Aging behavior of spin glasses under bond and temperature perturbations from laser illumination

0.25 MB·English

by  Ryuta Arai

Aging behavior of spin glasses under bond and temperature perturbations from laser
illumination
R. Arai, K. Komatsu, and T. Sato
Department of Applied Physics and Physico-Informatics, Keio University,
3-14-1 Hiyoshi, Kohoku-ku, Yokohama-shi, Kanagawa 223-8522, Japan
(Dated: February 4, 2008)
7
We have studied the nonequilibrium dynamics of spin glasses subjected to bond perturbation,
0
which was based on the direct change in the spin-spin interaction ∆J, using photo illumination
0
2 in addition to temperature change ∆T. Differences in time-dependent magnetization are observed
between that under ∆T +∆J and ∆T perturbations with the same ∆T. This differences shows
n thecontribution of ∆J to spin-glass dynamicsthrough the decrease in theoverlap length. That is,
Ja theoverlaplengthL∆T+∆J under∆T+∆J perturbationislessthanL∆T under∆T perturbation.
Furthermore,weobservethecrossover betweenweakly and strongly perturbedregimes underbond
6 cyclingaccompanied bytemperature cycling. These effects of bondperturbation strongly indicates

theexistence of both chaos and the overlap length.
]
n
PACSnumbers: 75.50.Lk,75.50.Pp,75.40.Gb
n
-
s
i I. INTRODUCTION fact,severalpapers18,19,20,21 claimthattherejuvenation-
d
. memory effects observed in temperature cycling can be
t
a Spin glass has been studied for the past several attributed to the differences among the length scales
m causedbythechangeintemperature. Ifthedirectchange
decades, but many questions about the nonequilibrium
- dynamics ofspinglassstill remain. To clarifythe nature in the bond,∆J, can be used in this kind of experiment
d without the change in time scales, it is expected that
of spin glass below the transition temperature, the ag-
n
o ing behavior1 in the relaxation of magnetization in spin the chaotic effect and the overlap length could be more
clearly analyzed.
c glasses has been actively studied. Especially, the aging
[ of spin glasses subjected to perturbations ∆X, such as The direct change in the spin-spin interaction

changesintemperature∆T andinbondinteraction∆J, ∆J can be realized through the photo excitation
3
of carriers using a semiconductor spin glass, E.g.,
v has been extensively studied because it shows character-
8 istic behaviors peculiar to spin glasses, such as memory Cd1−xMnxTe.22,23,24,25 The relaxation in thermorema-
4 and rejuvenation.2,3 These behaviorswere interpretedin nent magnetization and that in isothermal remanent
2 terms of the phenomenological scaling theory, called the magnetization of Cd1−xMnxTe were observed under un-
1 dropletmodel.4,5,6 Accordingtothistheory,thememory polarized light illumination.26 Recently, we studied the
0 andrejuvenationeffectsareexplainedintermsofthecon- aging behavior of Cd1−xMnxTe under photo illumina-
6
ceptofchaosaccompaniedbytheoverlaplengthL .4,6 tion, and showed that the ∆J contribution can be de-
0 ∆X
duced by comparing the data under the ∆T +∆J and
/ The correlation between two equilibrium states, before
t ∆T perturbationswiththesame∆T.27Todate,however,
a andaftertheperturbation,disappearsatthelengthscale
m L beyond the overlaplength L . However,the chaotic therehasbeennosystematicstudyofagingbehaviorun-
∆X
der bond perturbation. It is essential to obtain evidence
nature appears even at weak perturbation ∆X that sat-
-
d isfies L < L .7,8,9 At strong perturbation ∆X that of the existence of the chaotic effect and of the change
n ∆X in the overlap length expected in the droplet model4,5
satisfies L > L , the aging effect before the pertur-
∆X
o through the analysis of bond perturbation data.
bation is not easily removed, but the memory effect is
c
In this study we first confirm that bond perturba-
: observed. These contradictory aspects can be explained
v based on the ghost domain scenario.7,10,11,12 Thus, the tion using photo illumination affects the spin-glass dy-
i namics. We estimated that ∆J ∼ 0.14 ∼ 0.40K at
X crossoverbetweenaweaklyperturbedregime(L<L∆X)
and a strongly perturbed regime (L <L )11,12 should ∆T =0.26K.Thesecondpurposeistoclarifythecharac-
r ∆X
a be clarified so that we can gain an intrinsic understand- teristicsofoverlaplengthandtospecifythecrossoverbe-
tween weakly and strongly perturbed regimes to demon-
ing of the rejuvenationand memory effects based on the
droplet picture. strate the validity of the droplet picture.
