Treballs Finals de Grau de Física, Facultat de Física, Universitat de Barcelona, Curs: 2021, Tutor: Ferran Macià BrosSurface acoustic waves (SAW) are micrometric strain waves that propagate on the surface of a solid. They are good for a number of applications and have recently been used for their ability to couple with magnetic states in magnetostrictive materials. In this paper we study the SAW absorption of a magnetic material (Nickel) and ﬁnd the angle dependence between the SAW propagation direction and the magnetic ﬁeld orientation. We ﬁnd that when SAW and the magnetic ﬁeld are perpendicular or parallel there is no power absorption, but a maximum appears at 45 degrees. Furthermore, there is a dependence with the strength of the magnetic ﬁeld. At high enough ﬁelds the magnetic moments are saturated and have enough energy to overcome the coupling generated by SAW, whereas at lower magnetic ﬁelds there is SAW attenuation and a maximum appears at a resonant frequenc

Rovirola Metcalfe, Marc

English

Diposit Digital de la Universitat de Barcelona

Magnetoelastic effect with Surface Acoustic Waves in NickelAuthor: Marc Rovirola MetcalfeFacultat de F́ısica, Universitat de Barcelona, Diagonal 645, 08028 Barcelona, Spain.∗Advisor: Ferran Macià BrosAbstract: Surface acoustic waves (SAW) are micrometric strain waves that propagate on thesurface of a solid. They are good for a number of applications and have recently been used fortheir ability to couple with magnetic states in magnetostrictive materials. In this paper we studythe SAW absorption of a magnetic material (Nickel) and find the angle dependence between theSAW propagation direction and the magnetic field orientation. We find that when SAW and themagnetic field are perpendicular or parallel there is no power absorption, but a maximum appearsat 45 degrees. Furthermore, there is a dependence with the strength of the magnetic field. Athigh enough fields the magnetic moments are saturated and have enough energy to overcome thecoupling generated by SAW, whereas at lower magnetic fields there is SAW attenuation and amaximum appears at a resonant frequency.I. INTRODUCTIONModern electronics are largely based on magnetismand use electric current or magnetic field to modify mag-netization states. This, results in power loss due to heatand a non-local magnetization variation making it inef-ficient in small devices. A more power-efficient methodto produce changes in the magnetization is by applyingstrain.Ferromagnetic materials, such as Nickel, experiencechanges in shape when magnetized, and this propertyis called magnetostriction. This effect was first stud-ied by J. Joule in 1842 when he observed a change inshape of ferromagnets under the influence of a magneticfield. This effect is attributed to the rotation of the inter-nal magnetic domains due to a change in the preferredorientation. Furthermore, we can use the inverse mag-netostriction effect, also known as magnetoelastic effect,to generate changes in the magnetization when applyingstrain.Using elastic materials, such as piezoelectrics, we areable to generate elastic waves on the surface that can pro-duce strain on adjacent materials. These waves are calledsurface acoustic waves (SAW) and can be generated witha device called an interdigital transducer (IDT). An IDTconsists of two interlocking comb-like arrays of metallicelectrodes, and are commonly used as filters of frequen-cies, since the only frequencies they can accept are mul-tiples of the distance between their fingers (Fig. 3(a)shows a representation of an IDT). SAW are used dueto their small wavelengths, which makes them perfect fornano and micrometric devices.Recent studies have shown a variation in the ampli-tude of propagation of SAW when a magnetic materialsis placed on top [1], showing that the magnetic materialin fact interacts with the elastic waves. This interaction∗Electronic address: tfgac@ub.eduis made through the coupling between the SAW and themagnetic moments. The latter when placed under the in-fluence of a magnetic field will precess around its axis atcertain frequencies. This coupling mechanism has beenproven to be a great source for different studies such asacoustic spin-pumping [2, 3]. Acoustic spin