Low temperature two-dimensional behaviour of spin and orbital moments in Ni monolayers grown on Cu(0 0 1)

The Bloch T 3/2 law is obtained for three-dimensional magnons at low temperatures. When decreasing the dimensionality of the magnetic system, the 3/2 exponent is expected to be equal to one for two-dimensional (2D) systems. I present a theoretical sketch of 2D spin wave theory, in which a long magnon wavelength cutoff is introduced, connected to the lateral size of the 2D system investigated. I report a study by X-ray magnetic circular dichroism at the Ni L-edges on the onset of ferromagnetic order on 1.5 atomic Ni layers deposited on Cu(1 0 0), with spin and orbital moments’ dependence with temperature. A linear dependence is found for both spin and orbital moments with the same initial slope. This temperature dependence can be used to probe the size of the 2D magnetic islands, which is particularly useful for embedded 2D objects.