So far, the experimental studies12,13,14,15,16 and
simulations17,18,19 of spin glasses, have been conducted
exclusively under the temperature cycling protocol. In II. EXPERIMENTAL DETAILS
such an experimental protocol based on temperature
change, however, this change inevitably affects the ther- The sample was a single crystal of Cd Mn Te
0.63 0.37
mal excitation of the droplet and thus leads to strong (band gap energy E = 2.181eV) that was prepared us-
g
separation of the time scales.10 This makes it difficult ing the vertical Bridgeman technique. The magnetiza-
to demonstrate the existence temperature chaos. In tion of the sample, which was a plate 1.2 mm thick, was
2
660
6 LIGHT H
u] t
m p
e 4 t
640 FC -310 2 w D T
[
u] m 0 Tm ts
m 0 400 800
6 e 620 H [Oe] 0 t
-0
1
[ ZFC
m FIG.2: Experimentalprotocolofbond-cyclingprocessunder
photo illumination. The sample was first cooled to Tm =
600 Tf = 10.7 K 7K and aged during tw = 3000s (initial aging stage). The
perturbationwassubsequentlyaddedduringtp(perturbation
stage) using photo illumination. After the perturbation was
stopped,H of100Oewasappliedandthemagnetizationwas
580 measured as a function of t (healing stage).
4 6 8 10 12
T [K]
ble (∼10K/min)from30Kwhichis abovethe transition
FIG.1: TemperaturedependenceofZFCandFCmagnetiza-
temperature T . Then, the temperature T was held for
tionsofCd0.63Mn0.37TeinH =100Oe. Thefreezingtemper- t (=3000s) (ignitial aging stage). After mthat, the per-
ature of ∼ 10.7K estimated by this graph. The inset shows w
thefield dependenceof themagnetization at 7K (=Tm). turbation was given to the sample during tp using the
photo illumination (perturbation stage). After the light
was turned off, a magnetic field H of 100 Oe, at which
the linear field-dependent magnetization was held (inset
measured by a Quantum Design MPMS5 superconduct- of FIG. 1)), was subsequently applied. After t ∼ 60s,
s
ingquantuminterferencedevice(SQUID)magnetometer. the magnetic field H of 100 Oe is stabilized, and then
Figure 1 shows the temperature dependent magnetiza- themagnetizationM wasmeasuredasafunctionoftime
tion under FC (field-cooled) and ZFC (zero-field-cooled) t (healing stage).
conditions in H = 100Oe.29 The spin-freezing temper- The dynamics of a spin glass below T is governed
g
ature Tf ∼ 10.7K was evaluated. Light was guided to by excitations of the droplet.4 The size LTm(t) of the
the sample through a quartz optical fiber so as to be droplet, which was thermally activated at T within the
m
parallel to an external magnetic field. The light source time scale t, is given by the following equation,4
was a green He-Ne laser with λ = 543.5nm, (2.281eV),
where this photon energy was slightly larger than the k T ln(t/τ ) 1/ψ
B m 0
band gap energy of the sample. One side of the sam- LTm(t)∼L0(cid:20) ∆(T ) (cid:21) . (1)
m
ple was coated with carbon. If light was illuminated
on the carbon-coated side, the light was absorbed in a Consequently, a significant difference in time scales ex-
carbon black body and, thus only the thermal contri- isted even between two close temperatures, T and
m
bution ∆T appeared. When the light was illuminated T + ∆T. Therefore, we define the effective duration
m
on the opposite side, a change in bond interaction ∆J t (T ) of the perturbation10 according to
eff m
appeared in addition to ∆T.28 We determined the sam-
ple temperature during the illumination based on the L (t )=L (t ), (2)
Tm+∆T p Tm eff
change in field-cooled magnetization as shown in FIG.
