Documents of interest in support of your JEOL product
Application Note ER200011E
When an ESR spectrum of paramagnetic sample is measured in the state subjected to the Purcell effect, its line width broadens extraordinarily as shown in Application Note ER200006E. It would be a serious problem in which we must reduce the filling factor when a sample which has many spins is measured using a cavity. This is not a problem only with a ferromagnetic sample, but also with a paramagnetic one as well. How much should we reduce the filling factor by? To obtain a rough guide for it, ESR spectral line widths (ΔHpp) and shift widths of cavity frequency (Δf) were simultaneously measured on the respective sample position moved as shown in Fig. 1(a).
Fig.1 A drawing of the experiment which investigates a relation with sample moving and line width.
(a) Sample location in the cavity. (b) Measurement examples of Δf（upper) and ΔHpp (lower).
Relationship between frequency shift and line width in the state subjected to Purcell effect
As increasing the sample amount, frequency shift width also increases. Thus, it can be considered that there is a correlation between coupling constant 𝑔𝑚 and frequency shift Δf in the state subjected to the Purcell effect. Simulation results of frequency shift widths at several 𝑔𝑚 values based on S11 equation show a correlation according to quadratic function related to 𝑔𝑚 (conf. Fig. 2(a)). In this simulation, we have set Qu = 18000 and 𝛾𝑚 ∕ 2𝜋 (HWHM) = 3.39 MHz. Therefore, it can be considered that the observed line width ΔHpp is proportional to ∆𝑓, because ΔHpp is proportional to g2m. As a result, by plotting ΔHpp at respective ∆𝑓, sample intrinsic line width and optimal filling factor (optimal sample position) can be estimated. As shown in Fig. 2(b), ΔHpp can be fitted by linear function. By moving a sample to the position until the line width is no longer changed (in this case, more than + 30 mm), Normal spectrum and analysis which is not affected by a strong interaction between photon and spins is capable, even if spin density is high. This is a little troublesome experiment. However, this experiment is also effective on ESR/FMR measurements using more concentrated magnetic samples. Using this plot would be useful to study about the effect of the interaction between photon and spins.
Fig.2 (a) Simulation results about the relation with 𝑔_𝑚 and Δf . (b) Spectral line width ΔHpp plotted at respective observed Δf.
 E. Abe, H. Wu, A. Ardavan, and J. J. L. Morton, Appl. Phys. Lett. 98, 251108 (2011).
 Patent, US10288707B2 "Relaxation time measuring method and magnetic resonance measuring apparatus".
Application Note ER200010E
Using the transmission ESR/FMR measurement method, spectral analysis can be done in the situation that it is not affected by the spin-cavity coupling (interaction that produce the Purcell effect and a strong coupling state) due to the high spin density samples. Obtained spectral line width of a sample is necessary to estimate an important parameter, cooperativity (=g2m∕ 𝑘𝑐 ∙𝛾𝑚, 𝑘𝑐 and 𝛾𝑚 are HWHM (half width)) which means the degree of interaction between photon and spins. Figure 1(a) shows frequency dependence of line width obtained by paramagnetic resonance (sample is DPPH powder shown in Application Note ER200006E ). Figure 1(c) shows frequency dependence of line width obtained by ferromagnetic resonance (sample is YIG thin film shown in Application Note ER200008E - ER200009E ).
Fig.1 Frequency dependence of spectral line width by transmission ESR/FMR measurement method.
(a) DPPH sample (right photo) and frequency dependence of the line widths. (b) DPPH-ESR spectrum by transmission method. (c) YIG thin film (right photo) and frequency dependence of the line widths (Peak A). (d) YIG-thin-film- FMR spectrum by transmission method.
Damping constant and surface quality
Figure 1(a) and 1(c) show a difference on the frequency dependence of spectral line widths with respect to a paramagnet and a ferromagnet. The line width of FMR spectrum has a property that is proportional to the irradiated frequency. Its proportional coefficient is called damping constant. This damping constant α is very important on the evaluation of ferromagnetic materials. The line width (∆𝐻) of FMR spectrum and FMR frequency (𝑓) have a relation as
ΔH = 𝛼𝑓 / |𝛾𝑒| + ΔH0.
∆𝐻0 reflects the homogeneity of the film materials. Not zero value of ∆𝐻0 means the inhomogeneity of the film. In recent years, spintronics devices using ferromagnetic materials are actively studied. Therefore, evaluation of the damping constant is becoming more important. In this field, a vector network analyzer is usually used for FMR measurements. Introduced waveguide method in this application note is unfortunately not sensitive. However, there are not serious constraints for sample size and shape, and it has a merit on the homogeneity of B1 vector of microwave.
Fig. 2 Homogeneity of ferromagnetic thin films.
(a) Homogeneous film. (b) Inhomogeneous film.
Reference:  J. M. Shaw, H. T. Nembach, and T. J. Silva, J. Appl. Phys. 108, 093922 (2010).