arXiv:1110.1009v1 [cond-mat.str-el] 5 Oct 2011
Heat transport of the quasi-one-dimensional alternating spin chain material
L. M. Chen,1,2X. M. Wang,1W. P. Ke,1Z. Y. Zhao,1X. G. Liu,1C. Fan,1Q. J. Li,1X. Zhao,3and X. F. Sun1, ∗
1Hefei National Laboratory for Physical Sciences at Microscale,
University of Science and Technology of China, Hefei, Anhui 230026, People’s Republic of China
2Department of Physics, University of Science and Technology of China,
Hefei, Anhui 230026, People’s Republic of China
3School of Physical Sciences, University of Science and Technology of China,
Hefei, Anhui 230026, People’s Republic of China
(Dated: October 6, 2011)
We report a study of the low-temperature heat transport in the quasi-one-dimensional S = 1/2
alternating antiferromagnetic-ferromagnetic chain compound (CH3)2NH2CuCl3. Both the temper-
ature and magnetic-field dependencies of thermal conductivity are very complicated, pointing to
the important role of spin excitations. It is found that magnetic excitations act mainly as the
phonon scatterers in a broad temperature region from 0.3 to 30 K. In magnetic fields, the thermal
conductivity show drastic changes, particularly at the field-induced transitions from the low-field
N´ eel state to the spin-gapped state, the field-induced magnetic ordered state, and the spin polarized
state. In high fields, the phonon conductivity is significantly enhanced because of the weakening of
PACS numbers: 66.70.-f, 75.47.-m, 75.50.-y
Low-dimensional or frustrated quantum magnets were
revealed to exhibit exotic ground states, magnetic exci-
tations, and quantum phase transitions (QPTs).1,2For
a particular case of the spin-gapped antiferromagnets,
the external magnetic field can close the gap in the
spectrum, which results in a QPT between a low-field
disordered paramagnetic phase and a high-field long-
range ordered one.An intriguing finding is that this
ordered phase can be approximately described as a Bose-
Einstein condensation (BEC) of magnons.3Heat trans-
port of low-dimensional quantum magnets has recently
received an intensive research interests because it is very
useful to probe the nature of magnetic excitations and
the field-induced QPTs.4–8In particular, a large spin
thermal conductivity in spin-chain and spin-ladder sys-
tems has been theoretically predicted and experimen-
tally confirmed in such compounds as SrCuO2, Sr2CuO3,
CaCu2O3, Sr14Cu24O41, etc.9–12Most of these materials
have simple spin structure and strong exchange coupling,
which are necessary for producing high-velocity and long-
range-correlated spin excitations, while the low dimen-
sionality strongly enhances the quantum fluctuations and
ensures a large population of spin excitations. However,
the ground states of these materials usually have weak re-
sponse to the magnetic field because the laboratory fields
are too small, compared to the exchange energy. They
are, in this sense, not suitable for studying the field-
induced QPTs and the associated physics of magnetic
excitations. Apparently, some organic magnetic mate-
rials have obvious advantages since their larger crystal
unit cells and atom distances lead to much weaker ex-
change coupling of magnetic ions. Several materials have
been studied to reveal how the heat transport behaves
at the field-induced QPTs.8,13–15It seems that the spin
excitations are often playing a role of scattering phonons
and therefore strongly suppress the thermal conductivity
at the phase transitions. One alternative case is NiCl2-
4SC(NH2)2 (DTN), in which the thermal conductivity
is significantly enhanced in its BEC state.8,16Therefore,
the role of magnetic excitations in the heat transport at
QPTs still needs to be carefully studied.
