Magnetic order, metamagnetic transitions, and low-temperature spin freezing in Ca3Co2O6: an NMR study

0.61 MB·English

by  G. Allodi

Magnetic order, metamagnetic transitions, and low-temperature spin freezing in
Ca Co O : an NMR study.
3 2 6
G. Allodi,1,∗ R. De Renzi,1 S. Agrestini,2,3 C. Mazzoli,4,5 and M. R. Lees6
1Dipartimento di Fisica e Unit`a CNISM, Universita` degli Studi di Parma, Viale G. Usberti 7A, I-43100 Parma, Italy
2Laboratoire CRISMAT, UMR 6508, Boulevard du Mar´echal Juin, 14050 Caen Cedex, France
3 Max Planck Institute for Chemical Physics of Solids, No¨thnitzerstr. 40, 01187 Dresden, Germany
4European Synchrotron Radiation Facility, BP 220, 38043 Grenoble Cedex 9, France
5 Dipartimento di Fisica, Politecnico di Milano, Piazza Leonardo da Vinci 32, I-20133 Milano, Italy
6 Department of Physics, University of Warwick, Coventry, CV4 7AL, United Kingdom
(Dated: January 28, 2011)
1
1 Wereportona59CoNMRinvestigationofthetrigonalcobaltateCa3Co2O6carriedoutonasingle
0
crystal,providingprecisedeterminationsoftheelectricfieldgradientandchemicalshifttensors,and
2
of the internal magnetic fields at the non-magnetic CoI sites, unavailable from former studies on

n powders. The magnetic field-induced ferri- and ferromagnetic phases at intermediate temperature
a (e.g.10K)areidentifiedbydistinctinternalfields,wellaccountedforbypurelydipolarinteractions.
J Thevanishingtransferred hyperfinefield at theCoI siteindicates thattheCo3+(I) orbitals donot

7 participate in theintra-chain superexchange, in disagreement with a previous theoretical model.
2 The strong Ising character of the system is confirmed experimentally by the field dependence
of the resonance lines, indicating that local moments are saturated even at the phase boundaries.

] In the vicinity of the critical fields, nuclear spin-spin relaxations detect the spin reversal dynamics
l
e of large magnetic assemblies, either Ising chain fragments or finite size domains, which drive the
- metamagnetic transitions. Such collective excitations exhibit a glassy behavior, slowing down to
r
t subacoustic frequencies and freezing at low temperature. The relevance of such slow fluctuation
s modes for the low-temperature multi-step behavior reported in the magnetization is discussed.
.
t
a
PACSnumbers: 75.30.Kz,75.30.Et,75.60.Jk,76.60.-k.
m
-
d
I. INTRODUCTION
n
o
c Thenatureofmagneticorderinthegeometricallyfrus-
[
trated trigonal cobaltate Ca3Co2O6, an Ising-type mag-
2 netexhibitinglow-dimensionalbehavior,hasbeenapuz-
v zleforoveradecade. ThecrystalstructureofCa Co O
3 2 6
2 (Fig. 1) may be viewed as the result of the alternate
4
stackingalongthe c axisofface-sharingCoO octahedra c
1 6 b
1 (CoI) and CoO6 trigonal prisms (CoII) with a rather Co oct a b a
. short CoI - CoII distance c/4 = 2.59˚A, building up COo trig
1 chains arranged over the ab plane in a triangular lat- Ca
1
tice, with a much larger spacing (inter-chain distance
10 a/√3 = 5.24˚A).1,2 The Co3+ oxidation state at both FheIxGa.g1o:na(lCsoelottrinogn.linLee)ftL:aptteircsepesctrtuivcetuvrieewofoCfat3hCeos2pOin6cinhatihnes
v: sitesisnowestablished,3,4 contrarytoearlierpredictions formed bytheCoO6 polyhedraalong thec-axis; right: cross-
for a Co2+-Co4+ charge disproportionation.5 section intheabplane,evidencingthearrangement ofchains
i
X Magnetism resides on the CoII site, where a trigo- inthetriangularlattice. Thedarkandlightpolyhedrarepre-
r nal crystal field yields a high-spin ground state with sent the CoO6 octahedra and CoO6 trigonal prisms, respec-
a tively.
a large unquenched orbital component ( L 1.7,
z
h i ≈
2S +L = 5.3), while CoI is in a low-spin state
z z
h i
(i.e. non-magnetic).3 Spin-orbit coupling gives rise to
a single-ion anisotropy term DS2 of order 70 meV inter-chain AF coupling, giving rise to a complex mag-
(corresponding to an anisotro−py fizeld B 200T netic phenomenology as a function of temperature and
anis
along c), whence the strong Ising-type character≈of mag- magnetic field.
netism in this system.2,6 Exchange coupling between Susceptibility measurements actually demonstrate the
the Co3+II ions is ferromagnetic (FM) and relatively onsetofmagneticorderatT <T 25K.2,7 Thenature
c
≈
strong along the chains, whereas it is antiferromagnetic of magnetic ordering however, has been the subject of
(AF) and much weaker between chains. While the dom- a long-lastingcontroversy. Denoting spin-up, spin-down,
inant intra-chain exchange interaction promotes quasi ormagneticallydisorderedIsingchainsas , ,0,respec-
↑ ↓
one-dimensional Ising-type ferromagnetism, the actual tively,theoreticalmodelsindicatedeitheraferrimagnetic
magneticstructureistheresultofthecompetingresidual (FI) [ ] or a partially disordered antiferromagnetic
↑↑↓
2
(PDA) structure [ 0] as the stable zero-field arrange- sented in sections IIIA, and IIIB, respectively. The cal-
↑↓
ments of the three inequivalent chains on the triangu- culated dipolar fields at the CoI sites in the FI and FM
lar lattice inthe presence of geometricallyfrustratedAF phasesarecomparedwith experimentalvalues in section
inter-chain coupling.8,9 Early neutron diffraction experi- IV. The results are discussed in section V. Two appen-
ments seemingly supported either a PDA10 or a FI7 or- dices review in some detail the complex dependence of
der,althoughpoorquantitativeagreementofbothstruc- the 59Co resonanceson magnetic andquadrupolar inter-
tures with magnetic peak intensities was later pointed actions,andthelongitudinalrelaxationfunctionofa7/2
out.11 Recent x-ray12 and neutron scattering13 data on nuclear spin.
