Title: Lack of multiferroic behavior in BaCuSi₂O₆ is consistent with the frustrated magnetic scenario for this material

BaCuSi₂O₆ is a well-known quantum magnet that exhibits a Bose-Einstein Condensation quantum phase transition in applied magnetic fields. It contains Cu dimers that form singlets in zero magnetic field, and in applied fields as the singlet-triplet gap is suppressed a quantum phase transition occurs to canted XY antiferromagnetism between critical fields H_c1 = 23 T and H_c2 = 59 T. In addition, as the temperature is lowered, a rare frustrationinduced dimensional reduction has been proposed from three to two dimensions. Recently, however, a controversy has arisen about the details of the magnetic ordering due to the discovery of a tetragonal to orthorhombic structural transition at 100 K with an incommensurate modulation along the b-axis. Multiple magnon modes were observed in neutron diffraction studies, while NMR found modulation of the spin structure along both the ab plane and the c-axis. In this scenario the material is still a Bose-Einstein condensate system but the frustration is not perfect, calling into question the dimension reduction scenario. A recent study of BaCuSi₂O₆ combining inelastic neutron diffraction and density functional theory suggest that the material isn’t even frustrated at all and that the spins are ordered ferromagnetically in the a-b plane and antiferromagnetically along the c-axis. After a detailed symmetry analysis we have concluded that the magnetic scenario postulated by this most recent unfrustrated theory6 will render BaCuSi₂O₆ a multiferroic between H_c1 and H_c2, with electric polarization in easy axis of the a-b plane for magnetic fields along the c-axis via an inverse Dzyaloshinskii-Moriya mechanism. Electric polarization is a sensitive symmetry probe of magnetic order, since magnetic systems that break spatial inversion symmetry can induce an overall ferroelectricity in the crystalline lattice. In pulsed magnetic fields we can detect electric polarizations with unique sensitivity to sub-pC/m², which is orders of magnitude more sensitive than what can be detected in DC magnetic field.