Advanced Lab Course Tunneling Magneto Resistance M06 As of: 015-04-01 Aim: Measurement of tunneling magnetoresistance for different sample sizes and recording the TMR in dependency on the voltage. Content 1 INTRODUCTION 1 THEORY 1.1 Basics 1.1.1 The Schrödinger equation 1.1. The tunneling effect 1.1.3 Density of states 3. Tunneling Magneto Resistance 3.3 Magnetic Hysteresis and Domains 5 3 EXPERIMENT 7 3.1 Setup 7 3. Sample 7 3.3 Tasks 8 3.3.1 Recording of TMR characteristics 8 3.3. Size dependency 8 3.3.3 Recording of I/V characteristics 8 4 ANALYSIS 8 4.1 TMR characteristics 8 4. Size dependency 8 4.3 I/V characteristics 8 5 REFERENCES 9
M06: Tunneling Magneto Resistance 1 Introduction The influence of magnetic fields on the electrical resistance has long been known, but has not been the focus of interest for many years. The discovery of the giant magnetoresistance (GMR) in 1988 by P. Grünberg and, independently, A. Fert (Nobelprize 007), reanimated the research in the field of magnetoresistance. Nowadays, the tunneling magnetoresistance (TMR) attracts most attention, since the change of resistance due to magnetic fields can be large. Devices using this effect can be used as memory (MRAM) or magnetic and current sensors. Theory.1 Basics.1.1 The Schrödinger equation In the microscopic range, the behaviour of particles cannot be described by a time-dependent position vector r as in classical mechanics, but rather by the wave function ψ (,) rt. This wave function or probability density is a complex function of space and time; its square ψ (,) rt gives the probability to find the particle at the place r at the time t. To calculate ψ, one has to solve the Schrödinger equation ψ i = ψ + Vrt (,) ψ (0.1) t m where i is the imaginary unit, denotes Planck's constant, m the mass of the particle, = + +, and Vrt (,) the potential. The potential can be given by an electric or x y z magnetic field, or by a barrier such as an insulator between two metals (in the case of electrons). In the case of a one-dimensional time-independent potential, (1.1) reduces to d ψ + V( x) ψ = Eψ (0.) m dx where E gives the energy of the particle. In most cases, E can not be chosen freely but is, together with ψ, the result when solving (1.). E is the so-called Eigenvalue to the Eigenfunction ψ. Depending on the potential, there may be numerous solutions - for example, in the case of the hydrogen atom ( V( r ) 1/ r ), there are infinitely many solutions with the energies E 1/ n..1. The tunneling effect A very important application of the Schrödinger equation (1.) is the case of tunneling. As depicted in Figure 1, 1
M06: Tunneling Magneto Resistance Figure 1: Tunneling of electrons. A particle coming from the left hits a potential barrier of height V 0 and width d. Classically, the particle would be reflected, but in quantum mechanics, the propagating wave, describing the particle position, penetrates the barrier and leaves it on the right with lower amplitude. This way, the particle can pass the barrier. the potential is assumed step-like and given by 0 x < 0 V( x) = V0 0< x< d 0 d < x where d is the width of the barrier. The Schrödinger equation has to be solved for each area separately. The solutions are ψ ψ Ae Be k E ikx ikx m 1 = 1 + 1, =, ( ) iκx iκx m = Ae + Be κ = E V0 ψ Ae Be k E ikx ikx m 3 = 3 + 3, = (0.3) (0.4) (0.5) The solutions for every part consist of two terms: the term with positive exponent denotes a wave going from the left to the right, whereas the term with negative exponent denotes a wave going from the right to the left. This means, if an electron is coming from the left, the positive exponent describes the incoming wave, the negative exponent the reflected wave. This case will be discussed in the following.
