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APS/123-QED Lateral magnetic anisotropy superlattice out of a single (Ga,Mn)As layer R.G. Dengel, C. Gould, J. Wenisch, K. Brunner, G. Schmidt and L.W. Molenkamp Physikalisches Institut (EP3), Universität Wu¨rzburg, Am Hubland. D-97074 Wu¨rzburg, Germany (Dated: January 21, 2009) We use lithographically induced strain relaxation to periodically modulate the magnetic anisotropy in a single (Ga,Mn)As layer. This results in a lateral magnetoresistance device where twonon-volatilemagneticstatesexistatzeroexternalmagneticfieldwithresistancesresultingfrom the orientation of two lithographically defined regions in a single and contiguous layer. PACSnumbers: 75.30.Gw,85.75.-d,75.50.Pp 9 0 0 Strain control of the magnetic anisotropy in (a) 2 (Ga,Mn)As is currently a focus of spintronics re- n search. Recent reports include lithographic strain a control [1, 2] and related devices [3, 4, 5], as well as J the use of piezoelectric elements to electrically control 1 the imposed strain [6, 7]. So far, all of these devices 2 imposed an homogeneous anisotropy onto the targeted ] structure. In this paper, we show that this process can l be taken much further and demonstrate the fabrication l a and characterization of a lateral anisotropy superlattice. h Our method involves patterning of the surface of a fer- - s romagnetic semiconductor layer in order to allow partial e m strain relaxation. This is achieved by lithographically 2 µm 200 nm defining nanometer scale stripes into a (Ga,Mn)As layer . t and partially etching into the ferromagnetic layer. The a [010] m unetched part of the layer remains pseudomorphically H strained with its magnetic anisotropy relatively un- [100] - d changed, while the stripes anisotropically relax and gain φ n a strongly uniaxial magnetic anisotropy. By varying the o depth of etching, we can control the ratio of uniaxial to c biaxial anisotropy material. Our investigations reveal [ that for a specific ratio, the resulting structure has 1 alternating regions of uniaxial and biaxial anisotropy, J v and thus constitutes a anisotropy superlattice structure. 0 1 The principle of our method is based on the nature 2 of the ferromagnetism in (Ga,Mn)As. The magnetic in- 20µm (b) 3 teraction between the randomly distributed dilute Mn . 1 moments is mediated by itinerant holes through Zener 0 double exchange. Because of spin orbit coupling, the FIG. 1: a) SEM image of the mesa and the stripes after 9 wavefunction of these holes takes on anisotropies which patterning. Inset: high magnification cross sectional view of 0 reflect the symmetry of the lattice. When (Ga,Mn)As is a few stripes. b) Picture of the Hallbar geometry relative : v grown on GaAs (001), it is compressively strained, and to the crystal direction with a sketch of the current and the i applied magnetic field. X for the doping concentration used in our transport samples,at4K,theprimaryanisotropyisanin-planebiaxial r a anisotropy along the [100] and [010] crystal directions However,becausethestrengthofshapeanisotropyscales [8]. When lithographic techniques are used to trigger with saturation magnetization, it is a relatively weak ef- anisotropic deformation of the lattice along a given di- fectin(Ga,Mn)Asandcannoteffectivelycompeteagainst rection, this change in symmetry is reflected in the hole the crystalline anisotropy terms. For example, the uni- wavefunctions, and thus leads to a modification of the axial shape anisotropy field expected [9] from the 38 nm magnetic anisotropy. deep etched stripes used in this study is < 6 mT, much to small to compete with the crystalline anisotropy of An important distinction between the anisotropy in ∼100 mT. dilute magnetic semiconductors and traditional metals is worth noting. In metals, a common way to achieve The samples are made from a typical 70 nm anisotropy engineering is through shape anisotropy. Ga Mn As layer [10] with a Curie temperature 0.965 0.035 2 of 60 K grown on a semi-insulating (001) GaAs buffer and substrate. An array of 500 stripes of 150 nm width 3.12 (a) by 200 µm length, with a period of 400 nm, and aligned alongthe[100]crystallographicdirection,isdefinedbye- 3.10 beam lithography into a positive bilayer resist, followed 3.08 by deposition of 15 nm Ti and lift-off. This pattern is 3.06 3.10 90° transferred into the 70 nm (Ga,Mn)As layer by