Comparison between thermal and current driven spin-transfer torque in nanopillar metallic spin valves
CComparison between thermal and current driven spin-transfer torque in nanopillarmetallic spin valves
J. Flipse, ∗ F. K. Dejene, and B. J. van Wees Physics of Nanodevices, Zernike Institute for Advanced Materials,University of Groningen, Nijenborgh 4, 9747 AG Groningen, The Netherlands. (Dated: September 30, 2018)We investigate the relation between thermal spin-transfer torque (TSTT) and the spin-dependentSeebeck effect (SDSE), which produces a spin current when a temperature gradient is applied across ametallic ferromagnet, in nanopillar metallic spin valves. Comparing its angular dependence (aSDSE)with the angle dependent magnetoresistance (aMR) measurements on the same device, we are able toverify that a small spin heat accumulation builds up in our devices. From the SDSE measurementand the observed current driven STT switching current of 0.8 mA in our spin valve devices, itwas estimated that a temperature difference of 230 K is needed to produce an equal amount ofTSTT. Experiments specifically focused on investigating TSTT show a response that is dominatedby overall heating of the magnetic layer. Comparing it to the current driven STT experiments weestimate that only ∼
10% of the response is due to TSTT. This leads us to conclude that switchingdominated by TSTT requires a direct coupling to a perfect heat sink to minimize the effect ofoverall heating. Nevertheless the combined effect of heating, STT and TSTT could prove useful forinducing magnetization switching when further investigated and optimized.
I. INTRODUCTION
In spintronics the intrinsic angular momentum of theelectron (spin) is used to develop new or improvedelectronic components. In the spin-transfer torque(STT) mechanism proposed by Slonczewski and Bergerin 1996 , a spin polarized charge current entering amagnetic layer exerts a torque on the magnetization bytransfer of angular momentum. Nowadays STT is beingextensively studied and STT switchable random accessmemory (STT-RAM) is one of the prime candidates forreplacing dynamic RAM (DRAM) in the future . Thetwo spin channel model describes collinear transport, infor instance giant magnetoresistance devices, but is notable to explain and quantify the absorption of transversespins in STT. Therefore a so called spin mixing conduc-tance ( G ↑↓ ) was defined that gives the efficiency withwhich these spins transverse to the magnetization direc-tion are absorbed at the non-magnetic (N) | ferromagnetic(F) interface. G ↑↓ can be determined experimentally byperforming angular magnetoresistance measurements. In recent years research in the field of spin caloritron-ics, the interplay between spin and heat transport, hasled to exciting new results. In the spin-dependent See-beck effect (SDSE) heat flow is used to inject a spinpolarized current from F into N, which can exert anSTT on the magnetization of a second F layer. Indica-tions of such a TSTT have been reported by Yu et al. ,where they observed a change in the switching field of aCo | Cu | Co spin valve in the second harmonic response toa current sent through the nanowire. Nevertheless a com-plete study where the efficiency of the TSTT is quantifiedand a comparison with STT is made, is still lacking.The goal of this paper is to provide such a study ofTSTT in F | N | F GMR nanopillars. Using the same de-vice to study the GMR, the SDSE as well as their angle dependence we are able to reliably compare both. Fur-thermore we discuss measurements oriented at directlyobserving TSTT and the obstacles that come with it.This paper is organized as follows. In section II, wediscuss the theory of STT and TSTT and specificallydescribe how the angle dependent GMR and SDSE inmagneto electron circuit theory provides a way to quan-tify both mechanisms. Furthermore we show that a spinheat accumulation affects the aSDSE measurements, asthe energy dependence of the spin mixing conductancebecomes relevant. Section III describes the device fabri-cation as well as the measurement techniques that wereused. Section IV presents the GMR and SDSE measure-ment results and compares their angle dependences. Thedifference between the two leads us to conclude that aspin heat accumulation builds up in our devices. Sec-tion V presents measurements where the effect of TSTTon the magnetic switching field is studied. In section VIwe discuss the results presented and conclude that only ∼
10% of the response is due to TSTT.