pumping cantransfer spin current from ferromagnetic materials intononmagnetic metals and can be converted into chargecurrents that could be used in many applications.In this paper we aim to study the interaction betweenthe lattice motion and the magnetization to find howthe angle between them affects the magnetoelastic ef-fect. We use a hybrid device composed of a piezoelectricmaterial and a magnetic material. Placing the deviceinside an electromagnet we apply a magnetic field thatwill re-orientate the magnetic moments causing them toprecess. Then, through IDTs we are able to use the in-verse piezoelectric effect to generate a varying strain fieldthat will interact with the magnetic moments producingchanges in the magnetization. Furthermore, using a ro-tatory sample-holder we study the angle dependence ofthe magnetoelastic effect and the acoustoelectric effect,which is a new-found property in this kind of devices.II. THEORETICAL BACKGROUNDA. Surface Acoustic WavesSurface Acoustic Waves (SAW) are elastic waves gen-erated parallel to the surface of an elastic material. Thefirst appearance of SAW was published in a paper byLord Rayleigh in 1885 [4], where he characterized themas having a longitudinal and vertical shear that could in-fluence contacting layers. The amplitude of propagationof SAW in the neighbouring layer is directly linked to thematerial’s mechanical properties.The most common way of generating these waves arethrough Interdigital Transducers (IDT). Sending an ACvoltage signal to the one IDT we can generate acousticMagnetoelastic effect with Surface Acoustic Waves in Nickel Marc Rovirola Metcalfewaves by the inverse piezoelectric effect, where elasticdeformations are produced due to a difference of potentialbetween two electrodes of the IDT. An additional IDTwill receive these waves and by the direct piezoelectriceffect it will transform the elastic deformations into avoltage signal.The most important characteristic of SAW is the speedpropagation. Electromagnetic waves (EMW) have a ve-locity of 3×108 m/s whereas the propagation of acousticwaves on a substrate is approximately vs = 4000 m/s.We can obtain the SAW frequency from the followingformula fSAW = vs/λSAW and the λSAW will be twicethe distance between the IDT fingers. Therefore, for thesame frequency we will have wavelengths several ordersof magnitude smaller than on EMW.B. Magnetization dynamicsThe most accurate representation of the magnetizationdynamics in the presence of a magnetic field arises fromthe Landau–Lifshitz–Gilbert equation (LLG)∂M∂t= −γM×Heff + αM×∂M∂t(1)where Heff is the effective field composed of the externalstatic field, anisotropy field, exchange field and demag-netizing field, γ is the gyromagnetic factor and α is theGilbert damping parameter. It reproduces a precessingspin around the effective magnetic field axis with a damp-ing component as shown in Fig. 1.FIG. 1: On the left hand side, is a representation of the mag-netization dynamics from the LLG equation. On the righthand side, a polar plot of the first component (torque) as afunction of the angle between M and Heff.A solutions can be found when M and Heff are par-allel, resulting in no torque. When the angle betweenM and Heff is different than zero then there will be spinprecession and a maximum appears when they are per-pendicular. Plotting the first term - the torque - of theLLG equation in polar coordinates and taking the ra-dius as Ṁ/Ms results in a two-fold shape (Fig. 1). Thepower absorption will be linked to the precession ampli-tude, the energy provided by the magnetic field and theSAW frequency.C. Magnetization coupling with SAWSAW induce a time-varying strain field on the surfaceof a solid resulting in tensile (Sxx > 0) and compressive(Sxx < 0) phases (Fig. 2). The strain produced in theferromagnetic material will turn into lattice waves, quan-tized into phonons, that will interact with the generatedspin waves, quantized into magnons, in a phonon-magnoncoupling. In this coupling we can observe attenuationof the SAW transmission and a change in the magneticmoment oscillation amplitude proving an interaction be-tween them. It is shown that SAW can generate mag-netic waves in Nickel [5], obtaining variations up to 25◦between spin