High-order harmonics and the reverse of the squaring up process in the triangular-lattice magnet HoPdAl 4 Ge 2
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 HoPdAl 4 Ge 2 , 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 T N = 10.5 K and T t = 5.5 K. Below T N , Ho 3+ spins order antiferromagnetically as a transverse spin-density wave with the propagation vector k 1 = (001.5 – δ) with δ ≈ 0.18. Upon further cooling through T t , the high-order harmonics with k n = (001.5 – nδ), 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 HoPdAl 4 Ge 2 involves the conversion of k n = (001.5 – nδ) with n = 1, 3, 5, 7, to a ferromagnetic k F = (000) component. It is worth noting that the already weak seventh harmonic magnetic peak is enhanced by applying a small magnetic field in the ab plane at 1.5 K or warming up to 3 K, accompanied by a slight decrease of δ.