1. The photo-induced magnetization in Cd0.63Mn0.37Te or
wasscarcelyobserved(less than0.01ofthe totalmagne-
tizationchangebythephotoillumination),28andthuswe t (T +∆T)=τ (t (T )/τ )Tm/(Tm+∆T), (3)
p m 0 eff m 0
were able to neglect it. The light intensity was adjusted
so as to obtain the same increment of sample tempera- whereτ (∼~/J ∼10−13s)isamicroscopictimescale.30
0
turesunder boththe illuminationconditions. This made When we discuss the data below, we convert the actual
it possible to consideronly the ∆J contributionby com- durationofthe perturbationt (T +∆T)into the effec-
p m
paring the ∆T +∆J data with the ∆T data. We note tive duration t (T ).
eff m
that the change in temperature by the illumination was
given to a sample with step-like heating and cooling.28
Thus we could also neglect the effect of the finite cool- III. EXPERIMENTAL RESULTS
ing/heating rate.12,17
The time dependence of magnetization was measured We focused on the relaxation rate of the magnetiza-
according to the following procedure. (Fig. 2) The sam- tion, S = (1/H)dM/dlogt, measured under the various
ple was zero-field-cooleddown to T as rapidly as possi- conditions of strength and duration of the perturbation.
m
3
1.0 (a) D T=0.26K (b) D T=0.26K
D T D T+D J
0.8
x
a
m0.6
S
/
S
0.4 no illumination no illumination
teff=125sec teff=380sec teff=125sec teff=380sec
teff=1100sec teff=1900sec teff=1100sec teff=1900sec
0.2 teff=3800sec teff=13000sec teff=3800sec teff=13000sec

1.0
(c) D T=1.05K (d) D T=1.05K
D T D T+D J
0.8
x
a
m0.6
S
/
S
0.4 no illumination no illumination
teff=230sec teff=720sec teff=230sec teff=720sec
teff=2200sec teff=3700sec teff=2200sec teff=3700sec
0.2 teff=7600sec teff=26000sec teff=7600sec teff=26000sec

2 3 4 2 3 4
10 10 10 10 10 10
t [sec] t [sec]
FIG. 3: (Color online) Time dependenceof therelaxation rate S at 7K. Solid curvesshow S, measured after the waiting time
tw =3000swithoutillumination(isothermalaging). Figure(a)(filledsymbol)and(b)(opensymbol)showtherelaxationrates
S atvariousteff for∆T =0.26K under∆T and∆T+∆J perturbations,respectively. Figure(c)(filledsymbol)and(d)(open
symbol) show the relaxation rates S at various teff for ∆T =1.05K under ∆T and ∆T +∆J perturbations, respectively. All
thedata are normalized by themaximum height of S without photo illumination.
Since we observed the peaks in the perturbation time- and3(d)(∆T =1.05K),themainpeakinS isdepressed
dependent data of S, the height of each peak and the with increasingt in a more pronouncedway compared
eff
corresponding peak position are important for our dis- with the data at ∆T = 0.26K. For long t , S becomes
eff
cussion. almost flat, but the main peak is incompletely erased.
The solid curves in FIG. 3 show the time depen- Furthermore, in FIGs. 3(c) and 3(d), a small peak ap-
dence of the relaxation rate S, measured after the aging pears around t ∼ 100s (we call this the sub peak) ex-
timet =3000swithoutillumination(isothermalaging). cept for short t , and the sub-peak becomes more pro-
w eff
Thesecurvesshowapeakatt∼3000s,whichisatypical nounced with increasing t . The sub-peak in FIG. 3(d)
eff
behavior observed in many spin glasses.31 is less sensitive to t compared with that in FIG. 3(c).
eff
FIG. 3 also shows the typical data of perturbation In FIG. 3(d), the sub-peak is so close to the main peak
time-dependentS atT (=7K)ofthesample,wherethe that the two peaks are insufficiently separable. We note
m
constant temperature increment ∆T (=0.26K, 1.05K) is that some curves in S in FIG. 3 show a sudden increase
added during teff for the perturbation. The left figures at large values of t (e.g., S for teff ∼ 7600s in FIG. 3(d)
((a)and(c))andthe rightfigures((b)and(d))showthe (⋊⋉ symbols)). This may be due to a small fluctuation in
dataunder∆T and∆T+∆J perturbations,respectively. the sample temperature.
