Relaxation Phenomena of a Magnetic Nanoparticle Assembly with Randomly Oriented Anisotropy
The effects of a randomly oriented anisotropy on relaxation phenomena including the memory effect of a noninteracting magnetic nanoparticle assembly, are numerically studied with a localized partition function and a master equation, leading to the following results. During the zero-field-cooled (ZFC...
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| Published in | Japanese Journal of Applied Physics Vol. 50; no. 3; pp. 035001 - 035001-6 |
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| Main Authors | , , , , |
| Format | Journal Article |
| Language | English |
| Published |
The Japan Society of Applied Physics
01.03.2011
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| Online Access | Get full text |
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| Summary: | The effects of a randomly oriented anisotropy on relaxation phenomena including the memory effect of a noninteracting magnetic nanoparticle assembly, are numerically studied with a localized partition function and a master equation, leading to the following results. During the zero-field-cooled (ZFC) process, the energy barrier histogram changes with temperature, while during the field-cooled (FC) process it remains stable. In the relaxation process after ZFC initialization, the effective energy barrier distribution, which is derived from the $T\ln(t/\tau_{0})$ ($T$ temperature, $t$ time, and $\tau_{0}$ characteristic time constant) scaling curve, only reflects the low-energy region of the energy barrier histogram. The memory effect with temporary cooling during time evolution occurs in the studied assembly even without volume distribution and particle interaction involved. |
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| Bibliography: | Calculation results of the magnetic susceptibility obtained in ZFC and FC measurements at fields of 20, 300, and 1200 Oe. The peaks of the ZFC curves are marked by arrows. The particle radius is 2.5 nm and the unit heating duration is 60 s. Energy barrier histogram $f(E_{\text{b}})$ during the ZFC magnetization under a magnetic field of 1200 Oe. The thin and thick lines correspond to $T=24$ and 40 K, respectively. As the temperature increases, $f(E_{\text{b}})$ declines at the low $E_{\text{b}}$ and increases at high $E_{\text{b}}$. Energy barrier histogram $f(E_{\text{b}})$ during the FC magnetization under a magnetic field of 1200 Oe. The curves of $T=24$ and 40 K overlap, indicating that the energy barrier distribution almost remains stable even with a change in the temperature during the FC magnetization. $T\ln(t/\tau_{0})$ scaling curves of the normalized magnetization at magnetic field of 50 (a) and 2000 Oe (b). The inset shows the original relaxation process in natural logarithm. Energy barrier histogram $f(E_{\text{b}})$ for the randomly oriented magnetic particles in comparison to the relaxation rates $S(t)$ (insets) as a function of $T\ln(t/\tau_{0})$ at magnetic fields of 50 (a) and 2000 Oe (b). The open symbol and filled symbol correspond to the initial (i) and terminal (t) states of the assembly, respectively. The peak positions of $f(E_{\text{b}})$ and $S(t)$ are indicated in the figures for $T=50$ K ($H=50$ Oe) and $T=20$ K ($H=2000$ Oe). ZFC magnetic relaxation measurement of the magnetic nanoparticle assembly at 60 K with a decrease (a) and an increase (b) in temperature to 45 and 65 K for $t_{2}=9000$ s, respectively. The inset of (a) shows the data as a function of total time spent at $T=60$ K. During the temporary cooling (heating) in $t_{2}$, the magnetic field is removed. The TRM magnetic relaxation measurement of the magnetic nanoparticle assembly at 60 K with a decrease (a) and an increase (b) in temperature to 45 and 65 K for $t_{2}=9000$ s, respectively. The inset of (a) shows the data as a function of the total time spent at $T=60$ K. During the temporary cooling (heating) in $t_{2}$, a magnetic field of 50 Oe is applied. |
| ISSN: | 0021-4922 1347-4065 |
| DOI: | 10.1143/JJAP.50.035001 |