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2012 80 Edna Consuelo Corredor Vega Preparation and characterization of epitaxial thin films and patterned nanostructures of Ni/Cu and Fe/Cu Departamento Director/es Física de la Materia Condensada Ciria Remacha, Miguel Angel Arnaudas Pontaque, José Ignacio Director/es Tesis Doctoral Autor Repositorio de la Universidad de Zaragoza – Zaguan http://zaguan.unizar.es UNIVERSIDAD DE ZARAGOZA Departamento Director/es Edna Consuelo Corredor Vega PREPARATION AND CHARACTERIZATION OF EPITAXIAL THIN FILMS AND PATTERNED NANOSTRUCTURES OF NI/CU AND FE/CU Director/es Física de la Materia Condensada Ciria Remacha, Miguel Angel Arnaudas Pontaque, José Ignacio Tesis Doctoral Autor 2012 Repositorio de la Universidad de Zaragoza – Zaguan http://zaguan.unizar.es UNIVERSIDAD DE ZARAGOZA Departamento Director/es Director/es Tesis Doctoral Autor Repositorio de la Universidad de Zaragoza – Zaguan http://zaguan.unizar.es UNIVERSIDAD DE ZARAGOZA Preparation and magneti haraterization of epitaxial thin films and patterned nanostrutures of Ni/Cu and Fe/Cu ZAGUAN: Theses Digital Rep ository University of Zaragoza (Spain) Thesis submitted for the Degree of Dotor in Physis. University of Zaragoza, Spain (2012). Author: Edna Consuelo Corredor Vega Advisors: Dr. Miguel Ángel Ciria Remaha Prof. Dr. José Ignaio Arnaudas Preparation and magneti haraterization of epitaxial thin lms and patterned nanostrutures of Ni/Cu and Fe/Cu Edna Consuelo Corredor Vega Aragon Institute of Nanosiene and The Department of Condensed Matter Physis of the University of Zaragoza. The Materials Siene Institute of Aragon of the University of Zaragoza and the Spanish National Researh Counil. To my family. Growth of Ni/Cu thin films 5 Figure 3: Diagram of a eletron beam evap oration system where there is no diret line of sight from the lament to the material for evap orating. Courtesy of Wikipedia . is imp ortant b eause it grows in an UHV environment where we an ontrol with high preision the ontamination level, rates of dep osition and rystalline quality of the lms during evap oration. Go o d epitaxy is essential for the observation of p erp endiular magnetization in the nikel layer. The vauum in the main hamb er is ahieved by using a series of pumps, eah of whih has its own op erative pressure range. The hamb er is equipp ed with a load-lo k provided with a Varian sroll pump and a Pfeier Vauum turb o pump (60 l/s) that allows quikly reah pressure ab out 10−8 Torr. An ion pump (500 l/s) is then turned on to help bringing the pressure to ab out 10−9 after a few days of pumping. With a go o d bake (that is, the hamb er is heated to ab out 150◦ C for a few days), the pressure of less than 5×10−10 Torr an b e obtained. Figure 2 shows a piture of the MBE system. The main hamb er is equipp ed with a multip o ket linear eletron gun for four dierent materials (up to 6kW), two high temp erature eusion ells, a RHEED set-up (15 keV), fast ation linear shutters, a quartz rystal monitor thikness, sample heater up to 1000◦ C. During the Cu, Ni and Fe evap orations, the evap oration guns, the rystal monitor and the sample manipulator are water-o oled. The pressure do es not rise ab ove 10−8 Torr during the dep osition of the lms. Figure 3 illustrates the evap oration pro ess. Eletron-b eam evap oration makes use of a water-o oled ruible ontaining the desired metal, heated by an inoming b eam of eletrons from a tungsten lament. Typially the lament is lo ated adjaent to the ruible, with the eletron b eam b ent by magneti elds to impinge up on the ruible ontents, thus preventing evap oration of metal onto the lament itself. 6 Growth of Ni/Cu thin films Figure 4: RHEED patterns obtained for the silion with the eletron b eam along the (a) [100℄ and (b) [110℄ diretions, and for the opp er buer layer along the [110℄ diretion b efore () and after (d) the annealing pro ess. Substrate Preparation and Film Growth Prior to the loading in the hamb er, the Si(001) p-typ e substrate, whih have 2 inhes of diameter, are rst dipp ed in a 10 % hydrouori solution for twelve seonds and then rinsed with deionized water for ab ove 20 seonds. This pro ess removes the native silion oxide and leaves the surfae hydrogen passivated, whih is inert for several minutes in air and several days in UHV at ro om temp erature[1 , 2℄. The silion wafers are then immediately transferred into the load-lo k hamb er to b e pump ed down. After several hours in the load-lo k, the substrate is transferred into the main hamb er and heated at 150◦ C for 1 hour to eliminate the vap our of water that stay still on. One the RHEED pattern shows sharp streaky diration lines and Kikuhi lines, whih indiate a lean Si surfae (see Fig. 4 (a) and (b) ). Following these observations a Cu layer was evap orated at a rate of 0.5 /se on the Si substrate at ro om temp erature. The epitaxial relationships b etween the Si(001) and Cu were determined by in-situ RHEED observations and ex-situ with θ - 2 θ x-ray diration measurements. Comparing the lattie onstants of Cu, 3.616 Å , and Si, 5.431 Å , a mismath as large as 40 % exists b etween the two. However, up on the rotation of 45 ◦ of the Cu (200) lattie, a muh improved math is p ossible. This means a multipliation of the Cu lattie by a fator of √2 , making it 5,113Å . Thus, the epitaxy of Cu (100) on the (100) Si, have b een established with a 45 ◦ rotation.[3 6℄. Then, the Cu [100℄ axis is parallel to the Si [110℄ axis. The dep osition rate and the nal thikness of the lms were monitored by a quartz rystal mirobalane whih was alibrated using x-ray reetivity. The opp er buer layers for all the samples were annealed in situ to ab out 120 ◦ C for 40 minutes and then o oled down to 20 ◦ C prior to the dep osition Growth of Ni/Cu thin films 7 Figure 5: HRTEM image of the Si and Cu interfae. of the nikel layer. The annealing pro ess improved the atness of the buer layer surfae. Figure 4() shows the RHEED pattern of a 1000Å opp er lm on Si(001) b efore the anneal. The sp ottedness of the pattern indiates that the surfae of the opp er lm was atomially rough. Figure 4(d) shows the RHEED pattern of the same lm after the anneal. The streaky RHEED pattern suggests that the surfae was atomially at. Additional HRTEM exp eriments have shown the formation of a ≈ 5 Å opp er siliide layer at the Cu-Si interfae (see Fig. 5). Previous studies have shown the opp er-siliide forms slowly at ro om temp erature after the epitaxial relationship b etween the Cu layers and Si substrate has b een established sine the Cu layer lying ab ove the siliide remains a single rystal. [7 , 8℄. The opp er and nikel layers were grown at ro om temp erature and the substrates were rotating during dep osition in order to get a go o d thikness uniformity. Following eah dep osition, the Ni/Cu/Si thin lms were haraterized by RHEED. RHEED reveals the growing in the (001) orientation of the Cu and Ni layers with the following in-plane epitaxial relationships b etween silion, opp er and nikel layers: Si[110℄ k Cu[100℄ k Ni[100℄. The growth of Ni(001) on Cu(001) is more diret: the nikel lattie is totally or partially ommensurate with the Cu. Sine the lattie mismath b etween them is ab out 2.6 % , epitaxial growth of Ni is favourable and has b een frequently observed[7 , 22℄. The ritial thikness tc (the thikness b elow whih the nikel is totally ommensurate with the Cu buer layer) an b e found by setting the equilibrium strain ǫe k = 2.6 % (whih is the mist strain of Ni on Cu), and it is omputed to b e ab out 16Å. This value agrees with the exp erimental result on Ni/Cu(001) system rep orted by Matthews and Crawford [1970℄ and Ingleeld et. al. [1993℄ 8 Eletron Beam Lithography (EBL) Figure 6: Pitures of the equipments used for patterning rings on Cu/Ni/Cu/Si(001) lms. (a) Spin oater and hot plate. (b) Helios 600 dual beam equipment. () Eletron gun evap orator from Eduards . (d) Ion milling equipment by Siste . using TEM tehnique. Eletron Beam Lithography (EBL) A serie of Cu(5 nm)/Ni ( tNi )/Cu (100nm)/Si(001) ( tNi = 10 - 16 nm) thin lms were patterned by a subtrative pro ess using eletron b eam lithography, eletron b eam evap oration, lift-o tehniques and ion-milling. The lithography pro ess was p erformed with a dual b eam Helios 600 system equipp ed with Raith lithography hardware. The fabriation was arried out in the INA and LMA lab oratories where the equipments are installed in a lass 10.000 lean ro om, an image of the instruments used is shown in Fig. 6. Rings in arrays with dierent external diameter and width were fabriated. The distribution of the elements in the matries and numb er of strutures p er matrix were heked in dierent ongurations in order to nd the optimum preparation pro edure improving the quality of the elements and to make the MFM exp eriments easier. Thus, b efore eah exp eriment the starting p oint was to reate the mo dels to b e designed by using the ELPHY program of Raith. The separate steps involved in the fabriation are detailed as follow: Eletron Beam Lithography (EBL) 9 PMMA Resists Si(100) Cu/Ni/Cu Figure 7: Shemati of Cu/Ni/Cu patterning layers, pre-lithography pro ess. e-Sensibilized resist Figure 8: Shemati of exp osure step by using a Dual Beam equipment provided with Raith lithography hardware.  Spin oating: The Cu/Ni/Cu//Si thin lms were overed with a double layer of e-b eam resist. The spin oating of a lm of 50 Kg/mol p olymethylmetharylate (PMMA) resin (Allresist AR-P 639.04) at 2000 r.p.m. for 20 seonds to form a ≈ 120 nm thik layer. The sample was then soft baked for 10 minutes at 120 ◦ C on hot plate. A seond oated lm of 950 Kg/mol PMMA (AR-P 679.04) at 4000 r.p.m. for 20 seonds to form a ≈ 270 nm thik layer. One more, the sample was soft baked for 10 minutes at 120 o C on hot plate to remove exess solvents and prepare it for exp osure.  Eletron b eam writing: The designs are diretly dened by the sanning eletron b eam, then the resist is hemially mo died due to the energy dep osited from the eletron b eam. As the resist used is p ositive, the rings areas are sensibilized. The delivered dose area was 99 µ C/m 2 at 10 kV aelerating voltage and b eam urrent of ≈ 80 pA (see sketh in Fig. 8).  Develop: The energy dep osited during the exp osure reates a latent image that is materialized during hemial development. For p ositive resists, the development eliminates the patterned area. The exp osed sample was develop ed with AR 600-56 develop er for 30 s with a soft agitation followed for stopping in isopropil alohol for 30 seonds. A piture at this p oint pro ess is shown in Fig. 9.  Hard mask evap oration: After de development, a double metal layer was grown to protet the nanostrutures of the ion-milling pro ess. Both layers were grown by eletron b eam evap oration in a high vauum hamb er at a base pressure of 2×10−7 mbar. A hromium lm of 5 nm is 10 Eletron Beam Lithography (EBL) 10 µm 500 nm Figure 9: Shemati of the result of the development step (left) and orresp onding SEM images of an example of a p ost-development sample (right). Cr Al Figure 10: Shemati of the metal hard mask evap oration onto the patterned rings. dep osited for improving the adhesion followed by 14 nm of Aluminium, the rate of dep osition of the two layers was 1.3 Ao /s (see Fig. 10).  