Journal of Nanomaterials

Volume 2008, Article ID 329601, 12 pages

http://dx.doi.org/10.1155/2008/329601

## Atomic Layer Thermopile Materials: Physics and Application

^{1}Institute of Advanced Materials for Photoelcetrons, Kunming University of Science and Technology, Kunming 650051, China^{2}Max-Planck-Institut für Festkörperforschung, D-70569 Stuttgart, Germany

Received 20 August 2007; Accepted 16 May 2008

Academic Editor: Donglu Shi

Copyright © 2008 P. X. Zhang and H.-U. Habermeier. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

New types of thermoelectric materials characterized by highly anisotropic Fermi surfaces and thus anisotropic Seebeck coefficients are reviewed. Early studies revealed that there is an induced voltage in high oxide superconductors when the surface of the films is exposed to short light pulses. Subsequent investigations proved that the effect is due to anisotropic components of the Seebeck tensor, and the type of materials is referred to atomic layer thermopile (ALT). Our recent studies indicate that multilayer thin films at the nanoscale demonstrate enhanced ALT properties. This is in agreement with the prediction in seeking the larger figure of merit (ZT) thermoelectric materials in nanostructures. The study of ALT materials provides both deep insight of anisotropic transport property of these materials and at the same time potential materials for applications, such as light detector and microcooler. By measuring the ALT properties under various perturbations, it is found that the information on anisotropic transport properties can be provided. The information sometimes is not easily obtained by other tools due to the nanoscale phase coexistence in these materials. Also, some remained open questions and future development in this research direction have been well discussed.

#### 1. Introduction

The experiment of laser-induced voltage (LIV) effect, in which the (YBCO) thin films were used as a photosensor, was performed firstly by Chang etal. [1]. It was found that there is an induced voltage when pulsed laser light on the surface of YBCO thin films. It is proved that this LIV signal is induced by a thermoelectric anisotropy in the high superconductor (HTSC) oxides [2–5]. These films absorb incident laser radiation, the top surface of thin film is heated rapidly, and an instant temperature difference between the top and bottom parts of the films is generated. This temperature gradient produces an electric voltage through the difference between components of the Seebeck tensor. This anisotropy in thermoelectricity originates from the anisotropic shape of the Fermi surface, causing the different properties of atomic layers in the HTSC oxides with low and high conductivity.

They behave like the two metals of a thermocouple. Therefore, these materials are called atomic layer thermopile (ALT). LIV signals become even larger if the films are grown on vicinal cut substrates because the vicinal cut structure offers more atomic layer junctions upon the interface. Figure 1 shows the typical time response of an induced voltage with incident pulsed laser of duration of 20 nanoseconds. The first quantitative description of this phenomenon was due to Lengfellner etal. [3], subsequently these signals observed in the ALT materials were defined as laser induced thermoelectric voltages (LITVs). Since then several high superconductor oxides such as doped YBCO, , and so forth have been studied and all of them have shown a similar effect [6–8]. Based on these studies, light detection devices have been designed [9–13], this demonstrates some superior characteristics over traditional bolometer and photon counting devices. Most obvious advantages are that the device can function over a broad spectral range at room temperature, has a fast time response and no applied bias is required.

In 1998, Habermeier etal. observed a similar effect in thin films of the quasicubic grown on vicinal cut substrates [14, 15]. This discovery showed that the ALT property is not confined to HTSC oxide materials, but subsists in other materials. On the other hand, Lanthanum manganites, which are interesting for their colossal magnetoresistance (CMR) properties, have attracted a lot of attention both from the viewpoint of basic physics as well as potential applications. The discovery extends the field of application and also provides new insight for the understanding the discipline of “strong-correlated electrons.”

The LITV signal observed in ALT materials may be a general effect, and it has been well conscious of that the effect can be applied on several devices. However, there is no detailed relation between correlative macroscopic parameters of the used materials and the device performances. We derived a new formula based on a plane heat source and a thermal diffusion model [12]. This new formula does not only correlate the used material parameters with the device performances, but also facilitate the interpretation of physical mechanism of ALT materials.

