UNIVERSITY OF CALIFORNIA, IRVINE Wireless Microwave Detection Using Magnetic Tunnel Junctions THESIS submitted in partial satisfaction of the requirements for the degree of MASTER OF SCIENCE in Physics by Brian J. Youngblood Thesis Committee: Professor Ilya N. Krivorotov, Chair Professor Philip G. Collins Professor Michael Dennin 2012 UMI Number: 1529208 All rights reserved INFORMATION TO ALL USERS The quality of this reproduction is dependent upon the quality of the copy submitted. In the unlikely event that the author did not send a complete manuscript and there are missing pages, these will be noted. Also, if material had to be removed, a note will indicate the deletion. UMI 1529208 Published by ProQuest LLC (2012). Copyright in the Dissertation held by the Author. Microform Edition © ProQuest LLC. All rights reserved. This work is protected against unauthorized copying under Title 17, United States Code ProQuest LLC. 789 East Eisenhower Parkway P.O. Box 1346 Ann Arbor, MI 48106 - 1346 c 2012 Brian J. Youngblood TABLE OF CONTENTS Page LIST OF FIGURES iii ACKNOWLEDGMENTS v ABSTRACT OF THE THESIS vi 1 Magnetization Dynamics 3 2 Spin Transfer Torques 8 3 Magnetic Tunnel Junctions 17 4 Tunneling Magnetoresistance 23 5 Spin Transfer Assisted FMR 5.1 FMR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 Conventional FMR Measurement . . . . . . . . . . . . . . . . . . . . 5.3 STFMR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 27 28 29 6 Detector Design 33 7 Results 39 Bibliography 52 ii LIST OF FIGURES Page 1.1 Damped magnetization dynamics. . . . . . . . . . . . . . . . . . . . . 5 1.2 Torque contributions. . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 3.1 Schematic of free and fixed magnetic layers. . . . . . . . . . . . . . . 18 3.2 Typee A MTJ layer structure. . . . . . . . . . . . . . . . . . . . . . . 20 3.3 Type B MTJ layer structure. . . . . . . . . . . . . . . . . . . . . . . . 21 3.4 Type A MTJ Resistance vs. Field. . . . . . . . . . . . . . . . . . . . 21 3.5 Type B MTJ Resistance vs. Field. . . . . . . . . . . . . . . . . . . . 22 4.1 Spin-dependent band structure of a ferromagnet. . . . . . . . . . . . . 25 5.1 Free and fixed magnetic layers of an MTJ . . . . . . . . . . . . . . . 30 6.1 Schematic circuit diagram of an MTJ microwave detector . . . . . . . 34 6.2 Diagram of a bias-tee . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 6.3 Coplanar waveguide cross-section . . . . . . . . . . . . . . . . . . . . 35 6.4 Microwave detector components . . . . . . . . . . . . . . . . . . . . . 37 6.5 Dimensions of the assembled detector . . . . . . . . . . . . . . . . . . 38 7.1 Response of a type A sample to a direct microwave input . . . . . . . 40 7.2 Response of a Type A detector . . . . . . . . . . . . . . . . . . . . . 42 7.3 Response of a Type B detector . . . . . . . . . . . . . . . . . . . . . . 43 iii 7.4 Response of the best detector. . . . . . . . . . . . . . . . . . . . . . . 44 7.5 Response of a Type B detector to a direct microwave input . . . . . . 45 7.6 Power response of a GaAs Diode . . . . . . . . . . . . . . . . . . . . . 46 7.7 Diagram of spin-torque vectors 46 . . . . . . . . . . . . . . . . . . . . . iv ACKNOWLEDGMENTS I want to first express my gratitude to my research advisor, Professor Ilya Krivorotov. He has informed each step of this work and helped me to understand the physics that makes it possible and to see its further applications. He has listened to my ideas, both good and bad, and helped me to recognize the obstacles I was ignorant of and the implications I had not thought of. In the way he runs our group and through his personal example Prof. Krivorotov has made me a much better practitioner of physics and of science than I could have otherwise been. I also offer my thanks to the other members of my committee, Professors Philip Collins and Michael Denin both for their time and review of my thesis and for teaching me about undergraduate instruction and continuum mechanics, respectively. My thanks also go to my labmates in the Krivorotov Group, especially Jian Zhu, Graham Rowlands, and Yu-Jin Chen for technical advice and assistance in carrying out experiments. I thank my father Robert, for instilling and fostering both curiosity and a spirit of investigation in me. Finally, my deepest thanks go to my wife Marlette, for all of her support. RDECOM-TARDEC, NSF, the Western Institute of Nanotechnology, and the GAANN fellowship program provided financial support for this work. v ABSTRACT OF THE THESIS Wireless Microwave Detection Using Magnetic Tunnel Junctions By Brian J. Youngblood Master of Science in Physics University of California, Irvine, 2012 Professor Ilya N. Krivorotov, Chair I report on experiments demonstrating the detection of airborne microwave radiation using a magnetic tunnel junction as the sensing element. The detection is based on the technique of spin-torque assisted ferromagnetic resonance. In our version of this technique the RF current induced in an antenna by the microwave radiation is fed into the tunnel junction. The ac voltage across the junction is rectified by oscillations in the tunneling magnetoresistance of the junction which are caused by spin transfer torque due to the injected current. Compact coplanar waveguide antennas and non-magnetic, microwave-transparent, reusable device/antenna holder enclosures were designed and and assembled to carry out these experiments. Junctions with two different material layer structures were tested and compared. One of the tested structures gave superior sensitivities higher than those reported in the literature for similar devices and comparable to the sensitivities of commercial, diode-based microwave sensors. vi Introduction The use of conduction electrons to control the magnetic state of a material has broad applications from information storage and processing to sensors and microwave communication. Together, these technologies are often called spin electronics or spintronics. This thesis is concerned with the use of a magnetic tunnel junction as the sensing element in a passive detector for microwave radiation. Unlike an electromagnetic signal confined in a transmission line like a waveguide or cable, a radiated signal decays very quickly so a relatively sensitive detector is needed to measure it in technolgically relevant situations. Also, while a measure of control over source and cable impedances is possible when a source is connected directly to a detector, allowing improved matching and better overall detection efficiency, the impedance of air is fixed and some way is needed to couple microwave signals to the sensing element. The design presented here includes a compact antenna suitable for this purpose. The detector is based on a measurement technique called spin torque assisted ferromagnetic resonance (STFMR)[1]. Other work has explored the use of tunnel junctions as sensing elements [2],[3],[4], but until now wireless detection of microwaves using a magnetic tunnel junction has not been demonstrated. We also demonstrate an improvement in maximum detector sensitivity over the best sensitivities reported in the literature [4]. In this thesis I will describe the principles behind the operation of the magnetic 1 tunnel junction microwave detector, its design, and measurements obtained using two different layer designs for the tunnel junction. 