Table Of ContentLarge magnetothermal conductivity in GdBaCo O single crystals
2 5+x
X. F. Sun,1,2,∗ A. A. Taskin,2 X. Zhao,3 A. N. Lavrov,4 and Yoichi Ando5
1Hefei National Laboratory for Physical Sciences at the Microscale,
University of Science and Technology of China, Hefei, Anhui 230026, P. R. China
2Central Research Institute of Electric Power Industry, Komae, Tokyo 201-8511, Japan
3Department of Astronomy and Applied Physics,
University of Science and Technology of China, Hefei, Anhui 230026, P. R. China
4Institute of Inorganic Chemistry, Lavrentyeva-3, Novosibirsk 630090, Russia
5Institute of Scientific and Industrial Research, Osaka University, Ibaraki, Osaka 567-0047, Japan
(Dated: February 2, 2008)
8
To study the effects of paramagnetic spins on phonons, both the in-plane and the c-axis heat
0
0 transportof GdBaCo2O5+x (GBCO) single crystalsaremeasured at lowtemperaturedownto0.36
K and in magnetic field up to 16 T. It is found that the phonon heat transport is very strongly
2
affected by the magnetic field and nearly 5 times increase of the thermal conductivity in several
n Teslafieldisobservedat0.36K.Itappearsthatphononsareresonantlyscatteredbyparamagnetic
a spins in zero field and the application of magnetic field removes such strong scattering, but the
J
detailed mechanism is to be elucidated.
5
PACSnumbers: 66.70.+f,72.20.-i
]
l
e
- I. INTRODUCTION long-rangemagneticorderingofCospins,theirIsing-like
r
spin anisotropy prevents the low-energy magnon excita-
t
s tions, while the Gd ions remain paramagnetic and be-
. In magnetic materials,coupling of spins with other el-
t haveasalmostfreespinsdowntoverylowtemperatures.
a ementary excitations is a matter of fundamental impor-
m Furthermore, a lattice disorder in GBCO can be easily
tance. Inparticular,thespin-phononinteractioncausing
introduced by merely changing its oxygen content.
- unusualphysicalpropertiesincorrelatedoxideshasbeen
d In this work, we perform detailed studies of the low-
an issue of significant interest both by its own right and
n T heat transport of GBCO single crystals with various
because it provides a useful means to gain insight into
co frustratedmagnetismaswellasmultiferroics.1,2,3,4,5 The oxygen contents. It is found that both the in-plane and
the c-axis thermal conductivities (κ and κ ) show ex-
[ low-temperaturethermalconductivity is one ofthe most ab c
effective probes for studying the spin-phonon coupling,6 tremelystrongmagnetic-fielddependenceatlowtemper-
1 atures. Theκ(H)isothermsat1–2Kshowadip-likefea-
especially ininsulatorswhere magneticexcitations along
v
ture at low fields where the heat conduction is reduced
9 withphononsarethemainheatcarriers. Evenifthelong-
by as much as 50%, while at subkelvin temperatures the
7 range magnetic order is not established in a crystal or
magnetic field induces a step-like enhancement of κ by
7 the contributionofmagnonsto the thermalconductivity
0 is limited at low temperatures, the presence of localized nearly 5 times. The magnetic-field dependences of the
. thermal conductivity indicate that phonons are strongly
1 spins still can play an important role in the heat trans-
scatteredbytheGdspinsthataresusceptibletotheZee-
0 port as was observed long time ago in some ionic com-
8 poundsdopedwithmagneticimpurities.6,7,8 However,in maneffectinmagneticfields. Thelargemagnetothermal
0 stronglycorrelatedmaterials,thelow-T behaviorofther- effect illuminates the important role of free spins in the
: heat transport of novel oxide materials.