All the data are normalized by the maximum height of
S without photo illumination. In FIGs. 3(a) and 3(b)
(∆T = 0.26K), the peak in S at t ∼ t (we call this
w IV. DISCUSSION
the main peak) becomes gradually depressed compared
with the isothermal aging curve as t increases. The
eff
A. Theory based on the ghost domain scenario
depression of S in Fig. 3(b) is more pronounced than
that in FIG. 3(a) at the same t . In addition, the peak
eff
position in the main peak shifts to a longer time as t Recently, aging behavior under the bond or tempera-
eff
increases in both FIGs. 3(a) and 3(b). In FIGs. 3(c) ture cycle has been explained based on the behavior of
4
(a) D T = 0.26K (b) D T = 0.40K
c] 104
e
s
[
k
a
e
p
t D T D T
D T+D J D T+D J
103
3
(c) D T = 0.69K (d) D T = 1.05K 4
D T 2
ec] 104 D T+ D J 100
s 8
[k 6
a
tpe D T 103 104
t [sec]
D T+D J eff
103
103 104 103 104
t + t [sec] t + t [sec]
eff w eff w
FIG. 4: (Color online) The teff +tw dependent tpeak at various values of ∆T. The increments of temperature under photo
illumination, ∆T, are 0.26K, 0.40K, 0.69K, 1.05K. Solid lines satisfies the equation tpeak =tw+teff. Filled symbols and open
symbolsshowtpeak under∆T and∆T +∆J perturbations,respectively. Theinset shows teff-dependentt′peak. Thesymbolsin
theinset correspond to those in themain frame.
domains in terms of the ghost domain picture.10,11,12 In thanL ,astronglyperturbedregimeappears,inwhich
∆X
the following paragraphs, we interpret our results based the initial spin configuration is unstable with respect to
onthebehaviorofthedomainunderthebondortemper- droplet excitation and a new equilibrium state appears.
aturecycleinthe sameway. We divideourexperimental Thissuggestsachaoticnature. Thechaos,however,does
protocolinto three stagesaccordingto Fig. 2: the initial not appear abruptly7,8, and there exists a crossover be-
agingstage in whichthe equilibrium state Γ belongs to tween the weakly and strongly perturbed regimes.
A
the environment A−(Tm,J), the perturbation stage in In the weakly perturbed regime, the domain belong-
which the equilibrium state ΓB belongs to the new envi- ing to ΓA is weakly modified and the order parameter
ronment B−(Tm+∆T,J +∆J), and the healing stage ρ slowly decreases in the perturbation stage. The order
at the environment A. parameter in the domains is easily recovered during the
Intheinitialagingstage,thedomainsbelongingtoΓA healingstage. Thus,therecoverytime τrec,whichis nec-
atTmgrowduringtwaccordingtoEq. (1). Inthepertur- essary for the order parameter to saturate to 1, is given
bation stage, the perturbation∆X (∆T or ∆T +∆J) is as
appliedfromt tot +t . Duringtheperturbationstage,
w w p
the ”overlap” between the equlibrium states ΓA and ΓB τrweecak ∼teff. (5)
disappears at the length scale beyond the overlaplength
L∆X. The relation between L∆X and the perturbation Inthis regime,the size of domainbelongingto ΓA grows
∆X is given as4,6: accumulatively so as to neglect the perturbation.
