VOLUME 89, NUMBER 12 P H Y S I C A L R E V I E W L E T T E R S 16 SEPTEMBER 2002 Spin Flop Transition in a Finite Antiferromagnetic Superlattice: Evolution of the Magnetic Structure S. G. E. te Velthuis, J. S. Jiang, S. D. Bader, and G. P. Felcher Materials Science Division, Argonne National Laboratory, 9700 South Cass Avenue, Argonne, Illinois 60439 (Received 7 May 2002; published 3 September 2002) An antiferromagnetic (AF) superlattice of Fe=Cr 211 is used as a model system to study magnetic transitions in a finite-size geometry. With polarization neutron reflectometry the magnetic structure at the surface spin-flop transition and its evolution with field is determined. A domain wall created near the surface penetrates the superlattice with increasing field, splitting it into two antiphase, AF domains. After reaching the center the spin-flopped phase spreads throughout the superlattice. The experimental results are in substantial agreement with theoretical and numerical predictions. DOI: 10.1103/PhysRevLett.89.127203 PACS numbers: 75.70.­i, 61.12.Ha, 75.25.+z, 75.50.Ee Uniaxial antiferromagnets (AFs) have occupied the transition. The SL was chosen with a Cr layer thickness attention of researchers since Ne´el first predicted [1] the that gives AF coupling of adjacent Fe layers, and was magnetic field conditions under which an AF exhibits a grown epitaxially on a MgO(110) substrate to provide spin-flop transition, which is an abrupt decoupling be- uniaxial magnetic anisotropy [6]. Application of H tween the direction of the AF and the easy axis (EA). In parallel to the in-plane EA indeed initiated a magnetic Ne´el's microscopic description, below a critical field the transition at a field lower than HBSF. The surface character magnetic moments are ordered in two sublattices with of this transition was identified by magneto-optical opposite magnetization M. Their orientation is along the Kerr effect (MOKE) measurements. MOKE is surface EA, as is the applied field H, but at the bulk spin-flop sensitive since the depth penetration of the laser light transition HBSF the sublattice M is canted with a resulting is less than the film thickness, When the surface layer net M along H. Interestingly, it took over 30 years before was magnetized opposite to H it was not detected be- experiments confirmed Ne´el's model [2]. cause it nucleated at the buried surface. In contrast, AF coupled metallic superlattices (SL) offer novel magnetometry, probing the entire sample volume, templates to study the behavior of magnetic structures detected the surface spin-flop transition in both field in reduced dimensionality, in our case a finite AF. The directions. two outer layers (facing the surface and the buffer/sub- Following the experiments by Wang et al. in 1994 [7], a strate) are each magnetically coupled on only one side, robust body of theoretical and computational work and they respond more readily to an external field. In amassed to describe in detail the microscopic underpin- 1968 Mills proposed [3] that in an AF with a free surface, ning of this behavior [8­12]. The region of flopped spins, spins near the surface rotate into a flopped state at a field created at one end of the SL at HSSF, is described as smaller than HBSF. Later Keffer and Chow [4] refined the moving toward its center by jumps. The transition pro- description of the surface spin-flop (SSF). To describe the gresses with increasing H by a pair of layers of the inner behavior of bulk and finite antiferromagnets the impor- domain becoming part of the outer domain (whose M is tant quantities are the exchange field HE and the anisot- along H). There is ``discommensuration'' [11]: the mov- ropy field HA. The descriptions discussed here are limited ing wall separates the SL into two domains, with magnet- to systems for which HE and HA are of the same order of izations symmetric to the wall [9] or, as said in magnitude [5]. For a finite system composed of an even crystallography, in antiphase. Also its spreading toward number of AF coupled layers, a SSF transition takes place the edges of the SL occurs by a series of discrete jumps at HSSF 2 HEHA H2A and the bulk spin-flop field oc- [10]. The