singlecrystalshaverevealedtheincommensuratecharac-
ter of the magnetic order in this compound. They show
that the actual structure, referred to as modulated PDA II. EXPERIMENT
(MPDA),ratherconsistsoflong-wavelengthlongitudinal
spin-densitymodulationsalongeachchain,phase-shifted
The investigated sample was a single crystal of size
by 2π/3withrespecttothe neighboringchains.13 Nev-
± 1.2 1.2 5.8 mm3 (the long side parallel to the c axis)
ertheless, the MPDA phase is apparently metastable be- × ×
taken from a batch of several needle-shaped crystals ob-
low 14K, as indicated by the decreasein the intensity of
tainedbythefluxmethod. Thecrystalsweregrownusing
the MPDA magnetic peaks.11–13
the followingprocedure: a mixture ofCa Co O powder
3 2 6
The nature of the magnetic order in an externally and KCO (the flux), in a weight ratio 1/7, was heated
3
applied magnetic field is also far from clear. Increas- upto990◦Cinanaluminacrucibleforonehourandthen
ing magnetic fields applied along c tend to stabilize slowly cooled down to room temperature. A sample of
the FI phase and eventually FM inter-chain order. At thesamebatchwasemployedfortheresonantx-rayscat-
5K < T < Tc, the initial saturation of the magneti- tering study of Ref. 12. The high quality of the crystals
zation to a magnetic moment MFI 1.7µB per for- was confirmed by preliminary x-ray diffraction, energy
≈
mula unit at µ0H > Bc1 0.1T, followed by a step to dispersive x-ray, magnetization, and specific heat mea-
≈
MFM 3MFI at µ0H > Bc2 3.5T, actually points to surements.
≈ ≈
perfect FI and FM phases below and above H , respec-
c2 Magnetization measurements were performed after
tively. However,theM(H)curvesatlowertemperatures
zero field cooling, by using a vibrating sample magne-
displayapuzzlingmulti-stepbehaviorreminiscentofthe
tometer(OxfordInstruments)equippedwitha12Tmag-
quantumtunnelingofmagnetizationdetectedinmolecu-
net, with a field sweep rate of 1T/min in order to mini-
lar magnets.14,15 A number of complex magnetic super-
mize any relaxation effect. Susceptibility measurements
structures, distinct from both the FI and FM spin-chain
werecarriedoutbymeansofasuperconductingquantum
arrangements,havebeenproposedinordertoexplainthe
interference device magnetometer (SQUID) with mag-
fractional magnetization values. However, such super-
netic fields up to 5T and temperatures down to 1.8K
structures cannot account for all the plateaus observed
(Quantum Design MPMS). The magnetic measurements
in M(H).16
werecarriedoutforthe twogeometriescorrespondingto
In this paper, we address the issue of the field- the magnetic field applied parallel or perpendicular to
dependentmagneticorderofCa3Co2O6bymeansof59Co the c axis, i.e. parallel or perpendicular the direction of
nuclearmagneticresonance(NMR).Previous59CoNMR the chains and the spins. In the case of parallel geom-
research on Ca3Co2O6 polycrystalline samples, though etry the crystals were aligned using the magnetic field
successfulindemonstratingthepresenceofnon-magnetic itself at 5T as explained in Ref. 17. The alignment of
Co3+,couldonlyprovideverylimitedinformationonthe the crystals in the perpendicular geometry can be easily
magnetic structure, due to the angular averaging of the obtained thanks to their rod-like shape.
complex multi-line quadrupolar spectra into broad pow- The NMR experiments were performed by means of a
der patterns.4 The FMand FI surroundings,onthe con- home-built phase-coherent pulsed spectrometer18 and a
trary,canbeclearlyresolvedinourNMRinvestigationof fast-sweepingcold-borecryomagnet(OxfordInstruments
a high-quality single crystal, while the two field-induced EXA) equipped with a variable temperature insert as a
transitions,namelyMPDA-FIandFI-FM,wereprecisely sampleenvironment. Thecrystalwasmountedonasam-
identified at10K throughstep-like jumps inthe internal ple rotator,providing an angular span of 120◦ with re-
field and peculiar features of the spin-spin relaxations, spect to the applied field. Misalignment ±of the rotation
indicativeofglassyspindynamics. Ourstudy alsoyields axis(nominallyperpendiculartothefield)wasestimated
a detailed characterization of the chemical shift and the notto exceed5 degrees. In the caseof the c axisparallel
electricfieldgradient(EFG)tensorsatthenon-magnetic to the field, however, a precise alignment of the sample
CoI site. wasachieved,thankstoitslargemagneticanisotropy,by
The paperisorganizedasfollows. Samplepreparation loosely mounting it in the coil.
and the experimental methods are briefly described in NMRspectraweredetectedbyexcitingspinechoesby
section II. NMR spectra, providing information on the means of a standard P τ P sequence, with equal rf
− −
magnetic structures, and nuclear relaxation data, prob- pulses P of duration 3-5 µs and intensity suitably reg-
ingthedynamicalexcitationsofthespinsystem,arepre- ulated for optimum signal, and delays τ kept as short
3
as possible with respect to the dead time of the res- 40
onant probehead ( 10-25µs depending on the working
frequency). Record≈ing was carried out either by tuning 35 B =0.38T || c
ext
the probehead at discrete frequencies in a constant field
(frequency sweep mode), or by varying the applied field 30
andexciting the resonanceat aconstantfrequency (field u.]
b.25
sweepmode). Althoughanindirectmethod,wepreferen- r
a
tiallyemployedthe latterwheneverpossible(namely,far e [20
fromthemetamagnetictransitions)asityieldssmoother d
u
data, independent of the frequency response of the spec- plit15
trometer, in a fully automated procedure. m
A
Nuclear spin-spin relaxations were determined by the 10
decay of the signal amplitude in the same spin echo se-
quenceP τ P,asafunctionofvariabledelayτ. Spin- 5
− −
lattice relaxations were measured by the signal recovery
following a so-called fast saturation of the observed nu- 0
10 12 14 16 18 20 22
cleartransition(see Appendix B),obtainedwithanape- Frequency [MHz]
riodic train of 10-15 pulses.
FIG. 2: (Color online) Frequency-swept 59Co spectrum at
10 K from the majority spin-up chains of the FI phase,
III. EXPERIMENTAL RESULTS recorded in a field of 0.38 T applied along the c axis. Solid
lines are bimodal fits of the satellite peaks, vertical dash-
dotted lines mark their centersof gravity.