Recently, several new ALT materials were reported, which belong to members of Ruddlesden-Popper family [15, 16]. Due to their different physical properties, they are suited to function at different spectral ranges or time responses. A new experiment shows that the superlattice like multilayer thin films grown on vicinal cut substrates demonstrate enhanced LITV signals. We will discuss these new ALT materials in detail in Section 3.

The first application of ALT materials is in light detection with advantages of fast time and broad spectral response, operating at room temperature, with no bias required. Based on the reverse effect, the Peltier effect, one can design microcooler. Examples and device design consideration will be given in Section 4.

The LITV measurements of HTSC and CMR thin films provide some important microscopic information on these materials. The direct information obtained is the anisotropy of the Seebeck coefficients, which are valuable for studying the transport property. In strongly correlated electronic system, like HTSC and CMR, currently the discussion has the focus on the nature of the phase coexistence. The measured LITV signals from HTSC and CMR are very sensitive to the doping, strain, oxygen content, charge- and orbital ordering, as well as the external perturbations such as the temperature, the applied magnetic field, and pressure. The information on anisotropic transport in these materials is regarded as being very important and hard to obtain through other experimental methods.

Although the ALT model and the transport mechanism of CMR materials have been well established, a number of questions in these studies are still needed to be answered, for example, why do CMR thin films exhibit anisotropic Seebeck effect even they are mostly cubic and in a paramagnetic phase, are there other materials which contain even larger ALT property? These open questions will be summarized at the end of this paper.

#### 2. Basic Principles

A
thermoelectric field *E*
in a crystal can be induced by a
temperature gradient : where *S* is Seebeck tensor. For a thin film
grown on vicinal cut substrate (See Figure 2(a)), illuminated by a laser pulse
on the surface, a temperature gradient in -direction is
generated causing an induced voltage signal along the *x*-direction due to the nonvanishing off-diagonal components of the Seebeck tensor. Based on
the experimental observations in ,
Lengfellner etal. derived a formula according to (1) [3] as
follows: where is the
difference of the Seebeck coefficients in the *ab* plane and *c* direction
of YBCO, respectively. *l* and *d* are the illuminated length and thickness of the film, is the angle
between the surface normal and *c*-axis of the substrate, *ZT* the
temperature difference between the top and bottom part of the film. With this
formula, one can explain most of the observed experimental facts, and also
identify the nature of a laser-induced thermoelectric voltage from other
photoinduced effect experimentally. According to this formula, the key factor
is , that is, the anisotropy of Seebeck
coefficient. Large transport anisotropy implies large induced voltage. It is
well known that the properties of atomic layers in are very different: the CuO_{2} layer is highly conductive, while the Y(Ba)-O layer has a low conductivity, as
well as the Seebeck coefficients. Each two atomic layers form a junction like
the thermocouple. If the thin films are grown on vicinal cut substrate,
numerous of junction structures, which seem as the series thermocouples, form
spontaneously on the surface, as shown in Figure 2(c). With a pulsed light irradiating
on the film surface, the top surface is heated fleetly due to the light
absorption, and a temperature gradient is developed, thus a thermoelectric
voltage is produced in each junction. Due to the large number of junctions, the
total induced voltage is very high, and the time response is very short since
the distance for the carriers to move is very short.

Figure 3 shows tilting angle dependence of the LITV peak values measured in the YBCO
films grown on the (STO) substrate. The results
indicate clearly that relation between the peak value of induced
voltage and the tilting angle of the substrate is
followed. Due to the difficulty in growing high-quality YBCO film on the
substrate with high tilting angle, the exception of the sample grown on
tilted substrate does not increase with the increase tilting angle any more. depends on the incident photon fluency and the absorption of the film for
the corresponding photon energy. High absorption and small
penetration of the light in films lead to large and thus large
induced voltage. The longer the illuminated film length *l*, the larger
the induced voltage, that is, the more atomic scale thermocouples contributes
to the thermoelectric signals. The thinner the film thickness (smaller *d*),
the larger the induced voltage, this is correct when the films are relatively
thick. However, the description in (2) is proved to be unreasonable at very
thin films. Figure 4(a) shows the LITV peak values versus different thickness
in YBCO films grown on STO [5]. The increase of the peak value with reducing
thickness is followed above 250 nm, but the peak value undergoes a reduction
below 250 nm, this dependence cannot be simply ascribed to the loss of the perfection
of the thermopile arrangement. To explain this abnormal behavior, an improved
model has been derived to describe the LITV mechanism. We would like to discuss
this in the following.

