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Nanomagnetic Materials
Published in Ram K. Gupta, Sanjay R. Mishra, Tuan Anh Nguyen, Fundamentals of Low Dimensional Magnets, 2023
P. Maneesha, Suresh Chandra Baral, E. G. Rini, Somaditya Sen
Magnetism is governed by the exchange interaction, which is responsible for setting up magnetic order. Due to the indistinguishability of the electrons, there is no classical analogy for this quantum effect. A spin-spin exchange interaction between two contiguous spins, Si and Sj, can be described by the Hamiltonian H = −2J Si·Sj, in which J is the exchange constant, which indicates the value of the interaction known as the Heisenberg Hamiltonian. This describes several magnetic aspects of materials, especially insulators. The energy of a pair of spins is Eexpair= −2J Si·Sj and the angle between the two spins i and j as θ (i, j) = Δθ, Eexpair= −2J S2 cosΔθ ≈ J S2(Δθ)2, where the approximation cos Δθ ≈ 1−(Δθ)2/2! has been used by neglecting terms independent of θ.
Spin Transport in Hybrid Nanostructures
Published in Evgeny Y. Tsymbal, Igor Žutić, Spintronics Handbook: Spin Transport and Magnetism, Second Edition, 2019
Saburo Takahashi, Sadamichi Maekawa
In this section, we demonstrate that the spin exchange interaction between local moments and conduction electrons at the interface of normal metal and ferromagnetic insulator plays a vital role for the spin current across the interface. Making use of spin correlation functions and fluctuation‑dissipation theorem, we derive a formula for the spin current through the interface, and discuss the conversion efficiency of the spin currents.
Multiferroic and phonon properties near the phase transitions of pure and ion-doped Ca3Mn2O7
Published in Phase Transitions, 2021
A. T. Apostolov, I. N. Apostolova, J. M. Wesselinowa
The magnetic subsystem is described by the Heisenberg model: where is the spin–operator for the localized spins of the Mn ions with S = 3/2 at site i. stays for the spin exchange interactions between nearest-neighbors whereas between next-nearest-neighbors. is the constant of the single-ion anisotropy which is much smaller than . is an applied external magnetic field. x is the ion doping concentration. is the spin–operator for the doping ion and is the spin exchange interaction between the Mn and the doping ion.
Visible light photocatalytic activity of Mn-doped BiFeO3 nanoparticles
Published in International Journal of Green Energy, 2020
Caroline Ponraj, G. Vinitha, Joseph Daniel
where ω = ½ [(Π)-(Fe-O-Fe)] and dFe-O = Fe-O bond length. The bandgap is related to W as Eg = ∆-W, where ∆ is the charge-transfer energy. Fe-O bond length of rhombohedral phase is larger than orthorhombic phase and hence the decrease in effective bandgap energy can be a result of increase in the value of W indicating that Mn-doping increases orthorhombic phase (Athena et al. 2018; Radaelli et al. 1997). Similar results have been reported by Irfan et al. (2016). According to their studies, one of the reasons for the reduction in bandgap energy might be due to the metal ion doping which introduces an impurity level that may be an acceptor or donor level near the valence or conduction band leading to the decrease in the bandgap. The other reasons include the sp-d spin-exchange interaction between the manganese ions & the band electrons and the oxygen defects created in the system by doping. Hence, this reduction in bandgap with decreasing crystallite size (52–20 nm) can be attributed to the competing effects of micro-strain, columbic interactions and oxygen defects.
Chalconoid metal chelates: spectral, biological and catalytic applications
Published in Journal of Coordination Chemistry, 2019
The spin exchange interaction between Cu(II) centers is negligible (G > 4). Pyridine-based chalcone ligands DMAPP (see 17, Scheme 2) and DMEAPP (see 97, Figure 24) and their copper nanoparticles were prepared. The G value of DMAPP (see 17, Scheme 2) and DEAPP Cu(II) complexes are 2.15 and 2.0994, respectively, showing spin exchange interaction of Cu(II) in the solid state. The hyperfine splitting signal is absent, instead only a single signal appeared due to the strong dipolar and exchange interaction between Cu(II) ions in the unit cell [45]. The ESR data in pyridine solution reveal adduct formation; however, no nitrogen hyperfine splitting was observed [88]. ESR spectra of CuL2 (L = (E)-3-(3,5-dibromo-2-hydroxyphenyl)-1-(2-hydroxyphenyl)prop-2-en-1-one) (see 47, Figure 13) suggest square planar complex with the unpaired electron predominantly in the dx2–y2 orbital. The axial symmetry parameter value (G) was greater than 4 and there is no interaction between metal centers in the solid state [89].