Correlating supercooling limit and glass-like arrest of kinetics for disorder-broadened 1st order transitions: relevance to phase separation

0.11 MB·English

by  P. Chaddah

Correlating supercooling limit and glass-like arrest of kinetics for disorder-broadened
1st order transitions: relevance to phase separation.
P. Chaddah and A. Banerjee
UGC-DAE Consortium for Scientific Research (CSR)
University Campus, Khandwa Road, Indore 452 017, India.
S. B. Roy
6
Magnetic and Superconducting Materials Section,
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Raja Ramanna Centre for Advanced Technology, Indore 452013, India.
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(Dated: February 6, 2008)
2

n Coexistingferromagnetic(FM)andantiferromagnetic(AFM)phasesoverarangeoftemperature
a (T)andmagneticfield(H),havebeenreportedinmanymaterials. The1storderFM-AFMtransition
J is completed over a broad T (or H) range; this is ascribed to a landscape of free-energy density in

5 systems with frozen disorder. Kinetic arrest, akin to glass transition, has been reported in doped
CeFe2,La-Pr-Ca-Mn-O,Gd5Ge4,etc., suchthatthecoexisting fraction isfrozen. Thede-arrest,or

] melting, of this glass-like arrested state is seen to occur over a range of temperatures, implying a
l
e landscape (of TK or Tg). We argue that measuring magnetization along various specific paths in
- H-Tspacecanhelpinferwhetherthelandscapesoffree-energyandforkineticarrestarecorrelated.
r This will help to determine whether disorder affects glass formation, and the underlying 1st order
t
s transition, in contrasting (or similar) ways.
.
t
a
PACSnumbers: 75.30.Kz,75.60.Nt,75.47.Lx
m
-
d First order phase transitions (FOPT) that can be Since the correlation length is finite, the number N of
n
causedbyeithervaryingtemperatureorbyvaryingHare these regions (and thus of lines in the band) could be
o
ofcurrentinterestbecausetheseoccurinvariousmagne- large but would be finite. We propose to focus on the
c
[ tocaloricmaterials,colossalmagnetoresistancematerials, quasi-continuum of lines forming the band.