A. NMR spectra
We report separately the 59Co resonance spectra
thoughsizable,isneverthelessmuchsmallerthanthetyp-
recorded in the longitudinal geometry (external field
icalhyperfinefieldsdetectedinmagneticCo3+,whichare
B caxis),ageometrythatallowedusstudythefield-
indexutcked magnetic order in the system, and in transverse ofthe orderof-10T/µB and+60T/µB forthe spinand
orbitalhyperfinecomponents,respectively.21,22Thiscon-
applied fields. Interpretation of the spectra is relatively
firms that the present 59Co signals are from Co3+ ions
simple and model-independent in the longitudinal case,
in a low-spin state, in agreement with previous NMR
due to the collinearity of all the fields (internal and ex-
reports.4,19 We note that the dipolar field at site I gen-
ternalmagneticfields,andtheEFG).Inthegeneralcase,
erated by two nearest-neighborCoII moments of 5.2 µ
the dependence of the 59Co resonances on magnetic and aligned parallel to B accounts for both the positivBe
quadrupolarinteractionsisrathercomplex,asrecalledin ext
sign of the field offset B B , and its magnitude to
some detail in Appendix A. nuc− ext
withinafewpercentaccuracy. Thisisthefirstindication
thattheinternalfieldB B B arisesfromthe
int nuc ext
≈ −
1. Longitudinal applied fields surrounding magnetic ions essentially through the dipo-
A 59Co NMR signal could be detected below 15 K in lar coupling, as actually proven in detail by the internal
fieldcalculationsofSec.IV. Givenitsdominanton-chain
moderate longitudinal external magnetic fields B >
ext
dipolar origin, the positive sign of B then indicates
0.1T.SuchfieldvaluesassignthesystemtotheFIphase. int
that the nearest-neighbor Co3+ spins are aligned along
For such field values the FI phase is induced in the sys-
the direction of the applied field. The present positive-
tem. In contrast, no signal could be detected in the
offsetlinemultipletthereforeoriginatesfromnucleiatthe
MPDA phase at B <0.1T.
ext
CoI sites of spin chains aligned parallel to the external
A typicalfrequency-sweepspectrum, recordedat 10K
field, namely, the majority chains of the FI structure.
in 0.38 T, is plotted in Fig.2. The spectrum consists
in a septet of quadrupole-split Zeeman transitions ν , Qualitatively similar positive-offset spectra could be
n
n = 3,...,n = 3 (Eqn. A2), with constant frequency reproduced in increasing external fields parallel to the c
spacin−g νn+1 νn = 2.11(1) MHz, in agreement with axis (θ =0) at 10 K, up to Bext =3.5T. The resonance
Ref. 19. In th−is geometry (θ = 0), and in the presence frequency of the central line follows a linear dependence
of a cylindrical EFG (η = 0), as is actually the case on Bext (Fig. 3),
(see Sec. IIIA2), such a line spacing coincides with the
quadrupolarcouplingparameterνQ(Eqn.A3). Thereso- ν0 =aBext+b (1)
nancefrequencyν ofthecentralline,whichisunaffected
0
by the quadrupole interaction, corresponds to a field with best-fit parameters a = 10.21(1) MHz/T, b =
↑ ↑
B =2πν /59γ atthenucleuswhichislargerthanB 12.02(2) MHz (hereafter, in the subscripts denote
nuc 0 ext
byapproximately1.2T(here,59γ =2π 10.10MHz/T20 quantitiesrelatedtospin-up↑ m↓ajorityandspin-downmi-
is the gyromagnetic ratio of 59Co). Su×ch a field offset, noritychainsoftheFIphase,respectively). Ontheother
4
80 40
50
ν =16MHz
35 L 2
7048
30 1.5
z] 6046 arb.u.]25 1
MH 3.2 3.4 3.6 3.8 e [20 0.5
[0 ud 0
ν 50 plit15 3.35 3.4
m
A
10
40
5
30
2 3 4 5 6 0
B [T] 2.2 2.4 2.6 2.8 3 3.2 3.4
ext B [T]
ext
FIG. 3: (Color online) Central resonance frequency ν0 of the FIG.4: (Coloronline)Field-sweptspectrum(Bextkc)at10K
positive-offsetspectrafromthespin-upchainsineithertheFI
from the minority spin-down chains, recorded at a constant
(Bext <3.5T)ortheFMphase(Bext >3.5T),asafunction frequency ν = 16MHz. The solid line is a bimodal fit to a
of Bext kc. The dashed lines are fitsto straight lines for the septetofquadrupolarsatellites,withpositionsconstrainedby
two phases. The inset is a blow-up of thetransition region.
Eqn. A2. The inset is a blow-up of the rightmost satellite at
B−3 ≈3.36T.
hand
ν 59γB =59γ(1+K )(B +B ) (2) furthermore displaced from the expected position by ap-
0 nuc c ext int
≡ prox. -2mT (figure inset), a value well accounted for by
the demagnetization field, since the macroscopic mag-
as detailed in Appendix A. If the staggered magneti-
netization significantly deviates from the FI plateau at
zation is saturated all over the field span, the internal
field Bint is independent of Bext and, by symmetry, also H = µ−01B−3 (Fig. 11). The quadrupole coupling pa-
rameter is estimated as ν =1.97(1) MHz from the line
parallel to c. Working under this hypothesis, whose va- Q
spacing, ν = 59γ(1+K )(B B ), and is slightly,
lidity is demonstrated in the discussion, a comparisonof Q c n−1 n
−
but significantly smaller than in the spin-up chains.
Eqs. 1 and 2 simply relates the coefficients a, b to B
int
andthecaxiscomponentofthechemicalshifttensorK : The resonance frequency of the central line follows a
c
a=59γ(1+Kc),b=59γ(1+Kc)Bint,respectively. Best- similar linear dependence on Bext (Fig. 5), with slope
fit values for a↑ and b↑ then yield Bint↑ = 1.178(2) T, a↓ = 10.22(1) MHz/T, and a negative intercept b↓ =
and a sizable K 0.01. 12.48(3) MHz (Eqn. 1). The former coincides within
Resonances frco≈m the minority spin-down chains are −errorwitha↑,whencethesamechemicalshiftvalueKc
≈
marked by a negative field offset, comparable in abso- 0.01isobtained. Fromb↓,theinternalfieldatCoIinthe
lute value to the internal field in the majority chains. minority chains is estimated as Bint↓ = 1.221(4) T.