chloride, also known as DMACuCl3or MCCL) is an S =
1/2 alternating antiferromagnetic-ferromagnetic (AFM-
FM) dimer-chain system with weak inter-dimer AF
coupling.17–25MCCL crystallizes in the monoclinic struc-
ture (space group C2/c) with room-temperature lattice
constants a = 17.45˚ A, b = 8.63˚ A, c = 11.97˚ A, and β
= 125.41◦.18,26The crystal structure consists of Cu-Cl-
Cu bonded chains along the c axis with Cu-Cl···Cl-Cu
contacts along the a axis. These Cu-halide planes are
separated from one another along the b axis by methyl
groups, so the magnetic coupling is only expected in the
ac plane. The basic features of the spin structure are
illustrated in Fig. 1(a). All the spin interactions J1, J3,
JA and JB are AFM except that J2 is FM. The calcu-
lations using the diagonalization method found the re-
lations JB < JA < J1 < |J2|, and J3 is nearly zero.18
The magnetic structure can be regarded as an alternating
predominant AFM dimer(AF1) and FM dimer (F2) with
the practically equal magnitude of the intra-dimer inter-
actions J1and J2, respectively, which are linked by weak
AFM inter-dimer interaction J3. It can be modelled as
-F2-AF3-AF1-AF3-F2-.24This rather complicated mag-
netic structure results in interesting magnetic proper-
ties and multiple phase transitions, as shown in Fig.
1(b).19–21,24,25The ground state of MCCL in the absence
of the magnetic field can be viewed as a long-range or-
Field-Induced Gapped State
FIG. 1: (Color online) (a) A schematic plot of the spin struc-
ture of MCCL. There are two types of dimers along the a
axis: (i) the AFM dimers with the intra-dimer interaction
J1 and the neighboring AFM interaction JA; (ii) the FM
dimers with the intra-dimer interaction J2 and the neigh-
boring AFM interaction JB. Spin chain (along the c axis)
are contacted by alternating AFM dimers and FM dimers
through AFM interaction J3 between two types of dimers.
(b) The H − T phase diagram of MCCL obtained from the
former experiments.19–21,24,25The magenta area and the cyan
one represent the low-field spontaneous order state and the
high-field induced magnetic order state, respectively, with the
field-induced gapped state between them.
dered chain in which alternative S = 1 and S = 0 spins
coupled by an intervening weak interaction. A sponta-
neous AFM order is formed below the N´ eel temperature
TN = 0.9 K, but it is stable only in the low magnetic
fields (H < Hc1, Hc1 = 2 T at zero-T limit), and then
becomes a field-induced gapped state in Hc1< H < Hc2
(Hc2 = 3.5 T at zero-T limit) and finally turns into a
field-induced magnetic order (FIMO) phase at H > Hc2.
The rich magnetic phenomena of MCCL make it a good
material to study the low-T heat transport and its rela-
tionship with the QPTs.
In this work, we study the detailed temperature- and
field-dependencies of low-T thermal conductivity of high-
quality MCCL single crystals. It is found that the mag-
netic excitations do not transport heat directly and there
is strong scattering between magnetic excitations and
phonons at zero or low fields.
conductivity shows drastic changes across all the phase
transitions mentioned above. In high-field spin-polarized
state, the magnetic scattering is strongly weakened and
the phonon conductivity is significantly increased in a
very broad temperature region.
The phonon thermal
MCCL single crystals are grown using a slow evapo-
ration method.27Shining crystals with the typical size
of (3–6) × (1–3) × (1–2) mm3, with the bc crystallinity
plane the largest naturally formed surface, are selected
and polished into a parallelepiped shape for the specific
heat and thermal conductivity measurements. The spe-
cific heat is measured by the relaxation method in the
temperature range from 0.4 to 10 K using a commercial
physical property measurement system (PPMS, Quan-
tum Design). The temperature and magnetic field depen-
dencies of the thermal conductivity are measured using
a conventional steady-state technique in a3He refrigera-
tor and a 14 T magnet.8,28,29The heat flow is along the
bc plane, in which the spin chains are included. Note
that the MCCL crystals are somewhat fragile, so the tri-
als to make well-shaped samples with other orientations
are not successful. In both specific-heat and thermal-
conductivity measurements, the magnetic field is applied
perpendicular to the bc plane.
III. RESULTS AND DISCUSSION
The low-temperature specific heat data are measured
for verifying the H − T phase diagram of our MCCL
crystals. Figure 2 shows the data with magnetic field
from 0 to 9 T. The main features of the zero-field C(T)
curve include a narrow and sharp peak at 0.89 K and a
“shoulder” at about 5 K, as shown in Fig. 2(a). With
increasing the field, the low-T peak shifts to lower tem-
perature with the peak amplitude decreased and finally
evolves to a very small peak at 0.57 K when the magnetic
field is increased to 2 T. This low-T peak is clearly due
to the spontaneous N´ eel transition, which can be sup-
pressed by the magnetic field. With increasing magnetic
field further, this low-T peak completely disappears and
a new peak shows up. It can be seen from Figs. 2(b)
and 2(c) that the new small peak appears at 1.06 K in
4-T field and it becomes bigger and sharper and shifts to
a bit higher temperature with increasing magnetic field,
in contrast to the field dependence of the low-field peak.
