relaxed vs relaxing

Generally speaking, past participle (-ed) is used to describe someone's feeling. e.g. I feel relaxed.
present participle (-ing), on the other hand, is used to describe things that make people have the feeling. e,g, The drink is relaxing.

From the above, we can conclude that relaxing atmosphere is more appropriate.

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relaxed atmosphere = 不拘泥[緩和]輕松的氣氛
(comfortable, calm, casual, peaceful and informal)

relaxing atmosphere = 使人懶洋洋的氣氛
(making you feel relaxed; helping you to rest, and becoming less worried)

The difference is subtle.

-ed係感到，-ing係散發