Antiferromagnetic (AF) materials were described last century as "interesting, but useless" [1]. This paradigm has been changed upside-down in the second decade of the current 21^st century. Thanks to their inherent fundamental interest, have been thoroughly studied in the last decades. And the more we studied them, the more we got to know about their inherent assets, compared to the traditionally-used ferromagnetic materials, when coming to their potential implementation in the incoming spintronics-based technological devices [2]. Even more, from a fundamental perspective, antiferromagnetic structures are extremely appealing, since they can host complex magnetic arrangements that go beyond the basic antiparallel picture. To give some examples, these include helix, non--collinear and/or noncoplanar structures. Moreover, these structures are potential sources for topological spin textures to occur.

On the other hand-side, the experimental realization of the mesoscale, i.e., materials for which at least one physical dimension is comparable to a material correlation length, usually in the range of nanometers, opened a new research field, nanomagnetism, where new phenomena can occur. As an example, they are the interactions among magnetic nanoparticles which allowed to beat the Superparamagnetic limit [3].

Then, what if we put both together? Are complex magnetic structures also possible in nanoparticles, or the reduced symmetry and coordination, plus the interactions among nanoparticles would prevent these super-structures to occur? The access to the nanoscale also opens the room for more questions regarding the fundamental aspects of bulk materials. More precisely, we are all aware that quantum energy levels rely at the bottom of macroscopic behaviors. Determining precisely and experimentally how these change from bulk to nanoparticle is still an open challenge, mainly connected to the intrinsic difficulty of the experiments. In this work, we will provide answers for the previous questions for a 4f binary alloy, TbCu₂.

We have produced the TbCu2 alloys, both bulk and nanoparticle ensembles, using arc furnace for the alloy and ball milling for the size reduction to the nanoscale. In the MAGMA group at the Universidad the Cantabria, we have a long tradition working with 4f intermetallic alloys. While these binary Cu-4f alloys are AF ordered in bulk, when reducing their dimensionality, they develop magnetic frustration at the surface, building then the so-called superantiferromagnetic state, where the AF order is retained in the nanoparticle core, and the surface magnetic moments establish a spin glass-like state [4, 5]. Among all the possible combinations, we have selected TbCu2, as it has the highest Néel temperature of the series (48 K).

Then, the question arises on how to detect magnetic super-structures. Any magnetic structure has a correlation length among the magnetic moments. An ideal technique to probe correlation lengths in the range of 1-100 nm is Small-Angle Neutron Scattering (SANS), which can be employed in nanoparticle ensembles. This technique allows to quantify the elastic scattering with neutrons and matter. The lack of charge, and negligible dipolar electric moment, allow neutrons to penetrate in the material and interact via nuclear forces with the atoms. Moreover, neutrons do have a magnetic dipolar moment. This results in a “magnifier lens” that allows to probe both lattice (scattering with nucleii) and magnetic (scattering from unpaired electrons) structures. Our measurements were performed at SANS2D time-of-flight instrument in RAL-ISIS, (UK), in the temperature range of 5-285 K and from 0 to 6 T applied field. For the shake of avoiding complexity or too much details, we will briefly summarize our results by saying that, in our SANS patterns, we measured a Bragg peak at q = 1.15(1) nm^-1, which corresponds to a real space distance of 5.61 nm. This spacing is incommensurate with the crystal crystalline lattice, revealing that this correlation should correspond to an additional structure, larger than the crystalline one. The peak intensity is field-dependent, revealing the magnetic origin of these super-structure. We have calculated the magnetic moment carried by such super—structure, which is compatible with an helix configuration laying in bc-plane. We propose an helix to be the most reasonable configuration of the magnetic moments, as pure Tb, Dy, and Ho display such structure, so as metallic nanocrystalline Tb, which also presents a peak located at the same q value [6, 7]. Then, what happens for the case of nanoparticles? We found the same peak and field dependency for 8 nm nanoparticles, meaning that such super-structure, realized in the nanoparticle core, is robust against size reduction and microstrain.

