The magnetism of epitaxial Er films up to 1 pm thick differs from bulk Er in that no ferromagnetic transition is observed. Above a critical field that depends on temperature and film thickness the magnetization saturates at the bulk value. Both neutron scattering and magnetization data show lock-in transitions, but at lower temperatures than in the bulk. We have demonstrated in recent years [I] and in a paper on Er/Y at this conference [2], that rareearth multilayers, grown with crystalline perfection by molecular-beam epitaxy, have properties distinctly different from the bulk elements. Here we show that many of the property changes are consequences of the 4 epitaxy itself, rather than of the multilayer structure. $47 Er films of various thicknesses were grown epitaxia ally by first growing a layer of (110) Nb on sapphire, then a 300 A film of (0001) Y, and finally Er films o ranging in thickness from 400 A to 9500 A. All of the samples show excellent crystalline Bragg peaks, with cand a-axis lattice parameters within 0.6 % of those of bulk Er. Nonetheless, even the thickest films are magnetically distinct from the bulk. The Er samples are not lattice matched to Y (2 % difference). Dislocations formed during film growth permit the samples to relax toward bulk lattice parameters. However, the films remain clamped to the substrate, as a result of which no magnetoelastic deformation is possible in the growth plane without irreversible damage to the sample. Bulk Er orders in a sinusoidal c-axis -modulated (CAM) structure at 89 K, with a phase advance of approximately 52.5' per Er plane. Below 50 K, a basal plane spiral appears, the c-axis modulation becomes more square-wave-like and the CAM and spiral undergo a series of phase transition to unique lock-in states [3]. The lines in figure 1 indicate the phaseadvance per Er layer for the lock-in states, with the x's indicating the temperatures at which they first appear on cooling (nomenclature of Ref. [3]). At 20 K, the c-component of the magnetization becomes ferromagnetic, while the spiral remains. While some features of bulk Er are observed in epitaxial Er films, there are significant differences. Most notably, no c-axis ferromagmetic phase is observed to the lowest temperatures studied (4.2 K). The results of a neutron scattering study of the CAM structure in two representative thin films of 1750 A (circles) and I I I I I 10 20 30 40 50 Temperature (K) Fig. 1. Lock-in states us. temperature for bulk Er (x), 1750 A (circles), and 9500 A (triangles). 9500 A (triangles) are shown in figure 1. Both samples show a variation of wave vector with temperature, and each seems to pass through several of the lock-in states of bulk Er. However, the CAM structure persists below 10 K in each case. Each lock-in state appears at a lower temperature in the thin films than in the bulk and, further, the films fail to follow the entire sequence of lock-in states observed in the bulk. The presence of lock-in transitions is also evident in magnetization data. In figures 2a and 2b, we show, respectively, the magnetization of a 1750-A and a 9500-A film, each cooled in a field of 2 kOe. Both films show a small maximum at TN = 85 K, indicating the onset of the CAM phase, followed by oscillations in magnetization. The saturation magnetization of both samples is 230 f 10 emu/g, comparable to that of bulk Er, and appears abruptly above a temperature-dependent critical field. The number, amplitude, and position in temperature of the oscillations depend sensitively on film thickness and growth conditions. A 4000 A film grown under slightly different conditions (and with an ;axis lattice parameter identical to bulk Er) shows only a smooth increase in magnetization under the same measurement conditions. 'permanent address: Kamerlingh Onnes Laboratorium, Leiden, the Netherlands. 2 ~ a t i o n a l Bureau o f Standards, Gathersburg, M D 20877, U.S.A. Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19888764 C8 1686 JOURNAL I IE PHYSIQUE Temperature (K) Temperature (K) Fig. 2. Field-cooled magnetization (2 kOe) for 1750 A (a) and 9500 A (b) films. Neutron scattering data were taken on the 9500 Afilm in a 2 kOe field at temperatures corresponding to the extrema in figure 2b. The minima at 10 K and 32.K are consistent with the 112 and 3/11 lockin states, while the maximum at 20 K has a phase advance close to the 5/19 state. The observed phase advances appear to be systematically 0.3' larger than those of the lock-in states reported by Gibbs et al. The maximum in magnetization observed at 38 K is puzzling. It corresponds to a phase advance of 50.5', which is not one of the expected lock-in states. What is more, this state appears to be particularly stable in an applied field. At 30 K, the structure changes from the 48.4'-phase advance to the 50.5' advance at an applied field near 10 kOe; at still higher applied fields (> 35 kOe), the CAM structure is destroyed and the full bulk magnetic moment is observed. The so-called antiferromagnetic next nearest neighbour Ising (ANNNI) model was explicitly invented to explain the behaviour of Er. More recently, the model has extended to include a magnetic field [4]. The already rich phase structure of the ANNNI model becomes even more complicated in the presence of a field. We have considered a simple model of Ising spins on a cubic lattice with ferromagnetic coupling Jo between neighboring spins on a horizontal plane, J1, between neighboring spins on successive planes, and an antiferromagnetic interaction J2, between spins on nextneighbor planes. The ratio p = 52 controls the magnetic phase diagram. For p 0.5, the ground state is the antiferromagnetic (22) state (two up, two down). We have solved the coupled equations for a 264-layer system and calcu1ate.d the Gibbs free energy for all possible starting configurations. In figure 3, we plot the magnetization of the lowest energy state as a function of temperature at various magnetic fields for p = 0.55. At low fields (triangles), the magnetization has a maximum at 0.4 TN. Doubling the field (x's) leads to a ferromagnetic low-temperature state without intermeTemperature (arb. units) Fig. 3. Lowest energy states in the ANNNI model for p = 0.55 at fields of h = 0.1 (triangles); and h = 0.2 (x's). diate phases. This behaviour is qualitatively, and even semiquantitatively, similar to that observed in Er films. Why, if the ground state of ANNNI systems is antiferromagnetic, does Er have a ferromagnetic ground state? We have, in the ANNNI model, ignored the important contribution of magnetostriction, which possibly decreases p and thus favors ferromagnetism in Er. The minimization of the magnetoelastic energyrn bulk Er results in c-axis contraction and concomitant expansion in the basal plane. However, the clamped epitaxial condition restricts the magneto-elastic energy gain with the result that exchange energy is more important in epitaxial Er films. The ferromagnetic phase can be induced by an applied field in a completely reversible process. This suggests that no plastic deformation takes place. The critical internal fields required to induce ferromagnetism at 10 K decreases from 8 kOe for a 860-A film to 3 kOe for a 9500 A film. While we have not yet determined whether this decrease is continuous or occurs as a step at a well defined thickness, it is clear that films up t o 1 pm in thickness are still mostly clamped and behave differently from bulk Er. Further studies are underway to understand the relationship t o bulk behaviour.