Lift-o: This pro edure was arried out by submerging the sample in N-Methyl-2-pyrrolidone (NMP) solution at 75 o C for more than 2 hours and a quik ultrasoni bath. When the sample is immersed in NMP, the areas with resist b ehind the Cr/Al are removed.  Ion-milling: The sample is intro dued in an ion ething equipment where Argon ions impinge on the sample to remove the Ni unproteted areas with the Cr/Al hard mask. An eletron neutralizer gun is used b efore arriving the ions at the sample, making this pro ess softer to the surfae. The Ar pressure was 4.7 ×10−4 mbar and the milling rate was 10 nm/min for 2 minutes. Figure 13 shows examples of dierent patterned strutures fabriated along this thesis. (a) AFM image of a row of a matrix with 3 µ m external diameter and widths ranging from 130 to 540 nm. The top ographi and magneti images of a matrix of rings with 3 µ m external diameter and width = 900 nm are shown in Figs. 13 (b) and (), resp etively. In Fig. 13 (d), a tridimentional AFM image of one of the rings plotted in pane (b) is shown. Finally, magneti ontrast is observed only on the surfae of the ring indiating that the Ni layer out-side was removed with the ion-milling pro ess. Eletron Beam Lithography (EBL) 11 10 µm Figure 11: Shemati (left) and SEM image (right) of the Cu/Ni/Cu patterned rings overed with a Cu/Al double lm. Ar+ 10 µm Figure 12: Shemati (left) and SEM image (right) of the Cu/Ni/Cu patterned rings with a well dened prole due to the lak of the magneti layer in the surrounding area. 3 µm 3 µm (a) (b) (c) (d) (e) Figure 13: Examples of the patterned strutures and MFM haraterization. (a) Rings of 3 µ m external diameter and dierent widths. (b) and (), Matrix of rings of 3 µ m external diameter and MFM images, resp etively. (d) and (e), AFM and MFM image of a ring of the matrix shown in (b). Referenes I [1℄ J. Ehigoya, H. Enoki, T. Satoh, and T. Waki, Appl. Surf. Si. 56 , 463 (1992). [2℄ C. S. Liu, L. J. Chen, Appl. Surf. Si. 92 , 84 (1996). [3℄ Chin-An Chang, Joye C. Liu, and Joseph Angilello, Appl. Phys. Lett. 57 , 2239 (1990). [4℄ B. G. Demzyk, R. Naik, G. Auner, C. Kota, and U. Rao, J. Appl. Phys. 75 , 1956 (1994). [5℄ I. Hashim, B. Park, and H. A. Atwater, Appl. Phys. Lett. 63 , 2833 (1993). [6℄ R. A. Lukaszew, Y. Sheng, C. Uher, and R. Clarke, Appl. Phys. Lett. 76 , 724 (2000). [7℄ E. Ingleeld, Mist aommodation in thin lms of Ni/Cu as measured by magneti anisotropy, Ph.D. Thesis MIT (1995). [8℄ Chin-An Chang, J. Appl. Phys. 67 , 566 (1990). [9℄ J. W. Mattews and J. L. Crawford, Thin solid lms 5 , 187 (1970). X-ray haraterization 21 44 46 48 50 52 54 56 10 -3 10 -2 10 -1 10 0 10 1 10 2 10 3 10 4 s s Ni (200) N=4 N=3 N=2 Log i n t ensit y (arb. u n i ts) 2Theta (Degrees) N=1 Ni bulk Cu (200) s Figure 17: X-ray diration sans as a funtion of the numb er of Ni blo ks for [Ni(4 nm)/Cu(3 nm)℄xN strutures. The sup erlattie peaks are marked with s. The lattie p erio diity give rise to satellites aompanying the reetions of the average lattie parameter at p ositions in reipro al spae determined by the length Λ of the rep etition unit [4℄. The Λ value an b e diretly measured from the distane in the reipro al spae b etween the low-k satellite at −2π Λ ( k1 ) and its high-k satellite at +2π Λ ( k2 ) around the main Bragg p eak, so that[4℄ Λ = 4π k2−k1 (2) with k=4πsin θ λ (3) Then, the total numb er of planes in one bilayer is given by n=Λ p= Λ ×kBragg(200) 2π (4) where p is the averaged lattie parameter. By onsidering the Ni layers, the measured and alulated 2 θ p ositions, k Bragg values, p erio d and numb er of planes of a bilayer for the two strutures studied are presented in Table 1. 22 X-ray haraterization 48 50 52 54 56 Peak X position Peak height Peak width Peak area 2 Theta (deg) Peaks = 5 Shape = Pearson Error = 1.3868 1 48.737 2.25652 2.54887 3.18218 2 50.3845 6.04154 2.86111 9.56534 3 51.6412 2.47684 1.72703 2.3671 4 52.8986 3.27123 2.29808 4.16 5 54.3174 1.58241 1.68218 1.47294 Log intensity (arb. units) Exp. Fit Figure 18: Example of using an interative p eak tter program on a x-ray diration pattern for a sample with tN i = 40 Åand N=2. The onditions used for the adjustment are presented to o. X-ray haraterization 23 N 2 θ ( kBragg) 2 θ ( k1) 2 θ ( k2)kBragg k1k2ΛExp ΛCal n (deg) (deg) (deg) (Å −1 ) (Å −1 ) (Å −1 ) (Å) (Å) 1 53.3 2 53.15 51.04 54.79 3.65 3.51 3.75 60 52.58 30.54 3 52.95 51.17 54.72 3.63 3.52 3.74 60 55.55 32.15 4 53.14 51.21 54.71 3.64 3.52 3.74 60 56.35 32.72 5 52.93 51.07 54.82 3.63 3.51 3.75 60 52.59 30.42 Ni=40 Å 1 52.86 2 52.85 51.3 54.2 3.63 3.53 3.71 70 67.94 39.25 3 52.83 51.85 54.23 3.62 3.53 3.71 70 68.43 39.52 4 52.71 51.36 54.21 3.62 3.53 3.71 70 69.15 39.85 Table 1: Exp erimental 2 θ p ositions of the Ni(200) Bragg p eaks and parameters alulated by using Eqs. 2, 3, 4. N is the numb er of bilayers, n is the total numb er of planes, Λ exp eriment or alulated. 2345 50 55 60 65 70 75 Ni = 30 Ni = 40 B ila y e r th ick n e s s ( ) Number of Ni blocks Nominal thicknesses Figure 19: Bilayer thiknesses as a funtion of the numb er of Ni blo ks for multilayer with tN i = 30 and 40 Å. The nominal thikness values for b oth system are indiate with the dash lines. 24 X-ray haraterization Thus, from the values presented in Table 1, it is observed that the p erio d of the sup erlattie with [Ni(3 nm)/Cu(3 nm)℄ blo ks is in average ≈ 9 % smaller that the nominal value. This dierene is smaller for the [Ni(3 nm)/Cu(4 nm)℄ struture, where Λ has an average value of the ≈ 2 % lower than the nominal one. The data are plotted in Fig.19. Note that these deviation b etween the exp erimental and the nominal values of Λ translated to monolayer units means a variation in the average thiknesses of around 1 or 2 monolayers. Finally, in b oth series satellite p eaks lo oks to b e present at 2θ values smaller that the 2θCu p eaks. For example by omparing N = 1 and 3 sp etra of Figs. 16 and 17, the additional reetions around 2θ around 48 degrees b eomes more dened for N = 3. Large order satellites app ear if the variation of the omp osition of the bilayer is sharp b eause more higher orders in the Fourier o eients are neessary in repro duing omp ositionally abrupt proles. We note the large bakground due to the Cu buer layer preludes a full t of the sup erlattie exp erimental prole. Now the average p erp endiular strain is obtained by using the approximation that the value of the lattie parameters in the nikel and opp er layers is homogeneous and follow a step funtion. Therefore the sattering amplitude due to the opp er and nikel lattie do not interfere and, for strutures with a low numb er of rep eats, the maximum due to a single layer of Ni is very lose to the maximum obtained after multiplying that funtion with the term due to the sup erlattie p erio d. Therefore the out-of-plane lattie parameter and the average strain values, using the Ni bulk lattie parameter as referene, is alulated by using the 2 θ p ositions of the p eaks in the XRD patterns with the following expressions: a⊥ave =2λ sin θ (5) and the Ni out-of-plane strain: ǫ⊥=a⊥ave −aNibulk aNibulk , (6) The a⊥ave and ǫ⊥ values obtained for b oth strutures are listed in Table 2. In addition, in Fig. 20 the results for ǫ⊥ are plotted. In general, ǫ⊥ inreases with the numb er of bilayers indiating that the Ni lattie is getting relaxed. For the tNi = 3nm strutures there is a lineal dep endene up to N = 3 and the ǫ⊥ values hange from -2.5 % to -1.9 % while for the series with tNi = 4 nm the deformation is stable up to N = 3 with values around -1.7 % and then at N = 4 it inreases to -1.5 % . These results also reveal that the in-plane strain for strutures with tNi = 3 nm is larger than for the strutures with tNi = 4 nm. X-ray haraterization 25 12345 -0,025 -0,020 -0,015 Ni = 3nm Ni = 4nm Ou t-o fpla ne s tra in Number of Ni blocks Figure 20: Out-of-plane strain as a funtion of the numb er of Ni blo ks for multilayers with tN i = 30 and 40 Å. N a⊥ave (Å) a⊥ave (Å) strain⊥strain⊥ Ni 3 nm Ni 4 nm Ni 3 nm Ni 4 nm 1 3.43 3.46 -0.025 -0.017 2 3.44 3.46 -0.022 -0.017 3 3.45 3.46 -0.019 -0.017 4 3.44 3.47 -0.022 -0.015 5 3.45 -0.019 Table 2: Average p erp endiular lattie parameters and the alulated p erp endiular strain values for [Ni( tN i )/Cu(3 nm)℄xN strutures with tN i = 3 nm and 4 nm. 26 Magneti Properties -1 0 1 N= 1 (a) -1 0 1 (b) N= 2 -1 0 1 (c) N= 3 -1 0 1 M a g n e t i z a t i o n (N o r m a l i z e d ) (d) N= 4 -1000 -500 0 500 1000 -1 0 1 Per In -plane Applied field (Oe) (e) N= 5 Figure 21: Perp endiular and in-plane magnetization lo ops for Cu(1000Å)/[Ni(30Å)/Cu(30Å)℄xN strutures. The magnetization has been normalized to the saturation value Ms = 480 kA/m. The applied eld range is ± 15 kOe. Magneti Properties Volume Averaged Magnetometry The magneti prop erties have b een studied by means magnetometry and magneti fore mirosopy (MFM). Hysteresis lo ops with the magneti eld applied parallel and p erp endiular to the plane were measured for [Ni(3 nm)/Cu(3 nm)℄xN and [Ni(4 nm)/Cu(3 nm)℄xN strutures, the results are plotted in Figs. 21 and 22, resp etively. In b oth ases the sup erlatties show a lear p erp endiular magneti anisotropy with a large remanene of the out-of-the plane lo ops. For the strutures with tNi = 3 nm, at N = 1 and N = 2 the remanene ( Mr ) and the saturation ( Ms ) magnetization are equivalent, then Magneti Properties 27 -1 0 1 (a) Per In -plane M a g n e t i z a ti o n ( N o r m a l i z e d ) N= 1 (b) -1 0 1 N= 2 -1 0 1 (c) Applied Field (Oe) N= 3 -1000 -500 0 500 1000 -1 0 1 (d) N= 4 Figure 22: Perp endiular and in-plane magnetization lo ops for Cu(1000Å)/[Ni(40Å)/Cu(30Å)℄xN strutures. The magnetization has b een normalized to the saturation value Ms = 480 kA/m. The applied eld range is ± 15 kOe. for N = 3 Mr = 0.97 Ms , for N = 4 Mr = 0.9 Ms and, for N = 5 Mr = 0.78 Ms . On the other hand, the strutures with tNi = 4 nm up to N = 3 have similar Mr = 0.95 Ms values while for N = 4 Mr = 0.17 Ms . The eetive magneti anisotropy onstant, Keff is estimated from the dierene b etween the free energy of magnetization lo ops arried out in the lm plane and p erp endiular to the lm surfae. The in-plane lo ops were taken with H applied along the Ni[010℄ in-plane diretion. To eliminate the eet of hysteresis in the M(H) lo ops, we have used the anhystereti M(H) urve: for a value of M, the two orresp onding values of H, taken from the inreasing and dereasing eld branhes of the M(H) lo op, are averaged. Thus, Keff is p ositive in all ases and dereases as the numb er of layers N. For the strutures with tNi = 3 nm the alulated values are: for N = 1 Keff = 89 kJ/m 3 , for N = 2 Keff = 73 kJ/m 3 , for N = 3 Keff = 44 kJ/m 3 , for N = 4 Keff = 44 kJ/m 3 , and for N = 5 Keff = 39 kJ/m 3 . On the other hand, for the strutures 28 Magneti Properties 1 2 3 4 5 0 20 40 60 80 Ni3nm Ni4nm K eff (kJ / m 3 ) Number of layers Figure 23: Eetive magneti anisotropy onstants estimated from the anhystereti magnetization urves as a funtion of the Ni blo ks numb er for multilayers with tN i = 3 nm and 4 nm. with tNi = 40 Å the alulated values are: for N=1 Keff = 79 kJ/m 3 , for N = 2 