Some experimental approaches to study the aging phenomena in spin glasses Tetsuya Sato Keio University Yokohama, Japan

Outline Aging behavior of spin glass under bond perturbation · What is bond perturbation · Experimental procedure · Experimental result · What is bond perturbation · Experimental procedure · Experimental result Behavior of spin glass nanoparticle in magnetic field · Why is spin glass nanoparticle necessary · Experimental procedure · Experimental result · Why is spin glass nanoparticle necessary · Experimental procedure · Experimental result Concluding remarks

Outline Aging behavior of spin glass under bond perturbation · What is bond perturbation · Experimental procedure · Experimental result · What is bond perturbation · Experimental procedure · Experimental result Behavior of spin glass nanoparticle magnetic field · Why is spin glass nanoparticle necessary · Experimental procedure · Behavior of spin glass nanoparticle magnetic field · Why is spin glass nanoparticle necessary · Experimental procedure · Behavior of spin glass nanoparticle magnetic field concluding remarks

Aging behavior of spin glass under bond perturbation 1. What is bond perturbation Aging behavior of spin glass under bond perturbation 1. What is bond perturbation · Wait time dependence L( τ ) = L 0 [k B T ln( τ / τ 0 )/ Δ (T)] 1/ Ψ average size of excited droplet

· Temperature perturbation Temperature perturbations, e.g., temperature cycle has been extensively used to study slow dynamics of spin glasses. · Temperature perturbation Temperature perturbations, e.g., temperature cycle has been extensively used to study slow dynamics of spin glasses. Temperature chaos

· Temperature perturbation 1. temperature perturbation change in thermal excitation of droplet separation of time scale 1. temperature perturbation change in thermal excitation of droplet separation of time scale t p (T m + Δ T) =  0 [t eff (T m )/  0 ] T m /(T m + Δ T) ex) When T m = 7 K, ΔT = 1K, τ 0 = s 8 K : 75 s 7 K : s difference of 1K more than 100 times difference of time scale 2. temperature perturbation indirect change in bond interaction 2. temperature perturbation indirect change in bond interaction

· Bond perturbation bond perturbation Aging behavior of spin glass can be studied without separation of time scale. magnetic ion

· Bond perturbation bond perturbation magnetic ion Aging behavior of spin glass can be studied without separation of time scale.

· Bond perturbation bond perturbation magnetic ion · method for bond perturbation carrier excitation in semicondcutor change in interaction carrier excitation in semicondcutor change in interaction photo illumination

2. Experimental procedure A. Bond and temperature perturbations (Δ T perturbation + Δ J perturbation) - (Δ T perturbation) = Δ J perturbation

2. Experimental procedure B. Bond perturbation semiconductor laser polarizer PC control polarizer optical fiber Photo intensity is changed synchronously with temperature controller so as to decrease change in sample temperature. Deviation of temperature < 0.02 K Deviation of temperature < 0.02 K

2. Experimental procedure 1. bond and temperature perturbations 2. bond perturbation Sample temperature Field cooled magnetization

3. Experimental result t p (T m + Δ T) =  0 [t eff (T m )/  0 ] T/(T+ Δ T) A. bond and temperature perturbations

t peak t p (T m + Δ T) =  0 [t eff (T m )/  0 ] T/(T+ Δ T) 3. Experimental result A. bond and temperature perturbation

t p (T m + Δ T) =  0 [t eff (T m )/  0 ] T/(T+ Δ T) sub peak t peak sub peak 3. Experimental result A. bond and temperature perturbation

· t peak

isothermal aging : t peak = t eff + t w

· t peak isothermal aging : t peak = t eff + t w sub peak

· relative peak hight r

r is intrinsically equal to 1. r deviates from 1.

· relative peak hight r Difference between Δ T and Δ T+ Δ J perturbation disappears. r is intrinsically equal to 1. r deviates from 1.

· relative peak hight r sub peak r is intrinsically equal to 1. r deviates from 1. Difference between Δ T and Δ T+ Δ J perturbation disappears.

· Classification of aging behavior P.E.Jönsson. R. Mathieu, P. Nordblad, H. Yoshino, H. Aruga Katori and A. Ito: Phys. Rev. B 70, (2004). P.E.Jönsson. R. Mathieu, P. Nordblad, H. Yoshino, H. Aruga Katori and A. Ito: Phys. Rev. B 70, (2004). · Overlap length : L Δ X = L 0 | Δ X/J| -1/  Non-perturbed state and Δ X -perturbed state are completely different on large scale much beyond L Δ X. · Domain size after wait time t w : L i (t w ) (initial stage) · Domain size under Δ X- perturbation after time t p : L p (t eff ) (perturbation stage) · Domain size under Δ X- perturbation after time t p : L p (t eff ) (perturbation stage) · Domain size without perturbation after time t : L h (t) (healing stage)