2 Chapter 1 Magnetization Dynamics Magnetization dynamics are governed by the Landau-Lifshitz-Gilbert-Slonczewski equation: ~ = −γ0 M ~ × Ĥef f + ∂t M α ~ ~ + η µB I M̂ × (M̂ × P̂ ) M × ∂t M Ms eV (1.1) where γ0 is the gyromagnetic ratio for an electron, Ms is the saturation magneti~ is treated as uniform zation of the ferromagnet being studied.The magnetization M (macrospin approximation) and of constant magnitude. In this equation the effec~ ef f is the gradient of the free energy of the system with respect to the tive field H orientation of the magnetization. That is ~ ef f = dF = ∇M F H ~ dM (1.2) Typically, one includes terms in the effective field for contributions due to applied ~ ef f is given by field, anisotropy, exchange field, and demagnetization so that H ~ ef f = H ~ app + 2Ku (n̂ · M ~ )n̂ + 2Aex ∇2 M ~ +H ~ demag H 2 µ0 Ms µ0 Ms2 3 (1.3) where it is assumed that the anisotropy in the ferromagnet is uniaxial with coefficient Ku and direction n̂, in the following we will usually write such a uniaxial anisotropy ~ and the anisotropy direction. field as n̂Hk cos θ where θ is the angle between M ~ demag is the demagnetizing field arising from magnetic poles accumulated on the H surface of an object, such as a ferromagnetic layer. We approximate this field as ~ · û where û is the unit vector normal to the surface of the being proportional to M ~ demag is layer and also the direction of the demagnetizing field. This simple form of H only strictly true for an ellipsoid but it is close to true for thin ferromagnets. For the thin layers we deal with Hdemag = M/2 in SI units (Hdemag = 2πM in cgs). The second term of (1.1) represents the damping or tendency for the magnetization direction to return to the direction of the effective field. This results in a trajectory of the magnetization direction which is a contracting spiral about the effective field as shown in Fig.1.1. The damping constant α is an experimentally determined property of a material, though efforts have been made to compute it theoretically. For most ferromagnets the damping time determined by the damping term is on the order of 1ns. Broadly, the damping is due to spin-orbit coupling to the lattice [5]. In the absence of this damping the magnetization would precess uniformly around the effective field. The last term in (1.1) represents the pseudo-torque acting on the magnetization due to interaction with a spin polarized current (polarized in the direction of the unit vector P̂ ). Section 2 discusses the origin of this contribution but the main point is that this spin torque term can act opposite to the damping (see Fig.1.2) and if the current is sufficiently large it will cause the magnetization to switch to its other stable orientation (parallel or anti-parallel to the effective field). Expanding (1.1) to first 4 Figure 1.1: Damped magnetization dynamics. In this case the effective field is in the +ẑ direction and the magnetization is initially aligned with the +x̂ axis. Figure 1.2: Schematic of the action of the damping torque (Tdamp ) and the spin torque (Tst ). 5 order in the small damping constant α [6] gives ~ =M ~ × γ0 H ~ ef f + M ~ × (−αγ0 H ~ ef f + ∂t M ηµB I P̂ ) V (1.4) ~ × M̂ × (M̂ × P̂ ) = 0 for any P̂ . Considering a magnetization if we use the fact that M ~ initially oriented nearly parallel to both the effective field H ~ ef f and the incoming M conduction electron polarization direction P̂ means that the first term in (1.4) is approximately zero and we are left with ~ =M ~ × M ~ × (−αγ0 H ~ ef f + ηµB I P̂ ) ∂t M V (1.5) ~ also allows us to rewrite this in and our assumption about the initial direction of M a scalar form as ∂t θ = −αγ0 Hef f + ηµB I V (1.6) The condition for switching is ∂t θ = 0, giving a critical switching current of [7],[8] Icrit = Ms 2e α Vµ0 Ms (Happ + Hk + ) h̄ η 2 (1.7) Here we have chosen a particular form for Hef f which includes the applied, anisotropy, and demagnetization fields. The anisotropy is uniaxial and we are considering switch~ ,H ~ app ,and H ~ k are all aligned so that any factors ing starting from a condtion where M of cos θ, where θ is the angle between the magnetization and the various fields, are equal to one. The same expression for Icrit can be obtained by averaging the rate ~ about H ~ ef f and finding the of change in energy over a small angle precession of M condition for energetic instability [9]. Magnetization switching due to spin-transfer torque from a conduction current was predicted in [6], and observed for all-metal spin valve [9] and magnetic tunnel junction 6 [10] trilayer structures at similar current densities of order 107 A/cm2 . Of course, currents smaller than the critical current also modify the dynamics of the magnetization by stabilizing the precession and increasing the damping time. The effect of alternating currents will be described in Chapter 5. This effect is the basis for the measurements described in this thesis. 7 Chapter 2 Spin Transfer Torques Spin transfer torques arise from the transfer of spin angular momentum from a spin polarized current of conduction electrons to a ferromagnet, this transfer of angular momentum results in motion of the ferromagnet’s average magnetization. This effect was predicted independently by Slonczewski [6] and Berger [11]. Consider a (1D) electron wave function normally (x̂ propagation direction) incident on a planar ferromagnet (assumed to be single domain and magnetized in the ẑ direction) from a material whose band structure is spin-independent. At the interface the barrier for minority (spin down) states is greater than the barrier for majority (spin up) states. The incident electron wave function has the form [7] θ θ eikx x cos( )| ↑> +sin( )| ↓> ψin = √ 2 2 Ω ! (2.1) The reflected wave function has the form θ e−ikx x θ ψr = √ r↑ cos( )| ↑> +r↓ sin( )| ↓> 2 2 Ω ! 8 (2.2) While the transmitted wave function has the form ! 1 θ θ ψt = √ eikx,↑ x t↑ cos( )| ↑> +eikx,↓ x t↓ sin( )| ↓> 2 2 Ω (2.3) where kx is the wave vector x-component in the spin-independent medium and kx,σ are the spin resolved components in the ferromagnet. These wave functions can be immediately modified to reflect the 3D case by multiplying their terms by ~ e±φ/2 eq~·R (2.4) where the upper (+) sign is chosen for | ↑> terms and − is chosen for | ↓> terms and ~ is the transverse ~q is the transverse parts of the full wave function k vector and R position vector. The angles θ,φ give the orientation of the spin polarization direction of the electron with respect to the magnetization of the ferromagnet. For parabolic, free electron-like band structure in the ferromagnet and nonmagnetic region, the spin dependence of the transmission and reflection coefficients is determined by the spin dependence of the Fermi wave vector according to tσ = 2kx kx + kx,σ (2.5) rσ = kx − kx,σ kx + kx,σ (2.6) where we have assumed that q 2 ≤ (kF,σ )2 . Computing the incident, reflected, and transmitted spin currents according to Qxx h̄2 k = 2Re(ab∗ ) 2mΩ (2.7) h̄2 k 2Im(ab∗ ) 2mΩ (2.8) Qyx = 9 Qzx = h̄2 k (|a|2 − |b|2 ) 2mΩ (2.9) where a,b are the ↑,↓ coefficients of the wave function gives Qi,xx h̄2 = kx sin θ cos φ 2m (2.10) Qi,yx h̄2 = kx sin θ sin φ 2m (2.11) for the components of the incident current transverse to the ferromagnet’s magnetization. The same components are given by Qr,xx = h̄2 kx sin θRe[r↑∗ r↓ eiφ ] 4m (2.12) Qr,yx = h̄2 kx sin θIm[r↑∗ r↓ eiφ ] 4m (2.13) Qt,xx = h̄2 kx,↑ + kx,↓ sin θRe[t∗↑ t↓ eiφ ei(kx,↓ −kx,↑ )x ] 4m 2 (2.14) Qt,yx = h̄2 kx,↑ + kx,↓ sin θIm[t∗↑ t↓ eiφ ei(kx,↓ −kx,↑ )x ] 4m 2 (2.15) for the reflected current and by for the transmitted current. We have left out the component Qzx parallel to the magnetization because Qi,zx = Qt,zx − Qr,zx exactly, indicating that no angular momentum is transferred to the ferromagnet from this component of the spin current. If we take wσ = cσ + idσ (2.16) w↑∗ w↓ = (c↑ c↓ − d↑ d↓ ) + i(c↑ d↓ + c↓ d↑ ) (2.17) where w can be r or t. Then 10 From this equation we can see that when the reflection and transmission amplitudes are the same for up and down spin states the product in (2.17) is real and the reflected and transmitted spin currents have exactly the the same form (the factor exp[i(kx,↓ − kx,↑ )x] in the transmitted current must be unity if the reflection and transmission amplitudes and therefore kx,↑ and kx,↓ are the same) as the incident spin current (and must sum to the same value since |r|2 + |t|2 = 1). This would mean that no spin angular momentum at all would be transferred to the ferromagnet. When reflection and transmission amplitudes differ for different spins then there is transfer, this is called the contribution to the spin-transfer torque due to spin filtering. So far we have considered only a single electron mode incident on the ferromagnetic barrier. In order to go further we have to consider a distribution f~(~k) of incident electrons at the interface and