−
The signal could only be found in longitudinal fields ex- The negative-offset resonance lines from the minority
ceeding2T,sinceforsmallerexternalfieldsitsresonance spin-down chains completely disappear in external fields
frequency ν0 59γ Bint Bext falls below 10 MHz, Bext > 3.5T, while only a positive-offset septet can be
≈ | |−| |
outside the frequen(cid:12)cy range of ou(cid:12)r apparatus. A field detected, that is qualitatively similar to the one from
(cid:12) (cid:12)
sweep spectrum at 10 K, recorded at fixed frequency the majorityFI chainsbelow 3.5T andwith anidentical
of 16 MHz, is shown in Fig. 4. It consists of a mul- quadrupole splitting νQ = 2.11(1) MHz (Fig. 6). The
tiplet of quadrupole-spit lines centered at B ,23 similar integratedamplitudesofthepositive-offsetspectraabove
n
to those detected for the majority chains, with a cen- andbelow3.5T,andproportionaltothenumberof59Co
tral resonance at B = 2.792 T. The two satellites at nuclei excited in spin-up chains, have a ratio very close
0
B =3.172TandB 3.36Tarehoweverreducedin to 3:2. These facts indicate that all the spin chains are
−2 −3
≈
amplitude by approximately 75% and 90% with respect now aligned parallel to the external field, i.e. the system
to the symmetric peaks at B , B , respectively. The sig- is in a FM state.
2 3
nal loss at B B is due to the approach of the Thepositive-offsetseptetfromthespin-upchainscould
ext −2
≥
FI-FM transition at B 3.5T, which is accompanied be followed at 10K while increasing B in steps of ap-
c2 ext
≈
byanotablerelaxationphenomenonthatpartiallywipes prox. 0.1T across the field-induced FI-FM transition,
out the signal intensity over a wide field interval close without losing the signal. The resonance frequency of
to B (see below). The rightmost satellite at B is the central line is plotted vs. B in Fig. 3. Experi-
c2 −3 ext
5
25
22
ν =64MHz
21 c || B L
ext 20
B || c
20 u.] ext
Hz] arb.15
[M019 de [
ν u
18 plit10
m
A
17
5
16
2.8 2.9 3 3.1 3.2 3.3 3.4
0
B [T] 4.6 4.8 5 5.2 5.4 5.6 5.8
ext
B [T]
ext
FIG. 5: (Color online) Central resonance frequency ν0 of the
spectra from theminority spin-downFI chains,as afunction FIG. 6: (Color online) Field-swept (Bextkc) 59Co spectrum
of Bext kc. The solid line is a fit to Eqn.1. in the FM phase at 10 K, recorded at a constant frequency
ν =64MHz. Solidlinesarebimodalfitsofthesatellitepeaks,
vertical dash-dotted lines mark theircenters of gravity.
mental points clearly follow two different straight lines
aboveandbelow 3.5T (Eqn.1), whichsignalsthe occur-
rence of a transition at a critical field B = 3.50(5)T. sists of two septets of relatively sharp quadrupole-split
c2
Line parameters on the FM side are fitted as aFM = transitions, with positive (B0 < νL/59γ) and negative
10.23(1)MHz/T,ingoodagreementwiththe a valuesin offsets (B0 > νL/59γ) of their respective central lines.
the FI phase, and a reduced bFM = 11.40(1) MHz, cor- The integratedamplitudes of the positive- and negative-
responding to a step-like decrease of the internal field, offset multiplets are in a ratio very close to 2. Following
BFM =1.115(2)T. the above arguments, the two multiplets originate from
int
the majority spin-up and minority spin-down chains, re-
Thetransitionisalsoaccompaniedbyanabruptbroad-
spectively, in the presence of a sample misalignment of
ening by a factor of about 2 of the satellite lines above
the order of a few degrees, yielding a longitudinal field
B . A closer inspection of the resonance lines reveals,
c2
component of order a few hundreds mT, strong enough
onbothsidesofthetransition,anasymmetricalbimodal
to induce FI magnetic order in the sample.24 The effect
shape with a sharper peak and a broader negatively-
of sample rotation around an axis nominally coincident
shifted shoulder, that is more pronounced in the FM
with the crystallographicc axis is summarized in Fig. 8,
phase. Line shapes and widths, in contrast, are inde-
showing the dependence on the azimuthal angle φ of the
pendent of satellite order m. These facts indicate that
central lines B , B , and of the first-order quadrupole
the observed inhomogeneous broadening is magnetic in 0↑ 0↓
splittings,calculatedas(B B )/2.23 Overlaidonthe
origin. The increase in line width ∆ν above B quali- −1 1
L c2 −
experimentalpoints,thefigurealsoshowsforcomparison
tativelyagreeswithadominantlinebroadeningfromthe
simulated shifts (Fig. 8a) and splittings (Fig. 8b) pre-
demagnetization field, which is proportional to its net
dictedbyEqs.A2andA3forθ =81◦ (theanglebetween
magnetization, and inhomogeneousthroughout the sam-
c and B B , resulting from a vector addition of
pleduetoitsnon-ellipsoidalshape. Theagreementisnot nuc loc
≈
B = 7.45T with a perpendicular B 1.2T), and
quantitative, however,since a step in ∆ν by a factor of ext int
L ≈
rhombicityfactorsηoforder0.1. Clearly,theexperimen-
3 across B is expected from the corresponding step in
c2
talsplittingsdonotfollowthepredictedangularperiodic-
the macroscopicmagnetization. Such a discrepancy sug-
ityofπ,rathershowinga2π period(Fig. 8a). Moreover,
gests the presence of an extra broadening mechanism,
the quadrupolarshift is negligibleevenforlargeη values
relatively more important in the FI phase.
(Fig.8b),sinceitisasecondorderterminν /ν . There-
Q Z
fore, the entire azimuthal dependence of both quantities
2. Transverse applied fields must be due to a slight misalignment between c and the
The crystal was also mounted with its c axis perpen- rotationaxis,aswellasbetweenthe latter andthe plane
dicular to the external field, in order to study the trans- perpendicular to Bext, indicating that η is vanishingly
verse components of the EFG and Kˆ tensors in an az- small.
imuthal scan of B in the ab plane. A typical field- The spectrum of Fig. 7 is fitted to two septets of
ext
sweep spectrum at 10 K, recorded at a fixed frequency Lorentzianlines,withconstrainedpositionscalculatedas
ν = 75.6 MHz, is shown in Fig. 7. The spectrum con- functions of external and internal fields, chemical shift,
L
6
16 0.12
B ⋅B >0 T]
1124 Biinntt⋅Beexxtt<0 ) / 2 [100.1.11
rb.u.]10 νL=7B5.6 M⊥ Hcz B−B1−0.09 (a) η=0
e [a 8 ext ( 0.08 η=0.05
ud η=0.1
plit 6 T] 7.5 η=0.2
Am γ [
9
4 5
/ L7.4
ν (b)
2
7.3
0 0 50 100 150
7 7.2 7.4 7.6 7.8 8 φ − φ [deg]
B [T] 0
ext
FIG. 8: (Color online) Symbols: experimental first order
FIG.7: (Coloronline)Field-sweptspectrumat10K,recorded quadrupolesplitting(a)andcentralpeakposition(b),infield
at a constant frequency of 75.6MHz, in a nominally trans- units,asafunctionoftheazimuthalangleφinthetransverse
verse geometry (Bext ⊥c). The solid line is a global fit to geometry. Dashed lines are guides to the eye. Solid lines:
two septets of Lorentzian lines with positions constrained by simulationswith θ=81◦,correspondingtoBext ⊥c(seetext
Eqn. A2. Vertical dashed and dash-dotted lines mark peak and Eqn.A2), for increasing η values.
positions for themajority and minority spin chain signal, re-
spectively.