II. THEORY
If, in an F | N | F stack, the magnetization of one of theF layers is rotated while keeping the other pinned, non-collinear spin transport becomes important. The spincurrent flowing from one F layer to the other will have aspin component transverse to the magnetization directionof the second F layer. Contrary to the collinear case thesetransverse spin components are not eigenstates of the fer-romagnet and its angular momentum will be absorbed bydestructive interference in F over the decoherence length,expected to be ≤ The ab-sorbed angular momentum gives a torque on the magne-tization which, if large enough, can excite magnetizationdynamics or even reverse its direction. In magnetoelec- a r X i v : . [ c ond - m a t . m e s - h a ll ] J u l Al O insulating barrier M M parallel antiparallel stack Bstack A M M θ (a) (b)(c) M M FIG. 1. (Color online) (a) Schematic representation of the device structure used, where an F | N | F stack is sandwiched betweena Pt bottom contact and a Au top contact. Two Pt Joule heaters are used to produce a thermal gradient across the stack andare insulated form the Pt bottom contact by a thin Al O layer. (b) In the angle dependent measurements stack type A is used,consisting of a circular F layer and rectangular N and F layers. The circular shape of F ensures that there is no preferentialin plane direction for the magnetization, such that it easily aligns with a small magnetic field. Rotating this small field willnot influence the magnetization direction of F giving an angle θ between M and M . (c) For the thermal STT measurementsstack type B is used, consisting of in situ grown rectangular F | N | F stack. Because of shape anisotropy two stable magneticstates are present, namely parallel and anti parallel magnetization alignment. tronic circuit theory the real part of the spin mixingconductance ( G r ↑↓ ), in typical metals an order of magni-tude larger than the imaginary part, gives the efficiencywith which the electron’s spin component transverse tothe magnetization (M) direction are absorbed at an F | N interface: I s, ⊥ = V s, ⊥ G r ↑↓ (1)where I s, ⊥ is the transverse angular momentum currentabsorbed and V s, ⊥ is the the spin accumulation ( V ↑ − V ↓ )at the F | N interface with the electron spin pointing per-pendicular to M. The charge current through an F | N | Fstack depends on the angle between the two magneti-zations ( θ ) in the thermalized regime as follows: I c ( θ ) = G (cid:20)(cid:18) − P G tan ( θ/ η + tan ( θ/ (cid:19) ∆ V + (cid:18) − P G P (cid:48) tan ( θ/ η + tan ( θ/ (cid:19) S ∆ T (cid:21) (2)where ∆ V and ∆ T are the voltage and tempera-ture difference across the spin active part of F , S is the F’s Seebeck coefficient or thermopower, P G =( G ↑ − G ↓ ) /G is the spin polarization of the F’s con-ductance, P (cid:48) = (cid:0) P S + 2 P G − P S P G (cid:1) / P S =( S ↑ − S ↓ ) /S and η = 2 G r ↑↓ /G with G = G ↑ + G ↓ .The G r ↑↓ can be determined for a certain F | N inter-face by using η as a fitting parameter for angle depen-dent magnetoresistance (aMR) measurements, by setting∆ T = 0 in Eq. 2 (see appendix A): aMR = R ( θ ) R (0) = η + tan ( θ/ η + (1 − P G ) tan ( θ/
2) (3)A similar approach can be used for the angle depen-dence of the SDSE (aSDSE), which is given by Eq. 2 for I c = 0 (see appendix A): aSDSE = − ∆ V ( θ ) S ∆ T = η + (1 − P G P (cid:48) ) tan ( θ/ η + (1 − P G ) tan ( θ/
2) (4)Both the MR and the SDSE produce a spin currentrunning from one of the F layers to the other and there-fore lead to a spin transfer torque, either current driven(STT) or driven by a temperature difference (TSTT). τ ST T ( θ ) = (cid:126) e A ( θ ) P G I c (5) τ T ST T ( θ ) = (cid:126) e G A ( θ ) ( P (cid:48) − P G ) S ∆ T (6)with A ( θ ) = η sin( θ ) η (1+cos( θ ))+(1 − cos( θ )) η +tan ( θ/ η + ( − P G ) tan ( θ/ .The description given above holds in the thermalizedregime where strong inelastic scattering between the twospin channels leads to energy exchange and ensures thatthey remain at the same temperature. However if inelas-tic scattering is relatively weak the electron temperaturescan become spin-dependent and a spin heat accumula-tion will build up . Such a spin heat accumulationproduces an additional SDSE term which depends on thespin heat accumulation itself and the energy derivative of G r ↑↓ , and a normalized spin mixing thermopower can bedefined η (cid:48) = 2 (cid:16) δG r ↑↓ /δE (cid:17) E = E F / ( δG/δE ) E = E F . As aconsequence the aSDSE curve shape will differ from thatin the thermalized regime and Eq. 4 will not accuratelydescribe the observed aSDSE behaviour. III. FABRICATION AND MEASUREMENTTECHNIQUES