More exactly, the peak temperature is highest at 7 T.
Apparently, this new peak appeared in higher fields has
another origin, which is known to be the transition of the
FIMO phase. The phase boundaries determined from the
present specific-heat data have good consistency with the
former result (see Fig. 1(b)).20
Figure 3 shows the temperature dependencies of κ in
zero field and several magnetic fields up to 14 T. In the
zero field, the temperature dependence of κ is rather com-
plicated. The peak at ∼ 12 K is likely the phonon peak as
the insulators commonly have.30At lower temperatures,
there appear two “diplike” features in the κ(T) curve at
∼ 3 K and ∼ 0.6 K, respectively. In general, the possible
reasons of these behaviors in magnetic materials could
be either the strong phonon scattering by critical spin
FIG. 2: (Color online) Specific heat of MCCL as a function
of temperature for the magnetic field applied perpendicular
to the bc plane.
fluctuations at some magnetic phase transitions or the
phonon resonant scattering by some magnetic impurities
or lattice defects.28,30,31The underlying mechanism can
usually be judged from the magnetic-field dependence of
the diplike features of κ(T). As can be seen from Fig.
3 that applying magnetic field induces drastic changes
in the magnitude and the temperature dependence of
κ. As far as the lower-T dip is concerned, it is found
that applying magnetic fields up to 3.5 T suppresses the
very-low-T κ so strongly that the dip is markedly weak-
ened in 1 T and completely disappeared in 3.5 T. Ap-
parently, this dip is related to the spontaneous AF or-
dering, which is known to be suppressed with applying
magnetic field. More exactly, in zero field, the phonon
scattering by magnetic excitations or spin fluctuations
is strong at high temperatures; upon lowering tempera-
l / W
FIG. 3: (Color online) Temperature dependencies of the ther-
mal conductivity of MCCL single crystal in the zero field and
several different magnetic fields up to 14 T, which are applied
perpendicular to the bc plane. The dashed line indicates a
T2.7dependence of κ at subKelvin temperatures. The in-
set shows the temperature dependence of the phonon mean
free path l divided by the averaged sample width W in 14 T
ture to the spontaneous AF state, the spin fluctuations
are significantly weakened and the phonon conductivity
can be increased. Thus, a diplike feature is produced.
However, applying magnetic field (up to several Tesla)
can suppress the magnetic order and somehow enhance
the spin fluctuations and their scattering on phonons. In
passing, the temperature of the low-T dip locates at 0.6
K, a bit lower than the AF transition temperature 0.9
K from the specific-heat data. Similar phenomenon was
also observed in some other magnetic material.28
The 3-K dip is also weakened in magnetic fields al-
though its position is nearly independent on the field.
From the position of this dip, it is possible to be at-
tributed to the phonon resonant scattering by the en-
ergy gap in the spin spectrum.
ing measurements have revealed that in the paramag-
netic phase there are two magnon branches along the bc
plane; one is dispersive and the other one is dispersion-
less with gaps of 0.95 and 1.6 meV, respectively.22,23,26
In this situation, phonons with 0.95 meV (∼ 11 K) can
be resonantly scattered by producing magnetic excita-
tions. Since the phonon conductivity spectrum κ(ω) has
a (broad) maximum at ∼ 3.8kBT,30,31this magnetic scat-
tering on phonons is therefore the strongest at ∼ 3 K,
which agrees well with the position of the dip. The weak
dependence of dip position on the magnetic field suggests
that the gap of magnetic spectra is insensitive to the field
The neutron scatter-
at the paramagnetic state.
In magnetic field as high as 14 T, the thermal conduc-
tivity show very drastic changes. First, the magnitude of
κ is always enhanced in a broad temperature region from
0.3 to 30 K and the enhancement is rather large. Sec-
ond, the 3-K dip in zero field evolutes into a shoulderlike
feature, suggesting that the phonon resonant scattering
is still active at 14 T. Third, at subKelvin temperatures
κ(T) show an approximate T2.7dependence, which indi-
cates that the phonon boundary scattering is approached.