L =L |∆X/J|−1/ζ. (4) In the strongly perturbed regime, the spin configura-
∆X 0
tion in domains belonging to Γ is completely random
A
The chaos exponent ζ is given by ζ = d /2−θ (> 0), beyond the length scale of L , and the domains be-
s ∆X
where d is a fractal dimension and θ is a stiffness expo- longingto Γ growduring the perturbationstage. How-
s B
nent. Theoretically,temperatureandbondperturbations ever, the effect of the initial domain of Γ remains as
A
areequivalentwith respectto the overlaplength L .11 a ghost11,12, i.e., the domains, that grow up to L (t )
∆X Tm w
We candistinguish the weaklyandstronglyperturbed duringinitialaging,canvaguelykeeptheiroverallshapes
regimesbasedontherelationshipbetweenoverlaplength (whicharecalledghostdomain),andthedomaininteriors
L and the domain size grownduring eachstages.11,12 are significantly modified due to the growth of domains
∆X
If L (t ) < L , a weakly perturbed regime ap- Γ . Thus, the order parameter ρ significantly decreases
Tm+∆T p ∆X B
pears, in which the rejuvenation scarcely emerges.9 If (but does not reach zero). When the perturbation is re-
all the L (t ), L (t ), and L (t) are greater moved,the system recoversthe initial spin configuration
Tm w Tm+∆T p Tm
5
1.0 0.6
D T=0.69K 0.5
0.9 D T=0.26K
0.4
r 0.8 D T=0.40K 103 104
0.7 Filled: D T D T=1.05K
Open: D T+D J Filled: D T
Open: D T+D J
0.6

102 103 104 102 103 104
t [sec] t [sec]
eff eff
FIG.5: (Coloronline)Theteff dependentr atvariousvaluesof∆T. Theincrementsoftemperatureunderphotoillumination,
∆T,are0.26K,0.40K,0.69Kand1.05K.Thefilledandopensymbolsshowrunder∆T and∆T+∆J perturbations,respectively.
The inset shows teff-dependentr′. The symbols in the inset correspond tothose in themain frame.
(healing stage). The recovery time τ is given as other words, r is the measure of the memory after the
rec
perturbation.12 The value of r is shown as a function of
τrsetcrong ≫teff. (6) teff in FIG. 5.
In the completely weakly perturbed regime
In this regime, the domain belonging to Γ grows non-
A (L (t ) ≪ L ), the order parameter fully re-
Tm eff ∆X
accumulatively.
covers at t ∼ t according to Eq. (5). However, close
peak
to the strongly perturbed regime (the crossover regime
between the weakly and strongly perturbed regimes),
B. The role of the relaxation rate under the
the order parameter does not completely recover at
cycling
t = t +t . This leads to the decrease in the height of
w eff
main peak. In the strongly perturbed regime, the order
The relaxation rate S is characterized under the tem- parameter insufficiently recovers because of the long re-
perature or bond perturbations shown in Sec. IVA, coverytime τstrong giveninEq. (6). Thus,r isgradually
rec
through the peak position and height in the time de- depressed as t increases because of the rapid increase
eff
pendent S. First, we define the characteristic time tpeak in τrsetcrong. In addition, when the period ts is necessary
corresponding to the position of the main peak. The until the applied field is stabilized in a superconducting
value of tpeak is shown as a function of teff +tw in FIG. magnet after the perturbation is removed, the domain
4DIftheagingisaccumulative,thespinconfigurationat grows for t up to the size L (t ). This reflects the
s Tm s
Tm+∆T in the perturbation stage is equivalent to that sub-peak.12 Thus, the sub-peak becomes pronounced as
under the isothermalagingatTm forteff. This results in the rejuvenation effects become clear.
the following relation:
t ∼t +t , (7)
peak w eff C. Bond-cycling experiment
which corresponds to the reference line in FIG. 4. In
We try to classify our data, obtained under various
the strongly perturbed regime (L≫L ), on the other
∆X
perturbation conditions, into the following four cate-
hand, the chaotic nature becomes effective and the posi-
gories: the weakly perturbed regime (we call this the
tion of the main peak shifts to a shorter time compared
W regime); the crossover regime, which is close to the
with the accumulative aging curve. In this case, t
peak
weakly perturbed regime (we call this the WC regime);
satisfies the relation,
the crossover regime, which is close to the strongly per-
t <t +t . (8) turbed regime (we call this the SC regime); and the
peak w eff
strongly perturbed regime (we call this the S regime).