some of their correlations [12]. Considering only the electrons moving to the right, the incident spin current is given by Z h̄~k d3 k ~ i = h̄ f~(~ k)~ σ ] ⊗ T r Q 2 kx >0 (2π)3 m (2.18) The reflected current is given by h̄ Z d3 k ~ Qr = T r[R† f~R(~k)~σ ] ⊗ v~r (~k)] 2 (2π)3 (2.19) and the transmitted current is given by h̄ Z d3 k ~ Qt = T r[T† f~T(~k)~σ ] ⊗ v~t (~k)] 2 (2π)3 (2.20) In these equations v~r and v~t are the spin averaged velocities of reflected and trans- 11 mitted electrons and the transmission and reflection matrices are given by ik~↑ ·~ r k)e t↑ (~ T̂ = 0 ~ t↓ (~k)eik↓ ·~r 0 R̂ = 0 ~ r↓ (~k)eik·~r 0 (2.21) ~ k)eik·~r r↑ (~ (2.22) Integrating over the distribution reveals that although there could have been a contribution to the spin-transfer torque due to reorientation of the electron polarization upon reflection from the interface, the phase change due to this reorientation is randomized over the surfaces of integration (energies up to the Fermi surface) so that such a contribution averages to zero. The spin-transfer contribution that does remain after integration over the Fermi surface is due to the precession of the spins of the transmitted electrons about the magnetization direction as they travel through the ferromagnet. This change in momentum is expressed by the exp[i(kx,↓ − kx,↑ )x] factor in (2.14),(2.15) for the single electron case. The same information is contained in the transmission matrix (2.21) for the electron distribution case. Integrating gives the expression Qt,xx = Qi,xx 2 Z kF,↓ kx,↓ + kx,↑ |t↑ (q)t↓ (q)| dqq 2 kF 0 2|kx | for the total transmitted transverse spin current where q = q (2.23) kF2 − kx2 . At large x (far from the interface) this becomes [12] Qt,xx = 2Qi,xx kF,↑ kF,↓ kx,↓ + kx,↑ 1 |t↑ (0)t↓ (0)| . 2 kF 2kF (kx,↑ − kx,↓ )x (2.24) This shows that the transmitted spin current transverse to the magnetization decays with distance into the ferromagnet and we have already seen that the spin current parallel to the magnetization does not change so the spin angular momentum is being 12 transferred to the ferromagnet’s magnetization. Calculating the quantity Z ~i + Q ~r − Q ~ t ) = τst,|| dAx̂ · (Q (2.25) which is the total in-plane spin transfer torque acting on the ferromagnet, gives ~ i,⊥ τst,|| ≈ Ax̂ · Q (2.26) since the transmitted and reflected spin currents for Fermi surface states are collinear with the magentization of the ferromagnet [7]. This result indicates that spin angular momentum (the transverse component) was lost in the interaction with the barrier. This is the spin angular momentum which produces an effective torque on the magnetization in the ferromagnet. If an unpolarized (coefficients of | ↑> and | ↓> states equal) electron wave function is incident on a barrier like the one described, the transmitted wave function ψt is spin polarized since the spin component transverse to the ferromagnet’s magnetization will be absorbed. This will be the way that we obtain a spin polarized current of electrons, by passing an unpolarized current through a ferromagnet. This is the purpose of the second magnetic layer in the magnetic trilayers presented in section 3. The arguments above apply to an interface between a normal metal and a ferromagnet. Magnetic tunnel junctions include insulator/ferromagnet interfaces so that the reflection and transmission coefficients r↑,↓ ,t↑,↓ are different and (2.26) no longer holds quantitatively. However, the fact of spin polarized currents applying an in-plane torque to the magnetization of a ferromagnet remains. To treat the spin transfer torque in the case of a magnetic tunnel junction we will follow the scattering theory presented in [13]. We have introduced the idea that spin polarization of the condition electrons will be achieved by a ferromagnet so that we 13 will be discussing a trilayer consisting of a ferromagnet on either side of an insulator. The combined scattering matrices for right going electrons are # " ŝA,→ Tb = T̂1 (1 − Rb0 R̂2 )(1 − R̂10 Rb ) (2.27) Tb R̂10 Tb0 Rb0 + = T̂20 0 0 0 (1 − Rb R̂2 ) (1 − R̂1 Rb )(1 − R̂2 Rb ) # " ŝB,→ (2.28) while the components for left going electrons are given by Tb0 R̂2 Tb Rb = + T̂1 (1 − Rb R̂20 ) (1 − R̂10 Rb )(1 − R̂2 Rb0 ) (2.29) Tb0 T̂20 = (1 − Rb0 R̂1 )(1 − R̂20 Rb ) (2.30) " ŝA,← # # " ŝB,← (0 ) Here, R̂i ,T̂i (0 ) are the reflection and transmission matrices (like (2.22),(2.21)) for the (0 ) (0 ) interfaces 1,2 between the ferromagnets and the insulator. Rb ,Tb are the reflection and transmission matrices for the insulating barrier but since the insulator’s band structure is independent of spin they are proportional to the 2×2 identity matrix. By defining the normalized magnetizations of the two ferromagnets (m ~ 1 ,m ~ 2 ) it is possible to further approximate (by taking the impurity scattering in the insulating barrier to be zero ⇒ Rb = 0) the scattering matrices in terms of these two vectors as − ŝA,→ = tb (t+ ~ 1) 1 + t1 σ̂ · m (2.31) − − ~ 1 ×m ~ 2 ) (2.32) ~ 1 ·m ~ 2 ) + σ̂ · (r1− tb t+ ~ 1 + r1+ tb t− ~ 2 − ir1− tb t− ŝB,→ = (r1+ tb t+ 2m 2m 2m 2 + r1 tb t2 m − − ŝA,← = (r2+ tb t+ ~ 1 ·m ~ 2 ) + σ̂ · (r2− tb t+ ~ 1 + r2+ tb t− ~ 2 − ir2− tb t− ~ 1 ×m ~ 2 ) (2.33) 1 + r2 tb t1 m 1m 1m 1m − ŝB,← = tb (t+ ~ 2) 2 + t2 σ̂ · m (2.34) where t± i = (ti,↑ ± ti,↓ )/2 and ti,σ is the transmission amplitude for the spin σ at the 14 interface i. We can use these approximations for the spin scattering matrices in the following expression [13] for the spin current ~ = Q X 1 Z ~js (E, ~q, ~q0 ) dE (2π)3 q,q 0 (2.35) with ~js = 2T rσ [σ̂Im(ŝA,→ ŝ†A,← f1 (E) − ŝB,→ ŝ†B,← f2 (E + eV )] (2.36) where fi are the electron distribution functions of the two ferromagnets and V is the bias voltage applied across the multilayer. To determine the torque from this spin current on the magnetization of ferromagnet 2 we use the earlier determination that the entire transverse component of the spin current is absorbed as a torque, this gives ~τ = ~js − (~js · m ~ 2 )m ~2 (2.37) for the normalized torque. If we now put (2.36) into (2.37) we get two torque components ~n|| = t2b T1− T2+ (f1 − f2 )m ~ 2 × (m ~1×m ~ 2) (2.38) ~n⊥ = 2t2b Re(T1− r2− f1 + T2− r1− f2 )m ~1×m ~2 (2.39) where Ti± = |ti,↑ |2 ± |ti,↓ |2 . This result shows that for a magnetic tunnel junction there is both an in-plane or Slonczewski (2.38) and an out of plane or field-like (2.39) spin torque acting on the magnetization of the second ferromagnet. An alternative layer-by-layer nonequilibrium Green’s function approach [14] related to the microscopic approach to magnetoresistance [15] discussed in Chapter 4, which uses the true Bloch wave functions of the propagating electrons rather than a free electron approximation, predicts that the small fluctuations of thickness in real samples suppress the out of plane field-like torque for small biasing voltages. In addition, 15 the numerical calculations in this work indicate that the spin-torque acting on the ferromagnet’s magnetization (expressed as the decay of conduction electron spin components perpendicular to the magnetization) arises from majority propagating states interfering coherently with minority evanescent states in the ferromagnet. It should be noted that the magnetization of the second ferromagnet was initially perpendicular to the interface planes for these calculations in contrast to the usual cases where the magnetizations of both ferromagnetic layers are nearly in the plane of the interfaces. The Type B tunnel junctions described in this thesis (see Chapter 3) are, however, more like the ones in [14]. 