magneticshape-memoryalloysetc.,andarealsobelieved In a parallel development the disorder-broadened
1
v tobe the causeforthe functionalpropertiesofthesema- FOPTsandtheirslowdynamicsorhinderedkineticshas
5 terials [1]. In the absence of disorder, the FOPT occurs been under investigation [5, 6, 7, 8, 9, 10]. It is believed
9 at a sharply defined (HC, TC) line in the 2-control vari- that in variousmaterialsthe kinetics is actually arrested
0 able (H, T) space. Many of these functional magnetic (on experimental or laboratorytime scales)and a ‘glass’
1
materialsaremulti-componentsystemswhoseproperties isformed[11],andspecifically,theFOPTisfullyorpar-
0
6 become more interesting under substitution. Such sub- tially,arrestedatlowtemperatures. Thearrestoccursas
0 stitutionsareanintrinsicsourceoffrozendisorder. Early onecools,andthisstatemeltsorgets‘de-arrested’overa
/ theoreticalargumentsofImryandWortis[2]showedthat rangeoftemperature[8,9,10]asonewarms. Inaddition
t
a such samples would show a disorder-broadened transi- toCeFe2,these effectshavebeenseeninGd5Ge4 [7],La-
m
tion, with a spatial distribution of the (HC, TC) line Pr-Ca-Mn-O [9, 10], Nd-Sr-Mn-O [12, 13], Nd7Rh3 [14]
- across the sample. The first visual realization of such (seealsoreferences[5and6]). Ifsuchakineticarrestwere
d
n a local variation was provided by Soibel et al. [3] for to occur below a (HK, TK) line in the pure system, the
o the vortex melting transition. A similar visual realiza- disordered system would have a (HK, TK) band formed
c tion for an antiferromagnetic (AFM) to ferromagnetic out of the quasi-continuumof (HK, TK) lines. Eachline
:
v (FM) transition, in Ru-doped CeFe2, was provided by would correspond to a local region of the sample. If the
i Roy et al. [4] for the FOPT being caused by variation lines in each of these bands correspond to different re-
X
of temperature (with field held constant), and also by gions of the sample, can one seek a correlation between
r
a the variation of field (with temperature held constant). the position of a line in the (HK, TK) band and the po-
The occurrence of a landscape of free energy densities, sition of the corresponding (i.e. from the same region)
and a spread of local (HC, TC) values across the sam- line in the (H*, T*) band? We now consider isothermal
ples, would result in the (HC, TC) line being broadened MvsHmeasurements,afterfield-cooling(FC)invarious
into a band for samples with frozen disorder. The spin- fields, as a means of answering this question.
odallinescorrespondingtothelimitofsupercooling(H*, Let the high-T state be AFM and the low-T ground
T*)andcorrespondingtothelimitofsuperheating(H**, state be FM. Since a higher field favours the FM phase,
T**), would also be broadened into bands [5]. Each of the (H*, T*) band moves to higher T at higher H. We
these bands corresponds to a quasi-continuum of lines; take the (HK, TK) band to lie above the (H*, T*) band
eachlinecorrespondstoaregionofthedisorderedsample at zero field (to be consistent with the observation in
with length-scale of the order of the correlation length. La-Pr-Ca-Mn-O that zero-field cooling (ZFC) results in
2
fully arrested AFM), and to rise to higher H as T is same temperature in each case. The M(T) curves will
lowered(since FC inlargefieldgivesFM).This is shown then be as shown in the main panel of Fig. 1(c). It is
in the schematic in Fig. 1(a). The bands are actually trivialto arguethatifthe twolandscapesarecorrelated,
a quasi-continuumofN-lines, N=4 having been depicted then de-arrest will start at the same T in each case, but
in the schematic. We thus have 3 groups (say x, y and fullconversiontoFMwouldoccurathigherTforcooling
z) of these N lines in each of the T* and TK bands. We in the lower field. The M(T) curves would qualitatively
assumethatthehigh-Tendofthe(H*,T*)bandandthe resemble the schematic in the inset of Fig. 1(c) which is
low-Tendofthe(HK,TK)bandcorrespondtothesame verydifferentfromthe case whenthe twolandscapesare
local region (i.e. the two bands are anti-correlated), as anti-correlated.
indicatedintheschematic. Inpath1wecoolinzero-field, It is easy, given the schematic bands in Fig. 1(a) to
allT*linesliebelowTK lines,andentiresampleisfrozen visualize magnetization measurements under other H-T
in AFM at TO. As H is raisedat TO, regions in group x paths. Itisassertedthatthecaseofcorrelatedlandscape
will start de-arresting at the field marked by horizontal and that of anti-correlated landscapes predict qualita-
arrow 1. As H rises, group y and then group z regions tively distinct behavior.
will de-arrest into FM phase. For FC along path 2, the We have so far been considering the case where the
regions in group x will transform from AFM to FM, but low (H, T) ground state is FM; we now consider the
the regions in group y and z are arrested in AFM phase case where the low (H, T) ground state is AFM. This
at TO. On raising H isothermally, de-arrest of group corresponds to the observations in doped CeFe2 and in
y will start at the field 2 indicated by horizontal arrow, (NdSrSm)MnO3. Allargumentsmadeearliergothrough
andde-arrestwillbecompleteonexitingtheTK bandat with appropriate changes, the supercooling spinoidal
horizontalarrow4. Similarly,forFCalongpath3,group band (H*, T*) and the kinetic arrest band (HK, TK)
x and y regions will transform to FM on cooling to To, are depicted in Fig. 2(a). The frozen FM fraction is
andde-arrestofgroupzwillstartat3. ForFCalongpath larger at higher H. De-arrest occurs in isothermal case
4,entiresampleisinFMphaseatTO. Followingeachof by reducing H (however it may not be complete even at
the four FC paths depicted in Fig. 1(a) will thus result H = 0). Fig. 2(b) shows the qualitative M-H expected
in M-H curves shown in the main panel of Fig. 1(b); if the two landscapes are anti-correlated, while the inset
de-arrest will start at the corresponding points during shows these for the case when they are correlated. De-
