#### Nicolas MARTIN – Université Paris-Saclay, CNRS, CEA, Laboratoire Léon Brillouin

Spin glasses (SG) are diluted magnetic alloys whose behavior is dominated by disorder and interaction frustration. Their study has been mobilizing massive theoretical efforts for decades and has led to spectacular developments in various research fields, such as deep learning, neurosciences and fluid dynamics. The 2021 Nobel Prize in Physics has actually been awarded to Giorgio Parisi, in tribute to the concepts deduced from the study of certain models of SG which are the basis of our current understanding of complex systems.

Our recent paper focuses on amorphous alloys with formula (Fe_{1-x}Mn_{x})_{75}P_{16}B_{6}Al_{3} -so-called “reentrant” spin glasses (RSG)-whose concentration-temperature (x-T) phase diagram is shown in **Fig. a**. In these systems, frustration is driven by the distribution of nearest neighbor magnetic couplings: ferromagnetic (FM) for the Fe-Fe and Fe-Mn pairs, antiferromagnetic (AFM) for the Mn-Mn pairs. In the weakly frustrated case (x < 0.36), two mixed phases appear at low temperature in the FM sector, in agreement with infinite-range mean-field theories. In particular, the M2 phase displays macroscopic properties which strongly resemble the one of the “canonical” SG phase, stabilized for x > 0.36. *A natural question concerns the differences in the magnetic structures found in the M2 and SG phases, given that the former coexists with an underlying (long-range) FM order while the latter shows up within a regime where no long-range order can be established.*

Small-angle neutron scattering (SANS) is devoted to the study of objects with characteristic size in the ≈ 1-100 nm range. Here, it allows observing the signature of chiral textures, similar to quasi-2d vortices, induced by a magnetic field within the M2 phase (**Fig. b**). Their average radius (1-10 nm) is fixed by the inverse of position of the scattering peak which appears thanks to the correlations existing in the plane perpendicular to the applied field. This quantity is well-described by scaling laws using a “universal” exponent, showing that the size of these textures is driven by the ratio of the applied field over the average FM exchange term (**Fig. d**).

These structures however disappear in the SG phase, as a consequence of the loss of rigidity of the magnetic “vacuum” (**Fig. c**). In other words, they reflect the ground state of the material and potentially allow probing its properties in a fine manner, on a length scale with remains scarcely explored. In addition, our Monte Carlo simulations shows that the degree of exchange frustration between nearest neighbors is indeed the principal ingredient driving the emergence of these spin textures. These results reveal that the magnetic defects seen using SANS are anchored around AFM pairs (regions bordered in yellow in **Figs. e,f**), whichs explains their extreme robustness with respect to an applied field.

This work opens the way for a better understanding of the RSGs, while calling for deeper experimental and numerical studies. Notably, the role of anisotropy on the morphology of the vortex-like textures, their impact on electric transport and the nature of the spin dynamics close to the M2 → SG transition line remain to be elucidated.

Original paper: **Field-induced vortex-like textures as a probe of the critical line in reentrant spin glasses**, N. Martin, L. J. Bannenberg, M. Deutsch, C. Pappas, G. Chaboussant, R. Cubitt & I. Mirebeau, Scientific Reports **11**, 20753 (2021)

*The experiments described in this paper have been performed on the PAXY (LLB) and D33 (ILL) SANS instruments, as well as on the PPMS platform (Quantum Design, Dynacool 9T) of the LLB. This work is the result of a collaboration between the Laboratoire CRM2 of the Université de Lorraine, the **Technische Universiteit Delft and the LLB.*

On the same topic: Spin textures induced by quenched disorder in a reentrant spin glass : Vortices versus “frustrated” skyrmions, I. Mirebeau, N. Martin, M. Deutsch, L. J. Bannenberg, C. Pappas, G. Chaboussant, R. Cubitt, C. Decorse & A. O. Leonov, Phys. Rev. B **98**, 014420 (2018)