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 ...

The magnetization of three Pb 1Ϫx Eu x Se samples, with xϭ1.3,3.0, and 4.1 %, was measured at 30 and 50 mK in magnetic fields H up to 50 kOe, and at 0.6 K in fields up to 180 kOe. For xϭ1.3% and with Hʈ͓100͔, a magnetization step ͑MST͒ due to an energy-level crossing for isolated Eu 2ϩ ions was observed at 30 and 50 mK. The magnetic field at this MST, 1.76Ϯ0.2 kOe, was close to the predicted value H c ϭ1.98 kOe. At the same low temperatures ͑30 and 50 mK͒ but at higher fields, a magnetization ''ramp'' due to pairs was observed in all samples. For xϭ3.0 and 4.1 % this ramp consisted of well-resolved MST's arising from pairs. A ramp due to open triplets was also observed in these two samples. The MST's due to pairs were used to obtain the value J/k B ϭϪ0.24Ϯ0.03 K for the dominant antiferromagnetic exchange constant. Comparisons between the measured magnetization curves at 30 or 50 mK and theoretical simulations indicates that this J is the nearest-neighbor ͑NN͒ exchange constant J 1 . At 0.62 K the magnetization of each of the three samples rose rapidly with H in fields below several kOe. At higher fields a rounded ramp due to pairs and triplets was present. This ramp ended near 40 kOe, and complete saturation was achieved near 50 kOe. A model which includes only the NN exchange constant J 1 gave a reasonably good account for all the data at 0.62 K. Calculated magnetization curves for pairs, and for open and closed triplets, at various values of k B T/͉J͉ are presented. The effects of the single-ion and dipole-dipole anisotropies on the MST's due to pairs are also discussed.

Several exchange constants J i between Mn 21 ions which are not nearest neighbors were determined in Zn 12x Mn x X (X S, Se, Te) from magnetization steps at 20 mK. When the J i 's are listed in order of decreasing size, ratios between successive J i 's are material dependent, and differ from all predictions. The measured J i 's were identified by comparing the magnetization curves with simulations which assumed a random Mn distribution. Contrary to existing theories the second-largest exchange constant is not J 2 between next-nearest neighbors. The most likely alternative is J 4 , between fourth neighbors. [S0031-9007 (98)06413-8] PACS numbers: 75.30.Et, 75.50.Ee, 75.50.Pp, 75.60.EjThe distance dependence of the d-d exchange constants J i in dilute magnetic semiconductors (DMS's) has been discussed for more than a decade [1][2][3][4][5][6][7][8][9]. The focus has been on Mn-based II-VI DMS's with the zinc-blende structure. It has been established that the largest J i is the nearest-neighbor (NN) exchange constant J 1 . This J 1 is antiferromagnetic (AF), and is of order 210 K [5,6]. It is generally accepted that the second-neighbor (next-nearestneighbor) exchange constant J 2 , third-neighbor constant J 3 , etc., are all AF. What is at issue are the ratios J 1 : J 2 : J 3 : J 4 , etc.All existing theories, conjectures, and reported data as interpreted by their authors maintain that J 2 is the secondlargest exchange constant, after J 1 . The theory of Larson et al. [1] predicts that J 2 : J 1 , J 3 : J 2 , and J 4 : J 3 are all about 0.08. In the modified version by Rusin [9], J 2 : J 1 Х 0.08, and both J 3 and J 4 are less than 0.1J 2 . According to Bruno and Lascaray (BL), J 3 : J 2 J 4 : J 3 1͞2 (no prediction for J 2 : J 1 ) [4]. A power law dependence of J i on distance, J i~r

