Archimedes spiral in photoshop

In Photoshop there’s a Spiral option in the Symmetry feature of the Brush tool, and it actually produces a path, and if you copy the path you can stroke it. But I’m not sure if will help because it looks more like a seashell spiral than an Archimedes spiral, and you can’t customize the spiral. So a spiral from another source might be the way to go.

If your subscription includes Adobe Illustrator, it has a Spiral tool, although it isn’t in the default toolbar. But it does provide options. In the demo below, I change the spiral settings interactively by dragging while holding down the Ctrl key (Windows) or Command key (macOS). After you create the spiral in Illustrator, you can easily move it to Photoshop.

The first spiral that came to mind is the "golden spiral" crop overlay:

https://www.essentialdigitalcamera.com/2015/07/overlay-options-for-crop-tool-in.html

If the great suggestion from @Semaphoric doesn't work for you, then you would need to bring it in from an external source. A vector would be a good choice.

Photoshop does not have a Spiral tool, but you can construct one.

In a blank square image, draw a horizontal line from one side of the doc to the other with the Pen tool, and use Alt + T to drag a copy downward. Then use Control + Alt  + T to repeat the Transform.

With the Direct Selection tool, select all the points on one side (left or right), and drag them downward, so that they line up with the points on the other side.  Use a guide to help the snapping. You should end up with a series of equally spaced diagonal lines. Select the path, and stroke it with the Brush.

Run Filter > Distort > Polar Coordinates > Rectangular to Polar to make the spiral.