v malconductivitycanbesocomplicatedthatitisdifficult
i toselectivelystudythe effectofspin-phononinteraction,
X
especially when the electron transport, which can also
r depend on magnetic field, is contributing to the thermal II. EXPERIMENTS
a
conductivity. In order to gain insight into the impact of
spin-phononcouplinganditsunderlyingmechanism,one High-quality GdBaCo O single crystals are grown
2 5+x
needs a material in which the spin-phonon coupling can using a floating-zone technique9,10,11 and carefully an-
be treated independently. nealed to tune their oxygen contents to x = 0.50, 0.30
Forthispurpose,recentlysynthesizedlayeredcobaltite and 0.00. The thermal conductivity along both the ab
GdBaCo O (GBCO), which has attracted a great plane and the c axis is measured from 0.36 to 5 K in
2 5+x
deal of attention due to its rich phase diagram and fas- a 3He refrigerator by using a “one heater, two ther-
cinating physical properties (See Ref. 9 and references mometers” technique and from 5 to 300 K in a 4He
therein), wouldbe anidealsystemfor studyingthe spin- cryostat by using the Chromel/Constantan thermocou-
phonon coupling. This compound is a good electrical ple. Detailsofthe measurementsofthe temperatureand
insulator at low temperatures for a wide range of oxy- magnetic-field dependence of κ were described in pre-
gen content, and hence there is no need to consider the vious publications.12,13,14 All the parallelepiped crystals
electronic heat conduction. Although GBCO shows a are precisely cut along three crystallographic axes with
2
300 T
G dBaCo O CO 20 GdBaCoO 20 GdBaCoO
2 5.00 2 5+x 2 5+x
2.5
15 (a) 15 (b)
2.0 -1-1mol K) 200 (W/Km)ab10 x = 0.00 (W/Km)c10 x = 0.00
-2K) 1.5 C (J p 100 H // a05b T k 050 x1 0=0 0x. 5=0 0.32000 300k 050 x =x 0=1. 3000.050 200 300
1 10
-mol 13.5 T ( K) T ( K)
T (J 1.0 00 100 T (K) 200 300 101 x = 0.00x = 0.50 101 x = 0.00x = 0.50
C/p 100 x = 0.30 100 x = 0.30
m) T3 m) T3
0.5 W/K10-1 W/K 10-1
(ab10-2 (c10-2
k (c) k (d)
0.0
0 10 20 30 10-3 10-3
T (K) 1 10 100 1 10 100
T (K) T (K)
FIG. 1: (color online) The low-temperature specific heat of
GdBaCo2O5.00 in magnetic fields of 0, 5, 10, and 13.5 T ap- FIG. 2: (color online) Temperature dependences of the ther-
pliedalongtheabplane. SolidlinesshowcalculatedSchottky mal conductivity along the ab plane and the c axis in zero
contributions of paramagnetic Gd3+ ions assuming S = 7/2 magnetic field for GdBaCo2O5+x single crystals with various
(see text). The dashed line indicates the Schottky contribu- oxygen content. The data are displayed in both linear and
tion of paramagnetic ions with S = 1/2 at H = 13.5 T. The logarithmic plots. The dashed lines indicate the T3 depen-
inset shows theheat capacity in thetemperature range of 2– dence.
300Kmeasured atH =0and10T.Thearrow indicatesthe
charge ordering transition.
13.5TarewellfittedbyasimpleSchottkycontributionof
paramagnetic Gd3+ ions with a spin value of 7/2, which
◦
an error of less than 1 . The heat capacity is measured is determined by the area under the peak (the Schottky
by the relaxationmethod in the temperature rangefrom contribution of paramagnetic ions with S = 1/2 at H =
2 to 300 K using a commercial physical properties mea- 13.5T isshownforcomparison),andtheg factorof1.64
surement system (PPMS, Quantum Design). ±0.04, which is determined by the peak position. We
should note also that there is a finite splitting of the Gd
spin levels even in the absence of an external magnetic
III. RESULTS AND DISCUSSIONS field that can be a result of a weak magnetic interaction
ofGdionswitheachotherorwiththecobaltsublattices.
Before presenting the heat transport results of GBCO Figure 2 shows the temperature dependences of κ
ab
crystals,weshowinFig. 1therepresentativeheatcapac- and κ of GdBaCo O single crystals in zero field.
