How can I use a Nissin i40 as an off-camera flash with an A6000? Is it possible? What are the alternatives?
There are a number of different ways to trigger the i40 off-camera.
SD/SF slave modes
These are simple optical slave modes that are built into the flash, and can trigger it remotely on any flash burst, including the one from your α6000's pop-up flash. SD (slave digital) is if your pop-up is in TTL (has a single preflash), SF (slave film) is if your pop-up is in manual (has no pre-flash). Your pop-up flash will have to be up and turned on for this to work, and the sensor on the i40 has to "see" the flash burst from your pop-up. It may not work well outdoors in bright sunlight, without direct line-of-sight. And all you can do is tell the flash to fire. No TTL/HSS*, or remote power control.
AFAIK (I'm a Canon shooter, so...) this can only be accessed if you have a Sony wireless TTL master unit on the flash hotshoe (any of the Sony HLV flashes with controller capability). It's also optical, and has the same limitations, but will offer TTL and remote power control. Not sure about HSS.
You can also use radio triggers to get past the shortcomings of optical triggers. With radio triggers, you put a transmitter on the camera hotshoe, and it signals to a receiver you connect to the flash's foot. Because it's using radio, there are no line-of-sight requirements, and reliability in bright light is good.
However, finding TTL triggers that use the Sony multi-interface hotshoe is tough. They're not particularly common. The Sony versions of the Phottix Odin II and Godox X1 triggers, however, should have multi-interface hotshoes, and can communicate TTL and HSS.
You could also use manual-only triggers (e.g., Phottix Strato, Yongnuo RF-603II), but they won't communicate anything but the sync signal.
* For definitions of TTL and HSS, see: What features should one look for when selecting a flash?