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Magnetic frustration due to the competition between magnetic interactions is a promising stage for the discovery of novel phenomena in magnets. Under magnetic frustration, many different spin configurations can have nearly the same energy in a system, and thus, the ground state can degenerate magnificently, such as in the case of spin ice and spin glass. Among them, slow dynamics on the order of ms to µs can be observed, which is 6 to 9 orders of magnitude slower than the ordinary dynamics in non-frustrated magnets.

This study focuses on such extraordinarily slow dynamics in the vicinity of the phase transition at zero magnetic field in the frustrated magnet DyRu₂Si₂, where the oscillating RKKY interaction between Dy³⁺ spins causes frustration. At zero field, DyRu₂Si₂ exhibits multi-step phase transitions. One atT_N1 = 29.5 K, from the paramagnetic phase to the phase I, and the other at T_N2 = 3.6 K, from the phase I to II. The phase I and II are partially disordered antiferromagnetic (AFM) phases, where disordered and fluctuating spins remain. This is an outcome of the frustration effect, namely the cancel-out of interactions at specific spin sites. In the phase I, disordered a-planes (D_I planes) on which all spins fluctuate appear every 9 planes. The D_I-planes are decoupled from each other because the interactions from the ordered a-planes in between are canceled out. Therefore, the D_I planes are identified as emergent pseudo 2-dimensional (2-D) systems. In the phase II, these fluctuating spins on the D_I planes order into a stripe structure. Hence, the I-II phase transition in DyRu₂Si₂ can be considered as spin-ordering in the emergent 2-D systems.

We conducted detailed ac susceptibility measurements around T_N2 and revealed the strikingly anomalous dynamics attributed to the I-II phase transition as follows: ① the extraordinarily slow dynamics in the order of 10-100 ms appears around 6 K far above T_N2, ② the relaxation time reduces as temperature decreasing, indicating non-thermally activated origin, ③ the critical slowing down is absent at T_N2, and ④ the ferromagnetic (FM) spin correlations grow toward T_N2, even though it is an AFM phase transition.

On the basis of these findings, we propose a schematic of the I-II phase transition. Prior to the phase transition, large belt-like FM spin textures extending along c-axis emerge as precursors of the striped structure of the phase II. As approaching T_N2, they grow in size and number and couple antiparallel to each other. Finally, at T_N2, they spontaneously order into the striped structure. This anomalous ordering process to the phase II could be the highly fluctuating nature of the emergent 2-D systems.

Written by S. Yoshimoto on behalf of all the authors.