c 2 5+x
itydata,whichprovetobeveryinformativeregardingthe First of all, as we already pointed out, the insulating
magnetic excitations. In GBCO, regardless of the oxy- groundstateandtheIsing-likespinanisotropyofGBCO
gen content, the spins of cobalt ions undergo magnetic leave little room for carriers other than phonons to con-
orderingatratherhightemperatures,9,10 butGdions,in tribute to the heat transport, at least at low tempera-
contrast,remainparamagneticdowntoverylowtemper- tures. As can be seen in Fig. 2, the x = 0.00 crystals
aturesas suggestedby magnetizationmeasurements.9 In showalargephononpeakat∼20K,indicating the neg-
ordertoconfirmthis,wehavemeasuredtheheatcapacity ligible imperfection of the crystal lattice. In contrast,
of an x = 0.00 single crystal in different magnetic fields. for x = 0.30 and 0.50, the phonon conductivity is dra-
As can be seen in the inset of Fig. 1, the C (T) curve maticallyweakenedatlowtemperaturesandthe phonon
p
is insensitive to the magnetic field, except for the low-T peak is wiped out almost completely, which is not sur-
part: the peak around 248 K, which corresponds to the prising since the oxygennon-stoichiometrybringsstrong
charge ordering transition at this temperature,15 is not lattice disorder. Between the latter two compositions,
affected by applying a highmagnetic field either. At low the x=0.50 crystals have better heat conductivity, pre-
temperatures, on the other hand, the specific heat C /T sumablyduetotheoxygenionsbeingorderedintochains
p
shows a pronouncedSchottky anomalywith a maximum at this oxygen content.9,10 The worst heat conduction is
that shifts to a higher temperature with increasingmag- observed in x = 0.30 crystals, which have the largest
netic field. All the data measured in H = 0, 5, 10, and degree of oxygen-induced lattice disorder.9
3
The temperature dependences of κ in Fig. 2 are ac- 3 (a) 3 (b)
tually more complicated than those in conventional in- 0.36 K 0.36 K
0.50 K J //a(b) 0.50 K
sulators. At high temperatures, for example, the κ(T) JH//H//a(b) 0.70 K HH//c 0.70 K
data for the good phonon conductor x=0.00 cannot be 0) 2 5 K 2 5 K
wdehsiccrhibseudggbeysttshteheuseuxaisltepnhcoenoofnaUmmokrleacpopmspclaicttaetreidngs,c6a,1t6- kH)/( 01..9975 KK 01..9975 KK
(
tering mechanism or some other kind of heat carriers. k 1 1
In fact, the specific heat data in Fig. 1 indicate that
above ∼100 K, magnon excitations of the Co spin lat-
0 4 8 12 16 0 4 8 12 16
tice become important and may affect the high-T heat 5 5
transport properties. On the opposite side, the lowest-T (c) (d)
btheehabvoiournodfartyheshcaetattecrionngdulicmtiiotnoaflspohsoeneomnssteoxdpieffcetredfrofomr 4 JHH////ac(b) 000...573006 KKK 4 JH//H//c 000...573006 KKK
conventionalinsulators,6 in which case the magnitude of (0) 3 0.97 K 3 0.97 K
the phonon thermal conductivity should depend only on kH)/ 2 51 .K95 K 2 51 .K95 K
thesamplesize,andnotonimpurities,defects,oroxygen (
k
concentration(thedispersionofacousticphononsandthe 1 1
sound velocity do not change much upon changing the
oxygen content). Although both κ and κ below 1 K 0 4 8 12 16 0 4 8 12 16
ab c
arerathercloseto∼T3,theheatconductivityofthex= H (T) H (T)
0.00sample is nearlyone orderofmagnitude largerthan
thatofx=0.30and0.50samples. Notethattheκc data 100 (e) 100 (f)
for different oxygen contents were collected on one and
the same sample that was annealed each time to obtain
the required x; the samples for κab differ in size by less Km)10-1 T1.7 10-1 T1.7
than 20%. In addition, the low-T parts of the κ(T) data W/ J //a(b) J //c
arenot smooth: regardlessofthe oxygencontent,allthe k (10-2 H 0T 10-2 H 0T
crystalsexhibitclearwigglesintheirκ(T)curvesbelow2 T3 16T//JH//a(b) T3 16T//a(b)
K,whichsuggeststhe existence ofsome kindofresonant 10-3 16T//c 10-3 16T//c
phonon scattering.6 1 10 1 10
T (K) T (K)
Uponapplyingthemagneticfieldatlowtemperatures,
wehavefoundremarkablystrongchangesintheheatcon-
FIG. 3: (color online) (a–d) Magnetic-field dependences of
ductivity of all crystals. For instance, at the lowesttem-
perature0.36K,bothκ andκ oftheparentcompound the low-T thermal conductivity of the GdBaCo2O5+x single
ab c crystal with x = 0.50. Directions of the heat current (JH)
x = 0.50 show a step-like enhancement by several times
and the magnetic field (H) are shown in each panel. (e,f)
withincreasingfieldandsaturatesabove∼5T[Figs. 3(a- Temperature dependences of κab and κc in zero and 16 T
d)]. At higher temperatures, a dip-like feature appears magnetic fields. The dashed lines indicate the T3 and T1.7
atlowfield,while the subsequentenhancementathigher dependences.
