Coexistence of glassy antiferromagnetism and giant magnetoresistance (GMR) in Fe/Cr multilayer structures N. Theodoropoulou and A. F. Hebard Department of Physics, University of Florida, Gainesville, FL 32611-8440 M. Gabay Laboratoire de Physique des Solides, Bat 510, Universite Paris-Sud, 91405 ORSAY Cedex, France A.K. Majumdar Department of Physics, Indian Institute of Technology, Kanpur-208016, India C. Pace, J. Lannon, and D. Temple MCNC, Electronics Technologies Division, Research Triangle Park, NC 27709 (Dated: May 8, 2002) Using temperature-dependent magnetoresistance and magnetization measurements on Fe/Cr mul- tilayers that exhibit pronounced giant magnetoresistance (GMR), we have found evidence for the presence of a glassy antiferromagnetic (GAF) phase. This phase reflects the influence of interlayer exchange coupling (IEC) at low temperature (T < 140K) and is characterized by a field-independent glassy transition temperature, Tg, together with irreversible behavior having logarithmic time de- pendence below a "de Almeida and Thouless" (AT) critical field line. At room temperature, where the GMR effect is still robust, IEC plays only a minor role, and it is the random potential vari- ations acting on the magnetic domains that are responsible for the antiparallel interlayer domain alignment. PACS numbers: 75.70.Pa Given the established presence of GMR-based devices atures random potential variations rather than IEC are in technology, especially in the multi-billion dollar com- responsible for antiparallel alignment. puter hard disk drive market, it may come as a surprise Our Fe/Cr multilayer samples have been prepared on that there is still an incomplete scientific understand- silicon substrates by ion beam sputter deposition of sepa- arXiv:cond-mat/0205112 v1 6 May 2002 ing of the GMR effect[1]. The mechanism for GMR, rate Fe and Cr targets. Extensive characterization of the first observed in single crystalline (100) Fe/Cr multilay- deposited multilayers showed distinct compositional and ers grown by molecular beam epitaxy[2, 3] and subse- structural modulations with well-defined interfaces and quently in magnetron-sputtered polycrystalline films[4], a surface roughness on the order of 5 A. Ten and thirty- relies on spin-dependent scattering[5] and the associated layer stacks with the repeat sequence [Fe(20 A)/Cr(dCr)] dependence of resistance on the relative orientations of are typically deposited and passivated with a 50 A-thick the magnetizations in neighboring layers. It is important Cr layer. The Cr spacer thickness dCr is varied over to recognize that interlayer exchange coupling (IEC) is the range 8­12 A. The inset of Fig. 1 shows typical GMR not necessarily required for a GMR effect[1]. In a partic- traces at 300K and 10K for the magnetic field parallel to ularly simple manifestation, two neighboring films, sepa- the planes of a [Fe(20 A)/Cr(12 A) ]×30 sample. rated by a non-magnetic spacer layer, could have differ- In Fig. 1 we show a selected subset of temperature- ent coercive fields, thus giving rise to antiparallel align- dependent field-cooled (FC, open symbols) and zero- ment and a GMR effect, as the external field is cycled[6]. field-cooled (ZFC, closed symbols) magnetization data Randomness[7, 8] and competing interactions such as for a thirty layer sample with dCr = 12 A and a GMR ra- biquadratic coupling[9, 10] can also play a significant tio ((R(0) - R(H))/R(0), Fig. 1 inset) of 20.6% at 10K. role. In this paper we identify a glassy antiferromag- The data were taken using a SQUID magnetometer in netic (GAF) phase which by marking the influence of fields (indicated on the plot) oriented parallel to the lay- IEC at low temperatures implies that at higher temper- ers. At each field the corresponding FC and ZFC curves 2 Tg is the spin glass temperature. Although other cri- teria could have been used[12], we note that our choice of Tm(H) as the criterion determining the AT line has particular cogency because it obeys the scaling form of the AT prediction and extrapolates at zero field to a field- independent glass temperature Tg = 1.51×Tinfl = 140K, where Tinfl, an apparent fixed point, has been inde- pendently determined from the FC data (dashed line of Fig. 1). An additional and essential ingredient for a glassy phase is the presence of disorder measured by the variance, J, in the antiferromagnetic (AF) coupling strengths. This