orientations at each phase. This oscillatingstrain and magnetic waves are called magnetoacousticwaves.FIG. 2: From top to bottom. This shows the effect of strainphases in the magnetization dynamics. Bellow is a colormaprepresentation of the strain field in which the yellow showsthe tensile phase and the blue shows the compressive phase.Under it, we show the magnetization direction in each partof the strain field. We assume a 45◦ angle between the SAWpropagation and the magnetic field.The generated strain field will add an anisotropic com-ponent to the effective field (Heff) from Eq. 1. Math-ematically, we can express that anisotropy energy asa power series of even numbers, since the anisotropydoes not change under an inversion of the magnetiza-tion (Eani(M) = Eani(−M)). Taking the first term wecan express the anisotropy energy asEani ∝ −aMx2, (2)where a is a constant and Mx is the magnetization valuealong the SAW propagation direction. The anisotropyfield will therefore beHani =∂Eani∂M∝ −2aMx. (3)This field will give rise to interesting solutions that willbe discussed in Section III.B.Treball de Fi de Grau 2 Barcelona, June 2021Magnetoelastic effect with Surface Acoustic Waves in Nickel Marc Rovirola MetcalfeIII. RESULTSWe started out by measuring the power transmissionat 45 degrees between the magnetic field and the SAWpropagation direction at different frequencies on a Nickelfilm with a thickness of 50 nm. We set up the piezo-electric substrate with the Nickel film in between twoIDTs in-plane with the magnetic field. We send electri-cal signals to the IDT 2 with a Programmable NetworkAnalyzer (PNA) which are converted into SAW that willpropagate in the piezoelectric. As SAW has a penetrationdistance comparable to their wavelength we can assumethat the whole Nickel film is affected. As the Nickel isplaced on top of the piezoelectric, the strain field willproduce lattice motions that will couple with the mag-netic environment in a phonon-magnon coupling. ThePNA will then measure the resulting transmission fromIDT 1. The schematics of the setup are shown in Fig.3(a). In our case we can transmit frequencies of f0 = 125MHz and their harmonics. A frequency sweep is shownin Fig. 3(b) with the first peak corresponding to f0.FIG. 3: a) Experimental setup. The Network Analyzer sendsan electrical signal to IDT 2 and measures the result in IDT 1.SAW travel along the x direction creating longitudinal (sxx)strain in the Nickel film. C1 and C2 are contacts used tomeasure longitudinal voltage. b) Transmission as a functionof frequency. Shows the IDT working frequencies, 125 MHzand its harmonics.A. Magnetoelastic effectTo begin our study we measure the transmission ofSAW in the Nickel sample and compare it to a speciallymanufactured Permalloy (Py) with no magnetoelastic ef-fect. The common composition of a Permalloy is 19% Feand 81% Ni.Nickel has magnetostriction and experiences magne-toelasticity. When the field is large enough, the magne-tization is saturated and has enough energy to stay inthat state ignoring the lattice motions and experiencingno absorption. We use the saturation value to normal-ize the data so any absorption is detected as a negativeSAW transmission (Fig. 4(b)). As we decrease the fieldwe can see that we lose transmission of SAW due to theabsorption from the magnetic moments. When the SAWfrequency matches the spin precession frequency, therewill be resonance and the absorption will be maximum.This is represented as the 2 peaks at ±40 G. When ap-proaching zero magnetic field, at approximately 10 G, avalley appears corresponding to the start of the spin in-version in which the magnetization of the material is 0.This field is called the coercive field (Hc). As we keep in-creasing the magnetic field we see a symmetric response.The coercive field being at positive 10 G means that thefield sweep started at a negative field.FIG. 4: a) Transmission for different harmonics of Ni. b)Comparison between the Nickel and Permalloy. Permalloyonly shows noise. c) Angle dependence of transmission. d)Angle dependence of voltage. The dash lines represent thedifference between peaks in figures c) and d).On the other hand, Permalloy does not experiencemagnetostriction; therefore, there will be