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Physics of Nanomagnets
Published in Klaus D. Sattler, 21st Century Nanoscience – A Handbook, 2020
Ralph Skomski, Balamurugan Balasubramanian, D. J. Sellmyer
The Stoner criterion describes the transition from metallic paramagnetism (PM) to itinerant ferromagnetism but does not address possible transitions from PM to AFM, nor does it address the competition between FM and AFM. Let us assume, for the moment, that there are stable atomic magnetic moments and compare FM order, Figure 18.1a, with AFM order, Figure 18.1b. In this case, we can use the Heisenberg model H=--2∑i>jJijSi⋅Sj-gμoμB∑iHi⋅Si
Picometer Detection by Adaptive Holographic Interferometry
Published in Klaus D. Sattler, Fundamentals of PICOSCIENCE, 2013
What is the cause of the AFM ordering? This question was addressed by DFT calculations. This method allows us to scrutinize the electronic band structure of an Fe ML on W(001) as a function of the interlayer distance d between film and substrate. Figure 22.17 shows a plot of the total energy and magnetic moment per atom versus distance for the non-magnetic, FM, and AFM solutions. At the largest distance considered ( 6 a.u.), the Fe film hardly "feels" the presence of the W atoms, and the DOS is very similar to that of a free-standing, unsupported ML, exhibiting a very large non-magnetic DOS right at the Fermi energy. But this matches the Stoner criterion for ferromagnetism, and indeed at this distance, the p(1×1) FM solution has the lowest energy. Reducing d increases the Fe-W hybridization, and the energies of FM and c(2×2) AFM solutions become degenerate. Relaxing the film further to its equilibrium d results in a huge energy difference in favor of the AFM solution. Due to Fe-W hybridization, the DOS distribution near the Fermi energy is strongly modified and resembles that of prototypical AFM MLs of Cr and Mn on noble metal (001) surfaces [50]. One can now explain why the Fe ML is FM on W(110) and AFM on W(001): the effect of hybridization is stronger on the (001) than on the (110) surface because the number of nearest-neighbor substrate atoms is four for each Fe atom on (001) but only two in the (110) case. It is well known that an induced spin polarization is present in the W atoms when Fe is deposited on the (110) surface, contributing to the in-plane anisotropy of the Fe ML on that surface. This effect is absent on the (001) oriented surface: for symmetry reasons the W atoms below the AFM layer cannot be polarized.
Magnetism of Dilute Oxides
Published in Evgeny Y. Tsymbal, Igor Žutić, Spintronics Handbook: Spin Transport and Magnetism, Second Edition, 2019
Having discussed the messages that the experimental data seem to convey, we now summarize the generic models that have been proposed for ferromagnetism in dilute magnetic oxides. There are six of them. Five depend on whether the spin magnetic moments are localized or delocalized, and the nature of the electrons involved in the exchange. The sixth does not involve spin ferromagnetism, but collective orbital paramagnetism. The DMS model [191]. There are well-defined local moments on the dopant cations, which are coupled ferromagnetically via 2p holes, or by RKKY interactions with 4s electrons.The bound magnetic polaron (BMP) model [193]. Here again, there are well-defined local moments on the dopants, but they interact with electrons associated with defects, which form an impurity band. Each defect electron occupies a large orbit and interacts with several dopant cations to form a magnetic polaron, and ferromagnetism sets in at the percolation threshold for these large objects.A variant of the model (BMP), [131] dispenses with the magnetic dopants, but retains the idea of localized moments, which are now associated with electrons trapped at defects. Triplet pairs could form to give S = 1 moments, which are then coupled by electrons in an impurity or conduction band.The spin-split impurity band (SIB) model [196], which is based on a local density of states associated with defects where the density of states at the Fermi level is sufficient to satisfy the Stoner criterion.The charge-transfer ferromagnetism (CTF) model [172, 197] is a related model with a defect-based impurity band, but there is another charge reservoir in the system that allows for the facile transfer of electrons to or from the impurity band to create a filling that leads to spontaneous spin splitting. In dilute magnetic oxides, this reservoir is associated with the dopant ions.Lastly, there is the possibility that the effects are not essentially related to collective spin magnetism at all, but that the saturating magnetic signal is due to giant orbital paramagnetism (GOP) associated with a new collective orbital state of the electrons. The magnetic moments are then induced rather than aligned by the field.
Pd–H and Ni–H phase diagrams using cluster variation method and Monte Carlo simulation
Published in Philosophical Magazine, 2019
Natacha Bourgeois, Pierre Cenedese, Jean-Claude Crivello, Jean-Marc Joubert
In comparison with Pd metal, Ni presents more localised d-bands structure and, without spin polarisation, the DOS at Fermi level is higher for Ni (4.5 states by eV). As a consequence, to reduce its DOS() to 1.8 (Stoner criterion), a ferromagnetic state is found more stable for Ni and the majority spin bands are almost filled. The electronic structure is affected by hydrogen absorption. In Ni–H system, electrons given by H lead to a progressive filling of the -Ni bands and to an increase of the DOS() up to a maximum at y=0.33 (corresponding to the filling of a peak in minority spin), before a decrease of DOS() with y. This is detrimental to the formation of intermediate compounds. On the contrary for PdH compounds, the DOS() decreases as a function of hydrogen concentration y, with respect to its values for Pd and PdH. As a consequence, the energy of mixing for Pd–H system is negative which explains the presence of stable ordered super-structures.