We know Magneto is able to affect even adamantium as shown when he extracts all the adamantium from Wolverine's body.
Is he also able to affect or control vibranium? Has that been shown in any Marvel comic or maybe a crossover with Captain America?
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Magneto is able to use his magnetic powers to affect adamantium which is thousands of time more difficult to manipulate once it has been set into a particular form. Vibranium has no such rigidity or claims of durability.
Vibranium may need specialized tools to manipulate, but has never been shown to be particularly difficult to shape or alloy with other materials.
Vibranium has been seen used in a variety of formats in the Marvel Universe. The Black Panther wore body armor comprised of it, had claws made with it and boots which could absorb vibrational energy making them silent and decrease the damage the Panther took from falls and the Constrictor used them in his weaponized cables.
Non-ferrous metals have been affected by his powers in the past, so there is no reason to believe, despite its properties, it would be any more able to resist than any other non-ferrous metal.
In the panel shown below, Magneto is seen using his magnetic powers to repel:
Mjolnir, the hammer of Thor, which is comprised of the extra-dimensional metal, Uru, and
the shield of Captain America, which is made of proto-adamantium (an undisclosed mixture of adamantium and vibranium) and one of the most durable substances on Marvel Earth-616.
He is able to do this effortlessly, so there is no reason to consider he would be less able to affect the pure form of the metal, should he be confronted by it.
Magneto cannot manipulate vibranium. I saw a edition of Uncanny X-men where he fought Black Panther and didn't not manipulate his suit. In fact, the vibranium suit stopped him from even manipulating the iron in Black Panther's blood.
Wow this is a really tough one. While there are a few instances back years ago where Magneto and Captain America interact, I could not locate ANY instance where Magneto even attempted to take or manipulate the Shield. Most of the interactions are either non-combat or Captain wins by talking Magneto down using his diplomatic skills.
So I cant reference any canon proof as to yes or nay on this but, Given that the prevailing theory as to the reality of Magneto's powers is that he can create and manipulate localized Electromagnetic fields, it would then stand to reason than even a unique material as vibranium could still be manipulated by Magneto's powers. In some cases Magneto clearly moves non-magnetic materials using his powers, so even if the vibranium resisted magnetism he could create localized fields around the shield and move it that way.
Hope this helps.