In order to correlate the material parameters to the induced voltage and the
device performance, a new equation has been derived based on a plane heat
source and cascade power net model [12]: where is time-dependent LITV signal, and *D* are the
absorption coefficient, density, light penetration depth, specific heat, and
thermal diffusivity of the film material, respectively. *E* is the energy
of the incident pulsed laser integrated over the pulse duration, and all other
parameters share the same definition with that. This formula provides three important results. Firstly, the peak of LITV
signal is no more monotonic variation with the thickness *d*, in fact, an
optimum thickness which is corresponding to a maximum peak
of the induced signal does exist. Secondly, to achieve a fast time response,
materials with small thermal diffusivity *D* should be selected. This is
totally reasonable within the frame of this new mechanism, and the response
time now can be calculated quantitatively based on this formula. Thirdly, the
LITV signal is affected by the light absorption of the film materials. Large
absorption of the materials implies larger induced voltage. If a small penetration
depth *δ* for the incident light is fulfilled, then both large voltage and fast
time response can be achieved at the same time. On the other hand, Wang etal. has deduced the function of deciding the optimum thickness of film
materials by using them differential equation of (3) and some suitable boundary
conditions [17]. With inputting the material parameters of YBCO film, one can
obtain the calculated peak value *Up* as a function of *d*, as shown
in Figure 4(b). It is found that the optimum thickness of YBCO film for
producing the maximum *Up* is about 215 nm. The calculations agree with
the LITV experiments very well. As a result,
based on (3) and its derivative equations, it becomes easier for one to select
suitable materials to design a light detector in a specified spectral range
with desired time response and sensitivity [16–20].

According
to the LITV experiments under different perturbations, one can obtain some thin
film properties, which may not be easily measured from the bulk value. Figure 5
shows the experimental and calculated LITV signals of the YBCO thin films. The
film parameters of YBCO and LaCaMnO_{3} obtained from the fitting
process are listed in Table 1.

According to Mott’s band theory for non- or weakly interacting electrons, the Seebeck
coefficient is expressed as [21] where is the conductivity at Fermi level, and and *e* are Boltzmann’s constant and the elementary charge,
respectively. As an approximation, (4) in most of metallic and
insulating system can be expressed as . It
suggests that there is a close relation between the Seebeck coefficient and the
resistivity: the larger the resistivity, the larger the Seebeck coefficients.
Equation (4) provides the basic relation between the LITV effect and the
physical properties of the strong corrected electronic materials, especially
the anisotropic transport property, which is valuable information for studying
the mechanism of HTSC and CMR materials. On the other hand, it also offers the
important hints to seek the more effective ATL materials, since high anisotropy
in conductivity links with high Seebeck anisotropy.

#### 3. Alt Materials

The ALT behavior is firstly observed in high superconductor oxide YBCO [1]. Later, other HTSC materials, such as doped YBCO, , and so forth, are studied and all of them demonstrate ALT property, only the amplitude and time response of these induced voltages are discrepant in different materials. These oxides are known as highly anisotropic due to the special layer structure. However, they are not stable in normal environment. Therefore, it is very interesting to search more practical materials.