16 Chapter 3 Magnetic Tunnel Junctions Magnetic tunnel junctions (MTJs) are trilayers consisting of an insulator sandwiched between two ferromagnets, often referred to as an F/I/F structure. The detectors described in this thesis are based on an MTJ sensing element. As stated at the end of section 2 we obtain a spin polarized current to apply spin transfer torque to a magnetic layer by passing the current through another magnetic layer. The magnetizations of the two layers must be non-collinear for any torque to be applied so the question arises of how to cause the magnetizations of the two layers to behave differently under applied magnetic fields. This is accomplished in a variety of ways, one way is to make one ferromagnetic layer (the fixed layer) thicker so that it does not respond as easily to external fields. Another way is to have the fixed layer in close proximity to an antiferromagnet such as IrMn or PtMn, the exchange interaction between the antiferromagnetic layer and the ferromagnetic layer keeps the latter in place. In the case of the MTJs used for our detectors both methods are used. The ferromagnetic layer that is not constrained is called a free layer (see Fig. 3.1). The first reported MTJ was developed by Julliere [16] in 1975. These devices were 17 Figure 3.1: Schematic showing free and fixed magnetic layers and how the spin torque acts in an MTJ. Fe/Ge/Co trilayers but the experiments showing a dependence of their resistance on the relative orientation of the ferromagnets were never reproduced. Later, Slonczewski [17] studied Fe/C/Fe trilayers theoretically (see Chapter 4) but the effect has not been observed in this structure. The first successful magnetic tunnel junctions [18] were based on NiO barriers. Currently, tunnel junctions are based on either AlOx (usually Al2 O3 ) or MgO barriers [19]. The highest reported TMR ratio (see Chapter 4) for an MgO based junction is 604% at 300K (1010% at 5K)[20]. The current best TMR ratios of alumina barriers are significantly lower at 81% for room temperature (107% at 4.2K) [21]. The reason for this is that the crystalline MgO barrier, in combination with lattice matched ferromagnetic layers (such as CoFe) supports coherent tunneling of spin polarized conduction electrons while AlOx barriers, which are amorphous, do not. Coherent tunneling refers to the idea that for sufficiently perfect materials and interfaces impurity and interface scattering can be ignored, allowing quantum features of the tunneling process to emerge. More specifically, this can be taken to mean that the component of electron momentum parallel to the barrier is conserved. In the case of MgO tunnel junctions, theoretical studies [15],[22] indicate that, due to a small density of states, the conductance of the barrier for minority electron states with momenta nearly perpendicular to the barrier surface (that is, the electrons that are propagating) is much lower than that of majority states with the same momenta (this is dicussed in more detail in Chapter 4). The dependence of polarization on density of states is shown in (4.3), we can see that the barrier acts to increase spin polarization 18 for propagating states because it acts like a half metal for those states. Equation (4.2) shows that this increased polarization due to the crystalline barrier increases the TMR ratio for MTJs based on materials like MgO. Experimental support for the explanation of the higher TMR values for MgO tunnel junctions described above comes from a recent study [23] that compares junctions with barriers composed of AlOx , MgO, and a symmetric AlOx -MgO bilayer. This study found that the half AlOx junction had a TMR of 78%, like that of a pure AlOx junction instead of some intermediate value closer to the TMR of the MgO junctions (323%) which they fabricated. If the latter had been true it would suggest that some property of the barrier materials not related to coherent transport was responsible for the decrease in TMR. The observed results can be interpreted to mean that the presence of the disordered AlOx layer prevented coherent transport and thereby suppressed the TMR ratio. However, experimental considerations required that the combined AlOx -MgO barrier was about twice as thick as the pure barriers so the diminished TMR might be attributed to the increased thickness. In the range of thicknesses between 1.2nm and 2.6nm corresponding to the thicknesses of the pure barriers and the combined barrier resistance increases exponentially with thickness for both AlOx (approximately) and MgO while the TMR decreases by only about 20% for MgO and decreases quickly to around 1% for AlOx [24],[25]. From this we can see that the AlOx -MgO barrier does not behave like a simple combination or thicker version of the pure barriers and the coherent tunneling explanation is supported. For the detectors studied in this thesis, two different types of MTJs (which I will refer to as Type A and Type B) were used. Both are MgO tunnel junctions with CoFeB fixed and free layers. The Type A junctions, whose full layer structure is shown schematically in Fig. 3.2, are fairly standard MTJs (all samples were fabricated by J.A. Katine of Hitachi Global Storage Systems) with a free layer magnetization that is 19 entirely in the plane of the layer. The Type B junctions (Fig. 3.3) are the product of an at least partially successful attempt to produce MTJs with a free layer magnetized out of plane. Figure 3.2: Type A MTJ layer structure: 3 [nm] Ta / 40 CuN / 3 Ta / 40 CuN / 3 Ta / 10 Ru / 5 Ta / 16 PtMn / 2.5 Co70Fe30 / 0.85 Ru / 2.4 Co60Fe20B20 / MgO / 1.83 Co60Fe20B20 / 2 Cu / 5 Ta / 10 Cu / 5 Ru / 3 Ta The resistance of most Type A MTJs was between 300Ω and 350Ω at zero applied field. The resistance versus applied field plot of a typical Type A junction is shown in Fig. 3.4. For Type B junctions, resistances at zero applied field were higher, mostly ranging from 600Ω to 620Ω. A resistance vs. field plot for a Type B junction is shown in Fig. 3.5. 20 Figure 3.3: Type B MTJ layer structure. Figure 3.4: Type A MTJ Resistance vs. Field. 21 Figure 3.5: Type B MTJ Resistance vs. Field. 22 Chapter 4 Tunneling Magnetoresistance There is another consequence of the spin polarization of the conduction current. The argument at the end of the previous chapter shows that the current transmitted through a ferromagnet depends on the relative orientation of the incident electron polarization direction and the ferromagnet’s magnetization. Therefore the resistance of a trilayer (spin valve or magnetic tunnel junction) depends on the relative orientation of the ferromagnetic layers. When one layer’s magnetization is relatively stationary then the resistance of the trilayer depends on the magnitude of an external field (when the external field is applied in some direction other than parallel to the magnetization of the fixed layer). When the trilayer is a magnetic tunnel juction this variable resistance is called the junction’s tunneling magnetoresistance and is often defined as T MR = RAP − RP RP (4.1) Here RAP stands for the resistance of the trilayer when the magnetizations of the ferromagnetic layers are oriented anti-parallel to each other and RP stands for the resistance when they are parallel. 23 According to a model developed by Julliere [16] the value of the TMR ratio can be obtained in terms of the polarization coefficients of the two layers as T MR = 2P1 P2 1 + P1 P2 (4.2) In Julliere’s model P1 and P2 are given by the ratio P = N↑ (EF ) − N↓ (EF ) N↑ (EF ) + N↓ (EF ) (4.3) where N (E) is the number density of states as a function of energy. For magnetic MTJs, Slonczewski proposed an expression for tunneling polarization modified to include interface effects as follows [[26]]: P = k↑ − k↓ k02 − k↑ k ↓ · . k↑ + k↓ k02 − k↑ k ↓ (4.4) This expression is consistent with (4.3) when the parabolic dispersion relations 2mEσ h̄2 (4.5) 2m(EF − V ) h̄2 (4.6) kσ2 = k0 = are assumed (see Fig.4.1). A more accurate and detailed picture of TMR, applicable to magnetic tunnel junctions with epitaxial interfaces such as Fe/MgO/Fe, was developed in [15]. In this model the Bloch states of the electrons (near the Fermi level) in the first ferromagnet are used instead of free electron states as the incident states on the barrier. Bulk band structure calculations [27] show that the majority (↑) and minority (↓) electrons have four states available near the Fermi level in Fe. One of these, labeled ∆1 , is only available to 24 Figure 4.1: The spin-dependent parabolic approximation of a ferromagnet’s band structure. majority electrons and has spd hybridization, the others all have pd hybridization or are d states. In [15] Butler and co-workers use a layered