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Magnetization steps from Mn 2ϩ pairs in several single crystals of Zn 1Ϫx Mn x O (0.0056рxр0.030), and in one powder (xϭ0.029), were observed. They were used to determine the four largest exchange constants ͑largest J's͒, and the single-ion axial anisotropy parameter D. The largest two exchange constants, J 1 /k B ϭϪ18.2Ϯ0.5 K and J 1 Ј/k B ϭϪ24.3Ϯ0.5 K, were obtained from large peaks in the differential susceptibility, dM /dH, measured in pulsed magnetic fields H up to 500 kOe. These two largest J's are associated with the two inequivalent classes of nearest neighbors ͑NN's͒ in the wurtzite structure. The 29% difference between J 1 and J 1 Ј is substantially larger than 13% in Cd 1Ϫx Mn x S and 15% in Cd 1Ϫx Mn x Se. The pulsed-field data also indicate that, despite the direct contact between the samples and a superfluid-helium bath, substantial departures from thermal equilibrium occurred during the 7.4-ms pulse. The third-and fourth-largest J's were determined from the magnetization M at 20 mK, measured in dc magnetic fields H up to 90 kOe. Both field orientations Hʈc and Hʈ͓101 0͔ were studied. ͑The ͓101 0͔ direction is perpendicular to the c axis, ͓0001͔.͒ By definition, neighbors which are not NN's are distant neighbors ͑DN's͒. The largest DN exchange constant ͑third-largest overall͒ has the value J/k B ϭϪ0.543Ϯ0.005 K, and is associated with the DN at rϭc. Because this is not the closest DN, this result implies that the J's do not decrease monotonically with the distance r. The second-largest DN exchange constant ͑fourth-largest overall͒ has the value J/k B ϷϪ0.080 K. It is associated with one of the two classes of neighbors that have a coordination number z n ϭ12, but the evidence is insufficient for a definite unique choice. The dependence of M on the direction of H gives D/k B ϭϪ0.039 Ϯ0.008 K, in fair agreement with Ϫ0.031 K from earlier electron paramagnetic resonance work.

The title radical (F4BImNN) is a stable nitronylnitroxide that forms hydrogen-bonded NH... ON chains in the solid state. The chains assemble the F4BImNN molecules to form stacked contacts between the radical groups, in a geometry that is expected to exhibit ferromagnetic (FM) exchange based on spin polarization (SP) models. The experimental magnetic susceptibility of F4BImNN confirms the expectation, showing 1-D Heisenberg chain FM exchange behavior over 1.8-300 K with an intrachain exchange constant of Jchain/k = +22 K. At lower temperatures, ac magnetic susceptibility and variable field heat capacity measurements show that F4BImNN acts as a quasi-1-D ferromagnet. The dominant ferromagnetic exchange interaction is attributable to overlap between spin orbitals of molecules within the hydrogen-bonded chains, consistent with the SP model expectations. The chains appear to be antiferromagnetically exchange coupled, giving cusps in the ac susceptibility and zero field heat capacity at lower temperatures. The results indicate that the sample orders magnetically at about 0.7 K. The magnetic heat capacity ordering cusp shifts to lower temperatures as external magnetic field increases, consistent with forming a bulk antiferromagnetic phase below a Néel temperature of TN(0) = 0.72 K, with a critical field of Hc approximately 1800 Oe. The interchain exchange is estimated to be zJ/k congruent with (-)0.1 K.

Mixtures of 2-(4,5,6,7-tetrafluorobenzimidazol-2-yl)-4,4,5,5-tetramethyl-4,5-dihydro-1H-imidazole-3-oxide-1-oxyl (F4BImNN) and 2-(benzimidazol-2-yl)-4,4,5,5-tetramethyl-4,5-dihydro-1H-imidazole-3-oxide-1-oxyl (BImNN) crystallize as solid solutions (alloys) across a wide range of binary compositions. (F4BImNN)(x)(BImNN)((1-x)) with x < 0.8 gives orthorhombic unit cells, while x ≥ 0.9 gives monoclinic unit cells. In all crystalline samples, the dominant intermolecular packing is controlled by one-dimensional (1D) hydrogen-bonded chains that lead to quasi-1D ferromagnetic behavior. Magnetic analysis over 0.4-300 K indicates ordering with strong 1D ferromagnetic exchange along the chains (J/k = 12-22 K). Interchain exchange is estimated to be 33- to 150-fold weaker, based on antiferromagnetic ordered phase formation below Néel temperatures in the 0.4-1.2 K range for the various compositions. The ordering temperatures of the orthorhombic samples increase linearly as (1 - x) increases from 0.25 to 1.00. The variation is attributed to increased interchain distance corresponding to decreased interchain exchange, when more F4BImNN is added into the orthorhombic lattice. The monoclinic samples are not part of the same trend, due to the different interchain arrangement associated with the phase change.

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