Concerning the energy level schemes, we would like to highlight that the determination of the quantum energy levels is not an easy task for a J = 6 ion. A Crystalline Electric Field (CEF) with C_2v symmetry splits the degeneracy in 13 singlets, which would imply that calculations need to be performed in a non-lineal problem with at least, 13 variables. Then, below TN, the molecular field shifts the energy levels, which are going to be split on behalf of Zeeman interaction. On top of that, magnetic excitations may also occur below the ordering temperature. Indeed, probing experimentally the energy schemes in nanoparticles is challenging on its own. We decided to benefit from Inelastic Neutron Scattering, a very powerful technique that provides information on material excitations (single and collective). Our fabrication route (ball milling) allowed to obtain the large amount of crystalline nanoparticles (around 15 g) to achieve the required signal-to-noise ratio.

To answer the big question (how are the energy levels affected by size reduction to nanoscale), we decided to break it into smaller pieces. First, we have determined the pure CEF splitting of Tb³⁺ by measuring a non-magnetic bulk Tb_0.1Y_0.9Cu₂ alloy. As expected, these schemes hold in the paramagnetic region of TbCu₂. Second, we have resolved the TbCu₂ bulk alloy below T_N, where the energy levels are shift by 2 meV due to the molecular field of 60 T. We have also detected a magnetic excitation around 6.7 meV. Third, we have analyzed TbCu₂ nanoparticles ensembles of 7 nm. The CEF splitting in the PM region is soften (negative energy shift of the peaks), expected according to increased microstrain and reduced symmetry in the nanoparticles. Nevertheless, the most interesting fact comes below T_N, where no energy shift is found comparing with the bulk values. This means that there must exit a positive energy shift. The fact that this effect is “activated” only below T_N, and is enhanced as the T is decreased further T_N, reveals its magnetic origin. We propose to understand this contribution as an additional surface molecular field, imposed to the 60 T, which is preserved in the nanoparticle core. The idea of an active surface in the RKKY propagation has already been reported in NdCu₂ nanoparticles [8].

To sum up, the results shared in this work showcase the robustness of incommensurate magnetic structures, that are of primer interest for spintronic applications, plus improves the understanding on how the interplay between the size reduction and the magnetic interactions in ensembles of magnetic nanoparticles occur. So far to us, the present work constitutes one of the few case examples which shows and describes these claims experimentally in nanoparticle ensembles. The community of researchers working in complex magnetic materials requires still more (similar) combined SANS and INS evidences coming from other types of compounds within the nanoscale range to broaden a new field and to ponder to achieving an improved insight.

References

[1] L. Néel. Magnetism and local molecular field. Science, 1971, vol. 174, no 4013, p. 985-992.

[2] M. Jungfleisch et al. Perspectives of antiferromagnetic spintronics. Physics Letters A, 2018, vol. 382, no 13, p. 865-871.

[3] V. Skumryev et al. "Beating the superparamagnetic limit with exchange bias." nature 423.6942 (2003): 850-853.

[4] E. M.Jefremovas et al. Investigating the size and microstrain influence in the magnetic order/disorder state of GdCu2 nanoparticles. Nanomaterials, 2020, vol. 10, no 6, p. 1117.

[5] C. Echevarría-Bonet et al. Size-induced superantiferromagnetism with reentrant spin-glass behavior in metallic nanoparticles of TbCu 2. Physical Review B, 2013, vol. 87, no 18, p. 180407.

[6] T. Chatterji (ed.). Neutron scattering from magnetic materials. Elsevier, 2005.

[7] A. Michels et al. Influence of crystallite size and temperature on the antiferromagnetic helices of terbium and holmium metal. Physical Review B, 2011, vol. 83, no 22, p. 224415.

[8] E. M. Jefremovas et al. Observation of surface magnons and crystalline electric field shifts in superantiferromagnetic NdCu2 nanoparticles. Physical Review B, 2021, vol. 104, no 13, p. 134404.