M06: Tunneling Magneto Resistance As can be seen in eq. (1.3)-(1.5), there are two different wave vectors: k outside the barrier and κ inside the barrier. k is always a real number independent of E and therefore describes a propagating wave. κ can be imaginary when E < V0. In this case, the wave is not propagating any more but decaying into the barrier. Since it is not zero at the end of the barrier, the wave is still present on the other side. Classically, the particle can t pass the barrier, but in quantum mechanics, there is some probability for the particle to pass the barrier even when its energy is not sufficient. This is called the tunneling effect. The tunneling probability depends strongly on the thickness d of the barrier and the wave vector κ. In our macroscopic world, d and κ are usually rather large, therefore tunneling cannot be observed in everyday life..1.3 Density of states In a solid, the energy an electron can have is not arbitrary but restricted by e.g. the crystal structure and the sort of atoms. Furthermore, due to Pauli's principle, not all electrons can occupy the same state -- there is only a limited number of states at a given energy. The density of states (DOS) N( E ) gives the number of states in the energy interval ( E, E + de). It is mainly determined by the energy, but also by some quantum numbers similar to those used for atoms. This way, so called bands form -- areas in energy, where electrons can occupy a state. It is possible that for some energies there aren't any states for electrons to occupy; these areas are called band gaps. Since electrons tend to minimize their energy, the bands are filled continuously from low to higher energies. The highest occupied energy is called the Fermi level. In metals, the Fermi level lies within a band, so that electrons can easily be excited to (slightly) higher energies and move freely, whereas in insulators the Fermi level lies within a band gap and it takes higher energies to excite electrons to unoccupied states.. Tunneling Magneto Resistance The basic configuration of a Tunneling Magneto Resistance (TMR) element is depicted in Figure, upper row. It consists of two ferromagnetic (FM) layers separated by a thin insulating layer. The magnetizations of the layers can be oriented parallel or antiparallel ((a) resp. (b) in Figure ). 3
M06: Tunneling Magneto Resistance Figure : The TMR effect. Upper row: Typical configuration of a TMR element. It is made up of two ferromegnetic (FM) layers, separated by a thin insulating film (grey). Lower row: The density of states (DOS) of the electrons depends on the orientation of their spin relative to the magnetization of the layer: spin parallel to the magnetization shifts the DOS to lower energies (purple parabola), and the DOS at the Fermi level increases. Spin antiparallel to the magnetization leads to smaller DOS at the Fermi level (orange parabola). In case of parallel magnetization, many electrons with parallel spin can pass the TMR element (red arrow in (a)), whereas only a few electrons with antiparallel spin can pass (blue arrow).[3] The effect of the different magnetizations is shown in Figure, lower row. The density of states (DOS) of the electrons can be divided into two parts, depending on the spin: N for electrons with spin down and N for electrons with spin up. In case of spin orientation parallel to the magnetization, the energy of the electrons is lowered, which is why the DOS is shifted to lower energies (purple parabola in Figure ). In effect, the DOS at the Fermi level E F becomes larger. With antiparallel orientation of spin and magnetization the DOS is shifted to higher energies and the DOS at the Fermi level is smaller. When the magnetizations of the two FM layers are parallel (a), N ( E F ) is high on both sides, and many electrons with corresponding spin orientation can pass the element -- the resistance is low. Since N ( E F ) is low, only few electrons with spin antiparallel to the magnetization can pass and the resistance is high. All in all, the resistance R p is low (parallel connection of two resistances). In contrast, in the case of antiparallel orientation of magnetizations (b), the DOS is large on one side and low on the other side for each spin orientation. Therefore, the resistance is large for both 4
M06: Tunneling Magneto Resistance spin orientations, and the overall resistance resistance, one defines the TMR coefficient as R ap is large. To specify the relative change of Elements with TMR exceeding 400% have been developed.[4] Rap Rp TMR = (0.6) R By optimizing the layer structure and adding a so-called pinning layer, the magnetization of one layer can be fixed so it will not be influenced by external magnetic fields, while the magnetization of the other layer can be rotated easily. Such devices can be used e.g. as MRAMs and magnetic sensors. p.3 Magnetic Hysteresis and Domains In ferromagnetic materials, the magnetization M does not depend linearly on the external field H, but shows a hysteresis as depicted in Figure 3. Figure 3: Hysteresis loop of a ferromagnetic sample showing the saturation magnetization Ms, the remanent magnetization Mr and the coercive field Hc. Applied field H and the plotted magnetization component M are collinear. After magnetizing the sample to the saturation magnetization M s and reducing the applied field to zero, the remanent magnetization M r remains. To switch the magnetization to the opposite direction, a magnetic field equal to the coercive field H c is needed. The area enclosed by the loop is 5
