Dev should write unit tests and integration tests (some go even further to write functional tests using selenium). Asking QA to write unit tests falls into the

Dev should write unit tests and integration tests (some go even further to write functional tests using selenium). Asking QA to write unit tests falls into the category of busywork with extra overhead which a sure recipe of not being agile. You could ask them to write functional tests but not any lower than that. I do not do TDD but I always make sure my commits should have unit tests whenever possible because I do not commit without testing them first :)