Very fine particles reverse their magnetization spontaneously, passing the energy barrier by means of thermal activation. In the same way one could argue that small portions of larger particles could be spontaneously reversed, thereby serving as nucleii for reversed domains. These can then grow, because it is known that the energy favors subdivision into domains. In treating such a possibility, however, one should take into account the additional barrier for forming a wall around the ``nucleus,'' which is usually left out in standard domain theory calculations when the wall energy is used. This energy is rather small but the barrier for formation of the wall is large.The model studied is a small sphere, centrally located inside a spherical particle, the magnetization in which starts to rotate gradually from thezdirection in which the rest of the particle is magnetized. The angle between magnetization and thezaxis is assumed to vary linearily in the radial coordinate, from zero on the surface of the inner sphere, to its maximum value in the center. This value eventually reaches &pgr;, thus completing a wall around a reversed domain of radius zero, which should then start to grow by further supply of energy.Studying the energy barrier for such a process, it is seen that the main contribution is from the exchange energy, which practically forbids the process. The probability for a domain wall to nucleate at room temperature is thus shown to be negligibly small, which justifies the neglection of temperature affects in Brown's equations.