Keff = 70 kJ/m 3 , for N = 3 Keff = 59 kJ/m 3 , and for N = 4 Keff = 6.5 kJ/m 3 . Figure 23 displays these values so that b oth strutures with dierent Ni thiknesses an b e ompared. The lo ops show that the o erive eld, Hc , also dereases as the numb er of layers inrease, this dep endene is shown in Fig. 24 . The larger values of the reverse and o erive eld are observed for the single Ni blo k strutures.The measured values for the sup erlatties with tNi = 3 nm are: N = 1 Hc = 130 Oe, N = 2 Hc = 128 Oe, N = 3 Hc = 105 Oe, N = 4 Hc = 85 Oe and N = 5 Hc = 97 Oe. For the sup erlatties with tNi = 4 nm are: N = 1 Hc = 237 Oe, N = 2 Hc = 135 Oe, N = 3, Hc = 148 Oe and N = 4 Hc = 131 Oe. Magneti Domain Struture A deep er analysis of the magneti domain ongurations involved in the hysteresis lo ops is obtained by means of magneti fore mirosopy. Figure 25 shows MFM images taken at the virgin state for the [Ni( tNi )/Cu(3 nm)℄xN ( tNi = 3 nm and 4 nm) strutures with N = 2, 3, 4 and 5. The images were taken at onstant height sans over the lm surfae. The samples were demagnetized by applying a p erp endiular magneti eld. The distane b etween tip and lm was redued to improve the signal noise ratio up to a value where the top ography signal did not overome the magneti one or the magneti tip did not mo dies the domain struture. An estimation of the p erio d of the MFM images (i.e.,twie the domain size) was obtained from the prole of the self- orrelation transform of the MFM images[23 ℄. The set of images show learly Magneti Properties 29 1 2 3 4 5 80 120 160 200 240 Ni3nm Ni4nm H c (O e ) Number of layers Figure 24: Co erive eld for [Ni( tN i )/Cu(30 nm)℄xN strutures with tN i = 3 nm and 4 nm strutures vs the number of Ni blo ks. that the mean domain size D dereases as N inreases and thus D is virtually innity for N = 1 but b eomes measurable for the rest of lms b eing 1.5, 1, 0.45 and 0.3 µ m for the N = 2, 3, 4 and 5, resp etively, and Ni blo ks with tNi = 3 nm. For the blo ks with tNi = 4 nm, the average sizes are: 1.1, 0.7 and 0.3 µ m for N = 2, 3 and 4, resp etively. Notie that the N = 4 and 5 strutures show the formation of a maze domain struture. This transition from a state of virtual mono domain state to a multidomain state an b e explained by the derement of the demagnetization energy due to the dip olar interation b etween the Ni blo ks, therefore a larger numb er of domain walls an b e generated in the lms resulting in smaller value of D . Figure 27 shows eld dep endent MFM images taken in the struture [Ni(3 nm)/Cu(3 nm)℄x4 with the magneti eld applied p erp endiular to the lm plane. The domain pattern for eah H value is marked with an arrow on the p erp endiular hysteresis lo op. Notie that the inversion magnetization pro ess is taken plae through the nuleation of small bubbles and strip es (Fig. 27(b)), then they grow up (from Fig. 27() to Fig. 27(h)) and at the end near the saturation, some bubble domains are observed (Fig. 27(i)). In order to quantify the magneti energy of the domain strutures observed, two ontributions to the total energy are onsider: the magnetostati energy, ems , originating from the p oles at the interfaes b etween the Ni layers and the Cu layers, and the wall energy of the domain walls b etween neighb ouring domains, ew . Thus, we have used the expression of ems given by H. J. G. Draaisma and W. J. M. de Jonge[14 ℄: 30 Magneti Properties (a) (b) (c) (d) (e) (f) (g) Figure 25: MFM images for [Ni( tN i )/Cu(3 nm)℄xN strutures. In (a - d) tN i = 3 nm and (e - g) with tN i = 4 nm, for dierent N values. Notie that the sales are not the same. 2 3 4 5 0 1 2 [Ni(t Ni )/Cu(3nm)]xN D o m ain w id th ( m ) Number of Ni blocks t Ni = 4 nm t Ni = 3 nm Figure 26: Average domain size vs. N dep endene for the series with tN i = 3 nm and 4 nm. Coerivity in thin films 37 Figure 30: Burger vetor of one 60 o mist dislo ation. Coerive fore The mehanisms involved in the inversion of the M in nanostrutures that onsist of magneti blo ks separated by a non magneti spaer systems have manifold eets in their magneti prop erties. In strutures with in-plane magnetization, the dip olar oupling b etween DW survive large distanes b eause the magneti eld generated by the domain walls an b e large and favours a oupling b etween blo ks in the nanostruture. The result is the dereasing of Hc [12℄ in multilayers with resp et to the single lm, the dereasing of the remanene of the hard magneti layer by rep eated swithing of the soft magneti layer [13 ℄, sharp drops in resistane at Hc in trilayers [14℄ and dynamis of magneti domain wall motion in the soft eletro de of a trilayer [15 ℄. Therefore, the mehanisms involved in the inversion of the magnetization in nanostrutures whih may b e forming one of the funtional blo ks in a magneti struture show up as an imp ortant issue b eause the DWs interat with a spinp olarized urrent. Besides the tehnologial relevane of the knowledge of Hc , basi issues are b ehind the displaement of the DWs sine they are an example of fore-driven transitions that inludes harge-density waves in eletri eld, sup erondutors with large urrents, plasti-forming pro ess or earthquakes [16℄. Co erive fore in Ni/Cu/Ni bilayers In this setion the dep endene of Hc with the tNi is presented for several series of Ni/Cu/Ni bilayers and Ni lms. Figure 31 shows the variation of Hc with tNi in a series of Cu/Ni/Cu lms. A strong inrement for tNi ranging from 1.5 to 3.5 nm is observed, with Hc hanging from 100 Oe for tNi = 2 nm up to ab out 220 Oe for tNi = 4nm, while 38 Coerivity in thin films 0 2 4 6 8 0 100 200 Cu/Ni/Cu fil ms Ni/Cu wedge C o erc iv e F ield ( O e ) Ni Thickness (nm) Figure 31: Co erive fore as a funtion of tN i in a Ni wedge and in a series of Cu/Ni/Cu lms for larger thiknesses Hc remains roughly onstant. The same trend has b een observed previously [17℄ in Ni lms grown on Cu single rystal. The larger values of Hc found in the Cu/Ni/Cu trilayers an b e asso iated with the larger numb er of defets that are present in the 100 nm thik Cu seed layer ompared with a Cu single rystal after a standard preparation (ion milling and annealing yles) for thin lm grown in ultra high vauum environment. The variation of Hc with the tCu spaer in the double lms with tNi = 3 nm is shown in Fig. 32. From tCu = 0 to tCu = 1 nm, Hc,s dereases from ∼ 220 Oe to 125 Oe while for tCu > 1 nm, Hc,s do es not dep end of tCu and lo oks to take a value ∼ 130 Oe. A similar trend is observed for the in-plane strain measured by grazing inidene X-ray diration. Sine the anisotropy onstant K is prop ortional to the lm strain state, after Eq. (13 ) the generation of mist dislo ation an mo dify Hc diretly as a defet that pin the domain wall, and indiretly by mo difying the domain wall size δp∼(K/A)1/2 . Thus, Hc is ompared in strutures with similar values of p erp endiular magneti anisotropy. Figures 21 and 22 display out-of-plane M(H) lo ops taken for lms and double lms with tNi = 3 and 4 nm and tCu = 3 nm. All the lo ops show large remanene indiating that the Ni strutures have an out-of plane easy axis. For these strutures, the p erp endiular anisotropy onstant Kp is p ositive with Kp,s(4nm) = 2.2 10 5 J/m 3 and Kp,d(4nm) = 2.0 10 5 J/m 3 ; Kp,s(3nm) = 2.3 10 5 J/m 3 and Kp,d(3nm) = 2.1 10 5 J/m 3 . This fat suggests that δp should b e approximately onstant. Disussion 39 0 3 6 0.015 0.020 Cu thickness (nm) Strain 120 150 180 210 Coercive Field (Oe) Figure 32: Hc and in-plane strain for a series of Ni/Cu/Ni layers as a funtion of tCu Hc shows remarkable dierenes: for the strutures with tNi = 3 nm Hc≈ 120 ± 5 Oe, while if tNi = 4 nm, Hc is muh larger for the single lm ( Hc =220 ± 20 Oe) than for the double lm ( Hc = 130 ± 5 Oe). The lak of inrement of a quantity usually asso iated to the inrement of the density of defets (threading dislo ations) suggests that the preparation pro ess inhibits the propagation of dislo ations through the seond Ni blo k. On the other side, the presene δp app ears in Eq. (12) and (13) may also reveal the presene of a magneti mehanism that mo dies the interation range b etween defet and domain wall. Disussion To justify the use of the rigid wall approximation and Eq. 13 , it is onsider that the small value of the nikel layers prelude the formation of signiant b owing p erp endiular DW plane. Also, in plastially deformed single rystal of Ni [18℄, it has b een shown that in the low defet range investigated in this pap er, Hc∝ρ1/2 holds. Thus, the expression given in Eq. 13 is used to disuss the observed b ehaviour of Hc . 40 Disussion Figure 33: Geometry and initial onguration used to alulate the DW width Domain Wall Width First, we disuss the variation of δ in single and double lms to determine Hc . The redution of Hc in p ermalloy-silion multilayers with resp et to the value observed in the thin lms [12℄ has b een qualitatively explained attending to the nuleation of oupled Néel DW in double lms, with lower energy and larger width than the Blo h DW existing in single lms [19, 20℄. The domain walls struture in Ni nanostrutures is estimated using a Landau-Lifshitz-Gilb ert miromagneti solver [21℄. A retangular element (with dimensions Lx = 1000 nm and Ly = 400 nm) with p erio di b oundary onditions along the x diretion. Typial Ni material parameters were used: saturation magnetization Ms = 4.90 10 5 A/m and A = 0.8 10 −5 J/m, while Kp = 2.2 10 5 J/m 3 , a value within the range of the exp erimental values obtained for the strutures studied here. The element, divided in two domains with p erp endiular M and a entral strip, orresp onding to the DW, is set with random orientations of M, see Fig. 33. This onguration is used as the starting p oint in the simulation. Sine the DW volume is small ompared with volume of the simulation sp eimen and do es not move from the initial p osition, the dereasing magneti energy δE an b e assigned to a hange in the domain wall energy. One the DW is stable ∆ , we dene its thikness as δ = 2 ∆ , where ∆ is the distane from the enter of the DW to the p oints at whih Mz is 90% of the saturation value in eah domain. Figure 34.