During the healing stage, the order parameter of Γ ThecriteriafortheclassificationareabridgedinTABLE
A
starts to restore the domain structure grown during ini- 1. TheclassificationismainlyperformedbasedonFIG.4
tial aging, and this is probably reflected in the height of andFIG.5inwhicht andrarearrangedasafunction
peak
themainpeak. Thus,inordertocharacterizethechange of t under various amplitudes of ∆T. The condition,
eff
in the peak built in S, we define the relativepeak height i.e., t is variable and ∆T is constant, corresponds to
eff
r, which is the ratio of the height in the main peak un- the situation that the domain size L (t ) grown dur-
Tm eff
der the perturbation to that without perturbation. In ing the perturbation stage is variable while the overlap
6
Open: D T+D J
1.0 Filled: D T Open: D T+D J
t ~1400sec Filled: D T
eff
0.9 t ~2300sec
eff t ~4400sec
eff
t ~18000sec
r 0.8 Open: D T+D J eff
Filled: D T
0.7
t ~170sec
eff
t ~520sec
eff
0.6
0.2 0.4 0.6 0.8 1.0 1.2 0.2 0.4 0.6 0.8 1.0 1.2 0.2 0.4 0.6 0.8 1.0
D T [K] D T [K] D T [K]
FIG. 6: (Color online) The ∆T-dependent r at various values of teff. Almost the same values of teff are gathered together in
one graph. The left, middle, and right figures show r under teff ∼ 170 and 520s, teff ∼ 1400 and 2300s, and teff ∼ 4400 and
18000s, respectively. THe filled and open symbols show r under∆T and ∆T +∆J perturbations, respectively.
lengths L and L are constant. In addition, we Next, we turn to the data under the strongest pertur-
∆T ∆T+∆J
also pay attention to the sub-peak whose position and bation (∆T = 1.05K) prior to the discussion of complex
′ ′
relative height are shown as t and r in the insets in behaviorunderthemediumperturbation(∆T =0.69K).
peak
FIG. 4(d) and FIG. 5(b), respectively. At ∆T = 1.05K, tpeak cannot be determined at ∆T =
1.05K because the S curves are so flattened except for
First we pay attention to the data at ∆T =0.26Kun-
the short t (see FIG. 4(d)). The value of r rapidly de-
der ∆T perturbation. As shown in FIG. 4(a), the values eff
creases as t increases and becomes almost constant in
of t almost merge into the reference curve except for eff
peak
the long t region, in which r under both the perturba-
the dataatthe longestt +t , wherethe mainpeakfor eff
eff w
tionsmerge(FIG.5). Thesub-peakunder∆T perturba-
the longest t should appear at time much longer than
eff
the present observationtime window (∼104s). The sub- tion is observed except for the shortest teff and becomes
pronounced with increasing t (see the inset of FIG.5).
peak cannot be observed, and r scarcely decreases from eff
In the strongly perturbed regime, the chaotic effect sig-
1(FIG.5). Therefore,allthe dataat∆T =0.26Kunder
nificantlyemergesandthemainpeaksatisfiesEq. (8). In
∆T perturbation satisfy the criteriafor the W regime in
addition,thesub-peak,whichisattributedtotherejuve-
Table1. Thus, the accumulative aging proceeds in this
nation,isobservedaroundthetimenecessarytostabilize
condition.
the applied field, i.e., t ∼100s. Under the perturbation
Under the ∆J perturbation in addition to ∆T = s
with ∆T = 1.05K, thus, the system at long t may be
0.26K, the t except for the longest t satisfies Eq. eff
peak eff in the S regime, where the order parameter ρ becomes
(7), and the t , at the longest t , is shorter than
peak eff saturated to a level common to both kinds of pertur-
t +t (FIG. 4(a)). The value of r clearly decreases
w eff bations and the rejuvenation effect becomes noticeable.