variance arises because of the existence of domains and the concomitant constraints imposed by intralayer dipolar interactions The exchange energy be- tween two Fe moments separated by a spacer layer is of FIG. 1: Magnetization of a multilayer sample ([Fe(20 A)/Cr(12 A)]×30) normalized to the weight of iron the form E = JAF cos( ), where denotes their rel- plotted as a function of temperature at the indicated fields. ative angle. The intralayer domain structure imposes The data at each field are taken in pairs: the open(solid) sym- well-defined orientations of the spins and this constraint bols referring to the field-cooled, FC, (zero-field cooled, ZFC) will not be consistent, in general, with = (i.e. with a procedure. The vertical arrows and dashed line are described minimum value of E). Because of the long-range nature in the text. Inset, dependence of the giant magnetoresistance of dipolar interactions, lowering the exchange energy re- (GMR) ratio on applied field for the same film at 300K (left quires the overturning of one or of several clusters of Fe axis) and at 10K (right axis). moments, which is energetically inhibited at low temper- ature. In this regime, behaves like a pseudo random variable. A realistic estimate for J can be obtained by can be characterized by three distinct temperatures: an assuming a flat distribution for the values of on the [0, irreversibility temperature T 2 ] interval, leading to J = JAF / 2. At T > Tg, IEC irr(H) denoting the bifurca- tion point below which there is hysteresis (upward ar- is present but ineffective because the intralayer dipolar rows), a temperature T interactions dominate. m(H) (downward arrows) denot- ing the maximum in each of the ZFC curves, and an Many glassy systems, including the one discussed here, inflection temperature Tinfl (vertical dashed line) which marks the inflection point of each FC curve. Evidently Tinfl is quite robust and independent of field, having a value Tinfl = 93.0 ± 1.4K determined to relatively high precision from FC measurements at 5 different fields spanning the range 50-400 Oe. Compelling evidence for an interlayer rather than in- tralayer effect is found in the resistance measurements of Fig. 2 on the same sample. For each datum on this graph, the sample was zero-field cooled to the target temperature, the resistance R(0) measured, and then a field applied to measure the change in resistance R = R(0) - R(H). The ratio | R/R(0) | is plotted against temperature for the fields indicated in the legend. The striking aspect of these data is that although the peaks are not as pronounced as those in the ZFC magnetiza- tions of Fig. 1, their positions in an H-T plot of Fig. 3 (open triangles) show close similarity with respect to the FIG. 2: Temperature dependence of the relative changes in positions of the ZFC peaks (solid circles). resistance at the fields indicated in the legend for the same The presence of a spin-glass-like phase is buttressed by sample characterized in Fig. 1. For each data point, the sam- ple was zero-field cooled as described in the text. The vertical our finding that Tm(H) defines a critical field line (solid arrows indicate the positions of the maxima for each field and circles in Fig. 3) which delineates the onset of strongly ir- define a critical field dependence similar to that defined by reversible behavior and has the de Almeida and Thouless the maxima of the ZFC magnetizations in Fig. 1. (AT) form[11, 12], H/T (Tg/T - 1)3/2 (inset), where 3 show AT like boundaries without being Ising spin glasses and fields. Experimentally this is confirmed in Fig. 3 to which the theory[12, 13] strictly applies. The GAF where the AT line for the sample with dCr = 10 A (solid phase associated with our GMR multilayers is clearly squares) has higher critical fields and a correspondingly not an Ising system and is more reasonably described higher Tg than the sample with 12 A spacer. A second in terms of an anisotropic vector model in which the consequence is that the disorder-induced close proximity elemental spins, belonging to magnetized domains, are of Tg and JAF implies that at low H the presence of an coupled ferromagnetically in the X-Y plane and antifer- AF phase is obscured on the transition (Fig. 4, horizon- romagnetically in the perpendicular direction. For such tal dashed arrow) from the PM to GAF phase. If this vector glass systems there is an additional degree