Electron spin resonance for the detection of long-range spin nematic order

In this paper we propose that electron spin resonance (ESR) measurements enable us to detect the long-range spin nematic order. We show that the frequency of the paramagnetic resonance peak in the ESR spectrum is shifted by the ferroquadrupolar order parameter together with other quantities. The ferroquadrupolar order parameter is extractable from the angular dependence of the frequency shift. In contrast, the antiferroquadrupolar order parameter is usually invisible in the frequency shift. Instead, the long-range antiferroquadrupolar order yields a characteristic resonance peak in the ESR spectrum, which we call a magnon-pair resonance peak. This resonance corresponds to the excitation of the bound magnon pair at the wave vector $\bm k={\bm 0}$. Reflecting the condensation of bound magnon pairs, the field dependence of the magnon-pair resonance frequency shows a singular upturn at the saturation field. Moreover, the intensity of the magnon-pair resonance peak shows a characteristic angular dependence and it vanishes when the magnetic field is parallel to one of the axes that diagonalize the weak anisotropic interactions. We confirm these general properties of the magnon-pair resonance peak in the spin nematic phase by studying an $S=1$ bilinear-biquadratic model on the square lattice in the linear flavor-wave approximation. In addition, we argue applications to the $S=1/2$ frustrated ferromagnets and also the $S=1/2$ orthogonal dimer spin system SrCu$_2$(BO$_3$)$_2$, both of which are candidate materials of spin nematics. Our theory for the antiferroquadrupolar ordered phase is consistent with many features of the magnon-pair resonance peak experimentally observed in the low-magnetization regime of SrCu$_2$(BO$_3$)$_2$.