· Classification of aging behavior · L p (t eff ) << L Δ X Weakly perturbed regime Accumulative aging t peak = t eff + t w Recovery of order parameter in healing stage Accumulative aging t peak = t eff + t w Recovery of order parameter in healing stage · L i (t w ), L p (t eff ), L h (t) >> L Δ X Strongly perturbed regime Chaotic behavior t peak < t eff + t w Decrease in order parameter in healing stage Appearance of sub peak Chaotic behavior t peak < t eff + t w Decrease in order parameter in healing stage Appearance of sub peak · L i (t w ), L p (t eff ), L h (t) ~ L Δ X Crossover regime Intermediate behavior between weakly and strongly perturbed regimes r ~ 1 r < 1

· Classification of aging behavior S : Strongly perturbed regime SC : Crossover regime near strongly perturbed regime WC : Crossover regime near weakly perturbed regime W : Weakly perturbed regime S : Strongly perturbed regime SC : Crossover regime near strongly perturbed regime WC : Crossover regime near weakly perturbed regime W : Weakly perturbed regime

S : Strongly perturbed regime SC : Crossover regime near strongly perturbed regime WC : Crossover regime near weakly perturbed regime W : Weakly perturbed regime S : Strongly perturbed regime SC : Crossover regime near strongly perturbed regime WC : Crossover regime near weakly perturbed regime W : Weakly perturbed regime Shift of boundary curve · Classification of aging behavior

· Contribution of ΔJ Shift of boundary curve decrease in overlap length L Δ T+ Δ J < L Δ T Δ T+ Δ J data with Δ T= 0.26 K ~ Δ T data with Δ T= 0.40 K Δ T+ Δ J data with Δ T= 0.26 K ~ Δ T data with Δ T= 0.40 K contribution of Δ J perturbation with Δ T= 0.26 K ~  K contribution of Δ J perturbation with Δ T= 0.26 K ~  K

B. Bond perturbation · check of Δ J perturbation 1. Illumination on carbon side surface

· check of Δ J perturbation 1. Illumination on carbon side surface Independent of strength and duration of perturbation B. Bond perturbation

· check of Δ J perturbation 2. Photon energy h  smaller than energy gap E g h  eV E g = 2.18 eV h  eV E g = 2.18 eV > > B. Bond perturbation

· check of Δ J perturbation h  eV E g = 2.18 eV h  eV E g = 2.18 eV > > Intrinsically identical There is no contribution from photo illumination with low photon energy. B. Bond perturbation 2. Photon energy h  smaller than energy gap E g

B. bond perturbation

no illumination t w = 6000 sec B. bond perturbation

chaotic accumulative B. bond perturbation

· t peak B. bond perturbation

· t peak accumulative aging : t peak = t p + t w accumulative aging : t peak = t p + t w B. bond perturbation

· t peak chaotic accumulative B. bond perturbation

· relative peak hight r B. bond perturbation

· relative peak hight r slow decrease (chaotic) slow decrease (chaotic) decrease independent of strength of perturbation Two-step changes in bond interaction ? B. bond perturbation

· relative peak hight r Δ T = 0.40K temperature cycle Δ T = 0.40K temperature cycle Difference between Δ J and Δ T perturbations ? B. bond perturbation

4. Summary of aging behavior of spin glass under bond perturbation 1. Effective Δ J perturbation by photo excitation in spin glass semiconductor. 2. Observation of rejuvenation (chaotic) effect by Δ J perturbation. 3. Plausible features of decrease in overlap length with Δ J perturbation. 4. Difference between Δ J and Δ T perturbations in detail.

1. Effective Δ J perturbation by photo excitation in spin glass semiconductor. 2. Observation of rejuvenation (chaotic) effect by Δ J perturbation. 3. Plausible features of decrease in overlap length with Δ J perturbation. 4. Difference between Δ J and Δ T perturbations in detail. 4. Summary of aging behavior of spin glass under bond perturbation

1. Effective Δ J perturbation by photo excitation in spin glass semiconductor. 2. Observation of rejuvenation (chaotic) effect by Δ J perturbation. 3. Plausible features of decrease in overlap length with Δ J perturbation. 4. Difference between Δ J and Δ T perturbations in detail. 4. Summary of aging behavior of spin glass under bond perturbation

1. Effective Δ J perturbation by photo excitation in spin glass semiconductor. 2. Observation of rejuvenation (chaotic) effect by Δ J perturbation. 3. Plausible features of decrease in overlap length with Δ J perturbation. 4. Difference between Δ J and Δ T perturbations in detail. 4. Summary of aging behavior of spin glass under bond perturbation

Outline Aging behavior of spin glass under bond perturbation · What is bond perturbation · Experimental procedure · Experimental result · What is bond perturbation · Experimental procedure · Experimental result Behavior of spin glass nanoparticle in magnetic field · Why is spin glass nanoparticle necessary · Experimental procedure · Behavior of spin glass nanoparticle magnetic field · Why is spin glass nanoparticle necessary · Experimental procedure · Behavior of spin glass nanoparticle magnetic field Concluding remarks

Behavior of spin glass nanoparticle magnetic field 1. Why is spin glass nanoparticle necessary Quantitative evaluation of spatial length scales and critical exponents, e.g.,

