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We investigate the influence of critical spin fluctuations on electromagneticresponses in the odd-frequency superconductivity. It is shown that the Meissnerkernel of the odd-frequency superconductivity is strongly reduced by thecritical spin fluctuation or the massless spin wave mode in theantiferromagnetic phase. These results imply that the superfluid density isreduced, and the London penetration depth is lengthened for the odd-frequencypairing. It is also shown that the zero field Flude-Ferrell-Larkin-Ovchinnikovpairing is spontaneously realized both for even- and odd-frequency in the caseof sufficiently strong coupling with low lying spin-modes.

On the Meissner Effect of the Odd-Frequency Superconductivity with Critical Spin Fluctuations: Possibility of Zero Field FFLO pairing