H. Mamiya , I. Nakatani, T. Furubayashi Nanomaterials Laboratory

1. Experimental Approach to Macroscopic Quantum Tunneling of Magnetization in Single Domain Nanoparticles H. Mamiya, I. Nakatani, T. Furubayashi Nanomaterials Laboratory National Institute for Materials Science Tsukuba 305-0047, Japan International Workshop on "Physics on Nanoscale Magnets"

2. Outline • Introduction • Sample • Conventional approaches and their results (Suggestions of QTM) • Points to be noted • Modified approach and its results (Predominance of classical relaxations) • Summary International Workshop on "Physics on Nanoscale Magnets"

3. Introduction Macroscopic Quantum Tunneling of magnetization vector was observed in molecular magnets. How about larger systems ? Do antiferromagnetic nanoparticles show QTM ? International Workshop on "Physics on Nanoscale Magnets"

4. Sample Examined sample was natural horse-spleen ferritin protein, which stores antiferromagnetic ferrihydrite in its cage ( 8 nm) . Each core has a small magnetization vector ~300B due to its uncompensated spins. International Workshop on "Physics on Nanoscale Magnets"

5. A conventional approach and its results— Temperature dependence of relaxation rate — Decay function: Exponential: No Logarithmic: Yes Relaxation rate S, IRM/ln t is discussed as usual. S flattens out at lower T. Relaxations appear to be temperature-independent. Isothermal remanent magnetization IRM and its relaxation rate S International Workshop on "Physics on Nanoscale Magnets"

6. The conventional approach ( Next Step )— Scaling of relaxation curves at various T — Logarithmic decay : Sum of exponential decays of poly-dispersive particles IRM( t ) = Exponential function in ln t Step function IRM( t ) Except for If thermal process: k ( Happl=0, T ) = 0 exp[-Bk(Happl=0)/kBT] IRM( t ) Only As long as thermal processes, IRM( t ) can be scaled by Ec. International Workshop on "Physics on Nanoscale Magnets"

7. Results of the scaling analysis—Relaxations at various temperatures — IRM( t ) cannot be mapped onto an unique master curve at the lower temperatures. Non-thermal relaxations ? We observe Pure QTM ? Isothermal remanent magnetization as a function of EC/kB = T ln( t/0 ) International Workshop on "Physics on Nanoscale Magnets"

8. Points to be noted— Initial States of IRM( t ) — Though Happl = 30 kOe is large, M is not saturated owing to complex coupling with antiferromagnetic spins. The initial states of IRM( t ) are not always uniform at different T. The scaling ??? This problem is common to nanoparticles, since they have disorder of surface spins M-H curves of ferritin International Workshop on "Physics on Nanoscale Magnets"

9. A conventional approach — A maximum of ( T ) — Thermal energy kBT »Barrier height B  fluctuates and   1/T. kBT«B  is blocked and  is small. On their boundary, a maximum of  should appear. ( this temperature is Tmax ) Hence, Tmax  B is assumed, International Workshop on "Physics on Nanoscale Magnets"

10. Results — Field-dependence of the maximum — the rise in Tmax with H If Tmax  B Increase of effective B in H. Thermally assisted resonant QTM and its suppression by H ? M( T ) in various H International Workshop on "Physics on Nanoscale Magnets"

11. Points to be noted— Final states of zero-field-cooled M ( t ) —  Distance Relative Variation during to final states speed the observations Tmax depends not only on the relative speed but on unknown temperature-dependence of the final state International Workshop on "Physics on Nanoscale Magnets"

12. Modified approach—Initial and final states independent of T, Hmeas— For j th particle, equilibrium m: mjeq ( Hmeas, T ), j ( Hmeas, T ) Zero-field-cooled magnetization, MZFC(Hmeas,T ) is Reversed-thermoremanent magnetization RTRM: Their sum Msum is Note: mjFC ( Hcool,TB) is given by mj at TBon cooling in Hcool. Each distance of relaxation is independent ofT, Hmeas. International Workshop on "Physics on Nanoscale Magnets"

13. Scaling of Msum curves at various T, Hmeas— An overview — Msum( t ) at each Hmeas can be mapped onto a master curve at all the temperatures. Thermally activated mechanism The master curve shifts downward with Hmeas. Acceleration by the field Msum( t ) vs. EC/kB = T ln( t/0 ) International Workshop on "Physics on Nanoscale Magnets"

14. Distribution of barrier heights in Hmeas— An overview — Msum( Ec ) =mjFC of Bj>Ec A cumulative distribution with weights m(B). Msum/Ec ( = S/T )  n(B): Distribution of barrier heights. The barrier height Breduces with Hmeas in Hmeas> 1 kOe. International Workshop on "Physics on Nanoscale Magnets"

15. Distribution of barrier heights in Hmeas = 0 — Details at lower temperatures— Distribution of barrier heights Msum/Ec ( = S/T )  n(B) Msum( t ) vs. EC/kB = T ln( t/0 ) The scaling holds above 1.8 K. Thermally activated processes are dominant at a few kelvins. Only in the larger cooling field, lower barriers are observable. International Workshop on "Physics on Nanoscale Magnets"

16. The origin of non-zero-relaxation rate Why lower barriers appear when Hcool is large? A1. Since smaller particles with smaller B have smaller , they are magnetized only when Hcool is large enough. A2. Even when Hcool is large, M is not saturated owing to complex coupling with antiferromagnetic spins. The spin arrangement at that time may be metastable in Hmeas = 0 after cutting off Hcool. Escape from such local, shallow minima can be observed at the lower temperatures. International Workshop on "Physics on Nanoscale Magnets"

17. Relaxations during thermal cycles— Another approach using uniform initial states — The relaxation exponentially slows down during the temporary cooling while it exponentially accelerates during the temporary heating. An additional proof of predominance of thermal processes Relaxations with thermal cycles and effective time during the cycles International Workshop on "Physics on Nanoscale Magnets"

18. Distribution of barrier heights in Hmeas— Details in weak fields— As shown in the overview, the barrier height Breduces with Hmeas in Hmeas> 1 kOe. At the low fields Hmeas< 0.3kOe no detectable change of n( B ) is observed. Relaxations do not slow down when Hmeas is applied, in contrast with the prediction for resonant QTM. n( B ) in low Hmeas normalized by n( B ) in Hmeas= 0 International Workshop on "Physics on Nanoscale Magnets"

19. Relaxation time in weak fields— Explanation by classical fluctuations — The relaxation is accelerated, as predicted for classical activated mechanisms. Half-life t1/2 International Workshop on "Physics on Nanoscale Magnets"

20. Summary • We show that lack of the uniformity of initial ( or final ) states of relaxations seriously affects the results of the conventional approaches to QTM in nanomagnets. • For this reason, we propose a modified approach. • Its results clearly indicate that the relaxations observed in natural ferritin are dominated by classical superparamagnetic fluctuations in the Kelvin regime. • Existence of QTM below 2 K is still debatable. Further study using the modified approach is required. International Workshop on "Physics on Nanoscale Magnets"