Paramagnetic and antiferromagnetic resonances in the diamagnetically diluted Haldane magnet PbNi 2 V 2 O 8

The impurity-induced antiferromagnetic ordering of the doped Haldane magnet $\mathrm{Pb}({\mathrm{Ni}}_{1\ensuremath{-}x}{\mathrm{Mg}}_{x}{)}_{2}{\mathrm{V}}_{2}{\mathrm{O}}_{8} (0l~xl~0.06)$ was studied by electron-spin resonance (ESR) on ceramic samples in the frequency range 9\char21{}110 GHz. Below the N\'eel temperature a transformation of the ESR spectrum was found, indicating an antiferromagnetic-resonance mode of spin precession. The excitation gap of the spin-wave spectrum increases with increasing Mg concentration x in the same manner as the N\'eel temperature, reaching its maximum value of 80 GHz at $xg~0.04$. At small concentrations $xl0.02$ the signals of antiferromagnetic resonance were found to coexist with the signal of the paramagnetic resonance indicating a microscopic separation of the magnetic phases.