Spin-Wave Dispersion Relations in Ferromagnetic Fe-Si Alloys

Antonini, B.; Menzinger, F.; Paoletti, A.; Tucciarone, A.

doi:10.1103/physrev.178.833

Cited by 20 publications

(5 citation statements)

References 13 publications

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“…The evolution of bulk bcc Fe is also shown for comparison k can be written as ϭDk 2 , where D is the exchange stiffness constant that takes a value of Dϭ0,281 eV Å 2 for bcc Fe. 5 Note that in a ribbon with length l, width w and thickness t the incompatibility of the large wavelength, , spin waves with the reduced system dimensions leads to the following dependence of the number of magnons on : For l Ͼ Ͼw, k is constrained to be a vector lying along the longitudinal direction. For wϾ Ͼt, k behaves as a twodimensional ͑2D͒ vector lying in the plane defined by l and w. Finally, for tϾ , k becomes a 3D vector similar to the bulk material case.…”

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confidence: 99%

Spin-wave excitations in ribbon-shaped Fe nanoparticles

et al. 2004

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It has been found that in highly anisometric ribbon-shaped Fe particles with nanoscale dimensions that the magnetization decreases with temperature markedly faster than in bulk bcc Fe. This anomalous dependence, which becomes more remarkable as the length-to-cross section ratio increases, arises from the elongated shape of the particles. The analytical approximation performed on the thermal spectrum of magnons, compatible with the sample dimensions, unravels the correlated influences of shape and size on the thermal decreasing rate of magnetization. DOI: 10.1103/PhysRevB.69.012403 PACS number͑s͒: 75.30.Ds, 61.46.ϩw, 75.50.Bb, 75.50.Tt It has been observed that some magnetic properties considered as intrinsic when measured in the bulk exhibit an anomalous behavior when the size of magnetic entities decreases down to the nanoscale. 1 In particular, the thermal dependence of the magnetization deviates from that expected from the Bloch law. 2 Since in very small size particles magnons with wavelengths larger than the particle dimensions cannot be excited, a threshold of thermal energy is required to create spin waves. In this paper we present a nanoscale effect linked to the shape of very small particles. Opposite to the consequences of the known size effect, 2 which essentially contributes to stabilizing the magnetization, the shape effect analyzed here leads, in the low temperature range, to a decrease of the magnetization with temperature which is faster than that measured in bulk samples.The experimental magnetic behavior of wire shaped Cu-15 vol % Fe composite alloys, produced by the heavy working of spray-deposited billets, has been analyzed. A detailed description of material fabrication has been reported elsewhere. 3 With the cold working proceeding the spheroidal Fe particles, about 1 m in size, become drawn into elongated, flattened ribbons oriented along ͗110͘ direction with progressively smaller cross sections. Due to the high and positive enthalpy of mixing that characterizes the Fe-Cu system it is expected that Fe and Cu have not reacted, forming a FeCu solid solution. 4 Transmission electron microscopy shows that the thickness of the Fe ribbons decreases with the increase of the drawing strain from 14 nm down to 3.5 nm, while the ribbons width drops from 260 nm down to 27 nm. Hereinafter, the studied samples will be identified by their drawing strain measured by the wire diameter after drawing, ⌽.A magnetic characterization below room temperature was carried out by means of a superconducting quantum interference magnetometer, under a maximum applied field of 5 T strong enough to saturate the samples. Figure 1 shows the thermal dependence of magnetization M, measured in all the composite samples. Data corresponding to bulk bcc Fe were also included in the figure.It should be remarked from Fig. 1 that the magnetization of the composites decreases with T much faster than in bulk Fe. In addition, as the length-to-cross section ratio increases the magnetization decreasing rate enhances and deviates fro...

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Spin-wave excitations in ribbon-shaped Fe nanoparticles

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“…where z z a , , 1 2 1 and a 2 are the coordination number and the distance of the 1st and 2nd neighbor, respectively. The evaluated spin wave stiffness is presented in table 4, and the observed decreasing trend with the inclusion of vacancies follows the results of the neutron scattering experiments [48] and combined molecular-spin dynamics simulations (MD-SD) [49]. The results from table 4 are compared with the values of D(r) from the literature [35], and it can be seen that only at r ∼ a 0 , the value of Ni is lower than Fe.…”

Section: J Jmentioning

confidence: 61%

Influence of vacancy type defects on the exchange integrals in ferromagnetic metals: a Monte-Carlo-based approach

Billgates,

Joseyphus

2024

Phys. Scr.

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Estimating exchange interactions in real systems, particularly with defects like vacancies and impurities, poses significant challenges. A classical Monte-Carlo spin simulation within an atomistic machine-learning framework is utilized to predict the pairwise exchange interactions in ideal and defective bcc Fe and fcc Ni systems. The results closely replicate the experimental Curie temperature, with a reduction in exchange interaction by ~1 meV for the system with cluster vacancy concentration up to 6 %. An exponential relationship is established between the classical rescaling parameter α and microscopic exchange interaction enhancing α up to 3.35 and 2.5 in Fe and Ni, respectively. Additionally, the spin wave stiffness constant calculated using the near neighbor Heisenberg model demonstrates a dampening in both Fe and Ni with the inclusion of cluster vacancies.

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“…Graham [4] presented measurements only at two points below room temperature (77 and 195°K), and Argyle et al [5] in the region 4-29°K only. The stiffness constant was found to decrease with the decrease of Curie temperature or the increase of silicon content in silicon-iron steels [2,[6][7][8].…”

Section: Introductionmentioning

confidence: 95%

“…Most of the studies were mainly concerned in the range below room temperature. Antonini measured spin-wave dispersion relations in Fe0.93-Si0.07 and Fe0.85-Si0.15 steels by means of the so-called diffraction method in conjunction with polarised neutrons at room temperature [2]. Using FMR and FMAR methods, the saturation magnetisation of 3% silicon-iron single crystals was measured between 3.5 and 300 K [3].…”

Section: Introductionmentioning

confidence: 99%

Modelling of temperature dependence of saturation magnetisa-tion of silicon-iron steels

Shirkoohi

2017

2017 IEEE International Magnetics Conference (INTERMAG)

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The temperature dependence of saturation magnetisation of commercial 0.1 to 3 wt. % silicon steels is first measured using an air-cored solenoid and then modelled using a linear formula in accordance with the spin-wave theory, over the range of 20-100°C and in 100 KA/m applied field. The samples measured were heated by applying a heavy ac current along their length, and the measurement of temperature was made using thermocouples. The paper discusses the effect of temperature variation on magnetisation in high field regime approaching saturation in several grades of electrical steel.

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Spin-Wave Dispersion Relations in Ferromagnetic Fe-Si Alloys

Cited by 20 publications

References 13 publications

Spin-wave excitations in ribbon-shaped Fe nanoparticles

Spin-wave excitations in ribbon-shaped Fe nanoparticles

Influence of vacancy type defects on the exchange integrals in ferromagnetic metals: a Monte-Carlo-based approach

Modelling of temperature dependence of saturation magnetisa-tion of silicon-iron steels

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