M06: Tunneling Magneto Resistance proportional to the energy dissipated by the ferromagnet when driven around the loop and is characteristic for the ferromagnet as are the parameters M r and H c. Ferromagnets are classified by how easy they are remagnetized. Soft magnetic materials are easy to magnetize and have narrow hysteresis loops and small H c. They are used in transformer coils, generators and motors. In these applications the magnetization must be reversed many times a second and it is important that the energy dissipated in each cycle is minimized. An example is Permalloy which has a coercive field Hc Oe. In contrast, hard magnetic materials are difficult to magnetize and demagnetize. Important applications are permanent magnets (e.g. in motors), magnetic recording and data storage. In these applications, the magnetization needs to be preserved as long as possible. Consequently, hard magnets possess a broad hysteresis and the energy dissipated in a loop cycle is as large as possible so that the magnetization will not occur spontaneously. An example is Nd Fe 14 B which has a coercive field larger than 10000Oe. According to the theory of P. Weiss a not saturated ferromagnet is divided in small regions called domains, which are homogeneously magnetized to saturation. The direction of the magnetization of different domains need not be parallel. Two domains are separated by domain walls, in which the magnetization rotates continuously. Figure 4: Effect of an applied field on the domain pattern. a) In bulk. Domains with magnetization parallel to the applied field grow at the expense of domains with differently oriented magnetization. Domain walls have to move through the crystal. b) In thin films, domain wall motion is suppressed, and domains switch their magnetization abruptly to parallel to the external field. When an external magnetic field is applied, the domain walls move through the crystal, leading to a growth of domains with magnetization parallel to the external field while other domains shrink (see Figure 4 a). In small devices, the movement of domain walls is suppressed, and complete domains switch the orientations of their magnetization abruptly to parallel to the external field (Figure 4 b). This behaviour will lead to jumps in the hysteresis curve. 6
M06: Tunneling Magneto Resistance 3 Experiment 3.1 Setup For studying the tunneling magnetoresistance effect, the sample is placed between the pole pieces of a solenoid and contacted with precision needles. A sourcemeter supplies a constant voltage and measures the current (two-point measurement). To record the hysteresis loops, the magnetic field is sweeped from minimum to maximum value and back. Simultaneously, the current is measured and recorded. The regulation of the magnet and measurements are done using a computer. Attention! Make sure that the cooling of the magnet is turned on before starting the experiment! Turn on the cooling water and the cooling element for the magnet. Start measurement software. Turn on the power supply of the magnet and the Hall probe. Initialize the power supply and determine the I/H-ratio. Place the sample between the pole pieces and contact it using the precision needles. Check contact with the sourcemeter! Set parameters and start the measurements. For purposes of documentation and later evaluation store and print typical hysteresis curves and characteristics you have recorded. And remember to write down important parameters! 3. Sample Every TMR element consists of different layers with a thickness of some nm each. A typical structure of a TMR element is shown in Figure 5. Figure 5: Typical structure of a TMR sample. Top and bottom electrode provide electrical contact. The artificial antiferromagnet reference layer is magnetically hard, while the ferromagnetic sense layer is magnetically soft. MgO forms the tunnel barrier. 7
M06: Tunneling Magneto Resistance A silicon wafer is used as carrier of the element. For insulation a layer of SiO covers the Si. The bottom electrode for electrical contact consists of TaN/Ru/Ta layers. On top is the reference layer which is an artifical antiferromagnet: the ferromagnetic CoFe and FeCoB layers are separated by a Ru layer whose thickness is chosen so that the magnetic moments of the layers are antiparallel. The reference layer is magnetically hard, i.e. you need large external fields to switch the direction of magnetization. The tunnel barrier consists of MgO since which is an insulator. The magnetically soft sense layer is made of FeCoBSi which is covered by the top electrode for electrical contact. Since the sense layer is magnetically soft, its orientation can easily be changed by an external magnetic field, while for reorientation of the reference much higher fields are needed. Thus the relative orientation of the magnetisations of FeCoB and FeCoBSi, and therefore the TMR ratio, can be adjusted by a magnetic field. 3.3 Tasks 3.3.1 Recording of TMR characteristics To study the properties of the TMR stacks, the resistance is recorded in dependency on the external magnetic field. 3.3. Size dependency The aim is to study the size dependency of the TMR effect. Therefore hysteresis loops are recorded for TMR elements of different sizes. 3.3.3 Recording of I/V characteristics An important tool to characterize electronic parts is the recording of I/V characteristics. To do this, choose a TMR element and record the current in dependency on the voltage for positive and negative saturation fields. 4 Analysis 4.1 TMR characteristics Describe the resulting curves. What is the origin of the behaviour in the different parts? 4. Size dependency Calculate the areal resistance and the TMR ratio for different sizes. Is there a dependency? Describe and explain any unexpected behaviour in the hysteresis loops. 4.3 I/V characteristics Plot the I/V characteristics of the TMR element for positive and negative saturation. Explain the difference to 'normal' resistors! Plot the TMR ratio in dependency on the voltage. Can you explain the dependecy? 8
M06: Tunneling Magneto Resistance 5 References [1] G. Binasch, P. Grünberg, F. Saurenbach, and W. Zinn, Enhanced magnetoresistance in layered magnetic structures with antiferromagnetic interlayer exchange, Phys. Rev. B 39, 488 (1989). [] M. Julliere, Tunneling between ferromagnetic films, Phys. Lett. A 54, 5 (1975). [3] J.-G. Zhu, and C. Park, Magnetic tunnel junctions, Mater. Today 11,36 (006). [4] S. Yuasa, A. Fukushima, H. Kubota, Y. Suzuki, and K. Ando, Giant tunneling magnetoresistance up to 410% at room temperature in fully epitaxial Co/MgO/Co magnetic tunnel junctions with bcc Co(001) electrodes, Appl. Phys. Lett. 89, 04505 (006). [5] S. Blundell, Magnetism in Condensed Matter, Oxford University Press, New York, 001 9