chemical 3.06 assisted ion beam etching (CAIBE) using the Ti stripes 3.04 3.02 0° 0 nm as a mask. By properly selecting the etching depth, we 3.02 -40 0 40 fabricate samples with stripes from ∼ 20 to ∼ 60 nm in 3.00 thickness, leaving a continuous layer from 50 to 10 nm (b) betweenthestripes. TheTiisthenremovedbyadipinto HF:H O (1:200). A mesa of 20 µm × 200 µm, is defined 2 onto the center of the array, parallel to and containing 8.20 90° ∼ 50 stripes, by optical lithography using a positive re- 8.05 sist. Chemical wet etching is used to remove material 0° 7.90 18 nm around this mesa to a depth of ∼ 60 nm into the GaAs -40 0 40 substrate. Asecondopticallithographicstepisthenused todefineAu/Ticontactpadsforelectricalaccess. Fig.1a presents a scanning electron microscope (SEM) image of one of the ends of the 20 µm wide mesa containing the (c) stripes,wheretheymeettheAucontact. Theinsetshows a close up of some of the stripes, while Fig. 1b shows the finalsamplelayout. Theresultingthicknessofthestripes is determined from SEM images taken at tilted angles as well as by a stylus profiler system (Dektak 6M). 63 nm The samples are characterized by magnetoresistance studies in a magnetocryostat fitted with a vector field magnetcapableofapplyingfieldsofupto300mTinany direction. For our purposes, the magnetic field will be confined to the sample plane, and its direction ϕ = 0 is defined with respect to the current direction flow- FIG. 2: MR scans at4.2 Kof patterned (Ga,Mn)As for vari- ing along the stripes. Given that the contact resistance ous angles ϕ in steps of 10◦ between magnetic field and cur- (< 10 Ω) is negligible compared to the resistance of the rent. The field is swept from -300 mT to 300 mT. a) a Hall stripes , a simple two terminal measurement configura- barwithnoetching,b)Asamplewith18nmthickstripesand tion is chosen in order to maximize our sensitivity to biaxialbehavior; c)samplewith63nmthickstripeswhichis thedistributionofallthestripesinsteadofpreferentially fullyuniaxial. Theinsetsina)andb)showazoomofthelow measuring those near the edges. We apply a constant field region. voltage of 10 mV to the end leads of the Hall-bar and magnetization M(cid:126) rotates towards the nearest available measuretheresultingcurrentJ inordertodeterminethe easy axis. For this sample, we observe that for field di- resistance while the magnetic field is swept in the sam- rections closer to 90◦, the result of this relaxation is a ple plane. In ferromagnetic materials the longitudinal high resistance state, whereas for field directions nearer resistance of a sample is strongly dependent on the an- gle between the magnetization M(cid:126) and the current J(cid:126). In to 0◦ the sample relaxes to a low resistance state. At H = 0 mT two stable states exist corresponding to the (Ga,Mn)As, this anisotropic magnetoresistance (AMR) [11, 12] has a resistance minimum when M(cid:126) (cid:107) J(cid:126) and a typical biaxial behavior of (Ga,Mn)As. After H =0 mT in all curves, magnetization reversal takes place through maximum when M(cid:126)⊥J(cid:126) [13]. the nucleation and propagation of two subsequent 90◦ We first consider measurements on a sample with domain walls resulting in two distinct switching events. stripes of 18 nm thickness (Fig 2b). In all curves, the For reference, magnetoresistance curves on the unetched magnetic field is swept from -300 to 300 mT. For high layer are shown in Fig. 2a. In such a layer, the low field magnetic fields the magnetization M(cid:126) of the sample fol- features in the 0◦ and 90◦ curves are of similar width, lows the applied external magnetic field H(cid:126) and as ex- reflecting the near symmetry of these two directions. In pected, at ±200 mT, the sample has a maximum re- the layer with the 18 nm deep etched stripes, the much sistance for fields along 90◦, perpendicular to J, and a wider feature in the 90◦ curve and the near absence of minimum resistance for H (cid:107) J. When H(cid:126) decreases, the anyfeatureinthe0◦ curve, revealsasymmetrybreaking 3 switching event then follows decreasing the resistance to its minimum value corresponding to M(cid:126) parallel to J(cid:126). As (a) H(cid:126) continues to increase the resistance changes again to an intermediate level before returning to the maximum resistance. Comparing these curves to those of Fig. 2 H H S1 S2 leadstoanintuitiveinterpretationofwhatishappening: The sample breaks up into two regions having either biaxial or uniaxial magnetic anisotropy. Consider the gray curve of Fig. 3b showing an en- larged view of the low field part of the ϕ = 90◦ curve, and indicating by the thick (thin) arrows the direction of magnetization of the stripes (between the stripes) regions of the sample at various point in the field sweep. Athighfields, anddownto∼-30mT,thefieldalignsall moments into a uniform state H(cid:126) (cid:107) M(cid:126)⊥J(cid:126). As the field is reduced, a first magnetization reorientation event oc- (b) cursveryneartoH(cid:126) =0mT,asthemagnetizationofthe uniaxialstripeschangestoanalignmentalongtheireasy axis, and thus parallel to the current. This leaves the sample in a non-trivial configuration, where the magne- H tizationofthestripesandtheregionsbetweenthestripes are orthogonal to each other. As the field is further in- creasedtoabout16mT,themagnetizationofthebiaxial 0° J regions undergoes a 90◦ reorientation as part of its two step switching process. This reestablishes a co-linear, and thus low resistance state. Further sweeping of the field towards high positive value causes first the region between the stripes, and then the stripes to switch their FIG. 3: a) MR scan at 4.2 K for a (Ga,Mn)As layer with 38 nm thick stripes for various angles ϕ between magnetic field alignment to the magnetic field direction, creating a sec- and current. The field is swept from -300 mT to 300 mT. b) ond orthogonal state at 23 mT, and then the high resis- MR scan at ϕ = 90◦ (light gray) and minor hysteresis loops tance state where all moments are perpendicular to the from-300mTtothestatesat7(blue),16mT(red)and23mT current, from +30 mT onwards. (green). The thick (thin) arrows indicate the magnetization Inorderto verifythatallthese statesarenon-volatile, ofthestriped(bulk)regionsofthesampleatvariouspositions we proceed to a series of minor loops to verify their hys- in the field sweep. tereticbehavior. Thebluecurveisobtainedbysweeping between the two directions, highlighting a uniaxial easy the H(cid:126)-field from -300 to 7 mT, just after the first sharp anisotropy component along [100], the direction of the switching event, and then sweeping back to to negative patterned stripes. The sample thus shows primary biax- fields. Thesampleclearlyremainsintheintermediatere- ialbehaviorwiththeuniaxialcomponentimposedbythe sistance state confirming that the orthogonal configura- stripes playing only a secondary role. tionofthemagnetizationinthedifferentregionssurvives ThesituationisreversedinFig. 2cforthesamplewith intheabsenceofmagneticfield. Thesameistrueforthe stripe thickness of about 63 nm. While this sample’s be- second orthogonal configuration as well as the collinear havior is similar to the first at high fields, at H(cid:126) =0 mT low resistance state, as confirmed by the next two ex- all curves converge to a single low resistance value corre- perimentswhichrepeattheaboveprocedure,butreverse spondingtoM(cid:126) (cid:107)J(cid:126). Thesampleisnowtotallydominated field at 16 and 23 mT, at the point of emergence of each by the uniaxial character of the stripes, and behaves as relevant state. a simple uniaxial magnet. Toconfirmtherobustnessandreproducibilityofthere- We now consider this transition from biaxial to uniax- sults presented, we have fabricated a second set of sam- ial behavior in a sample with stripe thickness of 38 nm. ples. The fabrication is as above, except that the Ti Fig. 3ashowsAMRmeasurementsofsuchasample. The mask is left on the sample after processing. The sam- high field behavior is again unchanged. At low magnetic ple can thus be measured for a given stripe thickness fields however, when H(cid:126) is swept in directions nearly per- andthenre-etchedinCAIBE,resultinginthickerstripes pendiculartoJ(cid:126),thenumberofswitchingeventsincreases that can be measured again. This allows us to investi- from the two distinct features observed in Fig. 2, to four gate stripes of various thicknesses on the same piece of distinct features. Near H = 0 mT a first switching of M(cid:126) material, and thus ensure that the stripe thickness is the resulting in an intermediate resistance occurs. A second only parameter at work. Figure 4 shows measurements 4 1.269 60 H S1 H S2 40 1.266 1.269 1.267 20 1.265 1.263 1.263 -40 -20 0 20 40 0 -20 (a) 1.260 