(a) shows the variation of δ for Ni and Ni/Cu(3 nm)/Ni strutures as a funtion of nikel blo k thikness. The domain wall width dereases as tNi inreases for lms and tends to a onstant value in the ase of the double lms. The alulation of δ shows dierenes for single and double lms: δ is larger for the double lms than for the single lms ab ove tNi ≈ 3 nm, although the hange is size is minute, 2 nm for tNi = 4 nm, less than 5%. The energy of these DWs for strutures with nikel blo ks thiknesses smaller than 4 nm is in the range of 4.5 mJ/m 2 , Disussion 41 Domain wall width (nm) Nickel thickness (nm) Figure 34: Domain wall width for Ni lms (squares) and Ni/Cu/Ni strutures (irles) smaller that the theoreti value obtained for a Blo h wall ( ∼ 6 mJ/m 2 ). Thus, although the domain width dereases in double lms with resp et to the single lm values, that variation lo oks to b e small to justify the observed derement of Hc . Dislo ations in thin lms In thin lms, the relaxation of the epitaxial strain is asso iated to the glide of threading dislo ations at the interfae b etween two materials: existing dislo- ations of the substrate initially moves to the surfae without altering the seed struture and lattie parameter, but ab ove a ritial thikness tc the dislo ation line moves parallel to the interfae, adding or taking out a plane of the thin lm that faes a substrate plane, see Fig. 35. As a result, the averaged elasti energy of the lm dereases and a linear defet is intro dued into the thin lm [22℄. Magnetially, inreasing the density of linear dislo ations brings ab out an inreasing of the o erivity. In Fig. 31 the dep endene of the o erive eld vs. the thikness of a nikel lm grown on a Cu(001) single rystal shows that ab ove tc , Hc learly inreases reahing a relatively stable value; the low value of Hc for tNi < tc indiates the high p erfetion of the Cu(001) substrate. For the system under study, a hetero epitaxial Cu-Ni struture with a mist η = 0.025, the ritial thikness for the generation of mist dislo ations is 1.3 nm for unapp ed Ni lms and ab out 2.7 for lms with a apping layer. Therefore, ℓ in Eq. (13) inludes mist ℓm and threading ℓth segments and 42 Disussion (a) (b) Threading dislocation Misfit dislocation Figure 35: Generation of a mist dislo ation segment from a dislo ation line that initially extends from one sp eimen surfae to the other. Cu Cu Cu Ni Ni as bs cs ad bd cd Figure 36: Sketh for the three dierent senarious for the propagation of a threading dislo ation in single and double Ni lms. b oth of them an pin the domain wall. While ℓth go es with the total lm thikness, Lz b eause the dislo ation has to end at the lm surfae, ℓth may b e dierent dep ending on the layer struture:  Large strain without mist dislo ations (see Fig 36 ase a). If the strain relaxation is small, ℓth >> ℓm and the ratio ℓth/Lz will not hange if the lm struture is doubled. Therefore Hc remains with the value due to defets existing in the opp er buer layer and transmitted to the Ni/Cu/Ni struture and Hc (single) = Hc (double). The generation of mist dislo ations to relax the elasti energy of the lm is a omplex issue. Here we only intro due the extreme situations.  Relaxation by single kinks (see Fig 36 ase b). In this ase MD app ear only in the rst Ni-Cu interfae. The interfaes of the seond Ni lms do es not undergo es the propagation of the dislo ation along the interfae, see Fig. 35 , also if ℓmd >> ℓth the pinnig of the wall in the single and double lm is done by the same defet, and b eause the domain wall in two times larger in the double lm we have Hc (single)= Hc (double)/ √2 . Disussion 43 If ℓth is dierent at the interfaes of the seond Ni blo k by a fator γ < 2, ρs=γρd and the Hc ratio will b e equal to √γ .  Relaxation by double kinks (see Fig 36 ase ). Here symmetri distributions of MD are at the Cu-Ni interfaes. In this ase, segments in b oth lms are idential and doubling the domain area also doubles the dislo ation length, Hc (single)= Hc (double). The single-kink mo del implies the apping layer aquires some strain (of the opp osite sign to the layer) whereas the double-kink mo del implies the apping blo k remains unstrained. We note that the 4 nm thik Ni lm is strongly distorted, the opp er grown on top of a layer with a lattie parameter quite lose to the Cu bulk value implying small gain in elasti energy that may b e not large enough to favors the formation of double kinks. Thus, the next layer of Ni grows onto a Cu layer with smaller lattie parameter than the bulk value, b eause this layer of opp er is not ompletely relaxed, and the ritial thikness for the formation of MD inreases. Comparing this mo del with with the exp erimental values, for tNi = 3nm, Hc (single)/ Hc (double) = 1 while for tNi = 4 nm Hc (single)/ Hc (double) = 1.5, lose to √2 . This mo del yields that for the latter strutures the distribution of MD is asymmetri and dominates the pinning mehanism while for the strutures with 3 nm thik Ni blo ks the dislo ation segments have similar struture for the Ni blo k. Referenes I I [1℄ H. Hellwig, T. L. Kirk, J. B. Kortright, A. Berger, and E. E. Fullerton, Nature Mater. 2 , 112 (2003). [2℄ S. Mangin, D. Ravelosona, J. A. Katine, M. J. Carey, B. D. Terris, and E. E. Fullerton, Nature Mat. 5 , 210 (2006). [3℄ Mathlab Referene Guide (Math lab, 2010). [4℄ A. Segmüller and A. E. Blakeslee, J. Appl. Cryst. 6 , 19 (1973). [5℄ D. Navas, C. Nam, D. Velazquez, and C. A. Ross, Phys. Rev. B 81 , 224439 (2010). [6℄ H. J. G. Draaisma and W. J. M. de Jonge, J. Appl. Phys. 62 , 3318 (1987). [7℄ H. Barkhausen, Phys. Z 20 , 401 (1919). [8℄ G. Bertotti, Hysteresis in Magnetism (Aademi press, 1998). [9℄ H. Hilzinger and H. Kronmüller, J. Mag. Mag. Mat. 2 , 11 (1976). [10℄ L. J. Dijkstra and C. Wert, Phys. Rev. 79 , 979 (1950). [11℄ R. Labush, Crys. Latt. Def. 1 , 1 (1969). [12℄ H. Clow, Nature 194 , 1035 (1962). [13℄ L. Thomas, M. G. Samant, and S. S. P. Parkin, Phys. Rev. Lett. 84 , 1816 (2000). [14℄ W. S. Lew, S. P. Li, L. Lop ez-Diaz, D. C. Hatton, and J. A. C. Bland, Phys. Rev. Lett. 90 , 217201 (2003). [15℄ K. Fukumoto, W. Kuh, J. Vogel, F. Romanens, S. Pizzini, J. Camarero, M. Bonm, and J. Kirshner, Phys. Rev. Lett. 96 , 097204 (2006). [16℄ D. S. Fisher, Phys. Rep. 301 , 113 (1998). [17℄ W. L. O'Brien, T. Droubay, and B. P. Tonner, Phys. Rev. B 54 , 9297 (1996). [18℄ H. Rieger, Phys. Stat. Sol. 8 , 755 (1965). 46 Referenes I I [19℄ J. C. Slonzewski, J. Appl. Phys. 37 , 1268 (1966). [20℄ E. Feldtkeller, J. Appl. Phys. 39 , 1181 (1968). [21℄ M. Donahue and D. Porter, OOMMF Users Guide, Version 1.0 (National Institute of Standards and Tehnology, Gaithersburg, 1998). [22℄ J. H. Matthews, Phil. Mag. 13 , 1207 (1966). General features and magneti ontrast for tF e < 4ML 53 General features and magneti ontrast for tFe < 4ML The LEED patterns shown in Fig. 40(b) and () were taken at dierent p ositions of the iron wedge. The patterns in Fig. 40 (a) and () orresp ond to f and b  phases, while the pattern displayed in Fig. 40 (b), taken at an intermediate distane, shows a mix of b (110) and f(100) strutures revealing that the eletron b eam reovered information from dierent thiknesses on the wedge b eause the width of the LEED e-b eam (typially 1 µ m). The omplexity of the pattern shown in Fig.40 () has b een explained as the result of the arrangements of the b  struture on f (110) substrates [10, 11, 13℄ with the Pitsh orientational relationship in whih rows of nearest-neighb or atoms are mathed b etween {011} b  and {001} f planes [10℄. Thus, it is found that the Fe < 111 > diretion mathes the < 110 > Cu axis and four dierent variants an b e observed. Fig. 38 shows the orresp onding variants for the (110)Fe plane on (001)Cu: [110℄ bcc k [1 ¯ 1 1℄ fcc , [1 ¯ 1 0℄ bcc k [ ¯ 1 11℄ fcc , [1 ¯ 1 0℄ bcc k [ ¯ 1 11℄ fcc and [110℄ bcc k [ ¯ 1 11℄ fcc . Figure 40 displays a sketh of the reipro al lattie of a Fe lm on a Cu(001) surfae showing the [110℄ bcck [1 ¯ 1 1℄ fcc variant as it was rep orted by M. Wuttig et al [11℄. The ellipses represent the p ositions of the LEED b eams. Op en and lled ellipses distinguish the remaining variants. Moreover, in the LEED images the ontrast bakground indiates a low range order of the surfae. Figure 41 shows the SEM image and SEMPA vertial and horizontal p olarization omp onent images for the whole Fe wedge. The SEMPA images show no ontrast on the left half of the image exept for a wire in the vertial hannel. The lak of ontrast in this region indiates p erp endiular magnetization of the iron lm. The thikness of the iron lm, tF e , along the wedge was alulated based on the magneti ontrast observed and taken into aount a onstant ux of dep osition of iron on the opp er. Thus, based on previous results for the onset of the out-of-plane to in-plane spin reorientation [7, 9, 10 ℄, we have taken 11 ML for the x o ordinate where the magneti ontrast shows up in Fig. 41(b) and (). Another interesting fat is the observation of dierent ontrast in the SEM images parallel to the shutter edge (see Fig. 41 (a) and Fig. 45). Those dierenes in the ontrast ould orresp ond to the onset of the iron layer and the existene of b  and f rystal strutures whih will b e 54 General features and magneti ontrast for tF e < 4ML (c) (a) (b) (d) Figure 40: LEED patterns for lean Cu (100)(a) and Fe (b) and () lms with inreasing thikness. The diration patterns orresp ond with a mix of a f (100) and b  (110) phases, and a more dened b  (110) phase, in (b) and () respetively. (E= 233 eV).(d) Sketh from the Wuttig's artile. disussed later. A strip with magneti signal inside a non-magneti area is observed only in the vertial p olarization omp onent, see Fig. 41(b), for tF e b etween ≈ 1.6 and 2.3 ML forming a single domain struture. The domain is along one of the in-plane < 001 > diretions, whih is the easy axis of magnetization in Fe bulk. The width of the line is 5µm . We note that, for iron lms in this range of thiknesses, in-plane magnetization has not b een rep orted for Fe lms grown by thermal dep osition (TD), although the magneti phase diagram as a funtion of the growth temp erature rep orted by D. Liu et al [5℄ shows a weakening of the p erp endiular anisotropy for temp eratures larger than ro om temp erature. The presene of that strip an b e understo o d onsidering the work of O. Portmann et al. [18℄. This group has rep orted an anomalous variation of Tc with tF e for small values of tF e : Tc p eaks at tF e = 2.1 ML with a value of ≈ 320 K, b eing 1.8 ML the threshold of thikness for with whih Tc> = 300 K (see Fig. 2(a) of Portmann's referene). We note that the interval of tF e for whih Tc is larger than ro om temp erature rep orted in the ab ove referene is in exellent agreement with the values alulated for the strip observed in Fig. 41. However, an imp ortant fat in the magneti b ehavior of this system is related with dierent regimes regarding the strutural prop erties for Fe lms General features and magneti ontrast for tF e < 4ML 55 Figure 41: Magneti domain struture on a Fe wedge. (a) SEM image on the same region as in (b) and (). The SEMPA images show the distribution of the (b) vertial and () horizontal p olarization omp onents. (d) and (e) display the histogram of p olarization of the strip region (1) and in-plane domains region (2), resp etively. The p olarization values are 1 % in (d) and 2.6 % in (e). grown at ro om temp erature [7 , 9, 12℄. Although in general there is a onsensus ab out the rystallographi struture for lms thiker than 4ML, for thinner Fe lms the strutural prop erties seem to b e strongly dep endent on the growing onditions and tehnique used, providing lms with dierent magneti b ehavior [16, 20℄: M in-plane for lms grown by PLD and p erp endiular for lms with grown by thermal evap oration. Therefore, the o urrene of a ferromagneti island with in-plane ontrast inside of a paramagneti sea ould b e explained for small variations of the strutural prop erties of the Fe lms. We observe a redution of the spin p olarization on the iron lms, thus, the SEMPA p olarization value of the strip is 1% [see Fig. 41 (d)℄ inreasing up to 2.6 % at larger thikness [see Fig. 41 (e)℄. These values are omparable with those obtained by T. Bernhard et at [7℄ for equivalent thikness. In fat, it was found that the p olarization value