Magnetite, $\ce{Fe3O4}$ is able to capture $\ce{As(III)}$ and $\ce{As(V)}$ from drinking water through the following mechanisms.
Bidentate-binuclear complex
Monodentate-binuclear complex (both from here)
I'm assuming these are standard reactions in inorganic chemistry, but are there known mechanisms (I don't have a text available)? The first looks like an attack on the $\ce{As}$ by the $\ce{O}$, but the second seems to take place in two steps.
Unfortunately there are no (or only very hard to find) studies to the mechanism of the actual sorption of arsenic (acids) to magnetite. Most literature does describe it as a simple Ligand exchange, although I find that hard to believe. From what I have read[1-4] I will try to compose some hints on what may happen.
First of all lets have a look at arsenic acid. It is a medium strong acid and a quite well oxidising agent. \begin{align}\ce{ H3AsO4 &\equiv AsO(OH)3\\ AsO(OH)3 + H2O &<=> H3+O + AsO(O^- )(OH)2\\ AsO(OH)3 + 2H3+O + 2e- &<=> As(OH)3 + 3H2O }\end{align}
In presence of any electron rich material and acidic environment it will therefore not be unusual that arsenous acid will be formed.[5] We may therefore also focus on this, amphoteric molecule: \begin{align}\ce{ H3AsO3 &\equiv As(OH)3\\ As(OH)3 + H3+O &<=> As+(OH)2 + 2H2O\\ As(OH)3 + {}^{-}OH &<=> AsO^{-}(OH)2 + H2O }\end{align}
Depending on the pH of the solution one would expect to find many of different of these species. Arsenic is also somewhat oxophil, meaning that the $\ce{As-O}$-bond is quite strong.
The magnetite in aqueous solution reacts basic, also forming complex like structures or hydroxides, for example this fully hydrated cluster (ref. [2], stoichiometry omitted): \begin{aligned}\ce{ Fe3O4 + $x$\, H2O &<=> Fe2(OH)2(H2O)8^4+ }\end{aligned}
Of course one has to pay attention, that the used ferric nano particles for sorpting arsen(o)ic acid(s) are far larger than the used model complex. However, we can see, that there are functional groups like $\ce{-OH}$ or $\ce{-OH2+}$ (or maybe even $\ce{-O-}$) covering the surface.
Using this as prerequisites we can think about what might happen next. I generally would suggest to start with physisorption, i.e. the cluster and the acid molecules come in close range. Since we are dealing with contaminated water it is maybe safe to assume, that we can deal with soluble salts of arsenoic acid, hence focusing on $\ce{AsO3^{3-}}$.
When the complexes come into close range hydrogen bonds will form, with $ \newcommand{\nanoFe}{\bbox[lightgrey,3pt,border:1px solid black]{\ce{Fe}}} \nanoFe$ being the nano particle: $$\ce{\nanoFe-OH\cdots{}O-AsO2^{3-}}$$
Since the whole surface is covered with hydroxide groups, several of these hydrogen bonds may form. As we can see, with this we may now enter the realm of chemisorption. Once these complexes have formed, it is from an entropic point of view favoured to release smaller molecules, water in this case. Also the oxygen atoms bound to arsenic are now in close range to iron atoms. Since we are dealing with nano particle, there will be non-coordinated irons in proximity. This allows for a more permanent complet to form: $$\ce{\nanoFe-O-AsO^3- -O\cdots{}HO-\nanoFe}$$
With this monodentate complex we have an already stable complex of a bound arsenic to an iron. It is furthermore possible, and probably favoured, to form a bidentate complex with a somewhat similar mechanism.
Let us also consider a more basic scenario. In this case the surface of the magnetite will not be entirely covered with hydroxide atoms, but more freely accessible oxygen atoms will be present. Direct bond formation between $\ce{\nanoFe-O\cdots{}AsO3^{3-}}$ may occur.
After writing all this I also found a credible source that somehow proves my theory. In “Understanding Arsenate Reaction Kinetics with Ferric Hydroxides”[6] they used a model system of $$\ce{HAsO4^2- + Fe2O10H15+ -> Fe2O10H15-HAsO4-}$$ to explain the mechanism.
In this they describe that physisorption is barrierless, leading fast to the adduct that is $\Delta G^\circ_\mathrm{r}=-58~\mathrm{kJ/mol}$ more stable in energy. However, chemisorption and developing the equilibrium is a more lengthy process.
When the formed complexes become neutral, the activation barrier to release arsenate is very high, compared to adsorption. I will stop right here, please read the publication for further details.
You are talking about standard acid base reactions and formation of a salt (more covalent than ionic), so you can have an educated guess about the mechanism just thinking through what happens here:
As(III) and As(V) are simple inorganic (weak) acids, where a proton jumps up and down from the O. In literature, you may find estimations about the frequency about this jump. If not I would just use pKs and similar data of e.g. phosphoric acid to have an idea about the magnitudes.
The magnetite surface is a (weak) base, so the OH can accept a proton somewhere. The formed water stays there as a water ligand on Fe, or something kicks it out and dissociate.
Since both are weak, my guess would be that neither the unprotonated As acid nor the protonated magnetite surface is a dominant species. More probably the undissociated proton of the As-acids would attach to the OH of magnetite, and help to kick out the water while forming a salt. This salt is unlike NaCl or similar, and the Fe-O-As has a strong covalent character.
