You would need to be able to prove that he encroached on your land (or your tenancy to land) with his pesticide/herbicide. You should speak to him and let him know that you feel his herbicide made its way (it could've come with the wind if its just on the borders) to the land, and as a result your animals were harmed. It's always better to see if you can handle this by appealing to his sense of responsibility. Just ask him to not spray the border, or not spray on a day with any breeze if he insists on spraying the entirety of his land. If he denies spraying the border (or at all), you can try to catch him in the act and film it, or find neighboring witnesses, such that you can file a complaint for trespass. It is probably not illegal in the true sense of the word, but it may subject him to damages.
You may try contacting your department of agriculture.
If he is a commercial applicator there are likely regulations that dictate the necessity of following label instructions or specific regulations or laws in your community that may also subject him to liability under common law, if the pesticide drift enters the properties of others (like yours) and causes damage. While pesticide particles carried by air may cause harm to people, your type of damage or damage to another's agricultural crops is the typical claim made and the typical measure of damages. More-so when they drift to organic crops.
Generally, plaintiff(s) must show that defendant(s) breached either the label instruction or a regulatory provision to succeed in recovering damages outside of common law. Typically, there are labeling instructions or regulatory provisions that limit spray drift.
Is he spraying whole fields such that you think he is purchasing commercial amounts?
If he is just spraying his small field or plot of land, you will have to establish a claim for trespass in order to recover damages. You also must be able to prove damages – e.g., veterinarian bills, loss of use of the animals for plowing or whatever. You have to have show the act (spraying), causation (the cause and effect) and damages (the actual effect to you that brought about specific damages) to make a claim. So far, you don't seem to have actual evidence of the act, although if you can acquire that, causation seems to be met, as well as the potential to show specific damages.
Unfortunately, the pain and suffering of animals does not have the same impact or carry any of the same rights as people incurring some sort of physical harm. It must be some actual quantifiable damage to you. Only you can determine what this is.
In neighborly disputes, the measure of damages is often not worth the cost of litigation. Sad but true.
As a plaintiff (if it comes to that), you'll need to establish trespass or another common law cause of action as a basis for the recovery. Or you could seek equitable relief (ask the court to order he stop the practice). These claims prove challenging for plaintiffs to establish because of the common usage of pesticides. Also, strict liability is generally not available as a cause of action. You may have a claim in nuisance, but you still must show those three elements of proof. There are typically laws that preempt negligence claims concerning labeling (like in the US), and remaining negligence claims tend to be difficult to prove, for the very reason you stated (you didn't see him do it but you know he did).
This means that in order to show you (or your chattel) were injured by spray drift you will probably have to file a claim in trespass. However, chemical spray drift is so intangible it is difficult for plaintiffs to meet the requirements for a trespass claim. States’ approaches to trespass for securing damages resulting from spray drift vary, and this can mean that a plaintiff must carefully plead interference with exclusive possession (your right to the land) together with injury meaning substantial property damages or damage that is physical, to establish their cause of action in trespass.