T−1 2W (Eqn. B2) by at least 3 orders of magnitude,
1 ≡
and the two relaxations clearly follow quite different be-
quadrupoleinteraction,andageometricangleαbetween
haviors vs. B . The former exhibits a peak at B ,
thecaxisandB . Inthefit,thein-planechemicalshift ext c2
ext with such a large maximum value that it nearly leads
tensorcomponentK ,α,andν ,ν (whichareinprin-
a Q↑ Q↓ to the disappearance(wipeout) ofthe signalatthis tem-
ciple independent for the two chain types) were treated
perature. Incontrast,T−1exhibitsamonotonicdecrease
asfreevariationalparameters,whileB ,B ,andK 1
int↑ int↓ c withincreasingfields,exceptforashallowfeatureatB .
were kept fixed to the values determined by NMR with c2
Moreover, the time dependence of the spin-spin relax-
c B (longitudinal geometry). A further constant
pakrameextter, ρ dψ/dB = 3.4(2) 10−3T−1, account- ations exhibits a marked non-exponential decay over a
≡ ext × wide field interval across the FI-FM transition. The sig-
ing for a field-dependent tilting angle ψ of the electronic
nal decay is best fitted to a stretched exponential func-
moments, was calculated from the ab-plane macroscopic
tion, A(τ) = A exp[ (2τ/T )β], with stretching expo-
susceptibility, determined by SQUID magnetometry as 0 − 2
nent β peaked to a value of 1.5 at B , i.e. the intrinsic
χ = 1.8(1) 10−2µ /T. The fit yields a negative c2
K⊥ = 6.7(2)× 10−3,Band ν = ν = 2.11(1)MHz, lineshape(relatedtothespin-spinrelaxationfunctionby
a − × Q↑ Q↓ Fourier transform) is nearly Gaussian close to the tran-
coincident with the quadrupole line splitting of the ma-
sition.
jority signal in the longitudinal geometry, and so is in
The difference in magnitude and field dependence of
disagreementwith the value determinedfor the minority
theT−1 andT−1 ratesisnotpeculiartothelongitudinal
chains in large longitudinal fields. 1 2
orientation,asitcanbequalitativelyreproducedwiththe
caxisrotatedbyα=45◦ inB =4-7T (notshown),a
ext
B. Nuclear relaxations field interval encompassing the FI-FM transition in that
geometry. This indicates that the behavior of T−1 and
1
Nuclearrelaxationsweresystematicallystudiedonthe T−1 vs. applied field is essentially invariantwith respect
2
central quadrupole line (m = 0) in the longitudinal ge- to the orientation of the nuclear field B B rela-
nuc loc
ometry (B c) at 10K as a function of the external tive to the c axis (note that B B in≈this case, so
ext ext int
field. Thelongiktudinalnuclearpolarizationrecoversequi- that the B direction is approxim≫ately that of B ).
loc ext
libriumingoodagreementwithEqn.B2,indicatingthat Perfectly consistent data are recorded from nuclei in
spin-lattice relaxations are actually driven by magnetic the minorityspin-downchains,forB approachingB
ext c2
fluctuations, as expected in this system. from below. A qualitatively similar behavior of the two
Figure9bdisplaysspin-latticeandspin-spinrelaxation kinds of relaxations is also observed at 10 K close to
rates of the positive-offset septet at 10K over the 2-6 T the other metamagnetic transition, i.e. from the FI to
field span, an interval comprising the FI-FM transition the MPDA phase on decreasing the longitudinally ap-
B . Spin-spinratesT−1arelargerthanspin-latticerates plied B down to B 0.1T (Fig. 9a). Here again
c2 2 ext c1 ≈
7
T [K]

20 T1−1 T 101 14 12 10 8T−1
T−1/103 1.4 2 1
2 stretch. T−1/104
1] β 2
− 15 1.2
s
−310 [ 1 4−10 [s] 100
−1×210 2 3 4 5 6 1/1
−1, TT1 5 (a) (b) Bext [T] −−1, TT2110−1
B =4.749T
ext
ν =60MHz
0 L
0 0.2 0.4 2 3 4 5 6
B [T] 0.06 0.08 0.1 0.12 0.14
ext −1
1/T [K ]
FIG. 9: (Color online) Spin-lattice (triangles) and spin-spin
FIG. 10: (Color online) Spin-spin(triangles) and spin-lattice
relaxations(bullets)measuredonthecentralresonanceofthe
papopsirtoivaec-hoiffnsgetthseepFteIt-MatP1D0AKtarsanasfiutinocntiofrnomofBabeoxvtek,ca,n(da)(obn) rceelnatxraatliorensornataensce(b(uνl0le=ts)6m0MeaHsuzr,eBdeixntt=he4F.7M49pThapsaeraolnlelthtoe
c) as a function of temperature. The dashed line is a fit of
across the FI-FM transition. Inset of panel b: stretching
T−1 to an Arrhenius law. In the figure T−1 rates are scaled
tehxepofingeunrteβT−of1trhaetesspianr-espsicnalreedlabxyataionmufultnipctliicoantivosn. fBaecxtto.rIonf by1 a multiplication factor of 10−4 for clari2ty.
2
10−3 for clarity.
ementary excitations of an Ising spin chain system, will
be reported elsewhere.