It is useful to calculate the mean free path of phonons in
14 T and to judge whether the phonons are nearly free
from microscopic scatterings at subKelvin temperatures.
The phononic thermal conductivity can be expressed by
the kinetic formula κph=1
phonon specific heat at low temperatures, vpis the aver-
age velocity and l is the mean free path of phonon. Here
β = 3.15 × 10−3J/K4mol is obtained from the lattice
specific-heat data20and vp= 2440 m/s can be estimated
from β.32,33The obtained l from the 14 T κ(T) data are
compared with the averaged sample width W = 2?A/π
= 0.993 mm,30,34where A is the area of cross section.
As shown in the inset to Fig. 3, the ratio l/W increases
with lowering temperature and becomes close to one at
0.3 K, which means that the boundary scattering limit
is nearly established at such low temperatures. In other
words, the heat transport at such low temperatures is
mainly contributed by the phonons, on which the micro-
scopic scatterings are very weak. It is known from the
H − T phase diagram that 14-T field is strong enough
to suppress the magnetic ordering and fully polarize the
spins, so the low-energy magnons are hardly to be ex-
cited in such high field.28,29,32Therefore, it is naturally
expected that the phonon scattering by magnons is al-
most smeared out in 14 T. This means that in zero and
low fields, magnon excitations are mainly playing a role
of phonon scatterers.
To further clarify the roles of magnetic excitations and
magnetic phase transitions in the low-T heat transport
of MCCL, it is useful to study the detailed magnetic-field
dependence of κ. Figures 4(a) and 4(b) show the κ(H)
isotherms at temperatures below and above the zero-field
TN = 0.9 K, respectively. The qualitative behaviors of
κ(H) are essentially the same for temperatures below TN.
At low-field region, the κ strongly decreases with H, ac-
companied with three “dips” at ∼ 1 T, 2.25 T, and 3.5 T.
A “plateau”-like feature then appears at the intermedi-
ate field region, which is terminated by a quick increase
of κ at high fields, with the transition fields precisely co-
incided with the upper phase boundary of FIMO. The
strong increase of κ at the spin-polarized state can be
clearly attributed to the weakening of the phonon scat-
tering by magnons because the number of the low-energy
magnons is quickly decreased.28,29,32This result can be
compared to the observations of κ(T) in Fig. 3. As the
κ(H) curves show, even 14 T field is not strong enough to
completely suppress the magnetic scattering on phonons.
This is the reason that the 14 T κ(T) do not exhibit a pre-
3Cvpl,30where C = βT3is the
FIG. 4: (Color online) Magnetic-field dependencies of ther-
mal conductivity of MCCL crystal at low temperatures. The
magnetic fields are applied perpendicular to the bc plane. (a)
T = 0.38–0.7 K. (b) T = 0.97–3 K. (c) Zoom in of the low-field
plots for T = 0.38–0.7 K.
cise T3dependence at subKelvin temperatures.34Never-
theless, in zero and low fields, the magnetic scattering on
phonons are significant.
The low-field κ(H) behaviors are shown more clearly in
Fig. 4(c). Apparently, the dip fields at ∼ 2.25 and 3.5 T
correspond precisely to the lower and upper critical fields
of the field-induced spin gapped state, respectively. The
diplike features at these two critical fields are attributable
to the phonon scattering by the strong critical spin fluc-
tuations at the phase transitions.8,15The first dip at ∼
1 T locates in the low-field AF ordered state and is of
different origin. As can be seen in Fig. 2(a), the specific
heat data below 0.7 K do not show any anomaly or ob-
vious field dependence from 0 to 1.5 T. It is known that
the spin-flop-like transition of spin structure may not be
detectable by the specific-heat measurements. It is there-
fore very likely that the 1-T dip at very low temperatures
is related to some kind of spin-flop transition, which is
also reasonable considering the nearly temperature inde-
pendence of the dip field.28,29,32,35The spin-flop transi-
tion has been indeed observed in an earlier magnetization
measurement,19although the transition field found at ∼
0.5 T is somewhat lower than that in the heat transport
Another peculiar feature of the low-T κ(H) isotherms
is a “plateau” at the intermediate field region. At 0.38
K, for example, the κ is nearly field independent from 6
to 13 T. With increasing temperature, the plateau be-
comes narrower and disappears above 0.97 K. This field-
independence phenomenon is apparently in good agree-
ment with the specific-heat data shown in Fig.