process is completed at HBSF. A visualization of curs at HBSF 2 2HEHA H2A. HA 2Ku=Ms, where Ku the field evolution of the magnetic structure is presented is the uniaxial anisotropy and Ms is the saturation mag- in Fig. 1. Each compass represents M of an Fe layer in the netization, while HE 2J=Mst, where J is the exchange SL stack. H is the direction of the applied field, along the coupling and Mst is the moment per surface area [6]. AF easy axis in the film plane. The fields are scaled with Keffer and Chow pointed out that, with increasing H, respect to the bulk spin-flop field (h H=HBSF). The the SSF must penetrate the superlattice (SL) as an AF object of the present Letter is to show that, on the basis domain wall, until it reaches the center of the stack. Then of polarized neutron reflectivity (PNR) measurements, the spin-flopped region should expand to the full extent of the description given above is correct to a remarkable the SL. degree. Figure 1 actually has not been obtained by nu- In 1994 magnetic measurements by Wang et al. [7] on merical calculations [8­10], but is the result of a least Fe=Cr 211 superlattices confirmed the presence of a SSF square fitting of the neutron data. 127203-1 0031-9007=02=89(12)=127203(4)$20.00 2002 The American Physical Society 127203-1 VOLUME 89, NUMBER 12 P H Y S I C A L R E V I E W L E T T E R S 16 SEPTEMBER 2002 1 0 H 0.67 0.5 0.68 0.69 0 M/Ms 0.71 H Bulk SF 0.72 -0.5 0.93 H Surface SF -1 1.06 -20 -10 0 10 20 1.33 H [kOe] FIG. 1. The compasses in each row depict the magnetization FIG. 2. Magnetization curve of the Fe 14 A =Cr 11 A 20 direction in the Fe layers across the SL stack at increasing superlattice. applied fields, starting with the AF alignment at zero field. The applied field h H=HBSF is given to the left of each row. The gray shading indicates approximately the area of the domain the reflectivities: R , R ÿ, Rÿ , and Rÿÿ, where the wall, while the vertical dashed line indicates the position of the two superscripts denote the orientation of the polariza- discommensuration that divides the system into two domains tion, parallel ( ) or opposite ( ÿ ) to H, before and after in antiphase. The directions of the moments as shown are reflection from the sample, respectively. From R a chemi- obtained by fitting the PNR data in Fig. 3. cal and magnetic depth profile from the surface to the substrate can be determined [14]. Specifically, R ÿ and We studied the spin-flop transition of an AF coupled Rÿ are solely due to the components of M perpendicular Fe=Cr SL of the type Fe 14 A =Cr 11 A 20. The thick- to H. All four measured reflectivities were corrected for ness appears within parentheses and there are 20 repeats polarization efficiency. of Fe=Cr bilayers. The sample was prepared via dc mag- Initial PNR experiments indicated that at H 0, after netron sputtering onto a single-crystal MgO(110) sub- saturation in 50 kOe, the sample consists of lateral strate. A Cr buffer layer, nominally 200- A thick, was domains. This is given by the fact that the two non-spin first deposited at 400 C to establish epitaxy with the flip reflectivities, R and Rÿÿ, are equal. The lateral substrate. The SL was deposited at 100 C and found to domains are AF ordered throughout the thickness of the grow with a (211) orientation [6]. The SL was capped by a SL, but the top layer is either parallel or perpendicular to 100- A Cr layer. The epitaxy and the perfection of the SL the priming field. If the lateral domains had been of the were checked by x-ray diffraction. In particular, low order of a few m or less, off-specular scattering would angle x-ray reflectivity measurements indicate an Fe=Cr have been observed [15]. Since this was not the case, the interfacial roughness of 4 A. Magnetically the sample domains can be assumed to be significantly larger. Only was characterized by SQUID magnetometry as well as after cycling within the minor loop ( 6 kOe), a major- by MOKE, with H along the EA, in the plane of the film. ity of one domain state was formed, evidenced by a In SQUID measurements (Fig. 2) the induced M is inter- difference in R and Rÿÿ. The measurements of the preted as the onset of the SSF (HSSF). Further