linux - Can atomic ops based spin lock's Unlock directly set the lock flag to zero?

Say for example, I have an exclusive atomic-ops-based spin lock implementation as below:

bool TryLock(volatile TInt32 * pFlag)
{
   return !(AtomicOps::Exchange32(pFlag, 1) == 1);
}

void Lock (volatile TInt32 * pFlag) 
{  
    while (AtomicOps::Exchange32(pFlag, 1) ==  1) {
        AtomicOps::ThreadYield();
    }
}

void    Unlock (volatile TInt32 * pFlag)
{
    *pFlag = 0; // is this ok? or here as well a atomicity is needed for load and store    
}

Where AtomicOps::Exchange32 is implemented on windows using InterlockedExchange and on linux using __atomic_exchange_n.