no phonon-magnon coupling to change the magnetization. In Fig.4(b) Permalloy shows some noise and no sign of absorp-tion.Treball de Fi de Grau 3 Barcelona, June 2021Magnetoelastic effect with Surface Acoustic Waves in Nickel Marc Rovirola MetcalfeB. Power absorption angle dependenceIn Section II.B we explain how an external field pro-duces a torque on the magnetic moments of the Nickelmaking it precess around the field axes. SAW add an-other component to the effective field affecting the mag-netization. The lattice movement will modify the dis-tance between atoms, which will affect the orbit of theelectrons creating anisotropies from dipole-dipole inter-actions. This effective field will have only one componentin the direction of propagation of the SAW and will de-pend on the magnetization (Eq. 3). We would expect noeffect from SAW when it is perpendicular to the magne-tization, since there will not be any preferred orientationthat minimizes its energy, Fig. 5 shows a representation.FIG. 5: From left to right. When SAW and magnetizationare perpendicular, the magnetization will not have any ori-entation in which to minimize energy; therefore, it will notmove. As the angle changes the lattice motion will have moreeffect reaching its maximum at 45 degrees.Using the anisotropy field from Eq. 3 and solving thefirst component of the LLG equation (Eq. 1), we find3 important solutions. Taking the SAW propagation onthe x axis, then Hani = (−2aMx, 0, 0) and taking themagnetization at any direction M = (Mx,My,Mz), wefind:1. SAW ⊥ M: There won’t be any Hani since Mx = 0;therefore, there will not be any absorption.2. SAW ‖ M : Hani is at its maximum, but therewill not be any torque (τ = −M × Hani =|M ||Heff| sin θ) resulting in no absorption.3. SAW at 45◦ from M: Maximum absorption.These solutions can be visualized in Fig. 6. From aphysics point of view, when M and SAW are perpen-dicular the magnetization will not have any direction inwhich the energy will be lower; therefore, it will remainstatic and no absorption will occur. At an angle differentfrom 0 or 90, the magnetization will have a lower energystate when rotated along the SAW axis.Using the setup shown in Fig. 3, we can control theangle of the sample-holder with a screw that can movethe sample 1◦ in either direction. We start by measuringthe power transmission at 45◦ (between the SAW prop-agation and magnetic field) for different harmonics, andwe rotate 10◦ for each collection of data. We end up witha four-fold butterfly-shaped dependence as we expectedFIG. 6: Experimental data on the angle dependence of trans-mission at different magnetic fields for the third harmonic(H3: 375MHz).The radius shows the power transmission valuein dB and goes from -26 dB to -26.6 dB.(Fig. 6) reaching a maximum at 45 degrees. Additionally,there is field dependence. As the field decreases there ismore power absorption due to the spin having less energyto stay in one direction.C. Acoustoelectric effect in FMRecent studies have shown a new property producedby the magnetoelastic effect [6]. A longitudinal voltageappears when SAW propagates through the Nickel film.Using the same experimental setup (Fig. 3) and a lock-in system connected to the signal generator, we can syn-chronize the AC electrical signal to the internal frequencyof the lock-in and measure the longitudinal voltage fromthe contacts C1 and C2. With the lock-in system we canobtain voltage signals as low as 10−7V by multiplyingthe output signal by the input signal to neglect any noiseand filter the signal frequency that we want. Since thevoltage depends on the SAW power absorption we expectto obtain the same butterfly-like figure. As it is a recentstudy there are many missing experiments to determinethe exact answer to what generates this voltage but wecan theorize that there are two current components; anAC and a DC.• The DC component is the electrons moving in theSAW propagation direction.• The AC component is the ”wiggling” of the elec-trons due to an AC resistance change. As shownin Fig. 6(b) the strain field will excite the spin atdifferent amplitudes that will cause a time-varyingresistance in the form of a sinusoidal.There is a clear association between the magnetoelas-tic effect and the induced voltage, when more power isTreball de Fi de Grau 4 Barcelona, June 2021Magnetoelastic effect with Surface Acoustic Waves in Nickel Marc Rovirola MetcalfeFIG. 