Theoretical and numerical model for estimating unknown magnetic parameters in studying ferromagnetic and antiferromagnetic coupled films Influence of exchange energy and magnetic anisotropy on the nanocrystalline alloy A magnetic cluster is a group of magnetic ions ͑''spins''͒ that interact with each other but which, to a good approximation, do not interact with other magnetic ions. Such clusters are responsible for many of the interesting and useful properties of a large number of molecular crystals, and of dilute magnetic materials below the percolation concentration. In a molecular crystal the magnetic clusters are usually all of one type. In a dilute magnetic material, on the other hand, many cluster types are present. The magnetization-step ͑MST͒ method is a relatively new form of spectroscopy for measuring intracluster magnetic interactions, mainly exchange constants and anisotropy parameters. In dilute magnetic materials this method also yields the relative populations of different cluster types. This review focuses on the principles and applications of the MST method to relatively small clusters, no more than a dozen spins or so. It covers only MSTs from spin clusters in which the dominant exchange interaction is antiferromagnetic ͑AF͒, and MSTs from isolated magnetic ions. Such MSTs are the result of changes of the magnetic ground state, caused by energy-level crossings in a magnetic field H. At a sufficiently low temperature, each change of the ground state leads to a MST. Magnetic clusters may be classified by size. The smallest is a ''single,'' consisting of one isolated magnetic ion. Next are ''pairs'' ͑dimers͒, followed by ''triplets'' ͑trimers͒, ''quartets'' ͑tetramers͒, etc. Although the classification by size is useful, clusters of the same size may have different intracluster interactions, and also different geometrical shapes. More detailed classifications of magnetic clusters are therefore also needed. A cluster ''type'' specifies both the size of the cluster and the set of all intracluster magnetic interactions which are nonzero. Different geometries of clusters of the same type correspond to different ''configurations.'' MSTs from isolated spins ͑singles͒ are discussed first. When subjected to certain types of single-ion anisotropy, e.g., uniaxial hard-axis anisotropy, singles give rise to MSTs. Examples of anisotropy parameters which were determined from such MSTs are presented. An interesting application of MSTs from singles is the determination of the populations of Jahn-Teller distortions which are energetically equivalent at Hϭ0 but are inequivalent at finite H. For clusters larger than singles, the strongest intracluster interaction is usually the isotropic exchange. Using a model with one isotropic exchange constant J, predictions for MSTs from pairs, open and closed triplets, and the six possible types of quartets, are presented. Observations of some of these MSTs, and the exchange constants derived from them, are discussed. Recent studies of MSTs from AF rings in molecular crystals ...