First, let me get the definitions out of the way.
Atheism is nothing more than a rejection of the belief that god (or gods) exists. It is not even a position against supernaturalism. It is not even a pro-science position. It is only a “I do not believe gods exist” position.
As such, there may exist atheists who believe in ghosts, pseudo-scientific theories, mystic healing, and magic. There may also be atheists who are racist, ethnocentric, and politically conservative.
Atheism does not stop people from being any of these things. It’s only about not believing that gods exist.
Now to define spirituality.
No two people will define spirituality the same way. It can indeed be literally about spirits (ghosts and suchlike), or it can be about something more beyond words. When asked if they are spiritual, people nod in the affirmative. But when asked what they mean by it, they dissolve into ambiguity. I have heard people say, without using the word “god”, that their spirituality is about “a higher power” or “something above us all” or “just a feeling”.
Spirituality remains undefined, and because of that, it remains prevalent. Religion is easy to reject in modern times. But a lot of religious baggage sneaks into rational minds disguised as spirituality.
Depending on how we define spirituality therefore, there may be atheists who can be defined as spiritual. But they probably won’t define it as having anything to do with a higher power that exerts any influence on their lives. Their definitions will be more… how shall I put it… esoteric.
There is a worldview known as Religious Naturalism that Carl Sagan might be described as having subscribed to. It finds in the scientific understanding of the world something that resembles religious feeling. Some people feel it in shrines, temples, mosques, and churches. Some feel it when watching Cosmos.
I am an atheist. And I have a definition of spirituality also. To me, spirituality means the search for meaning. So the simple act of opening the dictionary to look up a word is spiritual to me. To understand something is, to me, the highest possible calling of a human being.
All religion and all spirituality stems from the human need to understand. In ages past, we explained the universe using stories. These stories were the best we could do, and to some extent, they hold meaning even today. They tell us about ways of being and methods of conduct.
What has changed is that we have come to a greater understanding of not only the universe, but also the impulse that causes us to look for meaning. The human condition is defined, not by supernatural influences, but by our species’ imaginative outlook.
This is, at least to this atheist, kind of spiritual.