# Magnetic frustration in a pentagonal network

In order to study magnetic frustration, researchers at our laboratory characterized the magnetism resulting from frustration in Bi_{2}Fe_{4}O_{}_{9}, where they identified for the first time a model of a pentagonal lattice of magnetic atoms. Neutron diffraction allowed them to observe the original ordered fundamental state of this compound. The inelastic neutron scattering gave them access to the microscopic ingredients at the origin of this orthogonal order.

*Published on 20 December 2020*

In order to be able to observe, characterize and understand these ground states, the model materials are usually chosen with a particular geometric pattern, characterized by an odd number of bonds between magnetic atoms, which does not allow all interactions to be satisfied. The most studied compounds actually consist of networks based on triangles (

*Figure 1*). To go beyond triangles, the polygon with the smallest odd number of bonds is the pentagon. It was therefore very tempting to probe such frustration phenomena in crystals whose atomic order is formed by networks of pentagons, in order to see what the similarities and differences with triangles are.

*Figure 1: Illustration of geometric frustration in materials where magnetic atoms occupy the vertices of a triangle. When the magnetic moments interact antiferromagnetically (they tend to point in a direction opposite to their nearest neighbor), then, in the case where two spins are antiparallel, the third spin cannot simultaneously satisfy the interactions with the other two. Frustration thus prevents magnetic moments from ordering antiparallel when subjected to a very low temperature.*

Researchers at our laboratory have been able to characterize more precisely the magnetism resulting from frustration in the compound Bi

_{2}Fe

_{4}O

_{9}, in which they identified for the first time a model of a pentagonal lattice of magnetic atoms. To do this, they used neutron diffraction below the ordering temperature (240 K). This way, they were able to observe the original ordered ground state of this compound exhibiting an orthogonal arrangement of magnetic moments (

*Figure 2*).

By inelastic neutron scattering, they were in addition able to gain access to the microscopic ingredients at the origin of this orthogonal order, and to better understand it. By quantifying the different magnetic interactions by comparing the measured excitation spectrum with that from different models, researchers at our laboratory have evidenced the mechanisms of frustration in Bi

_{2}Fe

_{4}O

_{9}resulting from the three competing interactions within the pentagons. They showed that there is a hierarchy in the strength of these interactions leading to a dominant network of pairs of antiferromagnetically coupled magnetic moments. The two magnetic moments of these pairs have a much weaker response to a magnetic field or to temperature than the other magnetic atoms in the unit cell because of their very intense mutual interaction. Even above the ordering temperature, in the paramagnetic state, where thermal fluctuations are supposed to suppress the magnetic order, these moments form an original magnetic state, neither totally disordered, nor totally ordered, consisting of spin dimers still very strongly coupled in an ocean of fluctuating spins.

*Figure 2: Magnetic arrangement of iron atoms (in blue and orange) on the pentagonal lattice of Bi2Fe4O9. Blue ellipses highlight pairs of strongly coupled antiferromagnetic magnetic moments (dimers).*

This study reveals new static and dynamic behaviors of certain materials exhibiting magnetic frustration connected to pentagonal geometry and hierarchical interactions. This work is part of the effort to gain a general understanding of the mechanisms of ordering in complex matter and has spread to other fields beyond magnetism.