The Defense Department and Microsoft are investigating an error that exposed at least a terabyte of military emails including personal information and conversations between officials, people familiar with the matter said, an episode that highlighted the security risk of moving sensitive Pentagon data to the cloud. The Pentagon’s Cyber Command has taken the lead on the investigation with Microsoft, which operates the Azure cloud-computing service that stored the data. Investigators have no sign yet that the exposed data was accessed but were still working to assess the fallout from the leak, the people said. They had differing assessments on who was at fault, with one saying it was the fault of a Pentagon employee and another saying Microsoft was to blame. The leak will draw new scrutiny to the Pentagon’s push to move much of its data over to commercial cloud-computing.