The samples are prepared on top of a thermally oxi-dized Si substrate by 8 or 9 consecutive electron-beamlithography (EBL) steps, depending on the stack type.All the materials are deposited by e-beam evaporationwith a base pressure of 3 × − mbar.In this paper two types of F | N | F stacks are used. Onefor the angle dependent measurements (section IV) andan other for the TSTT measurements (section V), forconvenience they are named stack type A (Fig. 1(b))and B (Fig. 1(c)) respectively. For both stack types thefull device consists of a bottom platinum (Pt) contact of60 nm thick and a 130 nm thick gold (Au) top contactwith the F | N | F stack sandwiched in between (see figure1(a)). On both sides of the Pt bottom contact Pt Jouleheaters of 40 nm thick are placed to produce a thermalgradient across the F | N | F stack. An 8 nm thick alu-minium oxide (Al O ) layer seperates these Pt heatersfrom side extensions of the Pt bottom contact, ensuringstrong thermal contact between the two but excludingany direct electrical pick up. Around the stack a ∼ layer of 15 nm thick Permal-loy (Py)(Ni Fe ) is deposited, with a diameter of 300nm. After cleaning the interface by Ar ion milling, tocreate a good Ohmic contact, the remainder of the stackis deposited consisting of a 10 nm thick copper layer (Cu)followed by a 10 nm thick Py layer with lateral dimen-sions of 150 ×
50 nm . Because F is circular there isno preferential in-plane direction for the magnetization.The magnetization of F (M ) will therefore easily followa relatively small rotating applied magnetic field. How-ever, the rectangular shape of F ensures an easy axis forM , parallel to its longest side, due to shape anisotropy. Therefore the rotation of M is negligible when the ap-plied field is much lower than the field needed to rotateM or to overcome its hard axis direction. Such magneticbehavior is ideal for magnetization angle dependent mea-surements, further discussed in section IV.Stacks of type B, see figure 1(c), are rectangular inshape (100 ×
50 nm ) and consists of 15 nm (F ) and5 nm (F ) thick Py layers separated by a 15 nm thickCu spacer. The full stack is deposited without breakingvacuum. Both magnetic layers have the same easy axisdirection giving two distinct stable states, namely paral-lel or anti parallel alignment of the two magnetizations.These stacks are used in section V to investigate changesin switching field due to TSTT.The electrical measurements presented in this paperare all performed using standard lock-in detection tech-niques, providing a way to distinguish first harmonic re-sponse signals ( V ∝ I ) from second harmonic responsesignals ( V ∝ I ). To ensure a thermal steady-statecondition a low excitation frequency of 17 Hz was used.All measurements are performed at room temperatureexcept for the temperature dependent measurement insection V, where a Peltier heating element together witha thermometer is used to bring and keep the sample at apreset elevated temperature. IV. ANGLE DEPENDENT EXPERIMENTS
To investigate the aMR and aSDSE an F | N | F stackof type A is used (see Section III). For characterizationpurposes we first measure the MR and SDSE.Fig. 2(b) gives the MR measurement where the resis-tance across the stack is measured as a function of theapplied magnetic field (B), parallel to the easy axis of F .Just after B passes through zero the magnetization in theF layer switches as it has no easy axis direction. Thefield necessary to switch the magnetization of F is sig-nificantly larger, around 80 mT, as it has to overcome theplanar shape anisotropy. Nevertheless the field to switchF is larger than expected for a single layer of its size andshape. This is caused by the dipole magnetic field cre-ated by the F layer coupling to the magnetization of F .For the angle dependent measurements we have to makesure that this coupling is canceled out such that it willnot influence M when rotating M . From separate mea-surements we conclude that the coupling corresponds toa 50 mT field, see appendix B. A constant B of 50 mT inthe angle dependent experiments is therefore sufficient tocancel out the dipole coupling field. Note that because wecompare aMR and aSDSE measurements directly, mea-sured on the same sample and using the same technique,any small differences between the angle set by the rota-tion of B and the actual angle, between M and M , hasno effect on the ability to compare both curves.The MR measurement corresponds well with theresults found from a Comsol Multiphysics three-dimensional finite element model (3D-FEM) with P σ, = −2 −1.5 −1 −0.5 0−0.100.20.610.40.8 −100 −50 0 50 1004.754.794.83 B (mT)
I=10 μA V H / I ( Ω ) I V −100 −50 0 50 1001.21.351.5 B (mT) V H ( μ V ) I=1 mA N o r m a l i z e d a M R a n d a S D S E θ / π MagnetoresistanceSpin-dependent Seebeck effect (a) (b)(c) aSDSEaMRaMR - aSDSE B = 50 mT I x V FIG. 2. (Color online) (a) The normalized, angle dependent magnetoresistance (aMR) (squares), angle dependent spin-dependent Seebeck effect (aSDSE) (triangles) and the difference between the two (circles) are plotted as a function of the anglebetween M and M . (b) The magnetoresistance (MR) measurement gives the resistance across the stack as a function ofapplied magnetic field B. (c) The spin-dependent Seebeck effect gives the Seebeck voltage as a function of applied magneticfield B. .
