x86 spinlock using cmpxchg

I'm new to using gcc inline assembly, and was wondering if, on an x86 multi-core machine, a spinlock (without race conditions) could be implemented as (using AT&T syntax):

spin_lock:
mov 0 eax
lock cmpxchg 1 [lock_addr]
jnz spin_lock
ret

spin_unlock:
lock mov 0 [lock_addr]
ret