isothermalincreaseoffield, and willbe completedatthe arrest can also be caused by heating, M(T) should be
highest H end of the (HK, TK) band. measured after lowering the field isothermally. Fig. 2(c)
On the contrary, if the two bands are correlated (i.e. is the counterpart of Fig. 1(c); again qualitatively dif-
the high-T end of the (H*, T*) band and the high-T ferent behavior distinguishes the case of correlated and
end of the (HK, TK) band correspond to the same local anti-correlatedbands.
region) then the frozen AFM regions will start getting To conclude, if a region with above average T* has
de-arrested as H rises into the lower end of the (HK, above average TK , then the M-H and M-T curves ob-
TK)bandindependentofthefieldinwhichthesampleis tainedbyfollowingspecifiedpathsinthe(H,T)spaceare
cooled. The field at which de-arrest starts depends only qualitatively distinct than if that region has below aver-
on the temperature at which H is raised isothermally. age TK (i.e. higher T* region has lower TK). It would
The de-arrestwill be complete when all the frozen AFM be important to understand why disorder influences T*
regions are de-arrested. Since freezing is less at higher and TK in contrasting (or similar) manner.
coolingfield, de-arreststops atlowerHwhenthe sample
is cooled in higher field. The inset of Fig. 1(b) shows
a qualitative schematic of how M-H curves would look
undercoolingindifferentfields,ifthetwolandscapesare
correlated. This is qualitatively very distinct from what [1] E Dagotto, T. Hotta and A. Moreo, Phys. Rep. 344,
is expected in the case of anti-correlatedbands. 1 (2001); E. Dagotto, Nanoscale Phase Separation
and Colossal Magnetoresistance, Springer Verlag, Berlin
We now consider measuring magnetization under one
(2003) and references therein.
more path in H-T space. We field-cool the sample, in [2] Y Imry and M Wortis, Phys.Rev.B. 19, 3580 (1979).
different fields, to TO and isothermally raise the field to [3] A Soibel et al., Nature(London) 406, 283 (2000).
that used for path 4 (H4) shown in Fig. 1(a). From [4] S. B. Roy et al., Phys. Rev.Lett. 92, 147203 (2004).
this field (H4), we raise the temperature with field held [5] M. A. Manekar et al., Phys. Rev.B 64, 104416 (2001).
constant at H4. The arrested AFM regions will get de- [6] K. J. Singh et al., Phys. Rev.B 65, 094419 (2002).
[7] M. K. Chattopadhyay et al., Phys. Rev. B 70, 214421
arrestedatdifferenttemperatures;thatcooledby path3
(2004).
will convert to FM starting at the T marked by vertical
[8] M. K. Chattopadhyay et al., Phys. Rev. B 72, R180401
arrow 3. Similarly for cooling by path 1 and 2. The
(2005).
de-arrest will start at lower temperatures for cooling in [9] P. A.Sharma et al., Phys.Rev.B 71, 224416 (2005).
lower field, but full conversion to FM will occur at the [10] L. Ghivelder and F. Parisi, Phys. Rev. B 71, 184425
3
(2005).
FIG.2: (coloronline)(a),(b)and(c)arethecounterpartsof
[11] Themetastablekineticallyarrested(orglass)stateisdif-
figures1(a), 1(b)and1(c) respectively,for thecasewhenthe
ferent from the metastable supercooled state in that the
low-TstateisAFM.M-Hcurvesof(b)areobtainedbyFCin
latter (but not the former) will undergo a metastable to
stable transformation on lowering of temperature. different fieldsto TO, and then reducingthethefield tozero
[12] H.Kuwahara et al., Science 270, 961 (1995). isothermally. M-T curves of (c) are obtained by reducing
[13] Y.Tokura et al., Phys. Rev.Lett. 76, 3184 (1996). the field at TO to a finite value, and then heating in the
same constant field. As seen from the insets of (b) and (c)
[14] K. Sengupta and E. V. Sampathkumaran, Phys. Rev. B
(Rapid, In press). correlatedTK andT*bandswouldgivequalitativelydistinct
M-H and M-T curves.
FIG. 1: (color online) Schematics of H-T phase diagrams as
well as the corresponding M-H and M-T curves after cool-
ing in different fields for the case with FM ground state. (a)
showstheH-Tdiagramwiththeanti-correlatedbandsforthe
case where the high-T state is AFM and the low-T equilib-
rium phase is FM. Only 3 regions (viz. x, y, z) out of the
Nregionsrepresentedbythequasi-continuous(H*,T*)band
areshown. Thehigh-Tsideofthe(H*,T*)bandisshownby
continuous line followed by dashed, dotted and dash-dotted
lines. The corresponding 3-regions and the dividing lines in
the (HK, TK) band appear in reverse order because of anti-
correlation. For the first measurement protocol, after FC in
differentHtoTO following paths1-4(1beingZFCpath)the
fieldsforonsetofde-arrestduringtheisothermalincreaseinH
(at TO) are shown byhorizontal arrows for therespectiveH.
Along the path-1 the sample is arrested completely in AFM
phase while along path 4 the sample completely converts to
FM phase during FC so does not have arrested phase. The
variation in M resultingfrom thisisothermal increase in H is
sketchedinmainpanelof(b). SteepincreaseinMstartingat
progressivelyhigherHisduetode-arrestfortherespectiveFC
paths starting at higher H, as depicted by horizontal arrows
in(a). Theinset of(b)showstheexpectedM-Hbehaviorfor
suitably sketched correlated bands (not shown). (c) depicts
the next measurement protocol, after FC along paths 1-3 of
(a) the H is isothermally raised to that of the path 4 (H4),
the M is measured while increasing the T from TO. The re-
sulting M-T is shown in the main panel. The abrupt change
in the slope of M occurring at progressively higher T indi-
cates the increase in the T at which de-arrest begins (during
heating) at H4, for the respective FC paths, as depicted by
verticalarrows in(a). Theinset of (c)shows theM-T curves
for suitably sketched correlated bands(not shown).
4
Fig. 1a
H
)
TK
(
,
HK z 4 H*,
( y z T
*
)
y
x 3
x
2
1
H 4
4
1 2 3
3
2
FM
AFM
1
T T
O
5
Fig. 1b
M
4
M
4
3
3 3
2
2
2
1
1 1 H
H
6
Fig. 1c
M
4 M
4
3
3
3
2
2
2
1
1 1 T T
O
T T
O
7
Fig. 2a
H
(
H
*) K,
T T
H*, z z K )
( y y
x x
3
2
3
1
2
AFM
FM
1
T T
O
8
Fig. 2b
M
3
M
3
2
2
1
1
H
H
9
Fig. 2c
M
4
M
4
3
3
2
2
1 1
T T
O
T T
O