ESR selection rules for direct transition of spin gap

The ESR direct transition from the ground state to the first excited state has been observed in some recent experiments on gapped spin systems, although such a transition is forbidden because of the conservation law of the spin quantum number. We consider the two possible mechanisms of the direct trasition between the singlet and triplet states; the Dzyaloshinsky-Moriya intraction and the staggered field due to the alternating g-tensor. The angle-dependent selection rules are presented for the two mechanisms, respectively. For the Dzyaloshinsky-Moriya interaction, non-zero intensity of the ESR can appear only in the two cases; (i) D → ∥ H → ⊥ h → rf or (ii) D → ⊥ H → ∥ h → rf , where D → , H → and h → rf are the characteristic vector of the Dzyloshinskii-Moriya interaction, the external magnetic field and the magnetic component of the rf-field, respectively. For the longitudinal staggered field, the singlet-triplet transition is possible for H → ⊥ h → rf . In contrast, the condition of the appearance of the transition is H → ∥ h → rf for the transverse staggered field, which is realized in the Haldane antiferromagnet NENP. Based on the present results, the mechanism of the singlet-triplet transition observed in the recent experiment on CuGeO 3 is discussed.