field gradually weakens with increasing temperature. At
the “high” temperature of 5 K, the magnetic-field de-
pendence is already rather weak and only a broad and T magnetizationandspecificheatdata.9,10Tobecapable
shallow dip remains. Here, the most impressive result is of scattering phonons, the Gd spins should not be com-
themagnitudeofthefield-inducedchangesinκ: the low- pletelyfree,butthespinstatesshouldbeslightlysplitted,
field suppression can be as large as a factor of 2, and the whichhasbeen confirmedbythe heatcapacitydata. (ii)
high-field enhancement can be nearly 400%. While the In magnetic fields, the energy splitting of the spin states
magnitude of the high-field enhancement in κ depends isincreasedbytheZeemaneffect. Thephononscattering
on the direction of the heat current [Figs. 3(a-f)], it is off these spins is most effective in suppressing the heat
surprisingly insensitive to the field direction, which con- transportwhentheenergysplittingisequalto∼3.8k T,
B
firms that magnon excitations in the long-range ordered wherethephononconductivityspectrum(definedbelow)
spins cannot be relevant to the low-T heat transport. peaks; therefore, the spin-phonon scattering generates a
Acluegivenbythe dip-likefeatureinκ(H)isthatthe dip-like feature in κ(H) at this energy and the dip posi-
low-T heat transport may be governed by the phonon tion shifts to higher fields with increasing temperature.6
scatteringby freespins,6,7,8 aswe previouslyobservedin (iii) In the high-field limit, the spin energy splitting be-
Pr La CuO (PLCO).12 Qualitatively, the κ(H) be- comes too large to exchange energy with phonons and
1.3 0.7 4
havior shown in Fig. 3 can be well understood in terms the spin-phonon scattering is completely quenched, en-
of magnetic scattering of phonons: (i) In zero field, the hancing κ above its zero-field value.
phononsarepresumablyscatteredbythespinsofGdions To illustrate the above picture, in Fig. 4 we show
thatbehavelikeS =7/2freespinsjudgingfromthelow- schematicallytherelationbetweentheenergysplittingof
4
D = D + gm H (a) T = 0.36 K (a) x = 0.00 (b)
0 B (b) 2.0 0.36 K 2.0 0.36 K
T = 1.95 K JH//H//a 00..5700 KK x = 0.00 JH//H//c 00..5700 KK
0) 1.5 5 K 1.5 5 K
) T = 0.97 K kH)/(0) T = 0.50 K k(H)/( 1.0 01..9975 KK 1 .0 01..9975 KK
kw ( T = 0.70 K k( T = 0.70 K k
0.5 0.5
T = 0.97 K
T = 0.50 K 1 0 4 8 12 16 0 4 8 12 16
T = 5 K
T = 0.36 K T = 1.95 K 2.5 (c) 0.36 K 2.0 (d) 0.36 K
0 2 4 6 8 10 12 0 4 8 12 16 x = 0.30 0.50 K x = 0.30 0.50 K
hw /k (K) H (T) 2.0 0.70 K 0.70 K
FIG. 4: (color oBnline) (a) Schematic picture of the phonon kH)/(0) 1.5 JH//H//a 051. .9K975 KK 11 ..05 JH//H//c 501 ..K9975 KK
conductivity spectrum κ(ω) at several temperatures (the ( 1.0
k
curves are normalized by their peak values and shifted verti-
0.5
cally for clarity). The phonons can be strongly scattered by 0.5
magnetic ions if their energy is close to the energy splitting 0 4 8 12 16 0 4 8 12 16
of the spin states, which gives rise to a “resonant scattering H (T) H (T)
band” centered at ∆ = ∆0 +gµBH, where ∆0 is the zero-
field splitting and gµBH is the Zeeman splitting. (b) Simu- FIG. 5: (color online) Representative data for the magnetic-
latedκ(H)byassumingthatthephononswithintheresonant field dependences of the low-T thermal conductivity of
scattering band donot carry heat. GdBaCo2O5+x single crystals with x = 0.00 and 0.30.