The
experimental procedures for investigating ALT materials are composed of two
steps: the film preparation and the LITV measurements. The films are grown on
vicinal cut substrates by pulsed laser deposition (PLD). Targets
used are synthesized by solid-state reaction or coprecipitation, and can
be characterized using X-ray diffraction, and other methods. The selection of
substrates depends on the lattice parameter of the films to be grown on them.
The most frequently used substrates are single crystal (STO), La (LAO), Si, LaSrGaO_{4}, and MgO, and so forth. The
selected films have been characterized by using X-ray, Raman, TEM, and other
techniques to ensure that they are single phase grown on substrates. High-quality films are patterned using typical photolithography technique, and after
the application of electrodes, one can directly measure the LITV signals. Two
LITV measurement methods can be used according to the light source: pulsed
laser or continuous-wave light sources [10, 20]. We first report the results of
CMR thin film with ABO_{3} structure,
and then that of other new materials.

##### 3.1. -type thin films

At the beginning, it was a surprise to observe the LITV signal in thin film grown on vicinal cut STO substrates, since no transport anisotropy is expected in such manganites due to their cubic structure and showing paramagnetic phase above . However, the signal is robust and also observed at several other doping levels. We prepared the films on substrates cut at different tilting angles to check whether these signals were induced by thermoelectric effect. Figure 6 shows the LITV obtained from Ag-doped LaCa thin films grown on LAO. It is clear that relation is followed the large tilting angle of substrate, the larger peak of LITV signal. Therefore, the physics origin of these signals can be assigned to anisotropic Seebeck effect, and the signals were thermoelectric voltages. These experiments have demonstrated that these CMR thin films are a new type of ALT material other than high superconductors. Two arisen questions then have to be answered. Firstly, whether do other manganite films with different compositions or doping levels possess strong LITV signal, so that one can apply these new materials. Secondly, why do these thin films show anisotropic transport properties. Inspired by the discovery, systematic experiments were performed, including that on different doping levels and dopant types.

In
the doping experiment of system,
it is revealed that the decrease in the doping level of Ca leads to a large
induced voltage. According to the phase diagram, it is found that the crystal
structure change from cubic to orthorhombic with the reduction of doping level *x*.
Therefore, a large structural anisotropy can be expected. On the other hand,
less doping also changes the magnetic order from ferromagnetic to A-type
antiferromagnetic, this process may facilitate the anisotropic transport of
electrons at the same time. Another interesting experimental result
arises from films grown on different types of substrates. Figure 7 shows the LITV signals from
LaCa thin films grown on STO and
LAO substrates with the same tilting angle and prepared using identical PLD
conditions. The result reveals that the strains due to the mismatch between the
lattice parameters of the substrate and the films grown on it have strong
influence on the induced thermoelectric voltage.

Except for the thin films, several other doped manganites CMR thin films have been tested and all show similar effect, such as LaSr, LaCaSr, LaPb (LPMO), and LaBa [22–25]. We also synthesized cobaltite and other transition metal oxides with perovskite structure, which also demonstrate ALT properties. One typical example is the grown on vicinal cut LAO substrates. is a conductive perovskite oxide and used as electrode in fuel cell and buffer layer to grown lead-zirconate-titanate (PZT) thin films on Si substrate. We found that the time response of thin films is extremely fast [18]. The half width of the response curve is almost the same as the duration of the incident-pulsed laser, as shown in Figure 8(b). Considering the limitation of the measuring method, the real time response should be in the order of picoseconds.

The fast time response of LITV in results apparently from the high-thermal diffusivity, as described in (3). In case of requirement of fast time response applications, would be a good candidate.

##### 3.2. Ruddlesden-Popper family

Most
of the ABO_{3}-type CMR thin films belongs to
the so-called infinite layer or 113 member of Ruddlesden-Popper family, in
which the anisotropy is relatively small due to their cubic structure.
Therefore, it would be interesting to test other member of Ruddlesden-Popper
family. One of the examples is (214
structure) grown on vicinal cut substrates [24]. Large LITV signals have been
measured. The first observation of LITV from this compound further enlarges the
range for seeking the more effective ALT materials. Comparing with 113 configuration,
the 214 structure demonstrates large anisotropic conductivity. Hence large LITV
signals can be expected. On the other hand, besides the cuprates, manganites,
and cobaltite, is
the first nickelate material which exhibits LITV effect. Other members of
Ruddlesden-Popper family of HTSC oxides have been measured, and all the
materials show high LITV signals [6–8].