saturates at ≈ 17 ML of Fe thikness. The loss of spin p olarization has b een observed for Fe lms with in-plane magnetization by D. P. Pappas et al. [5℄, and Allenspah et al. [3℄. In b oth 56 General features and magneti ontrast for tF e < 4ML ases, the in plane magnetization in Fe/Cu (001) lms saturates at ≈ 35% of the bulk value, whih is onsiderably lower than the p erp endiular p olarization of ab out ≈50% [5℄. On the one hand, Pappas et al., have argued that the derement of the spin p olarization would b e onsistent with a redution of ≈25% of the magneti moment in this range of tF e , where the value of Tc is onsiderably smaller that the bulk value. On the other hand, Allenspah et al. disagree with the last laim and suggest that the redued remanene magnetization, Mr , is a onsequene of the strutural transition from a tetragonally distorted to a more omplex phase. Figure 42: SEMPA domain images after three days on the same region as in Fig. 41. The strip breaks into big domains oriented on the [010] diretion. In addition, after three days, the strip e in Fig. 41 breaks into big domains oriented on the [010] diretion as it is shown in Figure 42. Notie that, the domains are visible in b oth hannels and the signal is even stronger in the parallel one. The width of the line is 7.2 µm and the domain size (vertial white zone) is ∼ 30 µm . These elongated domains in one diretion suggest an anisotropy within the lm plane. Time dep endent magnetization has b een observed b efore in Fe strip es grown on Cu (111) [21℄ where the remanent magnetization after saturating the sample deays slowly. However, the reasons why the single domain state is broken at lower iron thikness after some days is still unlear for us and may involve a weak ontamination of the sample by residual gases of UHV hamb ers. Spin Reorientation Transition, Fe films ( tF e > 11 ML) 57 Spin Reorientation Transition, Fe films ( tFe > 11 ML) Figure 43 shows a general view of the magneti domain struture for a Fe wedge with thiknesses ranging from ≈ 11 to 20 monolayers from the left to the right. It is lear that the domain size inreases with tF e . The histogram of p olarization shows that there is a preferred orientation of the M that ould b e understo o d if an uniaxial magneti anisotropy is present in the lm. Notie that, in this ase the radius of the SEMPA spin p olarization is 3 % , a larger value than that observed for the strip. 10 µm 10 µm abc Figure 43: In plane magneti domains of a Fe wedge. The thikness is inreasing from the left to the right (from ≈ 11 ML to 20 ML). (a) Perpendiular and (b) parallel SEMPA magnetization omp onents. () Histogram of the spin p olarization. Figure 44 shows the domain struture for a region near the transition from p erp endiular to in-plane magnetization with tF e b etween ≈ 11-13 ML. The domains are forming entwined ribb ons with M in antiparallel orientation b etween neighb or domains. The average domain size is 670 nm and 1350 nm for the vertial and horizontal omp onent, resp etively. The histogram of p olarization suggests the presene of an uniaxial magneti anisotropy. Remarkably, this nding ould b e explained as the result of the weakening of the p erp endiular anisotropy and the generation of a anted domain struture with alternating in-plane omp onents from the strip e domain struture; nevertheless magnetization measurements show that the spin reorientation transition is not mediated with intermediate orientation of M . On the other hand, on the region with the uniaxial anisotropy, the lose 58 Spin Reorientation Transition, Fe films ( tF e > 11 ML) 2 µm 2 µm 2 µm Figure 44: Domain pattern near the transition region at tF e ≈ 12-13 ML. The upp er plots orresp ond with the vertial, on the left, and horizontal, on the right, p olarization omp onents. The lower plots are: the in-plane magnetization pattern, on the left, and the histogram of the spin p olarization, on the right. examination of the SEM images reveal a orrelation b etween the struture and the magneti images. Bak-sattered eletron, Fig. 45 (a), and seondary eletron images, Fig. 45(b) and (e), show areas with two dierent tones at the transition region where the f to b  phase transformation takes plae. Notie that the ontrast is inverted in these images. The seondary eletron image were olleted with the in-lens detetor detetor(BSE) that shows dierenes in the work funtion (e.g., eletroni variations) on the sample with high lateral resolution. The ontrast in Fig. 45(b) was enhaned to highlight the shap e of the areas with dierent ontrast and establishes a orrelation b etween the top ographi and the magneti images. A more detailed view of a p ortion of the last image is shown in Fig. 45(e) where the dark lines are forming 90 degrees Spin Reorientation Transition, Fe films ( tF e > 11 ML) 59 45 degrees with the horizontal, see arrows. The magneti ontrast in Fig. 45(f ) and (g) follows the same orientation that the features observed in the SEM image, although the size of the magneti domain is larger. This shows the strong relation b etween the rystallographi phases and the magneti domain struture of Fe lms on the transition region. 2 µm e cd a 1 µm b f g Figure 45: Contrast phases and magnetism of Fe lms on Cu(100). (a) SEM image on the transition region using bak-sattered eletrons. (b) and (e) SEM images using seondary eletrons. ( - d) and (f -g) magneti domain mirostruture in the same region as in (b) and (e), respetively. Fourfold symmetry is observed in the SEMPA histogram when tF e in- reases, as it is shown for tF e ≈ 14-15 ML in Fig. 46. In this ase the domains follow a preferential alignment at around 45 degrees with the horizontal line 60 Spin Reorientation Transition, Fe films ( tF e > 11 ML) 2 µm 2 µm 2 µm Figure 46: In-plane Fe domains show fourfold symmetry at tFe≈ 14-15 ML. The upp er plots orresp ond with the vertial, on the left, and horizontal, on the right, p olarization omp onents. The lower plots are the in-plane magnetization pattern, on the left, and the histogram of the spin polarization, on the right. that orresp onds to the < 110 > Cu diretion, and further, taking into aount the rystallographi orientation of the Fe variants (Fig. 38), to the < 111 > or < 11 ¯ 2> b  Fe diretions. The sign of the magneto rystalline anisotropy onstant ( K1>0 ) indiates that these diretions are magnetially hard while the < 100 > diretion is the one of minimal energy. The angles that form < 100 > Fe and < 110 > Cu diretions are 55o , and 35o , dep ending on the variant onsidered (see Fig. 38). Therefore, another magneti anisotropy lo oks to b e present in iron lm. In addition, by evaluating the magneti domain dimensions in Fig. 44 and Fig. 46, we note that the domain dimensions hange their values with tF e . For the image taken at the p osition with thinner iron layer (Fig. 44 ), the typial values for the vertial and horizontal dimensions are 670 nm and 1350 nm , Magnetoelasti Model 61 resp etively, while, for the thiker region (Fig. 46), the average sizes are 1600 nm and 670 nm for the vertial and horizontal omp onents. The radius of spin p olarization is ≈1.8% in b oth ases. Magnetoelasti Model To justify the use of the ME energy for this system we disuss the presene of residual strain in the Fe(110) layer. The o urrene of the orientation relationships b etween the Cu(001) and Fe(110) planes is obtained using the onept of invariant line than orresp onds to a rystal line that remains unrotated and unstrethed during a rystal transformation [10, 22℄. For the Cu-Fe system the invariant line orresp onds to < 111 > diretions. Thus, along a < 111 > diretion of the unit ell the atoms of Fe and Cu are aligned, see sketh Fig. 38. This mathing intro dues a shear strain in the Fe layers along the < 111 > diretion as is observed by the measurement of the angle b etween the two < 111 > diretion lo ated in the (110) plane done by grazing sattering of fast H and He atoms or ions [7℄ and LEED [11 ℄. The strain b eomes anisotropi in the Fe(110) unit ell and inside eah variant but, from the p oint of view of the whole Fe lm, it has a fourfold symmetry b eause the distortion in the b  domains is linked to the Cu(100) plane. The mist b etween Cu[110℄ and Fe [111℄ is 2.7%, meaning that a thin iron lm will expand along this diretion to adapt itself to the Cu lattie. The inverse magneto elasti eet suggests that this [111℄ diretion b eomes a magnetially hard diretion sine the magneto elasti stress is p ositive [21℄ (i.e., M moves to the ompressed diretion), as it is shown b elow. To desrib e the ME ontribution to the total anisotropy energy eanis in eah rystallite forming the iron lm, due to the strain, we start onsidering the ME energy for a ubi symmetry, given by: emel =B1α2 z−1 3ǫzz −ǫxx +ǫyy 2+1 2α2 x−α2 y(ǫxx −ǫyy) + 2B2(αxαyǫxy +αyαzǫyz +αzαxǫzx) (14) First term on Eq. 14 is equal to zero, while for a shear strain along the [111℄ diretion ǫxy =ǫyz =ǫzx =ǫ0 . Then, the ME ontribution to magneti anisotropy energy an b e written as: emel = 2B2ǫ0(αxαy+αyαz+αzαx) (15) 62 Magnetoelasti Model x y z M ! "! Figure 47: Cartesian o ordinate axes and ( ¯ 1¯ 1 0) plane ( φ = 45 degrees). With this eletion the shear strain is applied along the [111] diretion For the (110) b  lm, M lays the lm plane, and the angular dep endene of emel an b e obtained pro jeting emel to the lm plane (¯ 1¯ 10) where M forms an angle θ with the [001℄ diretion, see Fig. 47. Thus, the diretion osines of M are obtained by xing φ = 45 o : αx=√2 2sin θ αy=√2 2sin θ (16) αz= cos θ Then, emel an b e expressed as: emel = 2Bǫ,2ǫ0 1 2sin2θ+√2 2sin 2θ! (17) Figure 48 displays the angular dep endene of emel/2B2ǫ0 , with B2ǫ0 p ositive, showing a lear uniaxial harater. The minima are found at θ≈ −57.5o and 122.5o , values that orresp ond to the [11¯ 2] diretions, i.e., p erp endiular to the invariant [111] axis, along whih the distortions happ en. We now ompare 2Bǫ,2ǫ0 with K1 . For iron K1= 5.2 × 10 4 J/m 3 , Bǫ,2 = 7.6 × 10 6 J/m 3 [25℄, therefore for values of ǫ0< 0.01 a spin reorientation ould b e IV. Strutural and Magneti Properties of Fe/Cu/Ni Films 69 Introdution The study of ultrathin lms on single-rystal substrates has ontributed greatly towards the understanding of surfae and interfae magnetism. By prop erly ho osing the substrate, lm thikness, and growth onditions, dierent rystalline phases of a magneti material an b e formed [1, 2℄. These systems are a very attrative eld b eause of the strong orrelation b etween small hanges in the epitaxial lm struture and magneti prop erties [3℄. The metastable f strutures of Fe have b een studied on dierent substrates. In partiular, two ferromagneti substrates with similar lattie parameters, f Co(001) and Ni(001) have b een used. The interest is based on investigate how the magneti moment of the substrates may inuene the magneti moment of the lm. By using LEED idential surfae unit ells of the three substrates were seen. Thus, it was found that the regions of dierent magneti b ehavior of Fe for growth on Co or Ni nearly oinide with the regions of dierent rystal struture for Fe growth on Cu. This is strong evidene that Fe has the same growth mo de on Cu(001), Co(001), and Ni(001) [1, 