Finite-Size Effect on Magnetic Ordering Temperatures in Long-Period Antiferromagnets: Holmium Thin Films

Abstract

The thickness dependence of the helical antiferromagnetic ordering temperature T(N) was studied for thin Ho metal films by resonant magnetic soft x-ray and neutron diffraction. In contrast with the Curie temperature of ferromagnets, T(N) was found to decrease with film thickness d according to [T(N)(infinity)-T(N)(d)]/T(N)(d) proportional variant (d-d(0))(-lambda(')), where lambda(') is a phenomenological exponent and d(0) is of the order of the bulk magnetic period L(b). These observations are reproduced by mean-field calculations that suggest a linear relationship between d(0) and L(b) in long-period antiferromagnets.

Structure and magnetism of Tm atoms and monolayers on W(110)

“…Extrapolating the thickness dependence of the Curie temperature leads to vanishing magnetic order for Gd films thinner than 3 monolayers (ML) [7]. Similarly, in Ho/W(110) thin films, resonant magnetic soft x-ray and neutron diffraction experiments [10] have shown that the helical antiferromagnetic ordering temperature T N decreases with the film thickness following a modified power law with an offset of about 11 ML, below which the long-period basal plane antiferromagnetic structure is not possible. It is worth mentioning that the decrease of the order temperature with thickness in these RE is stronger than in the case of transition-metal ferromagnets [41,42].…”

“…Interest in low-dimensional rare-earth (RE) magnetic structures has grown steadily in recent years, focusing on single atoms as model quantum spin systems [1][2][3][4][5] as well as ultrathin films that display either ferromagnetic [6][7][8][9] or antiferromagnetic [10] order when grown on nonmagnetic substrates. Ultrathin RE magnetic films and multilayers have also attracted attention due to their ability to induce perpendicular magnetic anisotropy in adjacent transition-metal layers [11], control magnetic damping in spin valve devices [12,13], as well as fabricate materials with higher magnetization compared to transition-metal alloys [14,15].…”

Size Dependence of Structures and Properties of Magnetic Materials

“…For thin Cr films, D 0 = 4.2 nm [252] suggests a close relation to the bulk period of the spin-density wave of 6 to 7.8 nm [254], and the separation of the finite-size effect in these multilayers is impeded by the strong influence of the interfaces. The magnetic behavior of thin Ho films closely resembling that of Cr [252] can be observed with a particularly interesting difference: D 0 = (10.8±0.5)h nm for Ho is much closer to the period of the bulk AFM superstructure than for Cr/Fe system [128].…”

“…This results in the inherent size dependence. For free-standing AFM nanocrystals, or AFM nanocrystals embedded in or supported by nonmagnetic matrix, their T N (D) continuously decreases with dropping D due to also the increase of surface/volume ratio as observed in systems of FeF 2 /ZnF 2 [230,231] superlattices, and CoO/SiO 2 [232,233], CoO/MgO [234], NiO/MgO [234,235], Ho/Nb/Y, Ho/Y/Nb [128] thin films, as well as NiO [236], CoO [237] and MnO [238] nanoparticles, and CuO nanoparticles [239][240][241][242], nanorods [242]. Compared with the superlattices of AFM layers with nonmagnetic interlayers [243,244], because of the interlayer magnetic coupling [245][246][247][248], weaker finite size effect for the superlattices of AFM/AFM insulators with exhibiting single transition temperatures have also been observed in the superlattices systems of FeF 2 /CoF 2 [249] and NiO/CoO [250] measured by thermal expansion and magnetic susceptibility, respectively.…”

Magnetoelectric effects due to elastic coupling in ferroelectric/ferromagnetic multilayers

“…Such a formulism has been introduced by de Gennes to empirically consider surface problems in superconductivity. 21 Generally speaking, the change in the density of states at the Fermi level on surfaces and interfaces in ferromagnetic thin films [22][23][24] also suggests that there should also be a change in the magnetization on the surfaces of the ferromagnetic thin films. It may therefore be proper to introduce a similar parameter ␦ m to account for the interface effect on ferromagnetic phase transition.…”