Single-molecule magnet with electrically-controlled permeability: How does the Titan Shield from Deus Ex work?
Is there any existing examples of single-molecule magnets with permeability that can be controlled via altering current flow just like in case of electromagnets? If not, is there an explanation why it is not possible?

Short answers: no, and not yet.
Longer answer, and a warning that I'm using recent results from my group as references:

Yes, single molecule magnets exist, but... The field of single molecule magnets is hot, but the working temperatures of single molecule magnets are still below liquid nitrogen. Things seem to be improving, but they do not seem to be improving a lot. See the plot below for how the maximum temperature at which long-term magnetic memory has been reported has improved over the years (for single-ion magnets based on lanthanides, which are the best single molecule magnets right now). While there is no consensus that room-temperature single molecule magnetism is impossible, it has not happened yet, and there is no explanation why it could not happen in the future.


Maximum magnetic hysteresis temperature vs year when the Single Molecule Magnet was reported. Plot generated dynamically by the SIMDAVIS (AGPL-3.0) web app: https://rosaleny.shinyapps.io/simdavis_dashboard/ [1]

Yes, magnetism in molecules can be controlled via electricity, but... In this work, and in several related works, Wernsdorfer and coworkers show electric control (and electric read-out) of the magnetic state of a single molecule magnet. [2] However, this happens at temperatures below liquid helium, and the machinery needed is only able to do this for a single molecule at a time. Furthermore, the device is so delicate that hundreds of attempts are needed to trap the molecule in the right configuration. If the device heats up by accident, the molecule is lost forever and one needs to start from scratch. Again, there is no solid reason why this could not be achieved at some point in the far future. As promised, an alternate way of coupling the magnetic (spin) state of molecules to electric current, reported recently by my group.[3] In this approach, molecular helicity can be used to generate magnetic current (like a molecular electromagnet), and in principle this could eventually be employed to control the magnetic state of a single molecule magnet (again, at some hypothetical point in the far future).

To complete the answer, while neodymium-based alloys behave very well, neodymium-based single molecule magnets are, so far, greatly outperformed by dysprosium, terbium and even erbium (see figure below). Since there are fundamental reasons for this, it is more likely that any future technology resembling the one described in the question will be based on dysprosium (as of may 2021 holding the record for highest temperature single molecule magnet) or terbium (the ion employed in the cited examples about electrical control of magnetism in molecules).



Maximum magnetic hysteresis temperature vs lanthanide ion. Plot generated dynamically by the SIMDAVIS (AGPL-3.0) web app: https://rosaleny.shinyapps.io/simdavis_dashboard/ [1]
References

Duan et al. Data mining, dashboard and statistical analysis: a powerful framework for the chemical design of molecular nanomagnets. Preprint at https://arxiv.org/abs/2103.03199 (2021).
Godfrin et al., Operating Quantum States in Single Magnetic Molecules: Implementation of Grover’s Quantum Algorithm,  Phys. Rev. Lett. (2017) 119, 187702, https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.119.187702
Torres-Cavanillas et al., Reinforced Room-Temperature Spin Filtering in Chiral Paramagnetic Metallopeptides, J. Am. Chem. Soc. (2020), 142, 41, 17572–17580, https://pubs.acs.org/doi/abs/10.1021/jacs.0c07531]