##### 3.3. Multilayer thin films

It is well known that man-made superlattices show strong anisotropy in conductivity. Is there the similar anisotropy in Seebeck tensors according to (4)? Following this question, multilayer thin films were prepared by PLD. The samples were composed with different periods and LaPb (YBCO/LPMO) combination. The thickness of each YBCO and LPMO layer was kept at 9 and 6 nm in these multilayer samples, respectively.

The
first group multilayer thin films is grown on vicinal cut LAO substrates with
the tilting angle of and between the surface normal and *c*-axis
by pulsed laser deposition technique. Details of the deposition process can be
found in our publication [25]. As shown in Figure 9(a), the experiments results
demonstrate clearly that the larger the tilting angles the higher the induced
voltages. Accordingly, our expectation has been confirmed in this experiment
that the observed effect originates from Seebeck effect. Furthermore, the LITV
signals are much larger than that of the individual single layer samples with
identically total thickness. The YBCO/LPMO superlattices in the second group
were deposited on LAO substrates with same tilting angle ,
but with different number of period as 7, 10, 15, and 20, respectively. The
LITV signals of these multilayer thin films with different periods have been
presented in Figure 9(b). In order to make a comparison, the LITV signals of
YBCO and LPMO single layer films with identical preparation process and
measuring condition are also shown in Figure 10. It is evident that the peak
value from multilayer YBCO/LPMO sample (20 periods) is about 7 and 34 times
larger than that of YBCO and LPMO single-layer films, respectively.

It
is known from (2) that the key factor for influencing the induced voltages is
the anisotropy of Seebeck tensor . In the
superlattice or multilayer film systems, it is difficult to predict the laser
absorption, penetration depth, and specific heat which also directly affect the
LITV signal, due to the large variation of these parameters in these special
systems. Therefore, one has to focus on the possibility of the enhancement from
the discrepancy of Seebeck tensor . For the multilayer
structure, it is obvious that the carrier transportation exhibits high anisotropy.
In the layer plane, the conductivity is rather high; while in the perpendicular
direction, that is relative smaller. With the increase of the period number,
the probability of carrier scattering enhances due to the increase of the
defects from the interface. As mentioned in (4), large resistivity leads to
large Seebeck coefficient, therefore, the large . Another
key influencing factor is the thermal conductivity. There are numbers of
discussion on the thermal conductivity of some manganites with layered
structures [26, 27]. Simkin and Mahan have calculated the phonon contribution
to thermal conductivity (*D*) in superlattices. It has been concluded that *D* is closely related to the number of superlattice periods (*n*)
and the phonon mean-free path. The heat conduction in perpendicular direction
of the layer plane is highest for the samples with small *n*, and rapidly
decreases with *n* increases, after reaching a minimum within the range of , increases
again. The smaller the mean-free path of phonon implies the smaller the *n*,
at which the minimum thermal conductivity is achieved. In superlattice
materials, the electrons are confined for certain situation, and the phonons
are scattered at the interfaces. Therefore, the high-thermoelectric figure of
merit (ZT) is expected, and indeed the ZT as high as 2 to 3 have been measured
in several experiments [28–30].

The
possible enhancement of may originate from
the stressed lattices. According to X-ray diffraction, both YBCO and LPMO films
are compressively stressed in *ab* plane due to the smaller lattice
parameter of LAO substrate. Therefore, the lattice parameters in *c*-direction
were enlarged assuming preservation of the volume of the unit cell. The large
mismatch and the sandwiched structure can keep this strain in the whole sample.
This leads to the variation of intrinsic properties of each component films.
Due to the strain effects, the stressed YBCO and LPMO films must show different
transport properties, this has been verified by several experiments [16–19, 31].