from 1 except for the shortest t (FIG. 5). This indi-
eff Exceptforthelongt ,thesystemwouldnotnecessarily
cates that ∆J perturbation decreases the overlaplength eff
beclassifiedintotheS regime,becauseρisnotsaturated
accordingtoEq. (4). Under∆T+∆J perturbationwith
althoughthe sub-peak is observable. Therefore,this sys-
∆T=0.26K,thus, the system is not completely in the W
tem may belong to the SC regime. The system at the
regimeexceptfortheshortestt ,andthechaoticnature
eff shortest t under ∆T perturbation is classified into the
partiallyemerges. Thus,thisregimeisintheWC regime eff
WC regime because of the absence of the sub-peak.
except for the shortest t , at which the system belongs
eff
to the W regime. At ∆T = 0.69K, t almost merges into the refer-
peak
Under both the perturbations with ∆T = 0.40K (see ence curve except for the data at the longest t +t .
eff w
Fig 4(b)), the values of t almost merge into the ref- At the longest t , however, the t under ∆T +∆J
peak eff peak
erence curve except for the data at the longest t +t . perturbation is shorter than that under ∆T perturba-
eff w
At the longest t +t , the values of t under both tion. Moreover, the sub-peak appears under ∆T +∆J
eff w peak
the perturbations merge together, but lie below the ref- perturbationonlyatthelongestt (seetheinsetofFIG.
eff
erence curve. Under ∆T perturbation, r is clearly lower 4). Under both the perturbations with ∆T = 0.69K, r
than 1 except for the small t , while r under ∆T +∆J rapidly decreases from 1 as t increases, but does not
eff eff
perturbation is clearly lower than 1 over all range of t become saturated(FIG. 5). Under the ∆T +∆J pertur-
eff
(FIG. 5). The sub-peak cannotbe observedunder either bationwith∆T =0.69K,thus,thesystematthelongest
perturbations. Therefore, at ∆T =0.40K under the ∆T t gets into the SC regime, whereas it does not under
eff
perturbation, the system belongs to the WC regime ex- the ∆T perturbation. Under the ∆T perturbation with
cept forshortt , atwhichthe systembelongs to the W ∆T = 0.69K, the system belongs to the WC regime ex-
eff
regime. Under the ∆T +∆J perturbation, the system ceptfortheshortestobservationtime,atwhichitbelongs
belongs to the WC regime. to the W regime because r scarcely deviates from 1.
7
To clearly evaluate the overlap length under both the 1.2 D T
perturbations,r isabridgedunderthe conditionthatteff 1.0 S
isconstantand∆T isvariable(FIG.6). Thismirrorsthe SC
0.8
situation that the domain size grown during the pertur- K]
bation stage is fixed while the overlap length L∆T+(∆J) T [ 0.6 WC
is varied. Atthe shortestteff (∼170s)under ∆T pertur- D 0.4
bation, r scarcely deviates from 1 as ∆T increases. This
0.2
indicatesthatτ issoshortthattheorderparameterin W
rec
ghost domains easily recovers. At long t , r rapidly de- 0.0
eff
creases as ∆T increases. This shows the crossover from
1.2
theweaklytothestronglyperturbedregimesthroughthe D T+D J
1.0
decreaseintheoverlaplength. Thevaluesofraresmaller S
SC
under ∆T +∆J perturbation than under ∆T perturba- 0.8
tion, but the difference in r between the perturbations K]
becomes indistinct as ∆T increases. Ultimately it dis- T [ 0.6 WC
appears at large ∆T due to the extremely long recovery D 0.4
time. 0.2
W
0.0
TABLE I: The defenition of classification of our data under 102 103 104
t [sec]
various perturbation conditions. (1) The condition tpeak = eff
teff+tw issatisfied. (2)Subpeakisobserved. (3)Thecondi-
tionr∼1issatisfied. (4)Thevalueofrattainsthesaturation FIG. 7: (Color online) Schematic phase diagram where our
value. For example, the data that belongs to the W regime dataareclassifiedintothefourregimes: theweaklyperturbed
satisfy theconditon (1) and (3), does not satisfy (2) and (4). regime(W regime);thecrossoverregime,whichisclosetothe
weaklyperturbedregime(WC regime);thecrossoverregime,
Regime (1) (2) (3) (4) which isclose tothestrongly perturbedregime (SC regime);
W Y N Y N the strongly perturbed regime (S regime) (bottom to top).
