Linear and nonlinear susceptibility effects in ${\mathrm{Y}}_2{\mathrm{Fe}}_{17}$ and ${\mathrm{Er}}_2{\mathrm{Fe}}_{17}$

The thermal dependence of the linear and nonlinear ac susceptibilities of the ferromagnetic ${\mathrm{Y}}_2{\mathrm{Fe}}_{17}$ and of the ferrimagnetic ${\mathrm{Er}}_2{\mathrm{Fe}}_{17}$ intermetallic compounds is investigated as a function of the amplitude and frequency of the applied ac field. In both compounds, the change of sign at $T_C$ and the behavior below and above the ferromagnetic or ferrimagnetic transition temperature are well explained in terms of divergence of the nonlinear susceptibility. Low temperature transitions detected by real and imaginary components of the fundamental ac susceptibility are related to the coupling of domain-wall dynamics and mobility defects. The thermal behavior of the linear and third order susceptibilities has been tentatively divided in different regions with different relaxation phenomena. Moreover, nonlinear effects due to the annealing procedure have been analyzed and discussed.

Figure 1

Real (left scale) and imaginary (right scale) components of the linear ac susceptibility for ${\mathrm{Y}}_2{\mathrm{Fe}}_{17}$. Measurements have been performed with $H_{\mathrm{ac}}=1\mathrm{Oe}$ and $\nu =333\mathrm{Hz}$. In the inset, details concerning the in phase nonlinear data at the same frequency are reported for different values of the applied ac magnetic field.

Figure 2

Real (left scale) and imaginary (right scale) components of the linear ac susceptibility for ${\mathrm{Y}}_2{\mathrm{Fe}}_{17}$ performed after the annealing procedure.

Figure 3

(a) Real and (b) imaginary components of the nonlinear susceptibility for ${\mathrm{Y}}_2{\mathrm{Fe}}_{17}$ performed after the annealing procedure for different values of the applied magnetic field and with $\nu =333\mathrm{Hz}$.

Figure 4

Thermal dependence of the real component of linear susceptibility for ${\mathrm{Y}}_2{\mathrm{Fe}}_{17}$ at different frequencies. The frequency dependence of the low temperature imaginary component is reported as inset in the upper left hand corner, while in the lower right hand corner the inset shows the high temperature details of the imaginary component at the same frequencies.

Figure 5

Thermal dependence of the nonlinear susceptibility (real component) of ${\mathrm{Y}}_2{\mathrm{Fe}}_{17}$ in the whole temperature range for different frequencies, with $H_{\mathrm{ac}}=0.5\mathrm{Oe}$.

Figure 6

Real component of the linear ac susceptibility for ${\mathrm{Er}}_2{\mathrm{Fe}}_{17}$ (as-cast and annealed samples) for $H_{\mathrm{ac}}=0.1\mathrm{Oe}$ and $\nu =133\mathrm{Hz}$.

Figure 7

(a) Real and (b) imaginary (b) components of the nonlinear susceptibility for ${\mathrm{Er}}_2{\mathrm{Fe}}_{17}$ performed after the annealing procedure for different values of applied magnetic field and with $\nu =133\mathrm{Hz}$.

Figure 8

Thermal dependence of the imaginary component of the linear susceptibility for the as-cast and annealed ${\mathrm{Er}}_2{\mathrm{Fe}}_{17}$. Details concerning the low temperature imaginary component of the annealed compound are reported for different frequency values as inset in the upper left hand corner, while in the lower right hand corner the inset presents the high temperature details of the imaginary component of the compound at the same frequencies.

Figure 9

Temperature dependence of the nonlinear susceptibility (real component) for ${\mathrm{Er}}_2{\mathrm{Fe}}_{17}$ in the whole temperature range for different frequencies, with $H_{\mathrm{ac}}=0.5\mathrm{Oe}$.

Figure 10

Temperature dependence of the real and imaginary components of the linear ac susceptibility for (a) ${\mathrm{Y}}_2{\mathrm{Fe}}_{17}$ and (b) ${\mathrm{Er}}_2{\mathrm{Fe}}_{17}$. The symbols represent the experimental data, while the continuous line represents the fitted results according to Eq. (2).

Figure 11

Temperature dependence of the real and imaginary components of nonlinear ac susceptibility in ${\mathrm{Y}}_2{\mathrm{Fe}}_{17}$ in the whole temperature range. For the meaning of the different regions displayed in the figure, see the text.