increasing spin-flop transition presented here were performed after H, the magnetic susceptibility steadily increases until cycling within the minor loop and with a final ``priming'' 4:14 kOe, indicating that at this field the entire SL has field of 6 kOe. undergone a spin-flop (HBSF). Saturation is reached at As a result of the periodic chemical and magnetic 16.7 kOe, with Mst 1:8 10ÿ4 emu=cm2 per Fe layer. structure of the sample, the PNR spectra include Bragg The experimental phase transitions and M fit well with reflections which have maxima at q 2 =d, where d is the values expected for superlattices, for which Ks the period of the structure. The first Bragg reflection that 0:06 erg=cm2 [5] giving JAF 0:81 ergs=cm2, HSSF appears at low q is an AF peak. In Fig. 3, R , Rÿÿ, and 3:3 kOe, and HBSF 4:4 kOe. Rÿ are presented for ascending values of h ( H=HBSF, PNR measurements were carried out at the ``POSY I'' with HBSF 4:14 kOe). The h 0 spectra are consistent reflectometer at the Intense Pulsed Neuron Source of with that of an AF alignment, with the magnetization of Argonne National Laboratory [13]. The sample, of the top Fe layer opposite to H. As h > hSSF 0:66, the 4 cm2 area was inserted in the gap of a conventional, intensity and width of the Bragg peak (at q 0:131 Aÿ1) split-coil electromagnet, with a maximum field of 6 kOe change. For R and Rÿÿ, the peak broadens and even- and with a field homogeneity of 5% on the sample. The tually seems to split into two parts (i.e., a minimum quantities measured as a function of the neutron momen- is created at the center). Correlated with this is the tum transfer perpendicular to the surface, q 4 sin = growth and sharpening of the Bragg peak in the spin ( angle of incidence, wavelength of the neutron), are flip reflectivity Rÿ . 127203-2 127203-2 VOLUME 89, NUMBER 12 P H Y S I C A L R E V I E W L E T T E R S 16 SEPTEMBER 2002 FIG. 3. The evolution of R , Rÿÿ, and Rÿ as a function of increasing h (going from the top to the bottom curve), the values of which are the same as those in Fig. 1. Symbols represent the data, while the solid lines are fitted to the data. For clarity, data at sequential fields are displaced by a decade downwards. Basic crystallography can explain these observations. shape of the Bragg peak in Rÿ is given by Eq. (1). The Within the first Born approximation, a periodic array of size of the flopped region, i.e., the extension of the 2N equal scattering objects, each of scattering amplitude domain wall, can be determined from the relevant qm a and of thickness d, gives rise to a Bragg reflection with around the Bragg peak position. These considerations intensity [16]: show how to extract in a straightforward way, by approxi- mation, the position and width of the domain wall, from I0 / a2fsin qd 2N =2 = sin qd=2 g2; (1) the reflectivities of Fig. 3. The results are shown in Fig. 4. which at its maximum at q 2 =d, is proportional to In agreement with results of numerical calculations, 2N 2. The distance between the first two minima and that the domain wall reaches the center of the SL when value is q h-hS m 1= 2N 2 =d, which depends on the SF 0:08. number of scattering objects 2N. When a displacement of More detailed magnetic depth profiles were obtained length d=2 is introduced in the center of the array, the by fitting the full set of measured spin-dependent reflec- array is divided into two equal domains in antiphase. The tivities using a least square minimization procedure [17]. diffracted intensity then becomes Data taken at h 0 were used to fit the chemical depth profile, i.e., the layer thickness and roughness, with the Ia / a2fsin qd N =2 = sin qd=2 g2 cos2fqd N =2 1=4 g; (2) which has a minimum at q 2 =d splitting the Bragg 20 reflection. Now qm 1=N 2 =d. In our case the ``scattering object'' consists of a pair of 15 adjacent Fe layers with opposite M, i.e., one period of the AF structure. At least for values of q far exceeding the 10 edge of total reflection, R and Rÿÿ are due to the component of M along H. The splitting of the Bragg Number of layers 5 distance peak observed for R and Rÿÿ above h 0:69 is due width hS to the formation of two domains where the components of SF M collinear to H are in antiphase. In the case in which 0.6 0.8 1 1.2 1.4 the two domains have different thicknesses, the intensity h close to q 2 =d has a smoother variation. However, the FIG. 4. Distance of the domain wall from the bottom layer, as qm of the auxiliary minima is dictated by the largest of obtained from the position of the auxiliary minima around the the two domains. R ÿ and Rÿ are nonzero only when AF reflection (R data). Width of the domain wall, in number there are components of M perpendicular to H. The of layers that are spin-flopped (Rÿ data). 