WC Y N N N Theupperandlowerfiguresshowthediagramunder∆T and
SC Y Y N N ∆T +∆J perturbations, respectively.
S N Y N Y
∆T +∆J perturbation than under the ∆T perturbation
(see the inset of Fig. 4(d) and Fig. 5).
FIG. 7 shows a schematic phase diagram in which
Inaddition,wepayattentionto the featureinwhichr
the perturbation conditions are classified into the four
under∆T+∆J perturbationwith∆T =0.26Kis signif-
regimes. In this figure, the boundary curves are guides
icantly smaller than 1 while r under ∆T perturbation is
to help the eyes grasp the qualitative aspect. As t
eff practicallyequalto1ast approacheszero,asshownin
and ∆T increase, a systematic change from the W to eff
FIG.5. Thissuggeststhatthe∆J perturbationdecreases
the S regime is observedin the case of both the ∆T and
the order parameter whereas the ∆T perturbation does
∆T +∆J perturbations. In FIG. 7, we find a feature in
not, even at infinitesimal t . Thus, at∆T =0.26K,the
which the boundary curve in the ∆T +∆J perturbation eff
effect of ∆T perturbation on the order parameter is so
data lies below the correspondingboundary curve in the
smallthatthe∆J perturbationmakesthedominantcon-
∆T perturbation data. This can be interpreted in terms
tribution. Basedonthefeatureinwhichrunder∆T+∆J
ofthedecreaseintheoverlaplengthduetotheadditional
perturbationwith∆T =0.26Kispracticallyequaltothat
perturbation ∆J.
under∆T perturbationat∆T =0.40K,weestimatethat
∆J =0.14∼0.40K at ∆T =0.26K.
D. The effect of the bond perturbation
V. CONCLUSION
The order parameter under ∆T + ∆J perturbation
are smaller than those under ∆T perturbation with the The bond perturbation ∆J, under photo illumina-
same ∆T as mentioned above. These indicate that ∆J tion, affects the aging behavior of semiconductor spin
perturbation decreases the order parameter through the glass. We then estimated that ∆J ∼ 0.14 ∼ 0.40K at
decrease in the overlap length. This is clearly demon- ∆T = 0.26K. Thus, the bond perturbation ∆J can sig-
strated in FIG. 7 through the shift of boundary curves. nificantly change the bond configuration, although the
The behavior of the sub-peak, observed under both per- photo-induced magnetization in Cd Mn Te is neg-
0.63 0.37
turbations with ∆T = 1.05K, suggests that the rejuve- ligible small.28 This effect cannot be explained in terms
nation effect becomes pronounced due to the additional of the strong separation of the time scales on different
′ ′
∆J,becausethe t islongerandr islargerunderthe lengthscales. Weattributeittothedecreaseintheover-
peak
8
lap length, i.e. L < L . Furthermore, we ob- anismofthe bondperturbationusingphotoillumination
∆T+∆J ∆T
served the crossover from weakly to strongly perturbed should be clarified.
regimesinthebondcyclingaccompaniedbythetempera-
turecycling. Theseexperimentalresultsstronglysuggest
that ”chaos” and the overlap length, which are the key
concepts in the droplet picture, exist because the contri-
Acknowledgment
bution of bond perturbation appears only in the overlap
length.
Inthefuture,itwillbenecessarytoconductthe”pure” ThisworkwasperformedduringtheFY200221stCen-
bondcyclingexperimentunderphotoilluminationwhere turyCOEProgram. WewouldliketothankS.Yabuuchi
thereisnochangeintemperature. Inaddition,themech- and Y. Oba for their fruitful discussions with us.
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