4℄. While Fe lms on Cu(001) are strethed in-plane sine the Cu lattie parameter ( aCu = 3.62 Å) is larger than that of f Fe ( afcc−F e = 3.59 Å), Fe lms on Ni(001)( aNi = 3.52 Å) are ompressed in-plane, and therefore the details of the atomi struture and magneti b ehavior are exp eted to b e dierent in the two systems [3℄. The surfae anisotropy favors the p erp endiular magnetization in Fe/Cu(001) lms for thiknesses less than 2 nm [5℄. On the other hand, Ni lms with thiknesses b etween 2 and 12 nm have out-ofplane magnetization whih arise from the fae-entered-tetragonal (ft) distorted rystal struture of Ni on Cu(001). The ombination of b oth Fe and Ni makes the oupled system an interesting ase to study the relation b etween the struture, magnetism, and oupling phenomena of Fe/Ni bilayers on Cu(001) [6℄. At present a few investigations have b een done in this system regarding to stru- tural and magneti prop erties using exp erimental tehniques suh as: spinp olarized low-energy eletron mirosopy (SPLEEM) [6℄, magneto-opti Kerr eet(MOKE) [7℄, low energy eletron diration (LEED) [3, 7℄, primary-b eam diration mo dulated eletron emission (PDMEE) [3, 4℄, photo emission ele- tron mirosopy (PEEM) [8, 9 ℄, x-ray magneti irular dihroism (XMCD) [1 ℄. As far as the magnetism onerns, most of the studies have b een done at the 70 Introdution (a) (b) (c) (d) (e) (f) Figure 49: RHEED patterns: for the Cu buer layer along the (a)[100℄ and (b)[110℄ diretions, for the Ni layer along the () [100℄ and (d) [110℄ diretions, and for the Cu apping layer along the (e) [100℄ and (f ) [110℄ diretions. rst spin-reorientation transition (SRT) of the Ni system, i.e., around Ni thiknesses of 2 nm in ombination with Fe layer thiknesses less than 2 nm. To the b est of our knowledge, however, no investigation on the eet of Fe layers on top of the Cu/Ni/Cu/Si system for Ni layers thiknesses near the seond SRT o urring at ab out 12 nm has b een done so far. In the present hapter, the strutural and magneti prop erties of Cu(5 nm) / Fe( tF e ) / Cu(5 nm) / Ni(10 nm) / Cu(100 nm) / Si(001) multilayers with tF e = 1, 2 and 4 nm are presented. The growth was ontrolled in situ using reexion high energy eletron diration (RHEED) and the strutural prop erties ex situ by x-ray reetivity (XRR), x-ray diration (XRD) and high resolution transmission eletron mirosopy (HRTEM). On the other hand, the magneti prop erties were measured by vibrating sample magnetometry (VSM), sup er- onduting quantum interferene devie magnetometry (SQUID) and magneti fore mirosopy (MFM). Growth and in-situ haraterization 71 Growth and in-situ haraterization Cu(5 nm)/ tF e /Cu(5 nm)/Ni(10 nm)/Cu(100 nm) multilayers were grown by eletron-b eam evap oration and using a high temp erature Knudsen ell on Si(100) substrates at ro om temp erature in ultra high vauum following a similar pro edure as the desrib ed in hapter 1. The Fe layer thikness, tF e , ranged from 1 to 4 nm. The rates of evap oration were ontrolled by using a quartz rystal monitor and a ux monitor, for the eletron b eam evap orator and the eusion ell, resp etively. Thus, the rates were 0.02 nm/s for nikel and opp er, and 0.008 nm/s for the iron layer (e-ell). The pressure during dep osition was not higher than 1 ×10−8 Torr. At the same time as the growth the samples were rotating 360o at a onstant velo ity for, on one hand, to get a high homogeneity over the whole surfae, and on the other hand, in order to study the full azimuthal dep endene of the RHEED patterns. 45o 0o 40o 35o30o 20o[110] [100] Figure 50: RHEED patterns taken for an iron layer with tF e = 2 nm along the angles and in b etween 45 to 0 degrees that orresp ond with the Cu [100℄ and Cu [110℄ azimuth diretions, resp etively. Figure 49 shows the RHEED patterns taken at the [100℄ and [110℄ azimuth 72 Growth and in-situ haraterization 0 50 100 150 200 250 300 Intensity (arb. units) X (pixeles) X= 2p/aCu[100] tFe=0,16nm tFe=1nm [100] (a) (b) (c) Figure 51: RHEED patterns taken for (a) tF e = 0.16 nm and (b) tF e = 1 nm. Proles on (a) and (b) are shown in (). The distane b etween two p eaks is 2 π / aCu[100] . diretions for opp er buer layer, the Ni lm and the 5 nm thik Cu layer prior to the growth of the iron layer. Figure 50 shows RHEED images taken along the [100℄ and [110℄ opp er azimuth diretions and, in b etween, at dierent angles for an iron lm of 2 nm of thikness. Note that we have hosen the Cu[110℄ azimuth diretion at 0 degrees. In omparison with the images in Fig. 49, the growth of an iron layer on top of the Cu/Ni/Cu system lead to unusual RHEED patterns. The relevant features in Fig. 50 are revealed from 30 to 45 degrees, where additional streaks app ear indiating a dierent mathing b etween the Fe and Cu/Ni/Cu rystal latties. Notie that the streak at 30 degrees (marked with an arrow) is hanging its p osition turning to the left on the pattern as the angle is inreasing from 0 to 45 degrees. At 45 degrees the pattern displays a splitting of the main streaks suggesting that the mist of the Fe lattie is present prinipally in the Cu [100℄ azimuth diretion. In order to study in detail the Fe growth pro esses dep endent on the thikness, in steps of 0.16 nm during the preparation of a lm with tF e = 4 nm, the evap oration was stopp ed and the whole angular variation of the RHEED pattern was reorded. Thus, the initial growth orresp onds with a well ordered f surfae with RHEED patterns that remain with the same struture and symmetries that the underlying Cu and Ni layers [see Fig. 51 (a)℄ b eing the ratio b etween the distanes determined from the images that san the [100℄ and [110℄ diretions ≈ 1.41, a value that indiates the observation of a square Bravais lattie. Then, at ab out tF e = 1 nm, broad and diuse streaks show up along the Cu[100℄ diretion as it is shown in Fig. 51 (b). Here, we observe a variation of the in-plane lattie parameter on the [100℄ diretion in Growth and in-situ haraterization 73 -40o -45o -50o -55o -60o -65o -70o -75o -80o -85o -90o -35o-30o-25o-20o -15o-10o-5o0o5o 10o15o20o25o30o 35o40o45o Figure 52: RHEED patterns dep endent on the surfae angle for a struture with tF e = 2 nm. 0 degrees orresp onds with the Cu [110℄ azimuth diretion. whih aF e is bigger than at the rst steps of the growth (less than 0.8 nm), this an b e seen by omparing the proles taken on the last patterns as in Fig. 51 (). Subsequently, the system keeps the same struture up to tF e = 1.44 nm. For larger values of tF e the images b eome more omplex suggesting the onset of the f to b  phase transformation. As desrib ed, in Fig. 52 the RHEED images for tF e = 2 nm in a omplete angular dep endene are shown. A fourfold symmetry of the rystal surfae is observed with patterns that are repro duible eah 90 degrees. By omparing these images with those showed in Fig. 50 for a lm with an equivalent thikness but dierent time of growth, the presene of wide sp ots in the rst one are indiating a surfae rougher than that grown ontinuously, probably as a onsequene of the stopping of the evap oration b eam. In theory, the RHEED patterns onsist of p oints resulting from the intersetion of the Ewald sphere with the ro ds of the 2D reipro al lattie. Due to the imp erfetion of the RHEED apparatus-angular and energy spread of the primary eletron b eam, and of the terraes of nite length, the RHEED patterns exhibit straight lines. Consequently, the b etter the qualities of the apparatus and the surfae are, the shorter the length of the straight line on the RHEED patterns. Therefore, by omparing the images presented 74 Growth and in-situ haraterization 0 10 20 30 40 50 80 90 100 110 D is ta nc e (pix e ls ) Angle (degrees) Figure 53: Variation of the in-plane lattie parameter with the angle on the surfae for the RHEED patterns shown in Fig. 52. in Figs. 49 and 50, longer streaks are observed in the last one revealing that the Fe apping layer is growing with a surfae formed by strutural domains or sup erstrutures. Notie that all the RHEED images shown in this hapter have the same dimensions. The distanes b etween the streaks in the RHEED patterns (see Fig. 52) were measured in order to have an idea ab out the variation of the lattie parameter with the angle. Thus, as it is shown in the plot in Fig. 53, there is not variation of the in-plane lattie onstant from 0 to 20 degrees, while at bigger angles it inreases almost linearly. By taking as a referene the distane b etween the streaks in the Cu buer layer (in Fig. 49) and assuming the value of the bulk Cu lattie parameter, we have alulated that the in-plane lattie onstants of the Fe layer are: aF e[110] = 4.99 and aF e[100] = 3.73 . These values demonstrate an in the plane expansion of the Fe f lattie (aF e,fcc = 3.58 ) . Finally, at tF e = 4 nm, the struture observed is basially the same although the images show o a tridimensional growth that is revealed for the presene of a sp otty diration pattern (see Fig. 54). In addition, the splitting of the streaks on the Cu[100℄ azimuth diretion displayed b efore is getting more and more dened with a variation of the angles in b etween as it is shown in Fig. 54 (b). Thus, we found that the tilt angle of the bifurations with resp et to the vertial are ≈ 6 degrees in b oth ases, at tF e = 2 and 4 nm. These results are onsistent with the exp eted epitaxial relationships for similar systems [2℄. The RHEED observations an b e explained by taking into aount the invariant line ondition for a b (110) lm grown on a f(100) substrate and state the optimum mathing b etween two rystal planes at an interfae is ahieved when there is at least one diretion along whih the two Ex-situ haraterization 75 0o45o 6,3o 6,2o [110] [100] Figure 54: RHEED patterns of an iron lm with 4 nm of thikness. The images were taken along the (a) Cu[110℄ and (b) Cu[100℄ azimuth. rystals math p erfetly on the interfae [10℄. Therefore, not variation is noted along the Cu[110℄ azimuth diretion and thus, we an onlude this is the invariant-line diretion. After the Fe growth the sample was overed with 5 nm of Cu in order to protet it from the oxidation. The RHEED patterns at this step orresp ond with remanent rough surfae that mainly follows the Fe surfae lattie. Ex-situ haraterization Strutural prop erties X-ray reetivity (XRR) and X-ray diration exp eriments were arried out by using a HRXRD Bruker D8 Advane with the Kα radiation of the Cu ( λ = 1.54056 Å). The XRR patterns were simulated with LEPTOS program so that the thiknesses and the roughness of the lms were obtained. X-ray reetivity measurements were done immediately after removing the samples from high vauum, in order to determine the Fe layer thiknesses as it is shown in Fig. 55. For omparison, the reetivity pattern for a Cu(5 nm) / Ni(10 nm) / Cu(100 nm) multilayer and the t p erformed are presented in Fig. 55(a). In this ase, the amplitude of the osillations is redued at 2 degrees, indiating an inrease of the roughness at the interfaes. The thiknesses for the simulation are well orrelated with the thiknesses exp eted. In Fig. 55 (b) a small variation in the p erio diity of the osillations is observed b etween ≈ 1.6 and 2.4 degrees due to the presene of a thinner iron layer. In Figs. 55 () and (d) two