Color of postponed magnetic noise in ${\mathrm{K}}_{0.4}\left[\mathrm{Cr}{\left(\mathrm{CN}\right)}_6\right]\left[\mathrm{Mn}\left(\mathrm{R}/\mathrm{S}\right)-\mathrm{pn}\right]\left(\mathrm{R}/\mathrm{S}\right)-\mathrm{pn}{\mathrm{H}}_{0.6}$ molecular ferrimagnet

Exotic conditions for the existence and evolution of nonlinear spin ensembles (domain walls, spin solitons, skyrmions) in molecular-based magnets are incarnated in the macroscopic response of magnetization corresponding to collective stochastic behavior. The molecular ferrimagnet ${\mathrm{K}}_{0.4}\left[\mathrm{Cr}{\left(\mathrm{CN}\right)}_6\right]\left[\mathrm{Mn}\left(\mathrm{R}/\mathrm{S}\right)-\mathrm{pn}\right]\left(\mathrm{R}/\mathrm{S}\right)-\mathrm{pn}{\mathrm{H}}_{0.6}$ manifests three types of magnetic relaxation: (a) continuous decay of magnetic moment, (b) stepwise relaxation by stochastic magnetization jumps, and (c) a single jump of magnetization in threshold magnetic field. Continuous relaxation at 20–50 K is provided by domain wall movement described in the frames of a strong pinning model, while a low-temperature continuous component of relaxation does not follow this model. Stepwise stochastic relaxation was observed below 8 K in both a sweeping reverse magnetic field and a stationary reverse magnetic field. Statistical treatment of the postponed magnetization jumps revealed a multimodal amplitude distribution of stochastic magnetization jumps corresponding to magnetic moment transitions between few clear distinguishable levels. Spectral density of magnetization jumps in a stationary magnetic field corresponds to white noise, while spectral density in a sweeping magnetic field manifests pink noise $\sim 1/f$ provided by self-organized criticality. Postponed emission of magnetic noise in the ${10}^{-6}-5\times {10}^{-1}\mathrm{Hz}$ frequency range was observed in stationary conditions in contrast to Barkhausen noise.

Figure 1

(a) Dependence of the magnetic moment on the magnetic field $M$($H$) at 8 K. Threshold magnetic fields initiating RJ $H_{\mathrm{C}1}$ and SJ $H_{\mathrm{C}2}$ are shown by arrows. (b) Superimposed time series of stochastic magnetization jumps collected from 16 independent measurements. Time dependence of magnetic field is presented in the upper panel.

Figure 2

(a) Distribution of amplitude Δ$M$ and magnetic field $H_{\mathrm{C}2}$ of the stochastic magnetization jumps at 8 K in sweeping magnetic field. (b) Spectral density $S$($f$) of the magnetization SJs in a sweeping magnetic field and its approximations by ${\left(1/f\right)}^{\alpha }$ function (theoretical curves for $\alpha =1$ and $\alpha =2$ are shown by dashed and solid lines, respectively).

Figure 3

(a) Time dependence of the magnetic moment $M$($t$) recorded after a magnetic field +10 Oe was stabilized at $T=2\mathrm{K}$. In the insertion, the derivative $dM\left(t\right)/dt$ is presented. Arrows indicate magnetization jumps. (b) Superimposed time series of stochastic magnetization jumps collected from 20 independent measurements. Time dependence of magnetic field is presented in the upper panel.

Figure 4

(a) Distribution of amplitude Δ$M$ and expectation time $t_{\mathrm{C}}$ of the magnetization SJs in stationary magnetic field at 2 K. (b) Distribution of amplitude Δ$M$ and starting magnetic moment $M_i$ of the magnetization SJs in stationary magnetic field at 2 K. (c) Spectral density $S$($f$) of the magnetization SJs in stationary magnetic field. Expected value is shown by horizontal solid line.

Figure 5

Sketch of (1) single kink and (2) double kink formed on the domain walls in periodical potential relief of crystal lattice ($a$ is lattice parameter), $U$ is potential energy of amplitude $U_{\mathrm{MAX}}$. Self-contraction forces are shown by arrows.

Figure 6

Jump-free fragments of continuous magnetic relaxation in stationary magnetic field (1) 30 Oe, (2) 20 Oe, and (3) −18 Oe at $T=2\mathrm{K}$. Approximations by the formula in Eq. (2) are shown by solid lines. The sample was magnetized in saturating magnetic field $H_{\mathrm{SAT}}=400\mathrm{Oe}$ during the 5 min before experiments.

Figure 7

Temperature dependence of normalized magnetic viscosity $S_{\mathrm{V}}$ in reverse magnetic field $H=-H_{\mathrm{coer}}$. Approximation of the high-temperature part of the $S_{\mathrm{V}}$ ($T$) dependence by the formula in Eq. (3) is shown by solid line.