In a word, there is a huge variety of strong correlated electronic materials which are not yet studied from the viewpoint of their ALT properties. According to our limited research so far, it is clear that most of the materials with layered structure demonstrate ALT properties. For the first time, an enhanced LITV signal from multilayer oxide thin films with a superlattice-like structure is observed. Compared with single-layer film of YBCO or LPMO, the LITV signals of the multilayer sample (the YBCO/LPMO structure with 7 periods) have been enhanced for several times than those obtained in YBCO and LPMO single films. This new observation is interesting for studying the transport properties in superlattice-like multilayer thin films. The unusual enhancement of the light-induced voltages in these multilayer films is possibly related to the large Seebeck anisotropy and the reduction of thermal conductivity in superlattice-like structures. The investigation of these materials and thin films provides candidates for different applications, such as light detection at different wavelengths or time responses. On the other hand, the measured LITV signals from the superlattices-likestructures provide information on the anisotropic transport property, which are hard to obtain by other experiments.

#### 4. Application

Two practical applications have been put forward and tested with the ALT materials. One is light and heat detection, and the other is local cooling based on the reverse of the Seebeck effect, the Peltier effect.

The
thermoelectric response of an ALT material has a linear dependence on absorbed
radiation power. Therefore, a radiation detector was designed and tested [14, 18–20]. To compare
the ALT detectors with those fabricated by other materials, Table 2 lists the
main parameters for three types of detectors. Due to the broad absorption of
the black surfaces of most of the ALT materials, the LITV detectors can work in
broad spectrum range. The experiment shows that these detectors can response
from ultraviolet to middle infrared. According to (3), the time response
depends on the thermal diffusivity *D* and the penetration depth .
By proper selecting the materials responded at special wavelength, response
time from micro- to picoseconds is easy to be realized. Other advantages of
this type of detectors consist in that they show good performance at room
temperature without any biases.

Considering that the importance for fabricating the devices with fast time response and high sensitivity, one can define a device figure of merit to describe the performance of the LITV detector [18]: where and are the peak value of induced voltage and the full width at half maximum of the response curve of the induced voltages. Therefore, synthesizing and searching for materials with high LITV sensitivity and fast time response at the same time, namely, higher is interesting.

We have prepared Ag-doped (Ag-LPMO) thin films by means of PLD, and investigated the doping level effect on the LITV amplitude. By optimizing the doping level of Ag, it is found that the of the LITV device is improved substantially.

The LITV signals of Ag-LPMO films with different Ag doping levels are shown in Figure 11. The value firstly increases with the increase of Ag doping level, then reaches a maximum at doping level of 4–6 wt%, finally decreases. At the same time, the time response varies with an opposite way, reduce first and then increase. According to (5), one can calculate the values of these devices. Table 3 lists the measured , , and the calculated at different Ag-doping levels. It is evident that value can be enhanced to several times by optimizing doping level of Ag.

There are lots of discussion on the enhancement of the ZT of thermoelectric materials, and several new concepts to obtain materials with ZT higher than 1 have been reported [28–30]. To form materials with “phonon glass and electron crystal” behavior become the central issue to realize large ZT, namely, high-electronic conductivity and low-thermal conductivity. Doping with monovalent ions, such as Ag, either in the lattice or at grain boundary, always enhances electronic conductivity. At the same time, the inhomogeneity is induced by doping Ag because the Ag ions form the centers of phonon scattering. Therefore, doping with Ag in the LaPb films can enhance the ZT, and this may be an effective method for other material system as well.

The
reverse effect of Seebeck is Peltier effect, in which a thermoelectric cooling
can be realized by simply applying electric current. In an anisotropic
material, an applied electrical current density can
produce a Peltier heat flow ,
which is described by where *P* is the Peltier tensor, related to Seebeck
tensor *S*, defined as . The largest temperature difference realized
in this effect depends on the thermoelectric figure of merit ZT and is
expressed as The cooling effect of ALT materials was firstly observed
in YBCO bulk [32]. Recently, more effective cooling effect was realized in a
Pb- multilayer
structure [33]. By applying a current in film plane, temperature difference up
to 22 K has been observed between top and bottom sides of the sample. The
cooling experiments on ALT materials are just launched. However, the renewed
interests in microcooling for various applications are pushing the related
investigations. The advantages of the type of cooling are easy to realize,
without moving parts, matching well with plane technology, and so on.

