Tunable finite-sized chains to control magnetic relaxation

The magnetic dynamics of low-dimensional iron ion chains have been studied with regards to the tunable finite-sized chain length using iron phthalocyanine thin films. The deposition temperature varies the diffusion length during thin-film growth by limiting the average crystal size in the range from 40 to 110 $\mathrm{nm}$. Using a method common for single chain magnets, the magnetic relaxation time for each chain length is determined from temporal remanence data and fit to a stretched exponential form in the temperature range below 5 $\mathrm{K}$, the onset for magnetic hysteresis. A temperature-independent master curve is generated by scaling the remanence by its relaxation time to fit the energy barrier for spin reversal, and the single spin-relaxation time. The energy barrier of 95 $\mathrm{K}$ is found to be independent of the chain length. In contrast, the single spin-relaxation time increases with longer chains from under 1 ps to 800 ps. We show that thin films provide the nanoarchitecture to control magnetic relaxation and a testbed to study finite-size effects in low-dimensional magnetic systems.

Figure 1

The scattered intensity from x-ray diffraction of a FePc/silicon sample shows three distinct peaks for FePc with the first peak position at $6.93{}^{\circ }$. The small satellite peak, indicated with a dashed line, near the FePc(200) main peak is due to the reflection at the FePc/silicon interface and used to determine the FePc thickness.

Figure 2

The remanence $M_r$ for the FePc/Si sample deposited at $180{}^{\circ }\mathrm{C}$ shows slow relaxation at temperatures in the range of 2.5 and $4.5\mathrm{K}$. The lines are fits of the stretched exponential function from the master curve.

Figure 3

Scaled remanent measurements are collapsed onto a single master curve for temperatures from 2.5 to 4 K for FePc/Si deposited at ${180}^{\circ }\mathrm{C}$. Each measurement is scaled by the relaxation time $\tau$. The gray line shows a fit to the stretched exponential form with $\beta =0.25$. The inset shows the FePc molecule with iron ion at the center.

Figure 4

The relaxation times are determined from fits to $M_r\left(t\right)$ using the stretched exponential form. Data for three samples are shown, and the dotted lines are linear fits to extract the energy barrier ${\mathrm{\Delta }}_A$ and the intercept ${\tau }_0$.

Figure 5

Energy gap ${\mathrm{\Delta }}_A/k_B$ vs chain length of sample. The gray line is added for reference for ${\mathrm{\Delta }}_{\xi }/k_B=64$ K determined from magnetic circular dichroism data in FePc/Au thin films. The chain length of five samples (circle) is determined from the crystal size using AFM, and the other two samples (square) are inferred lengths from coercivity measurements.

Figure 6

Single spin-relaxation times for seven samples with different chain lengths. For two samples (squares) deposited above $200{}^{\circ }\mathrm{C}$ the length $L$ is estimated indirectly. The inset shows a top view of the herringbone arrangement of FePc molecules, and the arrow indicates the direction of the magnetic field and the direction of the $b$ axis.