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The pseudogap phenomenon in the cuprates is arguably the most mysterious puzzle in the field of high-temperature superconductivity. The tetragonal cuprate HgBa 2 CuO 4+ δ , with only one CuO 2 layer per primitive cell, is an ideal system to tackle this puzzle. Here, we measure the magnetic susceptibility anisotropy within the CuO 2 plane with exceptionally high-precision magnetic torque experiments. Our key finding is that a distinct two-fold in-plane anisotropy sets in below the pseudogap temperature T * , which provides thermodynamic evidence for a nematic phase transition with broken four-fold symmetry. Surprisingly, the nematic director orients along the diagonal direction of the CuO 2 square lattice, in sharp contrast to the bond nematicity along the Cu-O-Cu direction. Another remarkable feature is that the enhancement of the diagonal nematicity with decreasing temperature is suppressed around the temperature at which short-range charge-density-wave formation occurs. Our result suggests a competing relationship between diagonal nematic and charge-density-wave order in HgBa 2 CuO 4+ δ .

High entropy oxides are emerging as an exciting new avenue to design highly tailored functional behaviors that have no traditional counterparts. Study and application of these materials are bringing together scientists and engineers from physics, chemistry, and materials science. The diversity of each of these disciplines comes with perspectives and jargon that may be confusing to those outside of the individual fields, which can result in miscommunication of important aspects of research. In this Perspective, we provide examples of research and characterization taken from these different fields to provide a framework for classifying the differences between compositionally complex oxides, high entropy oxides, and entropy stabilized oxides, which is intended to bring a common language to this emerging area. We highlight the critical importance of understanding a material’s crystallinity, composition, and mixing length scales in determining its true definition.

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We report the transverse relaxation rates 1/T2's of the 63 Cu nuclear spin-echo envelope for doublelayer high-Tc cuprate superconductors HgBa2CaCu2O 6+δ from underdoped to overdoped. The relaxation rate 1/T2L of the exponential function (Lorentzian component) shows a peak at 220−240 K in the underdoped (Tc = 103 K) and the optimally doped (Tc = 127 K) samples but no peak in the overdoped (Tc = 93 K) sample. The enhancement in 1/T2L suggests development of the zero frequency components of local field fluctuations. Ultraslow fluctuations are hidden in the pseudogap states.