Recent advances in human intracranial recordings have significantly deepened our understanding of complex cognitive functions like working memory (WM) at the circuit level. While single-neuron analyses, primarily within the medial temporal lobes, have elucidated how individual neurons contribute to memory computation, the role of local field potential (LFP) dynamics in complementing single-unit activity during WM tasks remains poorly understood. To address this, we developed biologically plausible spiking recurrent neural networks (RNNs) trained on a delayed match-to-sample (DMS) task which involves neural coding and persistent representation of sequential stimuli. In these spiking models, we computed LFP-like signals via post-synaptic input currents. Our results reveal that inhibitory power spectra vary significantly across frequency bands based on WM performance. Furthermore, disinhibitory circuits (inhibitory-to-inhibitory; I→I connections) are essential for generating neural synchrony in high gamma frequencies that are critical for WM maintenance. Inhibitory synchronization emerged as a key mechanism in maintaining memory representation, suggesting potentially universal computational principles of inhibition in memory. These findings advance our understanding in computational and systems neuroscience by providing a theoretical framework that integrates gamma oscillations and inhibitory signaling in cognitive function. Finally, we are currently in the process of validating these predictions using intracranial recordings from human participants performing DMS tasks, which will offer deeper insights into the circuit dynamics underlying working memory computation in humans and further bridge the gap between computational and biological neural networks.