127203-3 127203-3 VOLUME 89, NUMBER 12 P H Y S I C A L R E V I E W L E T T E R S 16 SEPTEMBER 2002 assumption that the magnetic configuration is AF and curred whose nature is as yet unexplained. It is our hope along H. Subsequently, for higher h, the orientation of that an expansion of the theories so far developed for the M of each of the 20 Fe layers was fitted. M is an additional spin-flop transition in finite systems will provide guid- fitting parameter, but it has one value for all 20 layers. The ance to further experiments. fitted reflectivities are the solid lines in Fig. 3, while the In conclusion, with PNR measurements we have suc- results for the direction of the layer-by-layer magnetiza- cessfully determined the layer-by-layer magnetization tions are displayed in Fig. 1. The results confirm that the profile in a finite, uniaxial AF at different stages of the spin-flop transition initially starts at the top surface, surface and bulk spin-flop transitions. Our results show forms a domain wall, and propagates to the center. The that the surface transition follows the general trend that region of fields where the wall is expected to widen was had been predicted, in particular, that the motion of the not well covered by the measurements. Yet at h 0:93 spin-flopped region toward the center of the SL results in there is almost a completely formed spin-flopped state. At two antiphase domains. the two highest fields, the moments are canted towards H. This work was supported by the U.S. DOE, Office of The fitting routine gives the error in the determined Science under Contract No. W-31-109-ENG-38. The au- directions of M to be 5 on average. However, taking thors thank J. Meersschaut, A. Hoffmann, C. Micheletti, into account the uniqueness of the solution, we estimate and A. Rettori for useful discussions. After completing that the real error is 20 . Still, the magnetic evolution this work we received a preprint (Lauter-Pasyuk et al. illustrated in Fig. 1 is strikingly similar to that calculated [20]) in which the splitting of the AF Bragg peak indicat- [8,9]. To attain the magnetic structure at each field with ing the antiphase domain in a SL of Fe=Cr 100 was also greater precision, it would be beneficial to calculate the observed. reflectivity expected from the computed magnetic struc- tures (which unfortunately so far have been reported in the literature only in graphical, rather than numerical form). Still remaining to be experimentally verified are the [1] L. Ne´el, Ann. Phys. (Paris) 5, 232 (1936). discontinuities as the domain wall propagates toward the [2] For a review, see Y. Shapira and S. Foner, Phys. Rev. B 1, center and spreads throughout the entire SL [8­12]. 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At this point the magnetization vectors of the two sublattices form an 209 (2001). angle of 90 . For larger values of , the rotation of [16] R.W. James, The Optical Principles of the Diffraction of magnetic moments with field is continuous. In order to X-Rays (Ox Bow Press, Woodbridge, Connecticut, 1962). ensure that H was parallel to the EA in our experiments, [17] R.W. E. van de Kruijs et al., Phys. Rev. B 65, 064440 (2002). we performed MOKE measurements as a function of [18] H. Rohrer and H. Thomas, J. Appl. Phys. 40, 1025 (1969). within the film plane. The character of the EA transition [19] J. M. Kosterlitz, D. R. Nelson, and M. E. Fisher, Phys. was preserved within the angular range c 6 . Rev. B 13, 412 (1974). Beyond this boundary other first-order transitions oc- [20] V. Lauter-Pasyuk et al. (unpublished). 127203-4 127203-4