unit, led by Björn Alling in the Theoretical Physics division at Linköping University. With recent publications in scientific journals, and two successful Master’s diploma projects, the researchers are bridging the gap between computational predictions and real applications in iron and steels.
New simulation technique
At first, they have developed a simulation technique that include the atoms vibrations, the magnetic moments rotations, and their fluctuation in magnitude, where the last effect has been often neglected in the past for computational and theoretical limitations. Application of this new technique to iron at very high temperature and pressure, conditions expected at the Earth’s core, predicts the presence of magnetic effects both in the solid inner core and in the liquid outer core, opening new scenarios in the investigation of phenomena related to Earth’s magnetic field.
In parallel, they have studied how the magnetic disorder influences a materials defect known as dislocation in iron. Dislocations are technologically important because they control the deformation process in metals, and as such their study at relevant application temperatures can improve the strength and mechanical properties of existing materials. They find differences in the local distribution of magnetic moments close to the dislocation at high as compared to low temperatures, which can be important in alloys like steels where other magnetic elements like chromium are added to improve mechanical properties and corrosion performance.
These research results have recently been accepted for publication in two articles in the scientific journal Physical Review B. The investigation of LSF in iron has been conducted by Davide Gambino, PhD student in the Theoretical Physics Division at LiU, Marian Arale Brännvall, Amanda Ehn and Ylva Hedström, Master students enrolled in the Master of science program in Applied Physics and Electrical engineering– theory, modelling and computer calculations (Teknisk fysik och elektroteknik – teori, modellering och datorberäkningar), who performed calculations during a summer internship under the supervision of Björn Alling. The study of dislocation has been mainly performed by Luis Casillas-Trujillo, post-doctoral researcher at LiU, and it is the result of an international collaboration with Lisa Ventelon, researcher at Université Paris-Saclay, France, a leading institution in the field.
Reference to the articles:
 D. Gambino, M. Arale Brännvall, A. Ehn, Y. Hedström, and B. Alling, “Longitudinal spin fluctuations in bcc and liquid Fe at high temperature and pressure calculated with a supercell approach”, Physical Review B 102, 014402 (2020)
 L. Casillas-Trujillo, D. Gambino, L. Ventelon, and B. Alling,
“Screw dislocation core structure in the paramagnetic state of bcc iron from first-principles calculations”,
Physical Review B, 102, 094420 (2020)
 Master Diploma work by Marian Arale Brännvall,
”Accelerating longitudinal spin fluctuation theory for iron at high temperature using a machine learning method”
Linköpings universitet (2020)
 Master Diploma work by Amanda Ehn,
”A theoretical study of longitudinal and transverse spin fluctuations in disordered Fe64Ni36 alloys ”
Linköpings universitet (2020)