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Various forms of spin and charge ordering have been identified in a widerange of cuprate superconducting materials, but whether these behaviors areubiquitous phenomena is not established. In this work we focus on one of thesimplest compounds, HgBa$_{2}$CuO$_{4+\delta}$ (Hg1201), a superconductor witha high transition temperature, 97 K, having only a single layer and tetragonalstructure, in contrast to one of the most extensively studied materials,YBa$_{2}$Cu$_{3}$O$_{6+y}$ (Y123). Using nuclear magnetic resonance we havediscovered a coherent spatial modulation of both spin and charge that istemperature and magnetic field independent, in competition withsuperconductivity similar to other cuprates. However, there is no evidence forthe magnetic field and temperature induced charge order observed in Y123.Electronic instabilities are a common feature of cuprates as in the presentwork on Hg1201, but their manifestations are not universal.

Coherent Charge and Spin Density Waves in Underdoped HgBa$_{2}$CuO$_{4+\delta}$