Your device is an analogue to a polarizing filter.
A polarizing filter is a passive device that allows some light to pass through it and blocks other light, depending on its polarization (the orientation of its waveform, loosely speaking). It is useful for when we want to selectively reduce a uniformly polarized component of incoming light (like the glare of reflected sunlight, for example) while allowing disorganized, ambient light to pass through in greater proportion.
Since you compare your "neural particles" to photons, perhaps you can handwave similar properties for them - analogues to wavelength, energy, and polarization - and have these properties contain the information that corresponds to the intention (or lack thereof) of the mind that generates them. Let's further handwave that the intent to do "magic" is encoded in the neural particles' "polarization"-analogue property.
Consider the following model:
1. A normal mind, or a mage's mind when not focusing on doing magic, produces neural particles (NPs) that are not polarized in any particular direction. Their polarization is distributed in relatively uniform randomness, and they all cancel each other out - no magic, deliberate or otherwise, is done.
2. A mage's mind, when focusing on an object with the intent to work magic upon it, bombards the object with a concentrated stream of NPs, all polarized in a particular direction which corresponds to the mage's intent. Unfortunately, due to an unhappy coincidence of physics (perhaps some sort of conservation law), NPs are always created in pairs with opposite polarization. So even though the mage is sending a beam of NPs that would accomplish the magic they desire, they are also unintentionally sending a beam that has the exact opposite effect. 70
So the two beams cancel out and no magic is done.
3. The same as case 2, but now the mage has positioned your device, made of the rare ore, in between their brain and the target object of their magic, in a specific orientation or using a specific configuration. The NPs polarized according to the mage's intentions pass through the device, reach the target and take effect, but the oppositely-polarized NPs are blocked by the device. Magic is accomplished!
Possible points to consider:
* Why the rare ore? How does the device work? Your rare ore, when processed with the proper metallurgy, forms a crystal lattice with the unusual property that it selectively blocks some NPs and passes others. However, it need not be passive filtering like a real-life polarization filter for light, where the only thing that matters is physical orientation. You're hand-waving the physics of the NPs, so you can choose to have the device need to have electricity or magnetic fields (or whatever else) applied to make it operative.
* If the unblocked beam's magic does work on an object, where does the blocked beam's energy go? If you want some elegance in your handwaved physics, perhaps your filter heats up as it blocks NPs, proportionally to how much work is done by the unblocked beam. Maybe your device would have a heat sink or cooling system attached to prevent it overheating and breaking or becoming ineffective.
* If this device blocks your own anti-magic, maybe it can block your opponent's magic. If magi are fighting each other, their devices may be useful not only to enable their own magic, but perhaps could also be used to protect themselves or other targets from an opponent's magic. 227