7: Longitudinal voltage (Vxx) at different angles andmagnetic field for the third harmonic (H3: 375 MHz). Theradius shows the voltage magnitude and goes from 0 to 6 µV .absorbed and the spin amplitude is maximized the volt-age is maximized. A difference between Fig. 6 and Fig. 7can be observed, there seems to be a preferred directionfor the SAW that results in a non-reciprocity betweenpeaks. This difference is marked with dashed lines inFig. 4(c) and (d). Non-reciprocity in Ni films has beenstudied thoroughly in the past [7], in our case the effectis very subtle in the SAW transmission results, but canbe clearly seen in the voltage. As Nickel is a conduct-ing metal; therefore, we should take into considerationthe free electrons since the SAW will couple with theircyclotron motion and can affect the results.IV. CONCLUSIONSWe provide an overview of the basic characteristics ofSAW and describe the phonon-magnon coupling that re-sults in changes in the magnetization. We studied howthe angle between the SAW propagation direction andthe magnetic field affects the absorption and thereforethe magnetoelastic effect. Furthermore, we find the ex-pected behaviour at high and low magnetic fields, ex-hibiting more magnetoelastic effect at lower fields due tothe lower energy provided to the magnetic moments. Fi-nally, we mention the acoustoelectric effect, a new-foundproperty of magnetostrictive materials resulting in a lon-gitudinal voltage and find a similar behaviour as the SAWtransmission. Further studies should focus on the differ-ence in peak magnitude (non-reciprocity). At a constantmagnetic field a change in SAW propagation and inducedvoltage can be produced by changing the angle betweenthe SAW and magnetic field leading to useful applica-tions. Furthermore, it would be interesting to study theseeffects at higher frequencies, ranging in the GHz, sinceit would give a faster magnetization state switch. Cou-pling between the lattice motion created from the SAWand the magnetic state pave the way for faster and moreefficient devices and give rise to research opportunities.AcknowledgmentsI would like to thank my tutor Ferran Macià for thehelp and motivation he has provided and for his greatenthusiasm regarding this topic which has been conta-gious. I would also like to thank J.M. Hernandez and M.Waqas for all their support in the laboratory. Lastly, Iwant to thank my family and friends for all their helpand encouragement over the last few years.[1] I.S. Camara, J.-Y. Duquesne, A. Lemâıtre, C. Gour-don, L. Thevenard. Field-Free MagnetizationSwitchingby an Acoustic Wave. Physical Review Applied, Amer-ican Physical Society, 2019, 11 (1),10.1103/PhysRevAp-plied.11.014045. hl-02187172[2] Fengyuan Yang and P Chris Hammel 2018 J. Phys. D:Appl. Phys. 51 253001.[3] Y. Pu, P.M. Odenthal, R. Adur, J. Beardsley, A.G.Swartz, D.V. Pelekhov, M.E. Flatté, R.K. Kawakami, J.Pelz, P.C. Hammel, and E. Johnston-Halperin, Phys. Rev.Lett. 115, 246602[4] Lord Rayleigh (1885). ”On Waves Propagated along thePlane Surface of an Elastic Solid”. Proc. London Math.Soc. s1-17 (1): 4–11. doi:10.1112/plms/s1-17.1.4.[5] B. Casals, N. Statuto, M. Foerster, A. Hernández-Mı́nguez, R. Cichelero, P. Manshausen, A. Mandziak, L.Aballe, J.M. Hernàndez and F. Macià, Generation andImaging of Magnetoacoustic Waves over Millimiter Dis-tances, Phys. Rev. Lett. 124, 137202 (2020).[6] T. Kawada, M. Kawaguchi, T. Funato, H. Kohno, M.Hayashi, Acoustic spin Hall effect in strong spin-orbit met-als. Sci. Adv. 7, eabd9697 (2021).[7] R. Sasaki, Y. Nii, Y. Iguchi, and Y. Onose, Nonrecipro-cal propagation of surface acoustic wave in Ni/LiNbO3,Physical Review B 95, 020407(R) (2017).Treball de Fi de Grau 5 Barcelona, June 2021

Magnetoelastic eﬀect with Surface Acoustic Waves in Nickel

http://diposit.ub.edu/dspace/bitstream/2445/180906/1/ROVIROLA%20METCALFE%20MARC_4253513_assignsubmission_file_TFG-Rovirola-Metcalfe-Marc.pdf

Magnetoelastic eﬀect with Surface Acoustic Waves in Nickel

Abstract

Similar works

Full text

Available Versions

Diposit Digital de la Universitat de Barcelona