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 , Japan International Workshop on "Physics on Nanoscale Magnets"

Outline 1.Introduction 2.Sample 3.Conventional approaches and their results (Suggestions of QTM) 4.Points to be noted 5.Modified approach and its results (Predominance of classical relaxations) 6.Summary International Workshop on "Physics on Nanoscale Magnets"

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

Sample International Workshop on "Physics on Nanoscale Magnets" 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.

A conventional approach and its results — Temperature dependence of relaxation rate — International Workshop on "Physics on Nanoscale Magnets" 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

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

Results of the scaling analysis —Relaxations at various temperatures — International Workshop on "Physics on Nanoscale Magnets" 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 E C /k B = T ln( t/  0 )

Points to be noted — Initial States of IRM( t ) — International Workshop on "Physics on Nanoscale Magnets" Though H appl = 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 ??? M-H curves of ferritin This problem is common to nanoparticles, since they have disorder of surface spins

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

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

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

Modified approach —Initial and final states independent of T, H meas — International Workshop on "Physics on Nanoscale Magnets" Note: m j FC ( H cool,T B ) is given by m j at T B on cooling in H cool. Each distance of relaxation is independent of T, H meas. For j th particle, equilibrium m: m j eq ( H meas, T ),  j ( H meas, T ) Zero-field-cooled magnetization, M ZFC (H meas,T ) is Reversed-thermoremanent magnetization RTRM: Their sum M sum is

Scaling of M sum curves at various T, H meas — An overview — International Workshop on "Physics on Nanoscale Magnets" M sum ( t ) at each H meas can be mapped onto a master curve at all the temperatures. Thermally activated mechanism The master curve shifts downward with H meas. Acceleration by the field M sum ( t ) vs. E C /k B = T ln( t/  0 )

Distribution of barrier heights in H meas — An overview — International Workshop on "Physics on Nanoscale Magnets" M sum ( E c ) =  m j FC of B j >E c A cumulative distribution with weights m(B).  M sum /  E c ( = S/T )  n(B): Distribution of barrier heights. The barrier height B reduces with H meas in H meas > 1 kOe.

Distribution of barrier heights in H meas = 0 — Details at lower temperatures — International Workshop on "Physics on Nanoscale Magnets" Distribution of barrier heights  M sum /  E c ( = S/T )  n(B) M sum ( t ) vs. E C /k B = 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.

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

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

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

Relaxation time in weak fields — Explanation by classical fluctuations — International Workshop on "Physics on Nanoscale Magnets" The relaxation is accelerated, as predicted for classical activated mechanisms. Half-life t 1/2

Summary 1.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. 2.For this reason, we propose a modified approach. 3.Its results clearly indicate that the relaxations observed in natural ferritin are dominated by classical superparamagnetic fluctuations in the Kelvin regime. 4.Existence of QTM below 2 K is still debatable. Further study using the modified approach is required. International Workshop on "Physics on Nanoscale Magnets"