which are also essentially independent on field above 6
T and at very low temperatures. One clear point is that
the plateau behavior shows up when the sample is in the
FIMO state, which indicates that the magnon spectrum
at such low-T phase does not change strongly with ap-
Above TN, the three low-field “dips” disappear; in-
stead, the κ(H) curves show a broad valley-like behavior
for T = 0.97, 1.4 and 1.95 K, as shown in Fig. 4(b).
In these curves, the fields for the minimum κ are all
located at 3.5 T, which indicates that it is not related
to the lower transition field of the FIMO phase. The
κ increase rather rapidly at higher fields, demonstrating
that the spin fluctuations are significantly weakened. At
even higher temperature of 3 K, the κ shows a mono-
tonically increase with increasing field. Note that the
high-field-induced increase of κ is actually happened in
a very broad temperature region, as also can be seen in
Fig. 3. Since the spontaneous or field-induced magnetic
orders are not relevant, the strong field dependence of κ
in this temperature region is apparently related to the
strong quantum fluctuations of the low-dimensional spin
systems. The data indicates that the strong magnetic
field tends to effectively suppress the spin fluctuations,
which can strongly scatter phonons.
From above data and discussions, it is reasonably con-
cluded that there is no clear signature that the mag-
netic excitations in MCCL have strong ability of trans-
porting heat directly.This is rather different from
some well-studied low-dimensional spin systems, like
SrCuO2, Sr2CuO3, CaCu2O3, Sr14Cu24O41, La2CuO4,
etc.,9–12,36–38in which the magnetic excitations show a
remarkably strong heat conduction and they are hardly
to be affected by the laboratory magnetic field.12,39The
main reason is that those inorganic materials usually have
much larger exchange coupling, typically being of the
order of magnitude of 100 meV. Furthermore, the spin
structure of MCCL is more complex. For example, in
the spontaneous AF phase only the FM dimers ordered
antiferromagnetically while the AF dimers are in the S
= 0 ground state with strong quantum fluctuations.
It is also useful to note that the low-T κ(H) shows a
minimum at the field-induced quantum phase transition
from the spin-gapped state to the FIMO state. This is
rather similar to another FIMO material, Ba3Mn2O8,40
in which the FIMO can be discussed on the basis of the
Bose-Einstein condensation of magnons.3In contrast, an-
other magnon BEC compound, DTN,8has shown strong
ability of magnetic heat transport along its spin-chain di-
rection at the phase transition from the gapped state to
the field-induced AF state.
The low-temperature heat transport in the quasi-
one-dimensional S = 1/2 alternating antiferromagnetic-
ferromagnetic chain compound (CH3)2NH2CuCl3 is
found to exhibit very complicated temperature and
spin fluctuations of this low-dimensional system scatter
phonons strongly in a broad temperature region from 0.3
to 30 K. The scattering is weakened when the sponta-
neous AF ordering is formed below TN, while it is en-
hanced when the AF order is suppressed in magnetic
fields. In higher magnetic fields, at the phase transitions
from the low-field N´ eel state to the spin-gapped state
(∼ 2 T) and the field-induced magnetic ordered state (∼
3.5 T), the thermal conductivity shows diplike anoma-
lies, which suggests the strong phonon scattering by the
critical fluctuations. In high fields, when the spins are
being polarized, the phonon conductivity is significantly
enhanced because of the weakening of spin fluctuations.
Due to the complex low-T phase diagram and the mul-
tiple field-induced QPTs, it is now difficult to perform
the quantitative analysis on either the temperature or
the magnetic-field dependencies of κ. Further knowledge
about the magnetic spectra of this material are necessary
for deeper understanding of the heat transport proper-
In zero field, the strong
We thank W. Tao for technical assistance. This work
was supported by the Chinese Academy of Sciences, the
National Natural Science Foundation of China and the
National Basic Research Program of China (Grant Nos.
2009CB929502 and 2011CBA00111).
∗Electronic address: firstname.lastname@example.org
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