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Correlation of Thermoelectric and Spin Properties in Magnetic Oxides University of Zaragoza Master in Physics and Physical Technologies Correlation of thermoelectric and spin properties in magnetic oxides Author: Supervisors: Alberto Dra. Myriam H. Aguirre Anad´onBarcelona Dr. Rafael Ramos Amigo June 23, 2013 Contents 1 Introduction 3 2 Thermoelectrics 6 2.1 Seebeck and Peltier effects . 6 2.2 Thermal conductivity . 7 2.3 Thermopiles and thermocouples . 8 2.4 Figure of merit . 8 2.5 Nernst Ettingshausen effect . 10 2.6 Anomalous Nernst effect . 11 3 Experimental techniques 11 3.1 Magnetic characterization . 11 3.2 Thermal transport measurements . 12 3.2.1 Seebeck effect and Thermal conductivity measurements 12 3.2.2 Electrical conductivity measurements . 13 3.2.3 Nernst effect measurements . 14 4 Results 16 4.1 Bismuth . 16 4.2 Magnetite . 19 5 Conclusions 24 1 INTRODUCTION Alberto Anad´onBarcelona Abstract Thermoelectrics are a potentially transformative power generation technology because they possess the property to convert directly heat into an electric voltage. In addition, thermoelectrics are a pollution- free method for generating energy. Until last decade, efficiency of thermoelectric materials has remained low, but due to the study of nanostructured materials they are becoming promising for commercial use. In this work we will be introduced in the world of thermoelectric characterization. For this purpose we are going to perform thermal, transport, thermoelectric and magnetic measurements in bulk single crystal magnetite and polycrystalline bismuth. 1 Introduction Power generation of renewable energy is one of the most important challenges for science and technology. Fossil fuel combustion is an inefficient way of generating energy, since only 25 % of the generated energy is usable [6]. The remaining 75 % is lost by different mechanisms: radiation and friction (5 %); exhaust gas (40 %) and dissipation in the engine (30 %). One way to exploit this wasted energy is the use of thermoelectric (TE) devices. Previously, TE materials were used mainly in concrete applications (see figure 1), but in order to improve waste-heat recovery technologies, TE devices are becoming more prominent. The origin of thermoelectricity dates back to 1822 when the Seebeck Effect[23] (SE) was discovered giving rise to devices such as thermocouples, very extended for measuring temperature nowadays. SE consist of a voltage difference that appears within any conducting material that is subjected to a temperature gradient ∆V = S∆T showing a proportional relation, where S is the Seebeck coefficient. Twelve years after, Jean Peltier discovered the reverse effect[18]. He found that the passage of an electric current (I) through a thermocouple produces a small heating or cooling depending on its direction q = πI; (1) where q and π are the heat flux and Peltier coefficient, respectively. In 1851, W. Thomson predicted theoretically (and observed experimen- tally) when a thermal gradient and an electrical current are induced to a conductor whose S magnitude is variable with temperature, a heating or cooling process is produced, due to the S variation[10]. The evolution of the heat flow can be described by equation 2. q_ = −τJ · rT; (2) Page 3 of 28 1 INTRODUCTION Alberto Anad´onBarcelona Figure 1: Robotic rover Curiosity is powered by a radioisotope TE generator. Radioisotope power systems are generators that produce electricity from the decay of radioactive isotopes. Heat given off by the decay of this isotope is converted into electricity by a TE system, providing constant power for fourteen years, the lifetime of the isotope used. Autor and copyright: NASA whereq _, τ, J are the heat flow per second, Thomson coefficient and cur- rent density though a homogeneus conductor. Thomson also related and summarized all the three effects in the following relations (1854)[1]: dS τ = T (3) dT π = ST (4) Today's thermoelectrics aim at increasing the heat to electricity conver- sion efficiency. The TE efficiency in power generation mode is defined in TH −TC equation 5[6], and is limited by the Carnot efficiency, C = . TE effi- TH ciency in power generation mode is calculated as the ratio of the electrical energy extracted from the source to the quantity of heat applied[10]. p 1 + ZTM − 1 = C p ; (5) 1 + ZTM + TC =TH Where TH ;TC and TM are the hot, cold and average temperatures respec- tively. An important magnitude to obtain the efficiency of a TE material is S2σT the figure of merit ZT = κ , where σ represents the electrical conductivity, T the absolute temperature and κ the thermal conductivity. We will define these quantities more precisely in section 2. For real applications it is desirable to have a figure of merit greater than one for the efficiency to be large enough. In literature, a ZT higher than Page 4 of 28 1 INTRODUCTION Alberto