Crystal electric field parameters determination for R_{2}Fe_{14}B compounds based on Yamada-Kato model

Semi-empirical model developed by Yamada-Kato enables calculation of magnetic spin directions for R_{2}Fe_{14}B compounds, based on minimization of free energy, and – in further steps – determination of spin reorientation temperatures for transitions from basal plane to axial easy magnetization direction. In our study, this model has been successfully used to determine crystal field and exchange field parameters for Er_{2-x}Ce_{x}Fe_{14}B compounds based on spin reorientation temperatures obtained experimentally from Mössbauer measurements

Search for canted spin arrangement in Er2−xTbxFe14BEr_{2-x}Tb_{x}Fe_{14}B with Mössbauer spectroscopy

The materials studied were polycrystalline compounds E$r_{2-x}Tb_{x}Fe_{14}B$ (x = 0.1, 0.2, 0.3, 0.4) which crystallize in a tetragonal lattice and display a variety of spin arrangements. The compounds have been measured with $^{57}Fe$ Mössbauer spectroscopy over the temperature range 80–320 K in order to investigate the spin reorientation processes. Each compound was studied in a wide temperature range, with precise Mössbauer scanning in the vicinity of the transition. The set of spectra obtained for a given compound was analyzed using simultaneous fi tting procedure to investigate the infl uence of the transition on the shape of the spectra. The fitting program was specifi ed to analyze the transition according to the ‘two state model’: spins fl ip abruptly from initial angle to fi nal arrangement ($90^{\circ} angle$ ). Obtained results suggest that spin reorientation process cannot be described using only the mentioned above model. Additional computer simulations based on the Yamada–Kato model were conducted to determine temperature range and the type of spin alignments in the vicinity of the transition. These theoretical results supported by spectra analysis suggest the existence of intermediate (canted) spin arrangements in the studied compounds. The spin arrangement diagram was constructed

Spin reorientation process in Tm_{2–x}Ho_{x}Fe_{14}B : analysis of conical arrangement based on Mössbauer spectra

The spin reorientation process in the Tm2–xHoxFe14B series of compounds was studied using 57Fe Mössbauer spectroscopy over the temperature range 5.2–320 K with a focus on the analysis of conical spin arrangement. Each compound was studied by precise Mössbauer scanning in the vicinity of the transition and during the transition. By applying computer simulations based on the simplified Yamada-Kato model, as well as on some literature data for R2Fe14B (R = Tm, Ho) compounds, the above series was selected for studies as it contains compounds with different spin arrangements (axial, planar, conical). It was a crucial requirement for obtaining unambiguous angular dependences when applying a simultaneous fitting procedure of Mössbauer spectra. Such an extended procedure was applied which allowed the temperature dependence of the angle describing the position of the magnetization vector to be obtained. The results were compared with those from theoretical simulations. The spin arrangement diagram was constructed. A conical spin arrangement was confirmed over a wide temperature range

Influence of carbon on spin reorientation processes in Er_{2-x}R_{x}Fe_{14}C (R = Gd, Pr) - Mössbauer and magnetometric studies

The $Er_{2-x}R_{x}Fe_{14}C$ (R=Gd, Pr) polycrystalline compounds have been synthesized and investigated with $\text{}^{57}Fe$ Mössbauer spectroscopy and magnetic measurements. The spin reorientation phenomena were studied extensively by narrow step temperature scanning in the neighborhood of the spin reorientation temperature. Obtained Mössbauer spectra were analyzed using a procedure of simultaneous fitting and the transmission integral approach. Consistent description of Mössbauer spectra were obtained, temperature and composition dependencies of hyperfine interaction parameters and subspectra contributions were derived from fits and the transition temperatures were determined for all the compounds studied. Initial magnetization versus temperature measurements (in zero and non-zero external field) for $Er_{2-x}Gd_{x}Fe_{14}C$ compounds allowed to establish the temperature regions of reorientation, change of magnetization value during the transition process. The results obtained with different methods were analyzed and the spin arrangement diagrams were constructed. Data obtained for $Er_{2-x}Gd_{x}Fe_{14}C$ were compared with those for $Er_{2-x}Gd_{x}Fe_{14}B$ series

The sound field around a tuning fork and the role of a resonance box

Atypical two-tine tuning fork is barely audible when held vibrating at an arm's length. It is enough, however, to touch its base to a table or, better, to a resonance box and the emitted sound becomes much louder. An inquiring student may pose questions: Why is a bare tuning fork such a weak emitter of sound? ; What is the role of the resonance box? ; Where does energy connected with larger intensity of emitted acoustic waves come from