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Implications of second harmonic generation for hidden order in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>Sr</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mi>CuO</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mi>Cl</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:mrow></mml:math>
Sr$_2$CuO$_2$Cl$_2$ (SCOC) is a model undoped cuprate with $I4/mmm$ crystallographic symmetry, and a simple magnetic space group $C_Amca$ with associated magnetic point group $mmm1'$. However, recent second harmonic spectroscopy in the antiferromagnetic phase has challenged this picture, suggesting instead a magnetic point group $4/mm'm'$ that co-exists with the antiferromagnetism and …