Korringa-Kohn-Rostoker method [28] to calculate the density of states for each state of both majority and minority electrons propagating through an MgO barrier as a function of penetration into the barrier. Their analysis is specific to modes propagating normal to the barrier, but these are the modes that dominate transport. They find that the details of the band structure have a significant effect on understanding the conductance of the tunnel junction. Specifically, the density of ∆1 states decays much more slowly than those of the other states as it traverses the barrier and since this state is only available to majority electrons these are conducted much more readily than minority electrons. When the magnetizations of the ferromagnetic layers are oriented parallel to each other majority states remain majority states throughout the trilayer but when the magnetizations are oriented anti-parallel to each other the states which start out as majority states on one side of the barrier are minority states on the other side and vice versa. This means that when the magnetizations are antiparallel the ∆1 state is not available in the second ferromagnet and is in fact completely reflected. This greatly 25 reduces the conductance of the trilayer (it now nearly matches the conductance for minority states alone) in the antiparallel state and explains the partial half metal behavior of the tunneling barrier mentioned in Chapter 2 and the large TMR ratio of this type of tunnel junction. The conductance for the minority states is not affected much by the relative orientation of the ferromagnetic layers. The dependence of the trilayer resistance on the angle θ between the magnetizations of the two ferromagnets is not yet completely understood. For simplicity, it is the conductance G that is usually expressed and this value is modeled and given to fair accuracy by [17],[29]: G(θ) = GP − GAP (1 + P1 P2 cos θ) 2 where Pi are the spin polarization factors given by Eq.(4.4). 26 (4.7) Chapter 5 Spin Transfer Assisted FMR In this section we will first consider FMR in general and its conventional measurement and then describe spin torque assisted FMR measurements. 5.1 FMR Earlier, in section 2, we discussed how the Landau-Lifshitz-Gilbert equation of motion ~ × ∂t M ~ ~ = −γ0 M ~ ×H ~ ef f + α M ∂t M Ms (5.1) (where we have suppressed the spin transfer term) describes a precessional motion of the magnetization of a ferromagnet. As mentioned before, in the absence of damping (5.1) describes stable circular precession. The frequency of such a precession is (for a spherical sample) given by the Larmor frequency ω = γHef f . Once it has been resonantly excited, this precession can be detected in different ways, two of which are described in more detail below. The resonance spectrum can yield information about the saturation magnetization, damping constant, magnetic anisotropy, spin-torque 27 vector, and bias response of a sample. 5.2 Conventional FMR Measurement For most of their history ferromagnetic resonance measurements have been made by determining the microwave absorption of a ferromagnetic sample in a DC magnetic field. The quantity determined directly is the imaginary component of the magnetic susceptibility so we would like to make the connection to magnetization precession. To do this we follow Kittel’s [30] derivation and consider a ferromagnetic ellipsoid with its axes aligned with a Cartesian coordinate system and a DC magnetic field applied along its longest (ẑ) axis. Microwave radiation is incident on the ellipsoid such that the RF magnetic field is aligned perpendicular to the DC field (along the x̂ axis). It is this oscillating magnetic field which drives the precession of the magnetization. In this situation the applied magnetic field has the form ~ app = ẑHDC + x̂HRF eiωt H (5.2) To take the shape of the sample into account we have to include the demagneti~ ef f of (5.1). In this treatment we will leave out the effect of zation fields in the H anisotropy, but if included it would cause a change in the FMR resonance frequency. The components of the magnetic field within the sample are then given by Hx0 = Hx − Nx Mx (5.3) Hy0 = −Ny My (5.4) Hz0 = Hz − Nz Mz (5.5) 28 Ignoring damping (which does not modify the resonance frequency significantly for ~ app ,Hz = ẑ · H ~ app the components physically realistic values of α) and taking Hx = x̂· H of (5.1) become ∂t Mx = γ[Hz + (Ny − Nz )Mz ]My (5.6) ∂t My = γ[Mz Hx − (Nx − Nz )Mx Mz − Mx Hz ] (5.7) ∂t Mz ≈ 0 (5.8) Solving these equations gives the susceptibility χx = Mz 1 Mx = Hx Hz + (Nx − Nz )Mz 1 − ( ωω0 ) (5.9) with the resonant frequency q ω0 = γ [Hz + (Ny − Nz )Mz ][Hz + (Nx − Nz )Mz ] (5.10) When a sample is placed in a microwave cavity its microwave absorption can be measured. For these types of measurements it is usually the magnetic field that is varied (since the frequency cannot be varied over a wide range in a microwave cavity). The resonant frequency can be observed from this measurement and if the geometry of the sample is well known then the magnetization Mz can be easily determined. 5.3 STFMR Spin transfer (or torque) assisted ferromagnetic resonance (abbreviated STFMR) [1],[31] is an all electrical technique for driving electrically detectable signals of ferromagnetic resonance. Briefly, the spin torque (section 2) due to a subcritical alter- 29 nating current drives a precession of the magnetization about the effective field. This results in an oscillation of the resistance of a spin valve or MTJ as the magnetization of the free layer is forced toward or away from alignment with the fixed layer magnetization depending on the instantaneous polarity of the RF current (see section 4). The product of this oscillating resistance with the alternating current that produces it is a rectified voltage whose average is measured as a DC signal (see Fig. 5.1). Specifically, the resistance in a trilayer can be expressed [1] as the expansion Figure 5.1: Schematic showing free and fixed magnetic layers and how the spin torque acts in an MTJ. ∆Rnf ein2πf t ) (5.11) 1 Vdc =< Irf cos(2πf t)R(t) >= Irf |∆Rf | cos(δf ) 2 (5.12) R(t) = R0 + ∆R(t) = R0 + Re( X n Then by Ohm’s law Where f is the δf is the phase of the resistance with respect to the current. 30 In terms of a DC bias (I,V ), Vdc can be approximated as [32] 1 ∂ 2V 2 1 ∂ 2 V h̄γ0 sin θ 2 (εk S(ω) − ε⊥ Ω⊥ A(ω)) + × Irf I 4 ∂I 2 rf 2 ∂θ∂I 4eMs Vσ (5.13) where " εk,⊥ # 2e/h̄ dτk,⊥ = sin(θ) dI (5.14) are dimensionless differential torques and S(ω) and A(ω) are symmetric and anti symmetric lorentzians given by S(ω) = A(ω) = 1 1+ (ω−ωm )2 σ2 (ω − ωm ) S(ω) σ (5.15) (5.16) In these equations ωm is the resonance precession frequency of the magnetization,Ω⊥ = γ(4πMef f + H)/ωm for an elliptical thin film. σ is the line width of the STFMR resonance peak. It is given by [32] σ= γτk (V, θ) αωm (Ω⊥ + Ω−1 ⊥ ) − cot(θ) 2 2Ms V (5.17) From this equation it is clear that the damping constant α can be obtained from an STFMR measurement of the line width at V = 0 giving αef f = 2σ ωm (Ω⊥ + Ω−1 ⊥ ) (5.18) Equation (5.13) shows that by fitting the symmetric and antisymmetric components of an STFMR voltage vs.frequency spectrum the contributions of the in-plane and out of plane spin torque components found in Chapter 2 can be determined experimentally. In the case of STFMR it is a spin polarized current and not an external magnetic field 31 that oscillates and causes resonant motion of the magnetization, the process described depends entirely on the spin transfer term in (1.1). In an STFMR measurement, both the frequency of the current and the magnitude and sign of the applied DC current are easy to vary. Usually the current frequency is swept at a constant field to obtain an FMR spectrum. Using this technique, samples much smaller than those accessible by the conventional absorption method can be measured. An STFMR measurement on a magnetic tunnel junction is the basis of the microwave detectors described in this thesis. 