osillation frequenies are revealed as a result of the inreasing 76 Ex-situ haraterization Exp Fit 2 (degrees) L o g in ten s i ty (a r b .u n its) Fe= 4nm Fe= 2nm (d) (c) (b) Fe= 1nm 1234 (a) W ithout Fe Figure 55: Exp erimental and simulated x-ray reetivity sp etra of Cu/ tF e /Cu/Ni/Cu multilayers with tF e ranging from 0 to 4 nm. Fe thikness, giving rise to a bilayer b ehavior, i.e., the Fe and Ni/Cu layers. These osillation frequenies are not observed in Ni/Cu layer due to the small dierene of their eletroni densities. At tF e = 2 nm, the osillations are extended up to ≈ 3.5, degrees showing that the roughness at the surfae is redued. This result onrms the RHEED diration patterns, where long strutural oherene on the surfae is shown. Also, there is a go o d adjustment of the osillations b etween the exp eriment and the t. Nevertheless, at 2.5 degrees the urve was not well followed by the simulation probably due to the presene of additional strutural domains on the surfae that were not intro due in the tting program. When the thikness is inreased at tF e = 4 nm, the bilayer osillations are b etter dened and the roughness is higher than at tF e = 2 nm, here the presene of additional rystal strutures is lear. In general, the reetivity observations are in agreement with the results rep orted from RHEED. Symmetrial θ - 2 θ x-ray sans as a funtion of the Fe thiknesses are shown Ex-situ haraterization 77 40 45 50 55 60 Fe 0nm Fe 1nm Fe 2nm Fe 4nm Cu (200) 2 (degrees) Fe (110) Ni (200) L o g in te n s ity ( a r b .u n its ) Figure 56: X-ray diration sans as a funtion of the Fe layer thikness for a Cu/Fe/Cu/Ni/Cu struture. For omparison the diration pattern for a sample without Fe is presented. in Fig. 56. The presene of the 200 reetion from the Ni lm near the [200℄ Bragg p eak from the Cu buer layer onrms its epitaxial growth. Thus, the out-of-the plane lattie parameter is aNi = 3.48 Åand orresp onds with a strain ǫ⊥ = -1.136 % . The Fe p eak is observed at tF e = 2 and 4 nm. Notie that the 2 θ p osition of the p eak is hanging with the thikness, thus as tF e inreases the lattie parameter is going towards the bulk Fe b  (110) value ( aF e−bcc[110] = 4.058 ). From the XRD patterns, at tF e = 2 nm, aF e,⊥= 3.9446 giving a strain value of ǫ⊥=−2.81% , and at tF e = 4 nm, aF e,⊥= 4.018 giving a strain value of ǫ⊥=−0.98% , with resp et aF e−bulk . These results show that at tF e = 2 nm the lattie is expanded in-plane to adapt itself to the Cu/Ni/Cu struture and as a result the p erp endiular parameter is ompressed, reveling that the Fe lattie is an intermediate region b etween a f and a b  struture. While at tF e = 4 nm the rystal struture is governed by the b (110) lattie, at tF e = 1 nm, we note the lak of an iron p eak indiating that for this thiknesses the f(100) lattie grows epitaxially on the Cu/Ni/Cu struture and its ontribution to the diration pattern an b e overlapp ed by the Cu(200) p eak. In order to omplement the diration tehniques that average the volume of the sample, a nanostrutural haraterization of a Cu(100 nm) / Ni(10 nm)/ Cu(5 nm) / Fe(2 nm) / Cu(5 nm) struture has b een arried out by means 78 Ex-situ haraterization Cu fcc Fe fcc Cu fcc Growth direction (c) (200) (220) fcc (200) (d) Cu fcc Fe bcc Cu fcc Growth direction (e) Cu(200)+Fe(110) Fe (200) (220) fcc (200) + bcc (110) (f) Cu Ni Cu Cu Fe Growth direction (200) (220) (a) Ni Figure 57: HRTEM images of a Cu(100 nm)/Ni(10 nm)/Cu(5 nm)/Fe(2 nm)/Cu(5 nm) multilayer. (a) Low magniation ross-setional image of the full system and its orresp onding FFT pattern. (b) FFT patterns for dierent regions on the multilayer as an b e identify by the numb ers. () High resolution image for a Fe(200) k Cu(200) area. (e) High resolution image for a Fe(110) k Cu(200) area. (d) and (f ) FFT patterns for the regions shown in () and (d), resp etively. of High Resolution Transmission Eletron Mirosopy (HRTEM) using a FEITitan Cub e mirosop e equipp ed with a CETCOR Csob jetive orretor and op erated at 300 kV (p oint to p oint resolution of 0.08 nm). The Fast Fourier Transform (FFT) images were obtained by means Digital Mirograph software. Figure 57 (a) shows a low magniation rosssetional image of the Cu/Fe/Cu/Ni/Cu region of the struture. The inset shows the FFT of the full image with diration sp ots that orresp ond with the { 200 } and { 110 } family of planes of the epitaxial f Cu/Ni/Cu struture. The inident eletron b eam is along the Cu[200℄ diretion. FFT images were made on dierent regions on the multilayer as it is presented in Fig. 57 (b). Note that the numb ers are indiating a zone and its orresp onding FFT pattern. The diration images Conlusions 85 Conlusions RHEED, XRR, XRD and HRTEM exp erimental results have shown that the Fe growing on a Cu/Ni/Cu struture an b e divided in three dierent ases. Firstly, down tF e = 2 nm where a Fe f(200) k Cu/Ni/Cu f(200) epitaxial relationship was observed. Seondly, in b etween tF e = 2 and 3 nm where the o existene b etween Fe f(200) and b (100) grains k Cu/Ni/Cu f(200) was demonstrated. Finally, for tF e = 4 nm or tiker, in whih ase the b  struture is the dominant one aording to the XRD patterns. The eet of the Fe thiknesses on the p erp endiular anisotropy of a Cu / Ni(10 nm) / Cu was studied. We found that the strong magnetostati energy of the iron layer is unable to overlap the p erp endiular anisotropy of the Ni layer due to the fat that the remanene magnetization do es not hange signiantly. Nevertheless, as tF e inreases the in-plane magnetization is favored. 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Owens, and Z. Q. Qiu, Phys. Rev. Lett. 98 , 207205 (2007). [10℄ M. Kato, S. Fukase, A. Sato, and T. Mori, Ata metall. Vol.34, No.7, 1179-1188 (1986). [11℄ M. Kato, M. Wada, A. Sato, and T. Mori, Ata metall. Vol.37, No.3, 749-756 (1989). [12℄ G. Bo hi, H. J. Hug, D. I. Paul, B. Stiefel, a. Moser, I. Parashikov, H.-J. Günthero dt, and R. C. O'Handley, Phys. Rev. Lett. 75, 1839 (1995). [13℄ A. Suna, J. Appl. Phys. 59 , 313 (1986). [14℄ H. J. G. Draaisma and W. J. M. de Jonge, J. Appl. Phys. 62 , 3318 (1987). [15℄ K. Janika, J. D. Burton and E. Y. Tsymbal, J. Appl. Phys. 101 , 113921 (2007). [16℄ N. S. Kiselev, I. E. Dragunov, V. Neu, U. K. Rler, and A. N. Bogdanov J. Appl. Phys. 103, 043907 (2008). 88 Referenes IV [17℄ M. Tekielak, R. Gieniusz, M. Kisielewski, P. Mazalski, A. Maziewski, V. Zablotskii, F. Stobieki, B. Szymanski and R. Shafe J. Appl. Phys. 110, 043924 (2011). Chapter V Transverse Magnetization in Ni rings V. Transverse Magnetization in Ni rings 91 Introdution The strain state in a nanostrutured material has b eome a ne tuning parameter to ontrol physial prop erties as the exiton sp etra in semiondutor ZnO mirowires [1℄, the p olarization in ferro eletri materials [2℄, the ritial temp erature in sup erondutors [3℄ or the order temp erature in magneti lms [4℄. Another fundamental prop erty ontrolled by the strain state is the magneti anisotropy through the inverse magneto elasti (ME) eet: the strain state in the lm is oupled to the magneti lattie and the ME stress o eients re- et the strength of the spin-orbit oupling. Strain dep endene of the magneti anisotropy energy has b een observed in nikel lms grown on opp er [59℄, and other 3d metal lms (Co/Au [10 ℄), and alloys (like Ni 90 Fe 10 [11℄) as well as rare earth sup erlatties [12℄. For materials with low magnetization values, whih give rise to lms with low magnetostati energy, and ubi rystal struture that results in a feeble magneto rystalline anisotropy, the ontribution of the ME density energy eME an b e partiularly imp ortant if the residual strain omp onents are 1% and the ME oupling o eient is, at least, in the range of MPa. This senario is found for Ni grown epitaxially on the (001) diretion on top of Cu with a tetragonal distortion of the ubi lattie: the in-plane strain is isotropi ( εxx = εyy = εk ) and the out of the plain strain prop ortional to the in-plane values: ( εzz = ε⊥=−(2c12/c11)εk ), and all of them are around 1% for Ni lms as thik as 10 nm [13 ℄. The total anisotropy energy inludes the ME term eME =−B1(ǫk−ǫ⊥)cos2θ with B1 b eing a bulk ME o eient and Ms the saturation magnetization, with θ the angle b etween the lm normal ([001℄ (rystallographi diretion) and the magnetization vetor. A further step is the ontrol of the magneti anisotropy and domain ongurations in magneti elements with submiron lateral dimensions, as that is the sale for atual spintroni devies. Planar nanowires and nanorings have b een investigated b eause of their p otential use in domain-wall devies prop osed for data storage [14℄ and logi appliations [15 ℄. Most rep orted work has b een fo- used on elements with p olyrystalline rystal struture, whose prop erties are dominated by shap e anisotropy. The stable domain ongurations are 180 o transverse or vortex-like domain walls (DW) dep ending on the element dimension [16℄. The ring geometry presents two dierent stable states, usually alled 92 Introdution PMMA Resist (Cr/Al) mask evaporation Si(100) Cu/Ni/Cu E-beam writing Lift -off Ion milling with Argon Development eSpin coating (a) (b) (c) (f) (d) (e) Figure 63: Shemati representation of the patterning of Cu/Ni/Cu/Si lms by a subtrative pro ess using eletron b eam lithography and lift-o tehniques. vortex and onion states, whih an b e easily reahed by applying a magneti eld in the lm plane [17 ℄. However, materials with dierent domain states and DW geometries ould oer advantages in spintroni appliations, as is the ase of metalli planar NWs with p erp endiular magneti anisotropy whih exhibit enhaned spin-torque eieny and higher thermal stability ompared to those of NWs with in-plane anisotropy [18, 19℄. Therefore, developing metho ds for tuning the magneti anisotropy in nanomagnets may oer new opp ortunities for spintroni devies. In this hapter we rep ort the fabriation and observation of magneti domain ongurations that defy the magnetostati anisotropy in magneti nanorings made in epitaxial Cu/Ni/Cu lms with a nikel lm thikness in the range where the eetive p erp endiular anisotropy o eient is ≈ 0 and magneti ongurations asso iated with in-plane magneti anisotropies are exp eted. These rings were fabriated by subtrative pro essing of epitaxial Cu/Ni/Cu lm using via eletron b eam lithography ombined with ion b eam ething using a metalli hard mask. Eletron beam lithography 93 Eletron beam lithography Beause the the elimination of the native oxide would damage a mask prepared diretly on the substrate, patterned ring strutures have to b e fabriated by a subtrative pro ess. The pro edure used in this thesis inludes eletron b eam (e-b eam) lithography, e-b eam evap oration of a hard mask, lift-o tehniques and ion b eam ething. A shemati representation of the patterned pro ess is shown in Fig. 63. The Cu/Ni/Cu thin lms were oated with a double layer, 120 and 270 nm, of p olymethylmetharylate (PMMA) resin with moleular weights, 50 kg/mol and 950 kg/mol resp etively, baked separately for 10 minutes at 120 o C. Exp osures were p erformed at 10 kV aelerating voltage using a b eam urrent of ≈ 80 pA suh that the delivered dose was 99 µC/cm2 . The exp osed sample was develop ed with AR 600-56 