25 and P σ, = 0 .
52. See Refs. 17 and 19 for a fulldiscussion of the model. The difference in P σ for thetwo F layers is because of the ion mill cleaning of the F layer, which leads to a stronger spin scattering andcan thus be taken as an effective lower P σ .The SDSE measurement in Fig. 2(c) gives the See-beck voltage measured across the stack while sweepingB. The temperature gradient over the stack is producedby sending a 1 mA root mean square current througheach Pt Joule heater. A clear difference in the Seebeckvoltage for the parallel and antiparallel case is observed.The SDSE signal and the background voltage correspondwell with previously reported results and with themodeled values, with P S, = 0 .
19 and P S, = 0 . π/
180 radian by the automated con-trol of a stepper motor. The sample holder is rotatedfrom − π to 2 π radian with a constant B of 50 mT whilerecording the voltage across the stack. M will follow Btherefore creating an angle θ between M and M , seefigure 1(b), equal to the rotation of the sample holder.In Fig. 2(a) the aMR and aSDSE measurements areplotted together and are normalized by the spin signalfrom the MR and SDSE measurements, respectively. Inthis way the angle dependence of both effects can directlybe compared. A small but distinct difference betweenthe two curves is visible, as the aSDSE is wider thanthe aMR, indicating that η (cid:48) starts playing a role. Fromthis we can conclude that a SHA builds up in our stacks, verifying previous results of direct SHA measurements. The TSTT, as described in Eq. 6, will be affected as wellbut from the relatively small difference between the aMRand aSDSE curves, of maximum 10% of the total spinsignal (see Fig. 2(a)), we can assume that this changewill be small and in first order can be neglected.
V. INVESTIGATION OF THERMALSPIN-TRANSFER TORQUE
The existence of an SDSE suggests that the spin cur-rent generated by a thermal gradient across an F | N | Fstack would produce a TSTT. The experiments discussedin this section are aimed at finding evidence for such aTSTT. For this purpose we use devices with F | N | F stackof type B (see Fig. 1(c)) to investigate the changes inminor loop switching fields.The magnetic minor loop measurement is presented inFig. 3(a), where the first harmonic response is plottedas a function of B. Here we only look at the switching ofthe 5 nm thick F layer. First M and M are saturatedparallel by applying a high positive magnetic field. NowB is sweeped towards zero until M switches, bringing thestack into the anti parallel resistance state. By reversingthe B field sweep direction, before M switches, a minorloop is obtained when M switches back to its originalparallel resistance state. The minor loop should normallybe centered around B=0 but is shifted to around B=45mT in our devices, because of the dipole field couplingbetween the two F layers.In Fig. 3(b) the STT switching experiment is givenfor characterization purposes. On top of the small alter-nating current (I ac ) of 10 µ A, which gives the resistanceof the stack via a lock-in detection technique, a directcurrent (I dc ) is sent through the stack responsible forinducing the STT. Sweeping I dc from -1.5 to +1.5 mAa STT switching from the parallel to anti parallel stateis observed, for a positive I dc of 0.8 mA, and a reverseswitch, for a negative I dc of -1.2 mA. A constant B of 40mT is applied to make sure that we are within the minorloop (Fig. 3(a)), where both the parallel and anti parallelmagnetization alignment constitute a stable state.The experiments discussed above show that the switch-ing fields B and B in the minor loop are changed bySTT, or in other words the barrier going from the P toAP state and vice versa is changed. Measuring these twoswitching fields as a function of I dc , through the F | N | Fstack, therefore quantifies