Behavior of spin glass nanoparticle magnetic field 1. Why is spin glass nanoparticle necessary Quantitative evaluation of spatial length scales and critical exponents, e.g., SG domain size Critical exponent Ψ Field crossover length Critical exponent δ ··· SG domain size Critical exponent Ψ Field crossover length Critical exponent δ ···

Behavior of spin glass nanoparticle magnetic field 1. Why is spin glass nanoparticle necessary · SG domain size Nanoparticles D D Domain growth is restricted to the particle size D. Bulk L → ∞ t → ∞ Large droplet cannot reach the equilibrium state in experimental time scale. L = D

Behavior of spin glass nanoparticle magnetic field 1. Why is spin glass nanoparticle necessary · SG domain size Nanoparticles D D Domain growth is restricted to the particle size D. Bulk L → ∞ t → ∞ Large droplet cannot reach the equilibrium state in experimental time scale. L = D D ~ L( τ ) ~ L 0 [k B T ln( τ / τ 0 )/ Δ (T)] 1/ Ψ Droplet picture Evaluation of SG domain size and 

Behavior of spin glass nanoparticle magnetic field 1. Why is spin glass nanoparticle necessary Qualitative evaluation of spatial length scales and critical exponents, e.g., SG domain size Critical exponent Ψ Field crossover length Critical exponent δ ··· SG domain size Critical exponent Ψ Field crossover length Critical exponent δ ···

Behavior of spin glass nanoparticle magnetic field 1. Why is spin glass nanoparticle necessary LhLh LhLh · Field crossover length D D L h > D LhLh LhLh D D L h < D

Behavior of spin glass nanoparticle magnetic field 1. Why is spin glass nanoparticle necessary LhLh LhLh · Field crossover length D D L h > D LhLh LhLh D D L h < D Observation of crossover Evaluation of field crossover length and  D ~ L h ~ l T h -  Droplet picture

2. Experimental procedure Reversed micelle method Ag(11 at.% Mn) nanoparticle Ag + Mn 2+ H2OH2O NaBH 4 H2OH2O Oactane TEM image Anneal in vacuum with excessive addition of surfactants Sample 1 : 400 °C for 6 hours Sample 2 : 400 °C for 6 hours Sample 3 : 450 °C for 6 hours

Sample 1 Sample 2 Sample 3 D ~ 44 nm D ~ 51 nm D ~ 53 nm 2. Experimental procedure

Sample 1Sample 2Sample 3 3. Experimental result

Sample 1Sample 2Sample 3 Field dependence of peak temperature T peak. 3. Experimental result

Relation between L and T peak 3. Experimental result

Relation between L and T peak 3. Experimental result D ~ L( τ ) ~ L 0 [k B T peak ln( τ / τ 0 )/ Δ (T)] 1/ Ψ

Relation between L and T peak 3. Experimental result D ~ L( τ ) ~ L 0 [k B T peak ln( τ / τ 0 )/ Δ (T)] 1/ Ψ  ~ 2.2 Θ  < d-1 = 2 a little large

Relation between H and T peak 3. Experimental result

Relation between H and T peak linear relation 3. Experimental result

Relation between H and T peak E(L) ~ B (L) -  q M L 3 ) 1/2 H H ~ - q M -1/2 L -3/2 k B T peak + q M -1/2 L -3/2 B(L) barrier energy Zeeman energy Appearance of peak at k B T peak ~ E(L) Linear relation between H and T peak L h < D 3. Experimental result

Relation between H and T peak deviation from linear relation 3. Experimental result

Relation between H and T peak Deviation from linear relation between H and T peak L h > D Estimation of L h 3. Experimental result Possible  estimation  of  in L h ~ h - 

4. Summary of behavior of spin glass nanoparticle in magnetic field 1. SG domain size and the critical exponent can be evaluated. 2. Field crossover length and the critical exponent can be evaluated.

4. Summary of behavior of spin glass nanoparticle in magnetic field 1. SG domain size and the critical exponent can be evaluated. 2. Field crossover length and the critical exponent can be evaluated.

Concluding remarks · Ambiguities in temperature perturbation can be removed using bond perturbation based on the photo illumination on SG semiconductor. · Effect of bond perturbation appears through the decrease in overlap length. · SG domain size, field crossover length and the corresponding exponent can be quantitatively evaluated using SG nanoparticle.

Concluding remarks · Ambiguities in temperature perturbation can be removed using bond perturbation based on the photo illumination on SG semiconductor. · Effect of bond perturbation appears through the decrease in overlap length. · SG domain size, field crossover length and the corresponding exponent can be quantitatively evaluated using SG nanoparticle.

Concluding remarks · Ambiguities in temperature perturbation can be removed using bond perturbation based on the photo illumination on SG semiconductor. · Effect of bond perturbation appears through the decrease in overlap length. · SG domain size, field crossover length and the corresponding exponents can be quantitatively evaluated using SG nanoparticle.