T−1isordersofmagnitudelargerthanT−1andincreases
2 1
as B approaches the critical field, while T−1 is non-
ext 1
divergent. As in the vicinity of B , the homogeneous
c2
IV. DIPOLAR FIELD CALCULATION
lineshape is quasi-Gaussian, as spin-spin relaxations are
fittedtostretchedexponentialdecayforms,withβ inthe
range 1.2-1.4. A calculation of the total dipolar field at the CoI site
Spin-lattice relaxations were also measured as a func- is required for a quantitative analysis of our experimen-
tion of temperature and applied field, both in the FI tal internal field values. We report such a calculation
and FM phase. Results of a typical temperature scan, hereforeachofthethreemagneticenvironments,major-
performed in a longitudinal field of 4.749T (i.e. in the ity FI-, minority FI-, and FM-ordered chains. The con-
FM phase) are shown in Fig. 10. The figure also shows tribution of nearby moments (referred to as the proper
thetemperaturedependenceofT−1 forcomparison. The dipolar field Bdip) is calculated by summing up the in-
2
spin-lattice rate clearly follows a thermally activatedbe- dividual dipolar fields from CoII spins SSj at posi-
ahuavthioorrsT.11−91Th=e AT∞r−r1heexnpiu−s∆la/wTi,saosbeaylesdo ofovuernda tbeymoptehraer- teiroanlsurnjitincseildleraadLiuosrecnetnztesrpehderaetwaithCoaIrasidtieusr0of=sev0-,
itnugretroanageTofv8a−ria1t3ioKnabtythmisopraerttihcaunlartwfioeldd,eccoardreess,pwonitdh- Boudtispid=e thPejLgoµrBen(t3zrjsrpjhe·rSeSajre−trrej2aSteSdj)a/srj5a,mwahcirleoscspopinics
1
activation energy estimated as ∆= 96(2)K. Above this magnetic moment density, giving rise to a demagnetiza-
temperature interval the signal is lost due to an exceed- tion field Bdem inside the sphere, as is customary. The
inglyshortT ,whileexperimentalT−1 pointsexhibitex- latter is strictly constant throughout the sample volume
2 1
cessrelaxationatT <8K,indicatingthattherelaxation onlyinthecaseofanellipsoidalsamplesurface,whereby
mechanism responsible for the Arrhenius behavior be- itissimply proportionaltothe saturationmagnetization
comesunimportantatlowtemperature,anditisshunted Ms and to the difference in demagnetizing factors of the
by other more effective relaxation channels. Spin-spin inner Lorentz sphere 1/3 and the outer sample surface
ratesseeminglysaturateatlowtemperatureandalsoex- N, Bdem = 4π(1/3 N)Ms. For a rotational ellipsoid
−
hibitasteeptemperaturedependenceatT >8Kaswell, magnetized along its principal axis c, the demagnetizing
although the evolution is clearly not Arrhenius-like. factor Nc is calculated as25
ThermallyactivatedT−1(T)weredetectedatallfields,
1 (1 ǫ2)(tanh−1ǫ ǫ)
irrespective of whether the system exhibits FI or FM N = − − (3)
order. The field dependence of the activation energy c ǫ3
∆(B ), as well as its interpretation in terms of the el- ǫ 1 (r /r )2
ext a c
≡ −
p
8
the presence of a large internal field which complicates
TABLEI:CalculateddipolarsumBdip,demagnetizationfield the unraveling of Kˆ components (see Appendix A). The
Bdem,andtotaldipolarfieldBtot≡Bdip+Bdemasafunction absolute magnitude of K, of order 1%, though sizable
ofmagneticchainordering,comparedwithexperimentalBint
in absolute terms, is however only slightly larger than
values.
the typical values reported for diamagnetic complexes of
Order Bdip (T) Bdem (T) Btot (T) exp.(T) cobalt.27 The relativelysmall value of K agreeswith the
FM 0.997 0.137 1.134 1.115(2)
knownlargecrystalfieldsplittingattheoctahedralIsite,
FI↑ 1.122 0.046 1.167 1.178(2)
of order 0.65eV,3 since a near-lying crystal field excited
FI↓ -1.246 0.046 -1.201 -1.221(4)
multiplet usually gives rise to a large chemical shift via
the van-Vleck mechanism, as often encountered in non-
magnetic transition metal ions.
A non-ellipsoidal sample may be approximated by an
The EFG exhibits cylindrical symmetry around c, in
effective ellipsoid accounting for the mean B , while
dem accordance with the fact that c axis is a C symmetry
3
deviations from the ideal shape gives rise to a distribu-
element of the point group of CoI. Consistent values of
tion in demagnetization fields, contributing only to the
thequadrupolarfrequencyν (proportionaltotheEFG)
Q
linewidth. We assume effective ellipsoid radii r = r ,
a b are estimated in different chain types and experimental
r equal to half of the sides of our square-base paral-
c geometries, with the notable exception of the minority
lelepipedalspecimen asa best ellipsoidalapproximation.
chainsinexternallongitudinalfieldsapproachingtheFI-
The choice of r and r does not critically affect the de-
a c FM transition value B , where an EFG deviation of or-
c1
termination of B , since N depends weakly on ǫ in
dem c der -7% is found, well beyond the experimental uncer-
the case of an elongated sample (e.g. ∂N /∂ǫ 0.3 for
c tainty. We argue that a magnetoelastic coupling of the
≈
our crystal). For instance, a 10% error on ǫ would result Co3+ ions in counter-oriented minority chains might be
in an error ∆B of order 5 and 2 mT in the FM and
dem the source of the observed EFG reduction, as already
FI phases, respectively.
proposed for other cobalt-based compounds studied by
The results of our calculations are summarized in ta- Mo¨ssbauer spectroscopy.28
ble I and compared with experimental results. Both the
The internal field B at the non-magnetic CoI site
dipolar sums and the demagnetization field were cal- int
can be accounted for by purely dipolar interactions with
culated by assuming the CoII moments saturated to
the surroundingCoII spins,within anabsoluteaccuracy
g S µ along c in all the three types of magnetic
± h zi B of2mTinallofthethreechaintypes. Thisresult,along
chains, with a ± sign as appropriate for the chain or- with the experimental value of Kˆ, sets a very stringent
der, and identical absolute moment values estimated as
upperlimittoatransferredhyperfinefieldatthenucleus.
g S =5.25(3)(inunitsofµ )fromanextrapolationof
h zi B The contact hyperfine field may originate from both a
M(H) data in high field. Lattice parameters were taken
tiny on-site magnetic moment on CoI, as that invoked
as a = 9.061˚A, c = 10.367˚A as reported in the litera-
in a neutron scattering refinement,7 and from the cou-
ture at 40K.1 Numerical convergence of B could be
dip pling to nearest neighbors CoII spins. These two con-
attained with a Lorentz sphere radius of the order 30 of
tributions might partially cancel out, since either sign is
unit cells. Calculated and experimental values differ by
possible.22Additionalinter-chaincontributionsarenegli-
lessthan2%inallcases. Agreementshouldbeconsidered
gibleinviewofthe largechainspacing. Nevertheless,we
satisfactory in view of the uncertainties in the magnetic
can safely rule out an on-site term, since a residual on-
moment (of order 1%) and the demagnetization factor.
site moment would require an admixture of the t with
This confirms that the internal field is dipolar in origin, 2g
the excited e orbitals, in contrastwith the large crystal
while transferred hyperfine contributions, if they occur, g
field excitation energy implied by the observed moder-
are negligible.
ate chemical shift value. For instance, a huge chemical
shift K 5 was reported for the resonance of 141Pr in
low-spin≈Pr3+, in combination with a small fractional
V. DISCUSSION AND CONCLUSIONS
moment 0.01µ on the Pr ion.29 Therefore, only the
B
≈
transferred contribution is to be considered.