0 10 20 30 40 50 60 70 -30) FIG. 4: Magnetoresistance measurements on the re-etched ain (x1 12..50 80 HMSo1d-eHlS2 sampleforstripesof37nmthickness,showingthesamemixed d str 1.0 40 e sotfattheeb9e0h◦avciuorrvaes.inFig.3b. Theinsetshowsthelowfieldpart Calculat 00..50 (b) 0 (c) on the re-etched sample for a stripe thickness of 37 nm, 0 20 40 60 0 20 40 60 and reproducing the mixed state behavior of Fig. 3b. In Etching depth ( nm ) this case, because the Ti mask which is still on the sam- FIG. 5: a) Magnetic fields of the switching events H(cid:126) and ple reduced the overall device resistance, we use a four S1 H(cid:126) for the individual samples with different etching depths terminalmeasurementconfigurationto fullyexcludeany S2 ((cid:4))andthesubsequentlyetchedsample((cid:78)). b)givestheav- role of the contacts. eragestrain(cid:15) asafunctionoftheetchingdepth. c)plotsthe x A figure of merit to quantify the strength of the im- separation between H(cid:126) and H(cid:126) , which is a measure of the S1 S2 posed uniaxial anisotropy term in the stripes can be ob- uniaxial anisotropy strength. The solid line is the anisotropy tained from the magnetic field positions H(cid:126) and H(cid:126) strength expected from modeling. S1 S2 where the resistance reaches the mid value between its minimum and maximum (see Fig. 3a), for the two uni- that not only the stripes, but also the regions immedi- axial switching events in the H(cid:126) ⊥J(cid:126) curves of each sam- ately under the stripe are significantly relaxed in both x ple [1, 14]. Results for both sets of samples are plotted andz directions,whereastheregionsbetweenthestripes in Fig. 5a, with the set comprised of individual samples areessentiallypseudomorphic,orevenpartiallycompres- given as squares and the set from re-etching as triangles. sively strained. This explains why the two regions have Towithinexperimentaldeterminationofthestripethick- such different anisotropy properties. Moreover, the fact ness, both sets reveal quantitatively identical behavior, that the relaxed strain extends to include the material and show a monotonic increase of the strength of the under the stripes explains why the uniaxial region car- imposed uniaxial anisotropy as a function of increased ries the majority of the current, as can be established etching depth. These results imply that the lithogra- from the data of Figs. 3 and 4 where the larger of the phy is capable of controlling the relative areas of biaxial two resistance changes occurs when the stripes change anduniaxialregionsandallowfordetailedengineeringof their magnetization direction. anisotropic superstructures. The measurements presented in this manuscript are To better understand the role that strain relaxation taken at 4.2 K. As temperature is increased, the qual- plays in setting up this mixed stated configurations, we itative behavior remains unchanged until about 20 K, turntofiniteelementcalculations. InFig. 6awepresent after which the bulk layer undergoes the biaxial to finite element strain simulations on a samples with 40 [110] uniaxial anisotropy transition commonly observed nm thick stripes. No strain relaxation occurs along the in (Ga,Mn)As [8]. The strength of the strain relaxation length of the strips, and we plot strain components per- induced uniaxial anisotropy in the stripes shows little pendicular to the stripe direction ((cid:15) ) and ((cid:15) ). (cid:15) = temperature dependence, as observed previously for this x z x 0.00 indicates full pseudomorphic strain, where the lat- anisotropy mechanism [1]. tice constant of the (Ga,Mn)As layer is equal to that Finite element calculations were carried out on stripes of the GaAs substrate. For (cid:15) > 0 the (Ga,Mn)As lat- ofvariousthickness,andtheaveragestraininthestriped x ticeconstantincreases, indicatingstrainrelaxation, with regionwasextractedforeachthickness. Thesewereused (cid:15) = 1.96× 10−3 corresponding to the Ga Mn As asinputfork·pcalculationstoextracttheexpectedvalue 0.965 0.035 fully relaxing to its natural lattice constant. Negative oftheanisotropystrength. FollowingRef.