the response of the sample toSTT, at currents below the STT switching current. Fig.4(a) gives this evolution of B and B , where every mea-surement point is an average switching field from 5 con-secutively obtained minor loops. B clearly shifts to lowervalues for higher I dc values, almost reaching 40 mT at anI dc of 0.8 mA, corresponding well to the STT switchingcurrent observed in Fig. 3(b). B on the other handonly shows a very small decrease consistent with mag-netic phase diagrams found for similar stacks. For TSTT a similar change in B and B should be ob-served when increasing the temperature gradient acrossthe stack. In the measurement presented in Fig. 4(b) thisis investigated by determining these switching fields as afunction of I heaters , sent through the Pt Joule heaters.The results are plotted versus I because the Jouleheating scales quadratically with I heaters . Indeed a clearquadratic decrease of B is observed as one would expectfor TSTT. However B now seems to slightly increase,instead of showing a small decrease as seen for the STTmeasurement. This could indicate that the changes in B and B are not purely due to TSTT, but overall heatingof F plays an important role as well. Namely, overallheating will lower the coercive field of the F layer. Tofurther investigate this we measured the evolution of theswitching fields as a function of the overall temperatureof the device, without any STT or temperature gradientapplied. A heating element together with a thermome-ter, positioned underneath and in good thermal contactwith the sample, was used to controllably set the overalltemperature of our device. Fig. 4(c) gives the resultsup to a temperature of 80 o C, showing a very similar be-havior as the “thermal” STT dependent measurement inFig. 4(b).To determine if the results in Fig. 4(b) are dominatedby overall heating the temperature of the F layer as func-tion of I heaters needs to be known. Experimentally this isdifficult to determine and therefore we use our 3D finiteelement model, successfully used in section IV as well asnumerous previously reported measurements. The −1.5 −1 −0.5 0 0.5 1 1.54.54.64.7 I dc (mA) V H / I ( Ω ) V H / I ( Ω ) B = 40 mT I ac V (a) (b) B (mT) B B I ac +I dc V FIG. 3. (Color online) (a) The magnetic minor switching loopof the F layer for a type B stack, where B and B representthe low and high switching field, respectively. (b) Resistanceof the stack as function of direct current (I dc ) sent throughit. The switching from the anti parallel resistance state tothe parallel state and vice versa is cause by the spin-transfertorque induced by I dc . A constant B of 40 mT is applied toensure that we are in the middle of the minor loop, whereboth the parallel and anti parallel magnetization alignmentconstitute a stable state. modeled temperature of F versus I is given in Fig.4(d). At an I heaters of 3 mA (I =9 mA ) F reaches atemperature of 57 o C. The same I heaters gives a B switching of 52 mT, according to the measurement in Fig. 4(b),which is also found for an overall heating of ∼ o C inFig. 4(c). In other words the change in B switching ob-served in Fig. 4(b) seems to be dominated by the overallheating of the F layer. VI. DISCUSSION AND CONCLUSION
The aSDSE measurement presented in section IVshows that the spin heat accumulation in our devices willinfluence the TSTT, however this changed is assumed tobe small and can effectively be neglected. Applying atemperature gradient across an F | N | F stack, presentedin section V, shows no evidence of TSTT. This we at-tribute to the dominance of overall heating of the mag-netic layer, masking the response due to TSTT. If weindeed neglect the relatively small efficiency difference inTSTT and current driven STT, then Eq. 5 and 6 describethe torques, respectively. The ∆ T needed to produce thesame amount