Yup, hawks are tough especially this time of the year when they are migrating. I free range (no fence, no run, just a secure coop at night). Recently I lost 4 8-week old chicks to a hawk. I live on the border of 3,000 acres of forest and this was my first predator loss (knock on wood) in 2 years.
I have never tried to deter hawks with CD's or any of the other methods suggested in the various threads that deal with hawk predation. What I have is 4 dogs who run my farm. They are 4 different breeds, all rescues from the shelter. One is a beagle mutt so she chases the rabbits. Another is a terrier mutt so she's always after the moles and mice. Another is a hound mutt so he's busy chasing anything in a tree. The last dog is an anatolian shepherd mutt. I'm not positive he's really an Anatolian (which is a guardian livestock dog) but that dog is alert! He watches the sky, the ground, close up, distance. He's on the JOB!
Dogs naturally defend and protect their territory. In my case, the dogs run off all the little critters that most natural predators want to eat. A dog chasing something will bark and a dog barking naturally scares away predators. My dogs also chase birds. We have a small pond and the dogs chase off any ducks or geese or herons who try to make the pond their home. They also chase hawks. They just naturally do. I didn't teach them this. They just do it.
Also, having more than one dog makes a difference. A single dog will bond with you and the rest of the family. Two dogs will not only bond with you but very likely with each other.
So, one idea is to get 2 dogs from your shelter. I don't know where you live and what your weather is like. I live in Kentucky and my dogs are outside alot during the day but inside at night. I don't chain or leash them because we live way out on a back country dead end road. But the idea is to get dogs that are a breed of dog that like being outside and that is not likely to bother chickens. In your 3/4 acre yard, I don't think a hawk is going to come down when there are 2 dogs laying about! Plus, 2 dogs are more likely to sit contentedly out in your yard and guard your place together as they are pack animals and will do it together.
I did have to train my dogs to not bother my chickens. The beagle mutt, hound mutt and anatolian mutt all needed minimal training. A few days of "these are my chickens, not your chickens" in a stern voice is all it took. The terrier mutt took more time but it wasn't hard. Now, the dogs all treat the chickens as part of the landscape. The dogs will lay asleep in the hay with the chickens 2 feet from their noses, open one eye, see the chickens, go back to sleep. But if they hear an unfamiliar sound or a shadow of a hawk passes by, they are up and running after whatever it is.
Some others do suggest more training for the dogs, so they learn what a chicken alarming sounds like and so they react appropriately, etc. This is great advice. I just offer this as an alternative. Dogs are natural protectors of your property and if they understand your chickens are just part of your property, they will by default protect them too. Dogs are natural predators too so they will chase most anything they think is prey or an intruder If you teach them that your chickens are not prey, they will naturally chase everything else. And again, in my case, my dogs all have their "niche" which is by accident. I just adopted these dogs for various reasons (on death row in a kill shelter, etc) and ended up with dogs all different from each other.
Back to my hawk that took the 4 chicks over a 2 day period. I believe he was migrating because I haven't seen him since and he was extra big so I believe I'd recognize him. I saw him eating one of my chicks a little distance from my barn and I simply tried to scare him away. That's all I had to do and I never saw him again. I've read that adult hawks are easier to scare than juveniles and by the size of him, he was an adult. And I've read extensively on the laws around harrassing or harming a hawk, all highly illegal. Plus, I honestly "get" that the hawk was just getting an easy meal and in a certain way, I feel OK about it because at least my chicks didn't go to waste. Three of the 4 were likely cockerals and I was going to eventally put them in the pot at some point anyway....
In terms of the dogs and this particular hawk, my dogs were not around when the hawk came as they were up the mountain with my husband working on a bulldozing project at the time. I suspect the local hawks have never (yet!) bothered my chickens because they know the dogs are "around." I suspect this is the reason because I had 14 baby chicks earlier this past summer, free ranging all over the place with their mothers and not one loss. And we see and hear hawks constantly overhead. So... it's just the way it goes sometimes. A hawk flies by on it's way to some migration spot, sees little chicks, dogs are gone for awhile and the hawk has himself a nice baby chick for lunch. Nature and chance at work, I guess.
Hope this helps,
Guppy