The Earth's magnetic field provides an important source of directional information for many living organisms, especially birds, but the sensory receptor responsible for magnetic field detection still has to be identified. Recently, magnetic iron oxide particles were detected in dendritic endings of the ophthalmic nerves in the skin of the upper beak of homing pigeons and were shown to fulfill the special prerequisites of a biological receptor. Here we study the proposed receptor theoretically and formulate the criteria for which it becomes operational and can be used for registering the weak magnetic fields as, e.g., the geomagnetic field, by a bird.