of STT, for a certain I dc through the stack,is then found by setting τ ST T = τ T ST T and gives∆ T = 2 G P G S ( P (cid:48) − P G ) I dc = P G RS ( P (cid:48) − P G ) I dc , (7)where R is the resistance of the spin active part of thestack and I dc is the current through the stack as plot-ted on the x-axis in Fig. 4(a). Using R=1.3 Ω (fromthe 3D-FEM), S=-18 µ V/K and for P and P’ the val-ues found in section IV we get; ∆ T = 2 . × [ K/A ] I dc . In order to switch the F layer using current drivenSTT an I dc of 0.8 mA is required (see Fig. 3 (b)), whichthen corresponds to a ∆ T of 230 K, across the spin active B s w i t c h i n g ( m T ) I dc + I ac V Spin transfer torque dependence Temperature dependence I ac V I dc (mA) I heaters2 (mA ) temperature ( o C) B B B B B B (a) (b) (c) I heaters x 2I ac V "Thermal torque“ dependence I heaters2 (mA ) T e m p e r a t u r e F ( o C ) Modeled temperature F (d) FIG. 4. (Color online) The evolution of the minor loop switching fields B and B for: (a) Spin-transfer torque, induced bysending a dc current (I dc ) through the stack. (b) “Thermal STT”, induced by a thermal gradient across the stack by sendingan I dc through the Pt Joule heaters. (c) Overall temperature change, induced by a controllable heater. (c) The temperature ofthe F layer extracted from 3D finite element modeling as a function of I dc sent through the Pt Joule heaters. part of the F layer, for pure TSTT driven switching.It can safely be said that such a large steady state ∆ T cannot be applied across such a short length and will leadto a significant increase in the background temperature.This becomes evident when determining the TSTT ver-sus overall heating contribution in the “thermal torque”dependence measurement (see Fig. 4(b)). For the largestJoule heating current ( I heaters ) in Fig. 4(b) B switching is52 mT, which corresponds to an I dc of 0.375 mA for theSTT dependent measurement in Fig. 4(a). The changein B switching observed in Fig. 4(b) would therefore need a∆ T of 110 K, across the spin active part of the stack , ifcaused purely by TSTT. The model gives a ∆ T ≈
12 Kfor the largest Joule heating current, which would meanTSTT is only responsible for a maximum of ∼
10% of theobserved B switching change.In conclusion we can say that although the angle de-pendent measurements show that a thermal gradient willinduce a TSTT, it is small and difficult to distinguishfrom overall heating effects. Overall heating leads to alowering of the energy switching barrier for both the Pand AP state, such that B and B move towards eachother and gives a narrower minor loop. In the case ofSTT, either induced by a thermal or voltage gradient,the two switching fields should move in the same directionproviding a way to distinguishing it from overall heating.Our results show that, in steady state experiments, itis difficult to avoid overall heating from being the dom-inant effect, unless the magnetic layer under investiga-tion is connected directly to an almost perfect heat sink.An alternative approach would be to use use short heatpulses and look at time dependent signals as discussed inRef. 14, 21, and 22 for tunnel magnetoresistance (TMR)structures. A combined effect of the lowering of the switchingbarrier by overall heating together with TSTT could ofcourse be beneficial as the torque needed to switch will besmaller. This route is currently being investigated in theform of heat assisted switching devices. However itrequires an in depth investigation and precise calibrationof the timing of the two effects.
ACKNOWLEDGMENTS
We would like to acknowledge B. Wolfs, M. de Rooszand J. G. Holstein for technical assistance. This workis part of the research program of the Foundation forFundamental Research on Matter (FOM) and supportedby NanoLab NL and the Zernike Institute for AdvancedMaterials.