of free- were not the case, then the field-cooled dc susceptibility dom in the order parameter and the true phase boundary would have a maximum at the AF boundary and then is delineated at higher temperatures and fields by the saturate at a smaller value as T 0. Such maxima are Gabay-Toulouse (GT) boundary[14]. A more compre- not observed! A third consequence supporting the ex- hensive viewpoint that facilitates understanding of our istence of a GAF phase comes from the scaling of the experiment can be gleaned from the schematic phase dia- field-cooled magnetization with H. Field- cooled (FC) gram, shown in Fig. 4 for the H-T plane at JAF / J > 1. magnetizations including those shown in Fig. 1 reveal (Note that the PM phase is not labeled as a ferromag- that M/H H-u as T 0. Here we find u=0.58(2) for netic (FM) phase, since in the presence of a field there is 5K magnetization data taken at 7 different fields rang- no spontaneous symmetry breaking as the temperature ing from 100 to 800Oe, thus confirming behavior char- is reduced through the Curie temperature.) In simplified acteristic of spin glass systems below the lower critical terms the GT line (solid) can be thought of as denoting dimension [12]. Finally, in addition to hysteresis, we also the onset of a phase transition to glassy behavior and the observe slow relaxations in the magnetization and resis- AT line (dotted) as the onset of pronounced irreversibil- tance that are logarithmic in time and which, but for ity. (The experimental signature of the GT line, which lack of space, can be explained by invoking constraints has not been measured here, is a divergence in the trans- on the dynamics imposed by a hierarchy of domain sizes verse ac susceptibility.) At H = 0 both lines terminate [15, 16]. at T = Tg. To fully appreciate the role of randomness in multilay- The following three consequences, confirmed by experi- ers, it is important to recognize the difference between ment, are immediately apparent: Firstly, since Tg JAF and J JAF , it is clear that as Tg increases, the bound- ary of the GAF phase moves out to higher temperatures H/ J Hs PM GT AF GAF AT T T/ J g FIG. 4: Schematic of phase diagram in the H-T plane FIG. 3: Critical field lines for the 30 layer [Fe(20 A)/Cr(12 A)] showing the relationship between the glassy antiferromag- (solid circles and open triangles) sample shown in Fig. 1 and netic (GAF), the antiferromagnetic (AF) and the paramag- for a second 30 layer [Fe(20 A)/Cr(10 A)] (solid squares) multi- netic (PM) phases. The axes are normalized as discussed in layer sample with smaller Cr spacer thickness. The solid sym- the text. The Gabay-Toulouse (GT) and de Almeida and bols refer to determinations using the experimental Tm(H)'s Thouless (AT) line (dashed) are described in the text. For of ZFC magnetizations and the open triangles are determined our samples the disorder is sufficiently large (i.e., J JAF ) by similar peaks in the resistance measurements. Inset, plot and the field sufficiently low to ensure that the presence of an of the high temperature points (solid circles) showing the de AF phase is obscured on the transition from the PM to GAF Almeida-Thouless (AT) scaling dependence for spin glasses. phase (horizontal dashed arrow). 4 GMR multilayers, in which there is a strong interac- der of magnitude for Fe which with a saturation magneti- tion between closely coupled interfaces, and bilayer or zation Ms = 1700Oe/cm3 implies a maximum saturation trilayer configurations in which such interactions can be field Hs = 4 Ms = 21kOe. For our three different sam- ignored since there are at most only two interfaces. Thus ples with dCr = 8, 10 and 12 A we find a linear dependence for example, in studies of exchange bias in single fer- of Hs on dCr which extrapolates to the origin (dCr = 0) romagnetic/antiferromagnetic (Co/CoO) bilayers[8], the to a value within 5% of Hs=21kOe, thus validating our onset of exchange bias, which is induced by random use of this analysis. interactions[7], is observed to occur at a single tempera- To associate field scales with energy (or equiv- ture, the Neel temperature. By contrast, in our case there alently, temperature), we use the conversion ratio, are two temperature ranges: T < Tg = 140K for glassi- 2.2µBB/kBT =1.5T/K, where the magnetic moment of ness and T > 250K where there is a loss of AF order Fe is 2.2 Bohr magnetons. Accordingly, the dipolar