High-order harmonics and the reverse of the squaring up process in the triangular-lattice magnet HoPdAl4⁢Ge2

We uncover high-order harmonics and the reverse of the squaring-up process, in terms of analyzing the evolution of magnetic orders in a centrosymmetric layered triangular-lattice magnet HoPdAl4⁢Ge2, based on a detailed study of the crystal structure, magnetic susceptibility, magnetization, heat capacity, and magnetic structure. Temperature dependencies of magnetic susceptibility and heat capacity show two magnetic transitions at 𝑇𝑁=10.5 K and 𝑇𝑡=5.5 K. Below 𝑇𝑁, Ho3+ spins order antiferromagnetically as a transverse spin-density wave with the propagation vector 𝒌1=(001.5−𝛿) with 𝛿≈0.18. Upon further cooling through 𝑇𝑡, the high-order harmonics with 𝒌𝒏=(001.5−𝑛⁢𝛿), 𝑛=3, 5, 7 develop, suggesting a squaring-up process. It is surprising that the squaring-up process does not continue down to 0 K but reverses the trend below 3 K. Magnetic-field-induced metastable transitions were observed in 𝑀⁡(𝐻) curves with the fields applied both parallel and perpendicular to the triangular-lattice plane. Neutron-diffraction results suggest that the magnetization process in HoPdAl4⁢Ge2 involves the conversion of 𝒌𝒏=(001.5−𝑛⁢𝛿) with 𝑛=1, 3, 5, 7, to a ferromagnetic 𝒌𝑭=(000) component. It is worth noting that the already weak seventh harmonic magnetic peak is enhanced by applying a small magnetic field in the 𝑎⁢𝑏 plane at 1.5 K or warming up to 3 K, accompanied by a slight decrease of 𝛿.