#### 5. Physical Mechanisms and Open Questions

All crystalline solid materials are composed of atomic layers, therefore, they should have ALT behavior and can be the candidates for the application and LITV measurements. So far, only few have been studied. Large unreached area remains to be explored. The studies of HTSC and CMR thin films have put forward several questions which should be answered, for example, why there is anisotropy in CMR thin films with cubic or quasicubic crystal structure? Even more interesting is that the LITV signals are recorded at temperature above , the films are in paramagnetic phase. What information can be followed by analyzing the LITV signals at different applied perturbations? Clear answer of these questions involves in the mechanisms of charge and phonon transport in the strongly correlated electronic systems, which are also the hot points of condensed matter physics.

We
now discuss the origin of LITV signals from CMR thin films and try to answer
the origin of the anisotropy in these films. In fact, the existence of LITV
signals is closely linked with the mixed phases of the complicated system.
Assuming that there are two competing phases near in
CMR materials [34–36], the ferromagnetic
metallic (FMM) and charge-ordered antiferromagnetic (COAF) insulating phase,
the total induced voltage based on (2) is composed of the contribution of the
two: where is
the peak value of induced voltages. and are defined as in COAF and FMM phases, respectively. *C* is the concentration of FMM phase, which can be evaluated from the
measured temperature or applied magnetic fields dependence of magnetization (*M*)
and expressed as [37].
A is a constant related to the geometric dimension of the sample and the
temperature gradient in the materials produced by the pulsed laser, which is
temperature independent in the first approximation. Considering no other phase
transition and only the two phases playing important role, two extreme cases
can be discussed. At the temperature range of , the FMM phase disappears, *C* approaches to zero correspondingly. Based on (8), one can evaluate high-temperature
Seebeck anisotropy of COAF phase: . While in the case of the contribution of COAF
phase is negligible, small one can obtain Seebeck anisotropy of FMM phase at
low temperature . Figure 12 shows the LITV
signals obtained from thin
films grown on STO substrates [14]. According to the above analysis and
estimation, the Seebeck anisotropy of COAF phase at high temperature is , for FMM phase at low
temperature is , and
a ratio was
obtained.

These
results are reasonable. For the FMM phase, the structure of is
cubic, and the anisotropy is small, while the COAF phase is possibly noncubic
[34], this implies that a large anisotropy can be expected. In fact, it is well
known that the Seebeck coefficient is closely related to the conductivity. According to (4), the larger
the resistivity the larger the Seebeck coefficients. For
the two coexistent phases near and above ,
the FMM phase is the one with higher conductivity and lower resistivity,
therefore the Seebeck coefficients are relative smaller. In addition, due to
the cubic structure, the anisotropy should be further suppressed at the same
time. On the contrary, the COAF phase is insulating (large resistivity), then a
large Seebeck coefficient is expected, and even a large structural anisotropy
occurs. With this argument and also considering the evaluated values and the ratio ,
one can further simplify (8) as . This
approximation is valid at temperature near and above . Since *C* can be
evaluated from magnetization measurements accordingly, and based on the
measured LITV temperature dependence [8], the temperature dependence of is easily estimated. Figure 13
shows the obtained dependence
from experiments, together with the used curve. Based on
these results, the concentration of FMM phase can be easily
estimated. With the decrease of temperature, it is shown that
the difference of the Seebeck coefficients or
the anisotropy of the resistivity in COAF phase increases firstly. After it
reach a maximum at around ,
then the decreases again. Since there
are significant LITV signals measured above , we
would like to emphasize that the anisotropic Seebeck coefficients are robust. Therefore,
an anisotropic transport behavior can be definitely observed above in
paramagnetic phase of thin
films. This is unexpected, since the sample is cubic or quasicubic in terms of
its structure, and magnetically is in paramagnetic phase, both factors should
not lead to anisotropic transport properties. In fact, the temperature-dependent
Seebeck coefficient has been measured at temperature near and above in bulk
by Jaime etal. [37], which is an isotropic value, and demonstrated
qualitatively the same temperature behavior as the deduced from
LITV measurements. This means that the difference of is roughly
proportional to the absolute value of *S* as a function of temperature.
The interesting point is that the obtained anisotropic components should be
correlated to the structural anisotropy as well as the conductivity anisotropy
of a possible COAF phases. Recently, there were a number of experiments which
reported the measurement of Seebeck coefficients from (D = Ca, Sr, Pb, and Ba) by Venkataiah et
al. [38, 39], by Battabyal and Dey [40], these results demonstrated similar
temperature behavior as the one observed in [37]. However, all of the results of their samples are obtained in the bulk materials, and
less information on the anisotropy of the thermoelectric effects is given.
Furthermore, there is no discussion on the contribution of the competing phase in
these materials. Therefore, it is hard to tell which phase is responsible to
the anisotropy.