Anad´onBarcelona two[28] has been estimated for p and n type TE materials by reduction of the thermal conductivity through heat transport control in nanostructured devices. Another novel approach to achieve higher thermoelectric efficiency is the study of thermoelectric effects in magnetic materials such as the Nernst Effect (NE)[30] or the recently discovered Spin Seebeck Effect (SSE)[26][20], which have already shown potential for possible applications[27]. Classic thermoelectric materials are usually semiconductor alloys, as we will see later. Most of the materials used are Bi2T e3 and Sb2T e3 alloys, since they have the greatest ZT value for n- and p-type bulk materials at room temperature. In this work we propose to study thermoelectric and thermomagnetic phenomena in Bismuth and Magnetite. Bismuth is a semimetal with one of the lowest thermal conductivity ob- served for metals (7:97 W/mK at room temperature). An image of a bismuth crystal can be seen in figure 2a. It was the material used by Nernst and Et- tingshausen in the discovery of the Nernst effect[8] (NE). Bismuth has also the largest NE coefficient[2] observed for correlated metals due to excep- tionally low value of carrier density and also due to a very long electronic mean-free path in clean single crystals. Bismuth is also the most naturally diamagnetic material and when it is deposited in thin films with a thickness comparable to its Fermi wavelength a transition to semiconductor occurs due to electron confinement. Magnetite is known since ancient Greece to attract metals. An image of a magnetite crystal can be seen in figure 2b. It is the strongest natural permanent magnet (ferrimagnetic material) with a Curie temperature of 858 K. It is an iron oxide (F e3O4) with inverse spinel structure (cubic) and for- 2+ 3+ 2− mula A B2 O4 . The oxygen anions are arranged in a face centered cubic lattice and the A and B cations occupy 1/8 of the tetrahedral and 1/2 of the octahedral interstices respectively. In magnetite the A sites are occupied by half of the F e3+ ions, while the B sites are occupied by equal number of F e2+ and F e3+ ions arranged in rows along the <110> directions (the double exchange between these ions is the main reason for magnetite being an electric conductor at room temperature). Magnetite also presents a metal to insulator transition at around 125 K called the Verwey transition. Page 5 of 28 2 THERMOELECTRICS Alberto Anad´onBarcelona (a) (b) Figure 2: Bismuth crystals (a) and magnetite crystal (b). 2 Thermoelectrics 2.1 Seebeck and Peltier effects - Heat flux + Hot Cold Carrier Current TA - + TB Figure 3: Detail of the Seebeck effect configuration. Plus and minus sign represent the relative electric potential sign with respect to the centre if dominant carriers are electrons. An electrical voltage difference (∆V ) appears within any conducting ma- terial that is subjected to a temperature gradient; this is called the Seebeck effect[23], and was discovered by the Baltic German physicist Thomas Jo- hann Seebeck in 1822. Seebeck saw that a compass needle was deflected when a temperature gradient was applied on two different metals connected in a closed loop. He did not understood the SE in the terms it is interpreted nowadays, but rather as a magnetic effect, so he called the phenomenon the thermomagnetic effect. Later on, it was discovered by Hans Christian Ørsted that the deflection was caused by a magnetic field generated by an electrical current in the loop, discarding the magnetic nature of the effect. Page 6 of 28 2 THERMOELECTRICS Alberto Anad´onBarcelona SE is due to carrier diffusion from the hot to the cold sides[5]. Figure 3 shows a diagram of SE. The Seebeck coeficient, S, is defined as the instan- taneous rate of change of the SE with respect to temperature (eq. 6) at a constant temperature. dV ! S = (6) dT T If S is independent from temperature, equation 6 can be written as: ∆V = S∆T (7) Where ∆T is the temperature difference between the hot and cold sides. In SI the Seebeck coefficient is usually expressed in µV=K. The inverse effect was discovered by French physicist Jean Charles Athanase Peltier in 1834. When a voltage difference is applied to a conducting ma- terial, a thermal gradient may appear in it. As T.J. Seebeck, Peltier saw the effect by applying a current (I) to a loop with two different conducting materials. In the junction between them heat was absorbed or generated depending on the current direction. This is the working principle of the thermopile (see figure 4). The heat flux in a Peltier junction between two conducting materials A and B is given by equation 8 q = (SATA − SBTB)I (8) 2.2 Thermal conductivity The thermal conductivity (κ) is the coefficient that relates heat flux (heat flowing through unit area every second) and temperature gradient for isotropic materials, as it is written in equation 9.
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