Not long after the birth of Yomigami, Amaterasu felt the same urge come upon her. This time, her aimless search brought her to the crucibles of the best smelters of jewel steel in the land of Nippon. From crucible to crucible she wondered in search of the finest jewel steel. She rejected ingot after ingot before she found what she was looking for.
With the steel obtained, she scoured the land in search of legendary sword smiths. She inspected the pieces of their work, searching for the skill and spirit worthy of forging a divine blade. Finally, she found a humble, pious, and above all skilled, smith to forge the sword of a god.
Night and day he forged and reforged the blade, attempts rejected dozens of times. He worked tirelessly for days, until at last the blade was perfect. It was a tsurugi style sword, the sword smith's greatest masterpiece, and he laid it reverently at Amaterasu's feet. She inspected the sword and found it suitable, and in thanks she blessed the sword smith and his descendants with good fortune, and in time they became one of the greatest and most legendary sword making families in Nippon.
Amaterasu brought the sword with her when she returned to the Celestial Plains. She took the sword's hilt between her jaws, the power in her soul rising up to fill her being. She raised the blade above her head, pushing the power of the sword, the Power Slash, through it. With a jerk of her head she swung the sword through the air. The sound of a sword being drawn swiftly from its scabbard rang out and the air itself parted with the force of her will.
As she put the sword down, her power flared. There, at the pommel of the sword, formed a small ball of white light. As Amaterasu watched, it grew and changed shape, forming a tail, ears, tiny paws and a pointed, twitching nose. It had become a large white rat, marked with divine red.
Once it was fully formed, it bowed to her and squeaked in a high-pitched voice, "Hail, Mother. By the strength of your will, I have come forth."
Amaterasu licked her newborn son in greeting, blessed him with his name, and gifted him his power over Power Slash, and the sword. She christened him Tachigami, Sword God, after a type of sword.
This is the account of the birth of Amaterasu's second son, Tachigami, God of the Sword and Brush God of Power Slash.
I have crossposted this story to Archive of Our Own and with extra info. Also, the story at Spacebattles is ahead by one chapter.