develop er for 30 s with a soft agitation followed by a quenh in isopropyl alohol for 30 seonds, b oth steps at ro om temp erature. Figure 64(a) shows a SEM piture of a ring at this p oint in the pro ess. 1 m 1 m (a) (b) Figure 64: Sanning eletron mirosopy taken on a ring after (a)the lift-of and (b) ion b eam ething steps. After the development, in order to improve the sharpness of the rings and to protet the Ni layer during the ion b eam ething step, a Cr(5nm)/Al(14nm) hard mask was evap orated. The b ottom Cr blo k favors adhesion for the high sputtering yield layer of Al. Ion b eam ething using Ar ions removes the Ni layer outside the hard mask. The Ar pressure was 4×10−4 mbar and the 94 Eletron beam lithography milling rate ab out 10 nm/min. Pro essing the sample for 2 minutes pro dues strutures like the ring shown in Fig. 64(b). Figure 65: (a) Reipro al spae map in the viinity of the symmetrial nikel and opp er (002) reetion. (b) Hysteresis lo ops with H p erp endiular to the the plane and in-plane for the Cu/Ni/Cu lm. The seleted nikel lm thikness is in the range where the net magneti anisotropy undergo es reorientation and the easy diretion for the magnetization is moving from out of the plane to the in-plane diretions as tNi inreases. In this range of thiknesses the ME stress ontribution is omp ensated by the magnetostati term. For the Ni lm studied here the ε⊥ is ab out 0.96% as an b e alulated from the reipro al spae map taken around the (200) ree- tion, see Fig. 65(a). Therefore B1(ǫk−ǫ⊥)≈ 0.12 MJ/m 3 while (1/2)µ0M2≈ 0.14 MJ/m 3 . This fat is also observed in the minor dierenes b etween the in-plane and out of the plane M-H lo ops measured by Vibrating Sample Mag- Analysis 101 -500 0 500 1000 -0.05 0.00 0.05 Stra y F i el d Distance (nm) Figure 72: Stray eld alulated for a segment formed by dierent ombinations of in-plane and p erp endiular domains that generate a eld with qualitatively the same shap e. Magneto elasti Energy Previous works [22, 23℄ suggest the imp ortant role of the ME energy in determining the magneti onguration in nanowires b eause of the presene of residual strain in the wires. We note that for Cu/Ni/Cu nanowires the sign of the anisotropi strain relaxation in ombination with the sign of the ME stress o eients favor a transverse ME anisotropy [22℄. Here we analyze the ME ontribution for a ring with a line width of 250 nm assuming an averaged in-plane anisotropi strain value omparable to that measured for an array of nanowires with similar lm thikness and wire line width. The general theory for the ME eets [24 , 25℄ expresses the ME density of energy emel of the undistorted rystal as a series of pro duts of tensor strain omp onents and p olynomials of the diretion osines of the magnetization related to the o ordinate axes. For the Cartesian o ordinate system emel an b e written as: emel =Bγ,2α2 z−1 3ǫzz −ǫxx +ǫyy 2 +1 2α2 x−α2 y(ǫxx −ǫyy) + 2Bǫ,2(αxαyǫxy +αyαzǫyz +αzαxǫzx) (21) The numb er of indep endent rst-order ME o eients is redued to two ( Bγ,2 and Bǫ,2 that orresp ond to the usual B1 and B2 ME o eients [21℄). 102 Analysis From Eq. ( 21) it an b e dedued that dierent lattie deformations pro due dierent magnetization states that are governed by the same ME o eient. Thus, for the γ -terms, inside eah square braket strain p olynomials prop ortional to α2 z−1/3 orresp ond to a tetragonal distortion (a, a, a)→(c, a′, a′) that indues a hange in the orientation of the p erp endiular omp onent of M , while the seond strain terms, whih are multiplied by α2 x−α2 y , desrib e the ontribution due to the breaking of the in-plane symmetry (a, a)→(a′, b′) . The last ontribution is fundamental in nanowires sine the isotropi in-plane strain is broken by the patterning pro ess. It is more appropriate to desrib e the problem in the ylindrial o ordinate system b eause it reets the symmetry of the ring. The strain tensor omp onents in the ylindrial referene basis an b e obtained by p erforming the tensorial transformation for 2nd order tensors: ǫij =aikǫklalj where the subsripts stand for the tensor o ordinates; i , j are assigned to Cartesian omp onents ( x , y , z ) and k , l to the ylindrial system ( r , φ , z ). The a 's orresp ond to the transformation tensor: a11 =a22 =cosφ , a12 =−sinφ , a21 =sinφ , a33 = 1 , a13 =a31 =a23 =a32 = 0 , therefore: ǫxx =ǫrrcos2φ+ǫφφsin2φ−ǫrφsin2φ ǫyy =ǫrrsin2φ+ǫφφcos2φ+ǫrφsin2φ ǫzz =ǫzz ǫxy = (ǫrr −ǫφφ)sinφcosφ +ǫrφ cos2φ−cos2φ ǫyz =ǫrzcosφ −ǫφzsinφ ǫzx =ǫrzsinφ +ǫφzcosφ (22) and for the osines of the magnetization: αx=αrcosφ −αφsinφ αy=αrsinφ +αφcosφ αz=αz (23) Analysis 103 obtaining for emel emel =B1α2 z−1 3ǫzz −ǫrr +ǫφφ 2 +1 2α2 r−α2 φcos2φ−2αrαφsin2φ ×[(ǫrr −ǫφφ)cos2φ−2ǫrφsin2φ] +2B21 2sin2φα2 r−α2 φ+cos2φαrαφ ×1 2(ǫrr −ǫφφ)sin2φ+ǫrφcos2φ +ǫrz [αrsin2φ+αφcos2φ]αz +ǫφz [αrcos2φ−αφsin2φ]αz (24) Therefore the dierene in emel if M is tangent to the ring ( αr =0, αφ =1) and aligned along the radius ( αr =1, αφ =0) is : ∆emel =−B1cos22φ+B2sin22φ(ǫrr −ǫφφ) (25) The magnitude of this ontribution dep ends on the existene of an inequality b etween the radial ǫrr and the tangential strain ǫφφ . Notie that we have assumed that the shear strains are negligible. The presene of a ombination of the two ME stresses multiplying the strain p olynomial in Eq.( 25) ompliates the variation of the sign of this ontribution with φ . This funtion osillates b etween the values of B1 and B2 every π/2 and, thus, if the sign of the B′s is dierent, the sign of the ME ontribution to ∆emel would osillate with φ . For nikel b oth ME stress o eients are p ositive and the sign of angular dep endene of ∆emel do es not hange with φ , see Fig. 74 . Magnetostati Energy For the sake of simpliity we onsider the ase of a uniformly magnetized ring to estimate the magnetostati energy ems b eause the alulation of the expression inluding the dep endene of M with φ is extremely ompliated and the uniform M ase provides a simple analytial expression to alulate an upp er limit to ems . That expression is given by ems =DxxµoMs2/2 , where Dxx is he demagnetization fator for a ring with M along a xed diretion [16℄: Dxx =d 2π(1 −r)ln(8/d)−1 2+r r+ 1ln(r) −21 + r2 (1 + r)2F2rr (1 + r)+ 2E2rr (1 + r) (26) 104 Analysis 0.0 0.2 0.4 0.6 0.8 1.0 0.00 0.05 0.10 0.15 0.20 W Dxx Figure 73: Calulation of the redued demagnetization energy for D = 3 µ m as a funtion of normalized ring line width. here, Dxx denes the demagnetization fator for rings of outer radius Ro and line width ω with tNi ≪ω , b eing d=tNi/Ro , 1−r=ω/Ro=W and, F and E are omplete ellipti funtions of the rst and seond kind, resp etively. Fig. 73 shows the numerial solution of Eq. ( 26) for rings with R0 = 3 µ m. Thus, if ω= 250nm , Dxx = 0.036, and ems = 5.4 kJ/m 3 . There are no magneti p oles for a vortex state ( αr =0, αφ =1) and the magnetostati energy is zero, therefore ∆ems takes the upp er limit value of 5.4 kJ/m 3 . Magneto rystalline Energy The magneto rystalline anisotropy for ubi rystals for the lowest order is expressed as: emc =K1(αx2αy2+αy2αz2+αz2αx2) , b eoming: emc =K1h(αrcosφ −αφsinφ)2(αrsinφ +αφcosφ)2i, (27) in ylindrial o ordinates, using the Eqs.( 23). From the p oint of view of the magneto rystalline energy, there is a ost of keeping M along the radial diretion that dep ends on φ and an b e evaluated by putting αr =1, αφ =0 in Eq( 27). ∆emc =1 4K11−sin22φ (28) Notie that this ost is zero for φ=π/4 and maximum ( K1 /4) for φ= 0 . Disussion 105 Figure 74: Angular dep endene of ∆eanis(φ) for a ring with 3 µ m diameter, ω = 250 nm width, and ǫ of 0.003. The ∆e(φ)mel , ∆e(φ)mc and ∆e(φ)ms are also shown Disussion The energy balane ∆eanis(φ) for a ring with ω = 250 nm and an averaged ( ǫrr −ǫφφ ) of 0.003, a value in the range of the exp erimental data measured for wires with similar width and Ni thikness, is displayed in g 74 , taking B1 = 6.9 MPa, B2 = 8.9 MPa [26℄ and K1=−4.5×103J/m3 . ∆eanis(φ) is negative indep endently of φ , meaning that the radial orientation of M is favored over the tangential diretion for the omplete ring. It an b e observed that ∆emel(φ) is the largest ontribution to ∆eanis(φ) . The alulations show ∆eanis(φ) is kept at negative values even if ( ǫrr −ǫφφ ) dereases to values as low as 0.001. Therefore the radial orientation of M observed in epitaxial rings an b e attributed to the ME ontribution. Finite elements analysis Now we disuss the prole of the miromagneti struture of the thiker rings. We note that an anisotropy in the relaxation of the isotropi in plane strain of Ni lm ( ≈ 0.75% for the lm) is required to justify the radial anisotropy term. Also, the observation of a domain struture dierent inside the ring than at its edges suggest that (ǫrr −ǫφφ) an hange along the ring. To analyze this fat nite element analysis is arried out for the estimation of a strain relaxation in the trilayer Cu/Ni/Cu struture for rings with D and W parameters based on the initial stress of 1.95 GPa for the unpatterned Cu/Ni/Cu struture. The stress is intro dued by setting the Ni layer to a a temp erature at whih the thermal expansion of nikel with resp et to the opp er is equivalent to the exp erimental in-plane strain. An example of the stress distribution for a ring with D = 1 µ m and W = 500 nm is shown in Fig. 75. The image shows, 106 Disussion Figure 75: Snapshot of the nite element alulation of the σxx for a Cu(5)/Ni(14)/Cu(100) trilayer. for a ring quarter, the stress along the x Cartesian o ordinate, therefore it orresp onds to the radial stress along the x axis and the tangential stress for the y axis. From the graph straightforward onlusions are observed: a) σrr is more relaxed at the edges of the ring that at the enter; b) the σφφ is quite uniform although there is a slight relaxation a the inner ring area. As a result, the alulated (ǫrr −ǫφφ) is maximum at the edges and minimum at the ring enter. This strain dep endene an b e related to the dep endene of the domain struture: transverse for edge areas loser to the ring edges and similar to the unpattern lm for the inner area of the ring where, lo ally the strain relaxation is smaller and therefore (ǫrr −ǫφφ)≈ 0 and the tetragonal distortion [ǫz−(1/2) (ǫrr +ǫφφ)] remains with a value omparable to the lm value. Conlusions 107 Conlusions This work shows the relevane of the ME interation in the ontrol of the magneti state in nanomagnets. For example, magneti iruits made on epitaxial layers will inlude nanowires with the axes along dierent rystallographi diretions, onneted with irular segments. The orientation of the magnetization of those elements an b e hosen through the eletion of the sign for the ME stress o eients. Thus, materials with dierent sign of the B oer the p ossibility of ombining elements with these transverse magneti orientations with the usual longitudinal orientation of M enabling new ongurations of domain walls to b e reated. Epitaxial ring of Cu/Ni/Cu has b een fabriated by e-b eam and fo used ion b eam tehniques is range of thiknesses where the eetive magneti anisotropy in the unpatterned lm is ≈ 0. The miromagneti struture show an unusual orientation of the magnetization along the radial diretion of the ring. 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