spinstatesandthepeakinthephononconductivityspec- ently, including other resonance bands related to higher
trum from the Debye model. The “phonon conductivity energy spin transitions of Gd ions with ∆m > 1 does
spectrum” κ(ω) represents the contribution to thermal not help, since the Zeeman splitting ∆mgµ H should
B
conductivity fromthe phonons with anenergyh¯ω and is quenchthesetransitionsatseveraltimeslowerfieldsthan
proportional to ω4exp(h¯ω/kBT)/T2[exp(h¯ω/kBT)−1]2 weobserveintheexperiment. Apossibleexplanationfor
which peaks at energy h¯ω ∼3.8kBT.6 Although Gd ions the extremely wide scattering band is the local fluctua-
have the spin state S =7/2 that splits into eight energy tion of the zero-field splitting ∆ , which would be quite
0
states in magnetic fields, allowing multiple transitions, natural if ∆ is determined by the dipole-dipole interac-
0
for simplicity we take just a single band, corresponding tionswithinthedisorderedGdsubsystem. Dependingon
to the spin transition with the lowest energy, ∆m = 1. the local environment, Gd ions feel different local fields
The energy of this transition changes with the magnetic and thus should exhibit a continuous spectrum of spin-
field as ∆ = ∆0+gµBH, and the phonons in a certain transitionenergies,ratherthanasingleresonanceline.18
energy range around this ∆ are considered to be reso- We have done the same experiments on x = 0.30 and
nantly scattered upon the spin transition. Figure 3(b) 0.00crystalsandshowtherepresentativeκ(H)isotherms
shows simulated κ(H) behaviors, where one can see the in Fig. 5. Obviously, the main features, including both
variations of κ as the position of the resonant scattering thehigh-fieldstep-likeenhancementandlow-fielddip-like
band is changedby the magnetic field. Upon calculating feature, are the same as those for x = 0.50crystals. The
theseκ(H),wesimply assumethatthosephononswhose essential similarity of the κ(H) behaviors for different
energyliesinaresonantscatteringbandcenteredaround oxygen contents seems reasonable if the phonon scatter-
∆ cannot contribute to the heat transport, and the rest ingbyGdmomentsisplayingthekeyrole,sincetheoxy-
of the phonons have the same relaxation time (which is gencontentapparentlyhasnomajorimpactonthemag-
the caseatverylowtemperature).17 Itis reassuringthat netic state of the Gd ions. This result clearly indicates
such a crude picture with only two adjustable parame- the separable effects of free spins and impurities/defects
ters,∆0 (≈2K)andthe widthofthe resonantband,can on the low-T heat transport of GBCO. It is worth not-
capture most of the qualitative experimental features of ing that the quantitative x dependence of κ(H)/κ(0) is
κ(H). Indeed, both the step-like enhancement and the rathercomplicated,namely,themagnitudeofκ(H)/κ(0)
dip-like feature are essentially reproduced. is slightly enhanced upon increasingx from 0.00to 0.30,
Nonetheless,thereis anobviousdifficulty inthe above while it becomes much more pronounced upon further
simple picture; namely, the magnitude of the observed increasingx to 0.50. Obviously,for quantitative descrip-
changes in κ(H) requires the resonance scattering band tion of the all experimental observations, not only the
to be extremely wide; indeed, the observed five-fold in- spin-phonon scattering but the oxygen-induced lattice
creaseinκimpliesthatatleast80%ofphononconductiv- disorder must be taken into consideration.
ity spectrum are affected by the spin scattering. Appar- Although the detailed mechanism of the large mag-
5
netothermal effect in GBCO calls for further investiga- singlecrystalsdowntoverylowtemperatures. Themain
tion, one can already capture some important informa- featuresofthemagnetothermalconductivity,i.e.,ahigh-
tion from the above experimental results. First, the fieldenhancementandalow-fielddip, canbewellunder-
phonon heat transport can be strongly dependent on stood in terms of the phonon scattering by the nearly
the magnetic field even at very low temperature for free Gd spins. The present finding demonstrates the po-
the materials containing paramagnetic moments, like tentially significant role of the spin-phonon coupling in
high-T cuprates12 and other strongly correlated com- correlated oxides.
c
pounds. Second, if the paramagnetic moments have a
small enough splitting between the spin states, the spin-
phonon scattering can survive down to very low temper-
ature and prevent phonons from entering the boundary
scatteringlimit. Thismakesthedataanalysisofthelow-
T thermalconductivityverydifficult,especiallywhenthe
boundary scattering limit is required for separating the Acknowledgments
electron and phonon terms.19,20,21,22
We thank J.Takeyafor helpful discussions. This work
IV. SUMMARY was supported by the National Natural Science Foun-
dation of China (50421201 and 10774137), the National
In summary, a surprisingly strong magnetic field de- Basic Research Program of China (2006CB922005),and
pendence of thermal conductivity is observed in GBCO KAKENHI 16340112and 19674002.
∗ [email protected] 13 X.F.Sun,S.Komiya,J.Takeya,andY.Ando,Phys.Rev.
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