The rare-earth orthorhombic perovskites (RMO3, with R = rare-earth and M = transition-metal) were discovered in the 1940’s and quickly attracted great interests due to their unique magnetic properties [1-2]. They exhibit two magnetic phase transitions associated to the two different magnetic sublattices (M and R). These two magnetic cations are also responsible for temperature-driven spin reorientations and magnetization reversals, and feature non-collinear canted spins that often result in weak ferromagnetism. Further, many RMO3 crystals exhibit bulk multiferroism, i.e., a combination of ferromagnetism and ferroelectricity with a high potential to yield large magnetoelectric responses. The latter has been measured in DyFeO3 and GdFeO3, where the magnetoelectric response appears to be 2-3 orders of magnitude larger than that of the most common magnetoelectric materials [1]. Most of the unique properties of the RMO3 perovskites are thus linked to the presence of both R and M magnetic cations, a fact was first identified and analysed theoretically by Yamaguchi in the 70’s [3]. Yamaguchi’s model has since been used as the reference theory to explain the temperature-induced magnetisation reversal and is often invoked to explain the multiferroic properties of RMO3 crystals.

The project is to work with an extended Heisenberg Hamiltonian for rare-earth perovskites that will include both rare-earth and transition-metal spin sub-lattices. The idea is to start from a generalised Heisenberg model and fit all the parameters from first-principles calculations, which will allow us to understand how the two magnetic sub-lattices influence each other and to scrutinise the origin of specific properties such as the temperature-driven reversal of the magnetization. An extension of the project will be to include the interaction between the spins and phonon vibrations to understand the magnetoelectric response. Such an analysis will be a primer of essential importance for fundamental studies and to propose new design rules to optimise these unique RMO3 properties, of great interest for technological applications such as in spintronics devices.

*Figure 1.- (left) Plot of the magnetization versus the temperature of SmFeO3. Between TSR1 and TSR2 a continuous spin reorientation occurs in the Fe sublattice that change the magnetization orientation from c to a axis. At Tssw = 278 K zero-field cooled (ZFC, black curve) and field cooled (FC, green curve) exhibit opposite sign of the magnetization and at Tcomp=3.9K the magnetization change its sign. From [4]. (right) Schematic view of the non-collinear magnetism exhibited by the two spin sublattices of RMO3 (M with red arrows, and R with blue arrows), from [2].*

The work will include first-principles DFT calculations on the reference systems, fitting of the second-principles parameters and second-principles simulations at finite temperature. It will also involve a few code developments.

### Project Partners

Eric Bousquet

Theoretical Materials Physics

Université de Liège

Jorge Iniguez

Dept. of Materials Research and Technology

Luxembourg Institute of Science and Techonology

The group at Université of Liège (ULg) has an extended experience in first-principles simulation of multiferroism, magnetoelectricity and non-collinear magnetism.

The group at LIST has a strong backgroung in first and second-principles simulations of large systems.

The PhD candidate was hired by the University of Liège. Roughly, he will spend two years at ULg to perform first-principles calculations, code development and fitting of the models and one year at LIST to perform large scale and temperature dependent simulations.

### References

[1] T. Kimura et al., Nature 426, 55 (2003); Y. Tokunaga, N. Furukawa, Sakai H, Y. Taguchi, T.H. Arima and Y. Tokura Nat. Mater. 8 558 (2009); Y. Tokunaga, S. Iguchi, T. Arima and Y. Tokura Phys. Rev. Lett. 101 097205 (2008).

[2] E. Bousquet and A. Cano, J. Phys. Condens. Matter 28, 123001 (2016).

[3] T. Yamaguchi and K. Tsushima, Phys. Rev. B 8, 5187 (1973).

[4] Y. Cao, et al., J Appl. Phys. Lett. 104 232405 (2014).

For more information on the work of the ULg and LIST groups, please visit:

ULG

http://www.phythema.ulg.ac.be

LIST

https://sites.google.com/site/jorgeiniguezresearch,

https://scholar.google.es/citations?user=hsLqX2UAAAAJ&hl=es