The Captured Nightmares item is a Legendary Crafting Material required to craft a legendary 1-H Weapon at Blacksmith Haedrig Eamon. The Captured Nightmare is found in Act IV. This material is really hard to farm due to the nature of the mob it drops from.
The Terror Demon can be found in the following Act IV locations:
Gardens of Hope Level 2
The Silver Spire Level 1
The Silver Spire Level 2
Take the waypoint to The Gardens of Hope Level 2 and thoroughly explore all the tier. Once you have explored all of it, use the Town Portal to reach Bastion's Keep. There take the waypoint to the Silver Spire Level 1; or take the gateway.
My first attempt, I only found two Terror Demon in the Gardens of Hope level 2. Based on the amount of time it takes to navigate that place it is not worth it. Skip it. About 4-5 in the Silver Spire level 1. Probably 3 in Silver Spire level 2. It might vary. However, through observation it seems Vile Lesions have a chance to spawn a Terror Demon. Thus, go kill all the Vile Lesions and Infernal Cocoons protruding off the ground. Seems clicking on Tortured Angels have a chance to spawn a Terror Demon.
My Captured Nightmares, however, dropped from Grimnight the Soulless (yellow elite Demonfire Nightmare/Enslaved Nightmare). Found him in Silver Spire Level 2. Not sure if it is relevant, but Grimnight the Soulless spawned during the Bounty: Kill Haures. Haures is an Enslaved Nightmare too.