32 Chapter 6 Detector Design As was mentioned earlier, the microwave detectors described in this thesis are based on an STFMR measurement made on an MTJ. In addition to the magnetic multilayer sample described in section 3, such a measurement requires a source of RF oscillating current, a way of applying a (preferably tunable) DC magnetic field, a means of separating DC and AC signals, and a way to measure the DC average of the rectified voltage signal produced across the MTJ. It is the purpose of this section to describe each of these components and the assembly of the whole device. A schematic circuit diagram of the detector is given in Fig. 6.1 below. The DC voltage across the MTJ is measured by connecting the top lead to the AC+DC port of a bias-tee and the DC port of the bias-tee to the signal pin of an SMA connector flange while the bottom lead of the MTJ is connected to the ground of the flange and the chassis of the device. The voltage measurements were made using a Keithley 2182A nanovoltmeter which can measure down to 1nV. The separation of DC and AC signals in the final device is accomplished using a biastee. A bias-tee (equivalent circuit shown in Fig. 6.2) can take a combined AC and DC 33 Figure 6.1: Schematic circuit diagram of an MTJ microwave detector input at its AC+DC port and output the components separately. For the final devices a small, surface-mountable model SM-101 bias-tee from Picosecond Pulse Labs was used. An earlier design using single or series connected inductors to suppress AC signals did not work. The DC magnetic field is provided by a permanent magnet affixed to a set screw. This gives a constant field which can be adjusted to obtain the best possible response from the magnetic tunnel junction. The magnet is a 3.175mm diameter × 3.175mm long Nd2Fe14B magnet from MagCraft which has a nominal surface field of 4kG. Its position in the detector allows fields between 0 and about 800G to be applied at the MTJ. This covers the fields which give maximum response which are about 700G for samples of type A and about 200G for samples of type B (see section 3). 34 Figure 6.2: Diagram of a bias-tee. The source of RF current in these detectors is a coplanar waveguide (CPW) acting as an antenna. This makes the detector capable of picking up ambient microwave radiation (of the correct polarization) and, via the MTJ, converting it to a measureable DC voltage. The coplanar waveguide antenna is the aspect of the detector design we had the most control over. The idea is to couple the microwave radiation to a signal at the tunnel junction as efficiently as possible. This came down to trying to match the impedance of the CPW to those of air and the MTJ as nearly as possible. Figure 6.3: Cross-sectional view of a coplanar waveguide showing relevant dimensions Analytically, the impedance of a grounded coplanar waveguide as depicted in Fig. 6.3 35 with a dielectric (r ) substrate of thickness h >> b = s + 2w is given by [33]: 60π √ ef f 1 K(k) K(k0 ) ef f = κ= K(k1 ) K(k10 ) 1 + r κ 1+κ (6.1) (6.2) K(k 0 ) K(k1 ) K(k) K(k10 ) (6.3) k = s/b (6.4) √ 1 − k2 (6.5) tanh(πs/4h) tanh(πb/4h) (6.6) k0 = k1 = + k10 = q 1 − k12 (6.7) As indicated by these equations the characteristic impedance of the CPW increases with increasing w or decreasing s. By modeling the coplanar waveguide structure in the finite element calculation software CST Microwave Studio, we were able to determine the parameters (s,w) that maximized the gain of the CPW antenna but were still relatively easy to fabricate. For the .254mm thick Duroid 6002 substrate that we used, the optimum values determined were s = 0.2mm and w = 0.1mm, which in the modeling software gives an impedance of 76Ω. We found that increasing w causes losses while decreasing s would lead to both losses and possible fabrication difficulties. The analytical approximation above gives an impedance of 86Ω for the same CPW dimensions. The discrepancy with the numerical result is explained by the fact that our coplanar waveguide does not satisfy the condition h >> b. An additional feature of this detector is an electrostatic discharge (ESD) protection circuit designed to prevent damage to the delicate magnetic tunnel junction. The 36 Figure 6.4: Microwave detector components - (1) Coplanar waveguide antenna, (2) MTJ Sample, (3) Bias-tee, (4) Brass screw holder, (5) Brass set-screw, (6) NdFeB magnet, (7) K-connector flange junction is susceptible to breakdown and shorting across its thin insulating layer when exposed to large transient voltages. The ESD protection circuit consists of two Schottky diodes connected in opposite directions which will shunt large voltages of either polarity to ground. The assembly of the detector’s components is shown in Fig. 6.4 and the major dimensions of the design are shown in Fig. 6.5. 37 Figure 6.5: Dimensions of the assembled detector 38 Chapter 7 Results Here we present the results of tests of the MTJ microwave detectors. First, in Fig. 7.1, is the voltage response of a Type A junction not mounted in a detector but instead measured in a standard STFMR setup with the oscillating current applied by a microwave signal generator (Agilent E8257D). In this case the power incident in the tunnel junction is easy to compute using [2],[34] Pinc = 1 2Z0 R + Z0 2 2 2 IRF (7.1) In our case the current applied was 0.1mA and the line impedance is 50Ω so the power applied to the MTJ was 1.5µW. The important figure of merit for our devices as microwave detectors is the sensitivity given by = V Pinc (7.2) Using our peak voltage of 48µV in this equation gives a sensitivity of 32 mV/mW. To explore the relationship between detector sensitivity and the parameters of the 39 Figure 7.1: Response of a type A sample to a directly(cable) fed microwave signal. detectors we can follow [2] and rewrite the frequency dependent part of (5.13) as " dτk dτ⊥ γ0 (Hz + 4πMef f ) dR µB 2 Irf S(ω) − A(ω) Vdc = dθ 2h̄(Ms V)σ dI dI ωm # (7.3) where Hz is the component of the applied magnetic field parallel to the initial orientation of the free layer magnetization and θ is the angle between the magnetizations of the two ferromagnetic layers before any RF current is applied. Mef f is an effective out of plane anisotropy which must be determined experimentally from resistance vs. field measurements with field applied perpendicular to the sample plane [32]. Now we can write (7.2) as " dτk dR dτ⊥ γ0 (Hz + 4πMef f ) µB Z0 = S(ω) − A(ω) 2 dθ 4h̄(Ms V)σ (R + Z0 ) ) dI dI ωm # (7.4) Next we use 1 1 1 1 1 1 1 = ( + )+ ( − ) cos θ R 2 RP RAP 2 RP RAP 40 (7.5) which expresses the sinusoidal angular dependence of TMR predicted in [17](see also (4.7)) to obtain R2 dR = (RAP − RP ) sin θ dθ 2RP RAP For the symmetric tunnel junctions we are studying we will treat (7.6) dτ⊥ dI as negligible or suppressed at zero bias in accordance with [14] and [32]. The differential torque in the plane of the ferromagnet dτk dI is given by dτk h̄ 2P R = sin θ dI 4e 1 + P 2 RP (7.7) Here P = P1 (= P2 ) is the spin polarization of the ferromagnet, also expressible as (see (4.1),(4.2)) s P = RAP − RP RAP + RP (7.8) Putting (7.6) and (7.7) into (7.4) gives = RAP − RP µB 2P R2 RZ0 sin2 θ RP 2eVσ (R + Z0 )2 1 + P 2 RP RA P (7.9) From this equation we can see how the sensitivity of a tunnel junction depends on the initial angle between the free and fixed layer magnetizations. This angle is generally set by the direction and magnitude of the applied magnetic field so information about θ is really information about the applied field. The sensitivity is maximized when θ is approximately 90◦ [2] and this means that the external magnetic field must be applied perpendicular to the fixed layer magnetization and be of sufficient magnitude to saturate the free layer magnetization but not so strong that it rotates the fixed layer magnetization. In terms of the resistance vs. applied field curves of Chapter 3 this occurs at fields where the derivative dR/dH is large, implying that dR/dθ is large for large sensitivity, as expected from (7.4). Also, we can see that if the applied field were zero, dτk dI would be zero and only the 41 dτ⊥ dI term could contribute to Vdc which could only happen if there were a relatively large biasing voltage. Tests on the full microwave detectors were run by placing