Appendix A: aMR and aSDSE formula’s aMR in a symmetric F | N | F stack is described by Eq.3, which is found by setting ∆ T = 0 in Eq. 2. Thisgives: I c ( θ )∆ V = G (cid:18) − P G tan ( θ/ η + tan ( θ/ (cid:19) (A1) R (0) R ( θ ) = η + (1 − P G ) tan ( θ/ η + tan ( θ/
2) (A2)The aSDSE is described in Eq. 4, which is found bysetting I c = 0 in Eq. 2. This gives: − (cid:18) − P G tan ( θ/ η + tan ( θ/ (cid:19) ∆ V = (cid:18) − P G P (cid:48) tan ( θ/ η + tan ( θ/ (cid:19) S ∆ T (A3) − ∆ V ( θ ) S ∆ T = (cid:18) η + (1 − P G P (cid:48) ) tan ( θ/ η + tan ( θ/ (cid:19)(cid:32) η + (cid:0) − P G (cid:1) tan ( θ/ η + tan ( θ/ (cid:33) (A4) −80 −40 0 404.074.094.114.134.15−80 −40 0 40 804.074.094.114.134.15 V H / I ( Ω ) V H / I ( Ω ) B (mT) B (mT)(a) (b)
FIG. 5. (Color online) Measurements on device with F | N | Fstack with negligible dipole field coupling (a) Resistance ofthe stack as a function of applied magnetic field B, spin valvemeasurement. (b) Minor loop switching measurement for theF layer clearly showing no coupling as the loop is well cen-tered around B=0. Appendix B: Dipole magnetic field coupling
To determine the dipole field coupling between the F and F layer for stack type A similar devices were fab- ricated, with a 1.5 µ m by 100 nm rectangular F layer.As the F layer is now much longer than the F layer thedipole coupling field will become negligibly small. As therest of the device and especially the N and F layer arekept the same we are able to determine the switchingfield of F without any coupling present. In Fig. 5 thespin valve and minor loop measurements are given. Theminor loop is perfectly centered around B=0 confirmingthat the dipole field coupling is negligibly small. Fur-thermore we observe a switching field of 35 mT, whichcan be seen as the uncoupled switching field. Comparingthis to the switching field of 85 mT for the coupled stacksused in the angle dependent measurements, see Fig. 2,we estimate a dipole coupling field of 50 mT. ∗ [email protected] J. C. Slonczewski, Journ. of Magn. and Magn. Mater. , L1-L7 (1996). L. Berger, Phys. Rev. B , 9353 (1996). J. ˚Akerman, Science , 508-510 (2005). T. Valet, A. Fert, Phys. Rev. B , 7099 (1993). A. Brataas, Yu. V Nazarov, G. E. W. Bauer, Phys. Rev.Lett. , 2481 (2000). A. Brataas, G. E. W. Bauer, P. J. Kelly, Phys. Rep. ,157 (2006). A. A. Kovalev, A. Brataas, G. E. W. Bauer, Phys. Rev.B , 224424 (2002). S. Urazhdin, R. Loloee, W. P. Pratt, Jr., Phys. Rev. B , 100401(R) (2005). G. E. W. Bauer, E. Saitoh, B. J. van Wees, Nature Ma-terials , 391 (2012). A. Slachter, F. L. Bakker, J-P. Adam, B. J. van Wees,Nature Physics , 879 (2010). F. K. Dejene, J. Flipse, B. J. van Wees, Phys. Rev. B ,024436 (2012). H. Yu, S. Granville, D. P. Yu, J.-Ph. Ansermet, Phys.Rev. Lett. , 146601 (2010). A. A. Kovalev, G. E. W. Bauer, A. Brataas, Phys. Rev.B , 054407 (2006). M. Hatami, G. E. W. Bauer, Q. Zhang, P. J. Kelly, Phys.Rev. Lett. , 066603 (2007). The spin active part consists of the F layers for a thicknessequal to the spin relaxation length ( λ F ). T. T. Heikkil¨a, M. Hatami, G. E. W. Bauer, Phys. Rev.B , 100408(R) (2010). F. K. Dejene, J. Flipse, G. E. W. Bauer, B. J. van Wees,Nature Physics , 636-639 (2013). L. Giacomoni, B. Dieny, W. P. Pratt, Jr., R. Loloee,M. Tsoi, (unpublished). A. Slachter, F. L. Bakker, B. J. van Wees, Phys. Rev. B , 174408 (2011). I. N. Krivorotov, N. C. Emley, A. G. F. Garcia, J.C. Sankey, S. I. Kiselev, D. C. Ralph, R. A. Buhrman,Phys. Rev. Lett. , 166603 (2004). X. Jia, K. Xia, G. E. W. Bauer, Phys. Rev. Lett. ,176603 (2011). J. C. Leutenantsmeyer, M. Walter, V. Zbarsky,M. M¨unzenberg, R. Gareev, K. Rott, A. Thomas, G. Reiss,P. Peretzki, H. Schuhmann, M. Seibt, M. Czerner,C. Heiliger, SPIN , 1350002 (2013). R. S. Beech, J. A. Anderson, A. V. Pohm, J. M. Daughton,J. Appl. Phys. , 6403 (2000). J. Wang, P. P. Freitas, Appl. Phys. Lett. , 945 (2004). H. Xi, J. Stricklin, H. Li, Y. Chen, X. Wang, Y. Zheng,Z. Ghao, M. X. Tang, IEEE Trans. Magn.46