There
are several possible phases coexistent with the FMM phase above [41–43]. Figure 14 shows
the spin structure in A, C, and G types of antiferromagnetic phases, together
with a ferromagnetic (F) and newly proposed CE, E, and types of charge-ordered
antiferromagnetic phases. The parent compounds of doped are La and Ca. The undoped La is
orthorhombic (space group *P _{nma}*),
with magnetic ground state of A-type antiferromagnetic structure. In

*a-c*plane, the alignment of spins is parallel, it indicates the configuration of two-dimensional ferromagnetism. While in the successive plane of

*b*direction, the orientations of the spins are antiparallel. Therefore, the transport anisotropy has been built accordingly, that is, the electrons can move easily in the

*a-c*plane, but difficultly in the

*b*direction due to the antiparallel spin orientation. The other doping end is Ca, which is cubic in structure (space group ) and with magnetic ground state of G-type antiferromagnetic structure. In this phase, there is no anisotropy originated from crystal and magnetic structure. With different doping levels, the COAF phases could be a mixture of all these phases at temperature near and above . The CE phase is most likely the candidate, which is responsible for an anisotropic transport property. The zigzag conductive chains are in

*ab*planes, while the conductivity in

*c*direction is very poor because the hopping of spin is forbidden. The E-type of COAF phase is similar to CE-type. However, the zigzag chains are composed of two parallel oriented spins. Therefore, there is also anisotropic transport property. The carrier transport may be easier in the zigzag chains than that in CE phase. Up to now, it is hard to directly correlate which phase is responsible for the measured Seebeck anisotropy. More theoretical and structural studies are required to make the question be clearer.

In summery, a new experimental method, laser induced thermoelectric voltage effect from CMR thin films, was used for the first time to reveal the transport anisotropy at temperature near and above in thin film. By neglecting the contribution of FMM phase, the temperature dependence of in COAF phase was evaluated, this dependence provides clear evidence for the existence of noncubic, highly anisotropic phase above .

The results show that the Seebeck coefficients difference in COAF phase increases firstly with the lowering temperature, and then reaches a maximum at around , finally decreases again. This information is unique, and may offer great help in correlating COAF phase type as well as the mechanisms of the complicated phase competition and coexistence in CMR materials. In fact, similar situation is also in high superconductor materials, where a is defined, and little is known on the region between and . Therefore, LITV measurements may contribute valuable information on the anisotropic transport, and hence the physical understanding of strongly correlated electronic systems.

#### 6. Conclusion

Atomic layer thermopile (ALT) materials are a new type of materials, which demonstrate novel thermoelectric property. The basic principle originates from the different transport properties in different atomic layers, this induces the anisotropic Seebeck effect. This effect can be used in light or heat detection, and local cooling based on its inverse effect. There are large amounts of materials which may exhibit ALT property, but not yet well studied. The investigations of LITV in different ALT materials provide unique information on transport properties at temperatures especially important for study the mechanism of high superconductor and CMR effect.

#### Acknowledgments

P.X. Zhang would like to thank Professor C. Wang (Yunnan University) for the fruitful discussion and technical assistance. Both authors would like to thank X.-H. Li, W.K. Lee, B. Leibold, G. Cristiani, G. Y. Zhang, H. Zhang, and L. Yu for their contributions covering various aspects of this work. The financial supports are from science foundation of China (10274026, 1999E0003Z).

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