We organizethe discussionofourexperimentalresults
An intra-chain transferred hyperfine term B would
hf
intoseparatesectionsforsakeofclarity,eachonefocusing
offset the total dipolar field B (Tab. I) by B for
tot hf
on one main conclusion of the paper. ±| |
theFI andFMchains,andby B fortheFI chains,
hf
↑ ∓| | ↓
dependingontherelativesignofB andB . However,
tot hf
A. Interactions of 59Co: evidence against a direct afiniteB biasingtermdoesnotimprovetheagreement
hf
CoI-CoII superexchange path betweenthecalculatedB B andtheexperimentally
tot hf
±
determined internal fields. We conclude therefore that
Our NMR study on a single-crystal provides a deter- the slight discrepancybetween the experimentaland the
mination of the chemical shift and the EFG tensors at calculated internal fields must be due to other sources
the CoI site. The chemical shift is less precise due to of error, and that the contact field, if present, is much
the uncertainty in the zero-shift 59Co reference26 and to smaller than 2mT.
9
A negligible hyperfine field at the CoI site is an un-
expected result. Transferred hyperfine fields at nuclei 5
of non-magnetic ions in magnetic compounds of tran- 10K
sition metals are typically of the order of several hun-
4
dreds mT or more, unless perfect cancellation occurs at 11.4
5
a symmetric site of an AF structure, which is not the
U]
case in Ca3Co2O6. For instance, the transferred hyper- F 3
fine field at 139La in the FM manganite La Ca MnO /B 4 11.6
1−x x 3 µ z]
equals 3T, i.e. approximately 10% of the on-site hyper- M [ MH
finefieldattheMnsites,wherethemagnetismresides.30 2 3 [011.8
Here, a virtually vanishing contactfieldat CoI indicates ν
∆
that there is no significant hybridization between the
1 2
Co3+(I)andthe Co3+(II) wavefunctions either directly 12
or through an oxygen bridge. 3 3.2 3.4 3.6 3.8 4
The mechanisms underlying exchange and hyperfine 0
transfer are similar, although not exactly identical.31,32 0 2 4 µ H [T] 6 8 10
Therefore, the lack of a detectable transferred hyperfine 0
field strongly suggests that Co3+(I) ions do not partici-
pate in the exchange interaction J between two neigh- FIG. 11: (Color online) Magnetization curves at 10 K as a
1
boringon-chainCo3+(II)spins. Westressthatthisfind- function of theexternalfield H applied along c. Inset: detail
of M(H) across the FI-FM transition, overlaid for compari-
ing constitutes experimental evidence against the cur-
rently accepted theoretical model by Fr´esard et al., who son to the frequency offsets ∆ν0 ≡ ν0−aBext of the central
NMR line of either FI↑ or FM chains, where a is the best-fit
instead proposedan exchangepath acrossCoI assuming
parameter to Eqn.1 (whence ∆ν0 ≈b∝Bint within error).
alargeoverlapofCo3+(II)withCo3+(I)wavefunctions,
yielding a direct integral t=1.5eV.33
eveninthevicinityoftheFI-FMtransition. Proofispro-
B. Nature of the metamagnetic transitions: perfect vided by the field proportionality coefficient a of Eqn. 1,
Ising behavior. whoseexperimentalvaluesforthethreechaintypeswere
foundtocoincidewithinanerrorδa 10kHz/T.Theob-
≈
At 10K two types of field-dependent magnetic struc- servedvalueof∂M/∂Hcontributesa15kHz/Tslope(i.e.
tures are detected, namely perfect FI and FM ones, in of order δa) to ν0(Bext) via the demagnetization field,
accordance with the two plateaus in magnetization data regardlessof the mechanism responsible for it, and inde-
at the same temperature. The two structures are clearly pendentofthemagneticorderinachain. Ahypothetical
identified by distinct localfields atthe CoI sites in good field dependent canting, however, would affect the dipo-
quantitativeagreementwiththe dipolarfields calculated larfieldatCoI,whichislargerthanthedemagnetization
for the correspondingspin arrangements. The transition field by an order of magnitude (Tab. I). Unless we as-
fromaFItoaFMphaseshowsupasasharpstepinB sume equal canting in the FM, FI spin-up, and the FI
int
at a threshold field B 3.5T, revealed by an abrupt spin-down chains, which is clearly unphysical, the lat-
c2
crossoveroftheresonance≈frequencyvs.fieldbetweentwo ter would produce differences in the a coefficients of the
distinct ν (B ) functions (Fig. 3). threelineswellbeyondexperimentalerrors,andcontrary
0 ext
Quantitative comparison between NMR and magneti- to experimental evidence.
zation data in longitudinal fields at 10K (Fig. 11) pro- As seen from NMR, the system apparently exhibits
videsaninsightintothemagnetizationprocess. Closein- perfect Ising behavior. Therefore, the rounded steps in
spectionof the magnetizationcurves asa function ofthe the M(H) data at the field-induced metamagnetic tran-
applied field H B /µ shows that the steps appear sitions, with unsaturated magnetization over broad H
ext 0
smootherintheM≡(H)curvesthanintheNMRfrequency intervals near them, must be due to a fraction of misori-
data ν (B ) (figure inset). Moreover, the plateaus in ented domains or spin chains.