the detectors at some distance from a microwave horn antenna (AH-118 from Com-Power Corporation) which was in turn connected to a microwave generator. The voltage reading from the nanovoltmeter was recorded as the frequency of the microwave emissions was varied. The next plot (Fig. 7.2) shows the output voltage at the applied field giving the best signal for a typical detector with a Type A tunnel junction. This result was obtained Figure 7.2: Response of a Type A detector with an external field of about 650G applied and a signal generator power output of 15dBm. Next, a figure (Fig. 7.3) showing the typical response of a Type B detector. Besides 42 Figure 7.3: Response of a Type B detector the stronger response of the Type B detector we also note that the resonance is at a lower frequency for this kind of MTJ. The constant external field applied for this measurement was about 200G, lower than the field at which the best response for Type A samples occurs. The last figure (Fig. 7.4) shows the signal obtained from our best performing sample, which was of Type B. As the figure shows, the response of this sample was atypically strong, though the resonance frequency was the same as for other Type B samples. This best performing sample was larger than the other Type B samples tested, measuring 210nm × 60nm while the other samples measured 150nm×70nm. Also, since these tunnel junctions were designed to have equal Resistance-Area (RA) products regardless of size, the MTJ in the detector of Fig.7.4 has a lower resistance (340Ω), closer to the impedance of air. 43 Figure 7.4: Response of the best detector. Finally, we show the response of a Type B sensing element under controlled conditions with the microwave power applied directly to the detector via a set of titanium probes in Fig.7.5. The RF power applied was -36dBm and the applied was 150 G. The signal corresponds to a maximum sensitivity of 240mV/mW since a power of 0.25µW was applied. For comparison, the best sensitivity for an MTJ detector reported to date [4] was 170mV/mW and the sensitivity of the commercial diode we used for calibration is quoted as 400mV/mW. We show the response of this GaAs diode microwave detector (Agilent 8474B) to different input powers in Fig. 7.6. The sensitivity we observed is well below the theoretical maximum of 10,000mV/mW predicted in [2]. To explain why the Type B sensing elements have a stronger response we can examine Fig. 7.5 and note the asymmetry of the resonance peak. We saw in Chapter 5 that an 44 Figure 7.5: Response of a Type B detector to a direct microwave input asymmetric component of the spectrum is likely a signature of an out of plane spin torque. Such an out of plane torque could cause the precession angle of the free layer ~ 2 about the effective field direction to be larger resulting in both a magnetization M lower resonant precession frequency and a larger change in resistance which would result in a larger signal. The natural perpendicular to plane anisotropy of the free layer that the Type B detectors were designed for would have the same effect. We still have to explain how an observable out of plain spin torque could arise at zero bias (no such torque was observed in [32] for an in plane free layer magnetization, though one is predicted in [13]). Figure 7.7(b) illustrates how a partially out of plane free layer magnetization can result in the stronger (Slonczewski) spin-torque component being directed out of the plane while the field-like torque is in the plane. Note that this does not happen in normal in-plane magnetized free layers (Fig.7.7(c)) or a completely out of plane free layer magnetization (Fig.7.7(a)). The picture we present here indicates that the spin-torque will be directed more out ~ 2 is with M ~ 1 . However, since the magnitudes of the plane the more closely aligned M 45 Figure 7.6: Power response of a GaAs Diode Figure 7.7: Diagram of spin-torque vectors: (a) Free layer magnetization perpendicular to plane, (b) Free layer magnetization out of plane, (c) Free layer magnetization in plane of both spin-torque components depend on sin θ where cos(θ) = M̂1 · M̂2 , the torque ~ 2 approaches M ~ 1 . If we restrict our attention to the case where M ~2 goes to zero as M ~ 1 are in the same x-z plane so that the field-like torque is completely in plane and M as in Fig. 7.7, the out of plane component of the Slonczewski spin-torque term is 46 proportional to sin(θ) cos(θ) so that its maximum value is obtained when the angle ~ 2 and M ~ 1 in the x-z plane is 45◦ . between M STFMR spectra obtained for other Type B tunnel junction samples [35] at various bias voltages indicate that the antisymmetric component of the peaks is the result of voltage induced magnetic anisotropy [36],[37],[38]. First, the spectra show a decrease in the resonance frequency as positive bias voltage is increased. The response frequency increases for negative bias voltages. This is in direct agreement with [37] but with much higher TMR junctions and is consistent with the results of other studies where methods other than STFMR were used. The bias changes the electron density at the interfaces in which in turn can modify the energy and therefore the occupancy of the different 3d electron states in the ferromagnet. This changes the surface magnetic anisotropy and through the change in the anisotropy field changes the resonance frequency according to a version of (5.11) modified to include anisotropy terms [30] q ω0 = γ [Hz + (Ny + Nya − Nz )Mz ][Hz + (Nx + Nxa − Nz )Mz ] (7.10) Nxa = −Hxa /Mx (7.11) Nya = −Hya /My (7.12) where with H a the anisotropy field. Here ẑ is the initial direction of the magnetization and we take ŷ to be out of the plane of the sample. The voltage across the tunnel junction due to the oscillating RF current used to make ~ ef f STFMR measurements induces anisotropy resulting in the addition of a term to H in the first term of the Landau-Lifshitz-Gilbert equation for magnetization dynamics 47 (1.1). We rewrite this first term ~ = −γ0 M ~ ×H ~ ef f ∂t M (7.13) and separate the contribution of voltage induced anisotropy from the rest of the ~ 0 giving effective field which we label H ef f 0 ~ ~ ~ = −γ0 (M ~ ×H ~ ef ∂t M f + M × Hvia cos θ) (7.14) The voltage induced contribution to the anisotropy is uniaxial, hence the factor of cos θ = Ĥvia · M̂ which makes the contribution zero when the sample is magnetized in plane. Equation (7.14) also shows us that this contribution is zero when the sample is magnetized completely perpendicular to the sample plane. The effect of voltage induced anisotropy is therefore important in MTJs with a significant component of magnetization perpendicular to the layer planes like our Type B junctions. This torque due to voltage induced anisotrpy is inherently field-like and appears as an anitsymmetric contribution to STFMR spectra that is not caused by current-induced spin-torque and therefore appears at zero bias and is linear in applied DC bias to the extent that the out of plane anisotropy responds linearly to voltage. When the bias and therefore the standard perpendicular field-like torque are non-zero, voltage induced anisotropy has an additional effect. To obtain (7.9) we treated dτ⊥ dI at zero bias as negligible, an assumption that is supported by theory [14] and experiment [32]. However, this is no longer true for non-zero bias and by examining (7.4) we see that there is a factor of Ω⊥ = γ(Hz + 4πMef f )/ω0 multiplying this antisymmetric term. Including both in plane and out of plane anisotropy [39] we can write Ω0⊥ = γ (Hz + 4πMef f − Hk sin2 β) ω0 48 (7.15) where Hk is the in-plane anisotropy field strength and 4πMef f is the effective out of plane anisotropy mentioned earlier in connection with (5.13), and β is the in plane angle between the free layer’s magnetization and its anisotropy (easy) axis when no currents are applied. We also assume that the fixed layer is aligned with the free layer in-plane anisotropy. Voltage induced anisotropy therefore modifies the effect of the current-induced spin-torque on the STFMR signal through its effect on Mef f as well as contributing the wholly independent field-like term discussed above. When the in~ k is weak compared to the out of plane anisotropy plane anisotropy represented by H (which can be strengthened by increasing the bias) the effects of voltage modification of anisotropy become increasingly significant. 