I have seen a number of people with rodent issues put hardware cloth on the bottom of the raised bed frame to prevent anything from digging into, and up, into the raised bed. That would be especially good against voles and the like. I don't know if it would keep out rats that could get into the raised bed from the top and make their tunnels down.
It's too bad you had to dismantle your raised beds, but I can understand wanting to get rid of those rats. I live on a lake, and I don't have the option of growing food in my sandy soil. It's just not good enough. Fortunately, I don't have a rat problem.
I have had hügelkultur style raised beds for about 10 years now and never had any rodent issues. Until this year. We had a really mild winter this past year, and this spring/summer I have seen an explosion of chipmunks in my yard. Some of them found harbor in a few of my raised beds and are digging tunnels.
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I don't mind chipmunks, and they don't seem to be eating much, so it's not a real problem this year. I have filled in the tunnels and put a protective chicken wire cage on top of some of my raised beds. That has helped.
That mainly keeps out the larger squirrels and rabbits which are doing real damage to my food plants. Also, I have built some cages with wire tops to keep out deer. I took a real heavy loss with deer eating almost all my tomatoes in my raised beds this year. I will have to build some kind of trellis and cage system that protects my plants from deer before I plant anything next year. If not, it's just no use to plant anything without protection.
I was very happy with the production of my plants in my hügelkultur raised beds this year. The hügelkultur method and my chicken run compost are great. My plants were tall and strong, full of fruit. Then, one morning, I went outside and discovered that almost all my tomatoes and pepper plants had been devastated by deer.

I really like the raised beds and using the hügelkultur method, but next I have yet to work out a solution to protect all my plants. Again, for the past 10 years, I never had a problem. But this year I got hit hard by rabbits, squirrels, and deer taking most of my crops.
I am working on a few ideas in my mind, and once I get something built, I'll post my efforts. I have built simple cages to put on top of my raised beds before, and they do work, but they are a real pain to take on and off all the time to work the beds. So, I am considering other cage build designs with hinges and/or removable panels so I can get to my plants. It will have to be strong enough to keep out hungry deer.
Speaking of wild animals getting into stuff this year, we have recently had a black bear getting into my neighbors' garbage cans the past few weeks. That is concerning because nobody wants a bear around their house. I don't keep any garbage cans outside, so I have not attracted any bears to my house.
Not the actual picture of the bear in our neighborhood, but here is a Google picture of a black bear in garbage cans for illustration...
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I don't think I could build a cage system around my plants to keep out a hungry bear, so I hope it never comes to that. If my neighbors get their act together and don't put garbage outside where a bear can get into it, I think the bear will move along to some other place.
I have been growing food in my gardens for about 25 years, and this was the first year I have ever had so much problem with losing my crop to rodents and deer. Again, some people are saying this might be a one-year problem because we had such a mild winter last year and our varmint population exploded.