0 ext
M(H)areonlyapproximatelyflat,withamoderatefield
dependence that is larger in the FI state (for instance, C. Two distinct magnetic excitations probed by
µ−01∂M/∂H ≈0.05µB/T for 1T<µ0H <3T). T1−1 and T2−1
In principle, incomplete saturation of M(H) over the
plateaus might be due to either unsaturated c axis com- Further insight on the spin reversal process close to
ponentsofindividualmomentsinahomogeneouslymag- the MPDA-FI and FI-FM transitions is provided by the
netized sample (e.g. due to spin canting), or inhomo- large and divergent spin-spin relaxations, accompanied
geneous magnetization, although the former could not by much smaller and non-divergent spin-lattice relax-
easily be reconciled with the known strong single ion ations. We recall that the spin-lattice relaxation rate
anisotropy of the system. NMR demonstrates experi- T−1 probes transverse random magnetic fields fluctuat-
1
mentallythatthecobaltspinsarecollinearandsaturated ing atthe Larmorfrequency ω ,while the spin-spinrate
L
10
T−1 isthesumofatermproportionaltoT−1 (thepopu- magnetic transitions finds a natural explanation within
2 1
lationterm)andaseculartermarisingfromlongitudinal this framework.
randomfieldsfluctuatingatvirtuallyzerofrequency.34,35 A peak in T−1 vs. B may arise in principle from
2 ext
In the presence of isotropic and fast fluctuations in the either a field-dependent correlation time of fluctuations,
so-called narrowing limit (such that ω is much smaller or a peak in the random field amplitude. In the nearly-
L
than the roll-off frequency of the fluctuation spectrum) static fluctuation regime, however, field dependence of
thetworatestendtocoincide.36 Here,thesimilarbehav- the correlationtime wouldimply faster spin fluctuations
ior of relaxations measured in longitudinal and oblique at the peak. The latter is apparently inconsistent with
external fields rules out the possibility that anisotropic the peaks in β vs. B reaching nearly-Gaussian values
ext
fluctuations, namely, entirely along the c axis and hence of1.5 atB andB , a signatureofa nearlyfrozenspin
c1 c2
ineffective for spin-lattice relaxations, are the source of dynamics, following the above argument. The T−1 peak
2
thehugedifferenceinT andT timescales. Excessspin- mustthereforeoriginatefromacorrespondingincreaseof
1 2
spin relaxation and T−1 peaks must instead depend on the quasi-staticmagnetic disorder,namelyalargernum-
2
fluctuations in a regime opposite to the narrowing limit, ber of misoriented domains or chain fragments, close to
namely with characteristic frequencies much lower than the transitions. We note that the peaks of β vs. B
ext
ω and hence contributing only to the secular term in coherently reflect changes in the spatial distribution of
L
T−1. Such a regime, which has already been reported in random fields on approaching the metamagnetic transi-
2
the literature for other oxides,37 is referred to hereafter tions. According to a well-known mechanism,34,40 the
as the nearly-static limit. transition from a quasi-Gaussian to a quasi-Lorentzian
To this end, the Kubo-Tomita theory of line shape line shape may be driven by an increasing dilution of
appropriateforcontinuous-wavemagnetic resonance38 is (nearly) static magnetic impurities or defects, and vice
modifiedinthecontextofpulsedNMRbyanexperimen- versa. Thus, the larger disorder probed by T−1 peaks
2
tallow-frequencycutoff,namelythe reciprocaltime win- consistentlycoincideswithalargerconcentrationofmag-
dowω =(2τ)−1 ofaspin-echoexperiment(here,τ isthe netic defects indicated by β > 1, which agrees with the
c
time separation of the two excitation pulses). Random shorteningofthe magneticcoherencelengthobservedon
fieldsfluctuatingatfrequenciesω ω 2 104s−1may approaching the field-induced transitions.41
c
≪ ≈ ×
beviewedasstaticovertheexcitation-detectiontransient Incontrast,spin-latticerelaxationsaregovernedbyin-
and contribute only to the inhomogeneous line broaden- dependentexcitations,whoseeffectonT2 isunimportant
ing, which is refocused by the spin echo sequence. Con- asitismaskedbytherelaxationchannelsketchedabove.
versely,fluctuationsatω <ω ω effectivelyrelaxthe The thermally activated behavior of T−1 reveals a gap
c L 1
≪
spin-echo signal. ∆ of order 100K in their spectrum. A thorough investi-
Withinthenearly-staticlimit,thedecreaseofT−1with gation of ∆ as a function of Bext for the different chain
2
types, and a fitting of the experimental energy gaps to
decreasing temperature (Fig. 10) then indicates the col-
a theoretical model, are the subject of a separate paper.
lapse of the fluctuation spectrum below the cutoff ω at
c
Here we anticipate that, according to the model, the ac-
lower temperatures, down to a complete freezing of the
tivated spin-lattice relaxations are essentially driven by
spin dynamics observed at T < 5K. It is worth noting
the spin-flip of a single Co3+ moment.
that evidence for comparable time scales in the spin dy-
namics was also reported from χ′ and χ′′ ac magnetic
susceptibilities in the zero-field phase, both showing a D. Spin freezing: relevance for the magnetization
strongfrequencydependenceovertheacousticandsuba- steps
coustic range.39 The nearly Gaussian T relaxationform
2
is another signature of nuclear spin depolarization from We conclude this discussion with a comment on the
quasi static random fields.34 In our case, random fields low-temperature multi-step behavior in M(H). The
are clearly electronic in origin, since the calculated sec- magneticstructuresunderlyingeachstepcouldnotbeac-
ond moment of the nuclear dipolar fields yields a T2−1 cessedinourNMRstudy,duetothenon-sphericalshape
ratesmallerthanthe observedonesbyatleastoneorder of our sample, inducing demagnetization-dependent line
of magnitude. broadening and offsets which prevent finer resolution of
The peculiar behavior of T−1 rates therefore reflects dipolar fields, as well as to exceedingly slow spin-lattice
2
the exceedingly slow spin dynamics, as in the case of relaxationsbelow5K.Nevertheless,T dataat7-15Kre-
2
massiveexcitationmodes involvingthe collectivemotion vealascenarioofglassyspindynamicsinvolvingfreezing
of several spins. In view of the strong Ising character of sizable magnetic aggregates and large quasi-static in-
of the system, such excitations probably consist in the homogeneitiescloseto the field-induced transitions. The
coherent reversal of large portions of the spin chains or collective arrangement of such frozen entities at lower
domains. The slowly fluctuating random fields respon- temperature is unknown. We may argue however that
sible for spin-spin relaxation are then straightforwardly it gives rise to complex field-dependent micromagnetic
identified with the stray dipolar fields originating from configurations or superstructures, resulting in a multi-
suchtransientdefectsinthemagneticstructure. Alsothe plicity of localminima separatedby potentialbarriersin
peaks in T−1 and the stretched exponent β at the meta- the free energy, becoming metastable below 2 K. If this
2