in- in Cr and disorder is still important. Accordingly, the teraction strengths measured by Hs, which are balanced picture described for FM/AF bilayers[8] is different for by domain wall energies, are on the order of a few Kelvin closely coupled multilayers where interactions between and hence not strong enough at T > Tg to determine do- multiple ferromagnetic (FM) layers and interactions be- main orientation. Rather, domain orientation at T > Tg tween interfaces should be taken into account. Simi- is determined by the much stronger potential variations lar considerations also apply to the magneto-optic Kerr associated with crystalline anisotropies and the presence effect (MOKE) and scanning electron microscopy with of impurities and defects. The presence of a GAF phase polarization analysis (SEMPA) studies[17] on Fe/Cr/Fe implies that IEC is effective in creating an anti-alignment trilayers and magnetization and ferromagnetic resonance effect beneficial to a large GMR effect only at low tem- studies of CoFe/Mn/CoFe trilayers[10], all of which spe- peratures (T < Tg) and low fields (H < HAT ). The cialize to a specific type of spacer layer and do not include shaded region in the inset of Fig. 1 illustrates just how the multilayer interactions responsible for our GAF be- narrow this region is. havior. Our results are thus complementary yet distinct In summary, we show that a heretofore-unrecognized from the results of bilayer/trilayer experiments. glassy antiferromagnetic (GAF) state coexists with GMR A consideration of the relevant energy scales and the in polycrystalline Fe/Cr multilayer stacks. The very pres- mutual interactions of the magnetized domains in the ence of this glassy phase sets an energy scale (T Fe layers solidifies this emerging picture of spin-glass- g =140K) for antiferromagnetic interlayer exchange coupling (IEC) like behavior in GMR multilayers. If adjacent Fe lay- that is well below room temperature. We therefore con- ers of thickness t and saturation magnetization Ms are clude that, for temperatures greater than T coupled through an antiferromagnetic exchange J per g , IEC plays only a minor role in forcing the antiparallel interlayer do- unit area, then saturation at a field H = Hs occurs main orientations that give rise to the (H = 0) high resis- when J = HMst/4, a relation found by equating the tance state of multilayer Fe/Cr GMR samples. Rather, field energy per unit area, HMst, to the energy dif- random potential variations, which constrain domain ori- ference, 4J, between the aligned and antialigned mag- entation, must be taken into account to understand GMR netic configurations . We note that a glass temperature in multilayer GMR devices. The origin of the depen- near 140K corresponds to an antiferromagnetic coupling dence of H energy 10 meV, in good agreement with theoretical s on spacer thickness in multilayers as observed here and by others[2, 4] as well as the origin of the AF calculations[18, 19] for Fe/Cr layers. In the first calcula- couplings for T < T tion by Fishman and Shi[18] the Fe layers are exchange g are totally open questions. This contrasts with the bilayer and trilayer cases[7, 8, 17] for coupled below the Neel temperature Tn of the Cr spacer which the AF couplings have a clear source. and a very strong AF coupling between the Fe and Cr mo- We thank S. B. Arnason, S. Hershfield, P. Kumar and ments at the interface is assumed. For our GAF phase Tn C. Yu for valuable discussions and suggestions. This work is in reality Tg. In the second calculation by Majumdar was supported by AFOSR, DARPA and NSF. et al.[19] magnetoresistance data is well described by a theoretical expression in which RKKY interactions give a best fit AF coupling strength of (70 ± 20)K. For T > Tg, the Fe layers are no longer AF cou- pled and the expression J = HM st/4 to calculate the Electronic address: afh@phys.ufl.edu IEC is no longer relevant. In its place we use the [1] U. Hartmann, ed., Magnetic Multilayers and Giant Mag- expression[20, 21] H netoresistance, vol. 37 of Surface Sciences (Springer- s = 4 Ms, to calculate the maxi- mum saturation field necessary to align dipolar-coupled Verlag, Berlin, Heidelberg, New York, 1999). domains within each layer. This expression is valid for [2] M. N. Baibich, J. M. Broto, A. Fert, F. Nguyen van Dau, F. Petroff, P. Etienne, G. Creuzet, A. 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