There was no Spartan-Persian War, unless you are talking about Agesilaus’ efforts in Asia Minor during the 390s BCE. He didn’t defeat them and they didn’t defeat him. He was recalled with his forces for urgent business at home.If you are talking about Thermopylai, The Persians invaded mainland Greece. The combined Greek fleet defeated the combined Persian fleet at Salamis in 480 BCE. The following year the combined southern Greek army defeated the combined Persian and northern Greek army at Plataia, while the combined Greek fleet defeated the remainder of the combined Persian fleet at Mykale.The Spartans were a very minor part of the Greek fleet. They were a small part of the Greek army. They were a small part of the 5,000 which defended the pass at Thermopylai.Read some of the other questions on the subject and the answers will fill in some gaps.