In 'The Twelve Dancing Princesses', what magical item helps the soldier spy on the princesses?

In “The Twelve Dancing Princesses,” a cloak of invisibility helps the soldier spy on the princesses. An old woman gives him the cloak after warning him not to drink the drugged wine they will offer.

The king has promised that any man who discovers where his twelve daughters go each night may marry one of them and inherit the kingdom. Earlier suitors fail because the princesses secretly leave their locked bedroom and dance in an enchanted underground kingdom. Many unsuccessful challengers are executed.

The soldier avoids the wine by pouring it into a sponge hidden beneath his chin. When the princesses leave, he puts on the invisibility cloak and follows them without being seen. He observes the silver, gold, and diamond trees, crosses the lake with the princesses, and enters the palace where they dance with twelve princes.

The Grimm tale was published in 1815 as KHM 133. It is also called “The Worn-Out Dancing Shoes.” The cloak belongs to a broader folklore tradition of magical garments that conceal their wearer, distinct from the seven-league boots or magic carpets found in other stories.