49 Conclusions In this thesis we have shown that it is possible to use magnetic tunnel junctions as sensing elements in microwave radiation detectors. In addition, we show that the junctions’ sensitivity (240 mV/mW) approaches that of current commercial semiconductor diode based detectors. An MTJ based detector has the feature of being intrinsically frequency tunable, which semiconductor RF detectors lack. We have also shown that the sensitivity of tunnel junctions with free layer magnetic anisotropy perpendicular to the plane of the layer have enhanced sensitivity when compared to junctions with in plane anisotropy. This enhancement is due to voltage induced anisotropy. According to theoretical models [2] for tunnel junctions similar to those used in our Type A detectors there is considerable room for improvement in sensitivity for the kinds of microwave sensors described here. Using MTJs with perpendicular magnetic anisotropy like our Type B sensing elements may result in even higher sensitivity especially in active, biased detectors for which voltage induced anisotropy and out of plane spin transfer torque will play a greater role. The maximum sensitivity possible in such an active detector will depend on the maximum biasing voltage the tunnel junction can sustain without breaking down and has not been determined yet. Besides improvements to the MTJ sensing elements, the microwave detectors described in this thesis would be improved significantly by better impedance matching between air, antenna, and sensing element. This kind of matching could possibly be achieved by a different antenna design or the inclusion of impedance matching circuitry in the detector. One promising note in this regard is the fact that MTJs are available with perpendicular anisotropy and impedances very much like that of air. So far we have discussed only the sensitivity of the MTJ microwave detectors, but to be technologically viable these detectors need to have not only high sensitivity, 50 but also low noise. Further work is needed to investigate the noise properties of tunnel junctions used as detectors and compare them to those of semiconductor diode detectors. 51 Bibliography [1] J. Sankey et al., “Spin-transfer-driven ferromagnetic resonance of individual nanomagnets,” Physical Review Letters, vol. 96, p. 227601, 2006. [2] C. Wang et al., “Sensitivity of spin-torque diodes for frequency tunable resonant microwave detection,” Journal of Applied Physics, vol. 106, p. 053905, 2009. [3] X. Fan et al., “Magnetic tunnel junction based microwave detector,” Applied Physics Letters, vol. 95, p. 122501, 2009. [4] S. Ishibashi et al., “Large diode sensitivity of CoFeB/MgO/CoFeB magnetic tunnel junctions,” Applied Physics Express, vol. 3, p. 073001, 2010. [5] C. Kittel, Introduction to Solid State Physics. John Wiley, 1996. [6] J. Slonczewski, “Current-driven excitation of magnetic multilayers,” Journal of Magnetism and Magnetic Materials, vol. 159, pp. L1–L7, 1996. [7] D. Ralph and M. Stiles, “Spin transfer torques,” Journal of Magnetism and Magnetic Materials, vol. 320, no. 7, pp. 1190–1216, 2008. [8] J. Sun, “Spin angular momentum transfer in current-perpendicular nanomagnetic junctions,” IBM Journal of Research and Development, vol. 50, pp. 81–100, 2006. [9] J. Katine et al., “Current-driven magnetization reversal and spin-wave excitations in Co/Cu/Co pillars,” Physical Review Letters, vol. 84, pp. 3149–3152, 2000. [10] G. Fuchs et al., “Spin-transfer effects in nanoscale magnetic tunnel junctions,” Applied Physics Letters, vol. 85, pp. 1205–1207, 2004. [11] L. Berger et al., “Emission of spin waves by a magnetic multilayer traversed by a current,” Physical Review B, vol. 54, pp. 9353–9358, 1996. [12] M. Stiles and A. Zangwill, “Anatomy of spin-transfer torque,” Physical Review B, vol. 66, p. 014407, 2002. [13] J. Xiao et al., “Spin-transfer torque in magnetic tunnel junctions: Scattering theory,” Physical Review B, vol. 77, p. 224419, 2008. 52 [14] C. Heilinger and M.Stiles, “Ab initio studies of the spin-transfer torque in magnetic tunnel junctions,” Physical Review Letters, vol. 100, p. 186805, 2008. [15] W. Butler et al., “Spin-dependent tunneling conductance of Fe—Mgo—Fe sandwiches,” Physical Review B, vol. 63, p. 054416, 2001. [16] M. Julliere, “Tunneling between ferromagnetic films,” Physics Letters A, vol. 54, no. 3, pp. 225–226, 1975. [17] J. Slonczewski, “Conductance and exchange coupling of two ferromagnetics separated by a tunneling barrier,” Physical Review B, vol. 39, no. 10, pp. 6995–7001, 1989. [18] S. Maekawa et al., “Electron tunneling between ferromagnetic films,” IEEE Transactions on Magnetics, vol. MAG-18, pp. 707–708, 1982. [19] S. Parkin et al., “Giant tunnelling magnetoresistance at room temperature with MgO(100) tunnel barriers,” Nature Materials, vol. 3, pp. 862–867, 2004. [20] S. Ikeda et al., “Tunnel magnetoresistance of 604Ta diffusion in cofeb/mgo/cofeb pseudo-spin-valves annealed at high temperature,” Applied Physics Letters, vol. 93, p. 082508, 2008. [21] H. Wei et al., “80Al-O barrier magnetic tunnel junction with cofeb as free and reference layers,” Journal of Applied Physics, vol. 101, p. 09B501, 2007. [22] J. Mathon and A. Umerski, “Theory of tunneling magnetoresistance of an epitaxial Fe/MgO/Fe(001) junction,” Physical Review B, vol. 63, p. 220403(R), 2001. [23] O. Schebaum et al., “Tunnel magnetoresistance in alumina,magnesia,and composite tunneling barrier and magnetic tunnel junctions,” ArXiv, vol. [cond-mat], p. 1008.0761v3, 2010. [24] J. Hayakawa et al., “Dependence of giant tunnel magnetoresistance of sputtered CoFeB/MgO/CoFeB magnetic tunnel junctions on MgO barrier thickness and annealing temperature,” Japanese Journal of Applied Physics, vol. 44, pp. L587– L589, 2005. [25] J. Du et al., “Investigation of magnetic tunneling junctions with wedge-shaped barrier,” Journal of Applied Physics, vol. 91, pp. 8780–8782, 2002. [26] J. Slonczewski, “Currents, torques, and polarization factors in magnetic tunnel junctions,” Physical Review B, vol. 71, p. 024411, 2005. [27] D. Papaconstantopoulos, Handbook of the Band Structure of Elemental Solids. Plenum, 1986. 53 [28] J. MacLaren et al., “Layer kkr approach to bloch-wave transmission and reflection: Application to spin-dependent tunneling,” Physical Review B, vol. 59, pp. 5470–5478, 1999. [29] F. Montaigne et al., “Angular dependence of tunnel magnetoresistance in magnetic tunnel junctions and specific aspects in spin-filtering devices,” Journal of Applied Physics, vol. 108, p. 063912, 2010. [30] C. Kittel, “On the theory of ferromagnetic resonance absorption,” Physical Review, vol. 73, no. 2, pp. 155–161, 1948. [31] A. Tulapurkar et al., “Spin-torque diode effect in magnetic tunnel junction,” Nature, vol. 438, pp. 339–342, 2005. [32] J. Sankey et al., “Measurement of the spin-transfer-torque vector in magnetic tunnel junctions,” Nature Physics, vol. 4, pp. 67–71, 2008. [33] R. N. Simons, Coplanar Waveguide Circuits Components Systems. Wiley-IEEE Press, 2001. [34] D. M. Pozar, Microwave Engineering. Wiley, 2004. [35] J. Zhu et al., “Voltage-induced ferromagnetic resonance in magnetic tunnel junctions,” Pysical Review Letters, vol. 108, p. 197203, 2012. [36] T. Marayuma et al., “Large voltage-induced magnetic anisotropy change in a few atomic layers of iron,” Nature Nanotechnology, vol. 4, pp. 158–161, 2009. [37] T. Nozaki et al., “Voltage induced perpendicular magnetic anisotropy change in magnetic tunnel junctions,” Applied Physics Letters, vol. 96, p. 022506, 2010. [38] Y. Shiota et al., “Quantitative evaluation of voltage-induced magnetic anisotropy change by magnetoresistance measurement,” Applied Physics Express, vol. 4, p. 043005, 2011. [39] C. Wang et al., “Bias and angular dependence of spin-transfer torque in magnetic tunnel junctions,” Physical Review B, vol. 79, p. 224416, 2009. 54

1/--страниц