[15, 16]wecal- values indicate stronger compressive strain than that of culate the ground state energy of the hole system under the pseudomorphic layer. The simulations clearly show the assumption that the magnetization is aligned along 5 The authors thank T. Borzenko and V. Hock for as- 40nm sistanceinsamplefabrication,andacknowledgefinancial (Ga,Mn)As support from the EU (NANOSPIN FP6-IST-015728). GaAs εx(x 10 - 3 ) -2.70 -1.50 0.00 1.50 3.00 [1] S. Hu¨mpfner, K. Pappert, J. Wenisch, K. Brunner, C. Gould, G. Schmidt, L. W. Molenkamp, M. Sawicki, and T. Dietl, Appl. Phys. Lett. 90, 102102 (2007). [2] J.Wenisch,C.Gould,L.Ebel,J.Storz,K.Pappert,M.J. Schmidt,C.Kumpf,G.Schmidt,K.Brunner,andL.W. εz(x 10 - 3 ) Molenkamp, Phys. Rev. Lett. 99, 077201 (2007). [3] K. Pappert, S. Hu¨mpfner, C. Gould, J. Wenisch, K. -0.90 0.00 1.20 2.40 3.60 4.80 Brunner, G. Schmidt, and L. W. Molenkamp, Nature Phys. 3, 573 (2007). FIG.6: Finiteelementstrainsimulationsforstripesof40nm [4] J. Wunderlich, A. C. Irvine, J. Zemen, V. Holy, A. W. thickness Rushforth, E. De Ranieri, U. Rana, K. Vyborny, J. Sinova, C. T. Foxon, R. P. Campion, D. A. Williams, a given crystal direction. We then repeat this calcula- B. L. Gallagher, and T. Jungwirth, Phys. Rev. B 76, tion of all possible directions of magnetization, to get a 054424 (2007). profile of the magnetic anisotropy, where the directions [5] E. D. Ranieri, A. Rushforth, K. Vyborny, U. Rana, E. yielding the lowest total energy are obviously magneti- Ahmed, R. Campion, C. Foxon, B. Gallagher, A. Irvine, cally easy axes. For the strain Hamiltonian, we treat the J. Wunderlich, and T. Jungwirth, Cond-mat\ 08023344 strain in the stripes as homogeneous and given by the (2008). [6] A.Rushforth,E.D.Ranieri,J.Zemen,J.Wunderlich,K. average value of the calculated strain in both the x and Edmonds, C. King, E. Ahmad, R. Campion, C. Foxon, z directions (the y direction is pseudomorphic) and the B.Gallagher,K.Vyborny,J.Kucera,andT.Jungwirth, off diagonal components of the strain matrix are taken Cond-mat\ 08010886 (2008). to be zero. The average strain (cid:15)x as a function of etched [7] M.Overby,A.Chernyshov,L.P.Rokhinson,X.Liu,and depthextractedfromthefiniteelementcalculations,and J. K. Furdyna, Cond-mat\ 08014191 (2008). usedinthek·pmodelingaregiveninFig. 5b. Theother [8] M. Sawicki, F. Matsukura, A. Idziaszek, T. Dietl, material parameters used in the modeling are as in Ref. G. M. Schott, C. Ruester, C. Gould, G. Karczewski, G. Schmidt, and L. W. Molenkamp, Phys. Rev. B 70, [17]. 245325 (2004). UsingthemethodsdescribedinRef. [1,2]torelatethe [9] A.Aharoni,JournalofAppliedPhysics83,3432(1998). uniaxial anisotropy strength to the opening in the mag- [10] G.Schott,G.Schmidt,G.Karczewski,L.W.Molenkamp, netoresistancecurves, weplotasthesolidlineinFig.5c, R. Jakiela, and A. Barcz, Appl. Phys. Lett. 82, 4678 the expected opening from the model, and compare it (2003). [11] T. R. Mcguire and R. I. Potter, Ieee Transactions On to the experimental values (solid symbols). Given the Magnetics 11, 1018 (1975). oversimplification in the model that the strain for each [12] J. P. Jan, Solid State Physics ((Eds: F. Seitz, D. Turn- thickness can be reduced to a single homogeneous aver- bull), Academic Press Inc., New York, 1957), pp. Vol. 5, agevalue,thecorrespondencebetweentheoryandexper- p.1. iment is quite remarkable. [13] D. V. Baxter, D. Ruzmetov, J. Scherschligt, Y. Sasaki, Inconclusion,wehavedemonstratedhowcarefullyen- X. Liu, J. K. Furdyna, and C. H. Mielke, Phys. Rev. B 65, 212407 (2002). gineered strain relaxation in (Ga,Mn)As can be used to [14] F. West, Nature 188, 129 (1960). createnontrivialmagneticanisotropieswithinacontinu- [15] M. Abolfath, T. Jungwirth, J. Brum, and A. H. Mac- ouslayeroutofwhichdevicescanbepatterned. Wehave Donald, Physical Review B 6305, 054418 (2001). used this method to demonstrate a new device function- [16] T. Dietl, H. Ohno, and F. Matsukura, Physical Review ality. The structure behaves like a two state magnetore- B 6319, 195205 (2001). sistancememoryelement,witharesistiveresponsetothe [17] M. J. Schmidt, K. Pappert, C. Gould, G. Schmidt, R. differencebetweentwonon-volatilemagnetizationstates. Oppermann, and L. W. Molenkamp, Physical Review B 76, 035204 (2007). Unlikepreviousdeviceswherethetwostatesdifferinthe relative alignment of the magnetization of separate lay- ers, here the two regions of differing magnetization are contained within a single layer. Apart from the obvious advantages in applications, this method can also be use- ful for studies relying on the interplay between regions of different magnetization, such as domain wall or spin torque studies.