Imprinting Vortices into Antiferromagnets

J. Sort,* K. S. Buchanan, V. Novosad, A. Hoffmann, G. Salazar-Alvarez, A. Bollero, M. D. Baró, B. Dieny, and J. Nogués Institució Catalana de Recerca i Estudis Avançats (ICREA) and Departament de Fı́sica, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Spain Materials Science Division and Center for Nanoscale Materials, Argonne National Laboratory, Argonne, Illinois 60439, USA Departament de Fı́sica, Universitat Autònoma de Barcelona, 08193 Bellaterra, Spain SPINTEC (URA 2512 CNRS/CEA), CEA/Grenoble, 17 Rue des Martyrs, 38054 Grenoble Cedex 9, France (Received 7 April 2006; published 7 August 2006)

In ferromagnets and antiferromagnets, there are often domains with differently ordered spin states observed instead of a single homogeneously long-range ordered region.It turns out that domain structures in antiferromagnetic (AFM) materials have been far less studied than domains in ferromagnets [1].This is partially due to the fact that the staggered AFM spin structure with its lack of a net magnetization makes the detection of domains and domain walls more challenging [2,3].Moreover, the physical properties of AFM domains differ significantly from ferromagnetic (FM) domains.Domains in a ferromagnet are generally determined by balancing magnetostatic with exchange and anisotropy energies.Thus, in nanostructured systems, ferromagnets can develop welldefined unusual spin states, such as magnetic vortices [4 -9].The absence of a net magnetization in antiferromagnets means that magnetostatic energy is vanishing, and, therefore, domains in antiferromagnets are generally metastable, since typically the gain in configurational entropy is not sufficient to overcome domain wall energies.Without any direct explicit driver for domain formation, the AFM domains may originate from random nucleation of long-range order due to randomly distributed defects [10].For these reasons, the formation and evolution of AFM domains remain a research area with many open questions.
Nevertheless, domains in antiferromagnets have received increased attention recently due to their role in exchange bias, i.e., the shift of the hysteresis loop observed in FM-AFM coupled systems [11,12], which is a key ingredient in spintronic devices [13].Many exchange biased systems exhibit unusual properties, one of which is a pronounced asymmetry in the hysteresis loop, caused by different irreversible reversal mechanisms on either side of the hysteresis loop [14 -18].Since the ferromagnet and the antiferromagnet are exchange coupled, measurements of the FM behavior provide an indirect probe of the properties of the antiferromagnet, for example, the spin-flop field [19], the surface order parameter [20], the crystalline anisotropy [21], or the domain wall width [22,23].Furthermore, it has recently been demonstrated that nonuniformly magnetized ferromagnets can modify the antiferromagnetic spin structure in a way that allows tuning of the hysteresis loops over a wide range [24 -26].
In this work, we show that it is possible to imprint a welldefined nonuniform magnetization state, such as a magnetic vortex, into the antiferromagnet.Investigations of the role of magnetic vortices in exchange bias systems have begun only recently [27][28][29][30][31].In previous experiments, we have shown that the interplay between the unidirectional exchange bias and vortex structures can give rise to angular-dependent magnetization reversal, when the exchange bias is established with a saturated ferromagnet [27,31].In contrast, here we investigate the magnetization reversal of circular disks composed of FM-AFM bilayers after cooling them in unsaturated magnetization states.This allows imprinting symmetric as well as displaced vortex spin structures into the AFM.The resulting hysteresis loops exhibit a new type of asymmetry characterized by a curved, reversible, central part with nonzero remanent magnetization, which can be accurately controlled by varying the cooling field magnitude.This asymmetry originates from the competition between the intradot magnetostatic energy and the FM-AFM exchange energy with the imprinted structure.
Arrays of circular disks (1 m diameter) were fabricated by e-beam lithography and subsequent ion etching of continuous films, previously deposited onto thermally oxidized Si wafers by dc magnetron sputtering, with the compositions Ta5 nm=Py12 nm=IrMn5 nm=Pt2 nm (where Py, i.e., permalloy, stands for Ni 80 Fe 20 and is FM, whereas IrMn, i.e., Ir 20 Mn 80 , is AFM) and Ta5 nm= Py12 nm=Pt2 nm.The patterned structures were heated to 550 K (i.e., above the blocking temperature of the system, T B 420 K) and subsequently cooled to room temperature both in zero field and with in-plane magnetic fields 0 H FC , with values ranging from 2.5 to 250 mT, applied parallel and perpendicular to the direction of measurement (arbitrarily taken as 0 ).The dots were separated by 2 m to minimize dipolar interactions.Hysteresis loops were recorded at room temperature using a Durham magneto-optics Kerr effect (MOKE) setup and detecting both the longitudinal and transverse magnetization components, i.e., the in-plane magnetization components parallel and perpendicular to the applied magnetic field, respectively.Magnetic force microscopy (MFM) imaging (using a Nanoscope III Digital Instruments, Inc.) was also performed [32].
To interpret the magnetization curves, micromagnetic simulations were performed using a Landau-Lifshitz-Gilbert micromagnetic solver [33].Typical material parameters for bulk permalloy were used: saturation magnetization M S 8 10 ÿ5 A=m and exchange stiffness constant A 1:3 10 ÿ11 J=m.The magnetocrystalline anisotropy was neglected.Hysteresis loops were calculated by allowing the disk magnetization state to relax to an equilibrium state in successively applied magnetic fields.The patterned exchange bias is represented by an additional position-dependent pinning field with local magnitude 0 H E 9 mT and with the direction defined by calculations of the unbiased vortex state for an applied field equal to H FC .Full hysteresis loops were obtained using cells of 5:4 5:4 nm 2 , 12 nm thick at a temperature of 300 K. Simulations of the reversible portion of the curve were repeated with smaller cells (3 3 nm 2 , 12 nm thick) at zero temperature in order to obtain more refined estimates of the remanent magnetization and core trajectories.
The hysteresis loops of Py and Py-IrMn disks after field cooling (FC) along 0 from T 550 K in 0 H FC 250 mT are shown in Fig. 1(a).Both loops are constricted in their central part, as observed for magnetization reversal via nucleation and annihilation of a vortex state [4 -9].For the disks without IrMn, the loop shape is insensitive to the field cooling.In contrast, in the Py-IrMn disks measured along the FC direction, a symmetric vortexlike loop is observed, shifted along the magnetic field axis by 0 H E 9 mT.For both the biased and unbiased Py, no transverse magnetization signal is detectable.If the Py-IrMn disks are zero-field cooled (ZFC) from T 550 K, the resulting hysteresis loop becomes closed (i.e., reversible) at its central part [see gray curve in Fig. 1(b)], again without any detectable transverse component.In this case, the nucleation and annihilation fields of the vortex increase by approximately 9 mT with respect to the unbiased Py, an enhancement of the same magnitude as the loop shift observed in the case of field cooling in saturation.This suggests that during ZFC the vortex state is imprinted into the AFM, and, once at room temperature, the coupling with the AFM acts like a 9 mT local effective pinning field with the cylindrical symmetry of a centered vortex state, thus enhancing the magnetic stability of the vortex in the FM.
When the Py-IrMn disks are FC in small H FC values, the resulting hysteresis loops recorded along the FC direction become asymmetric [Fig.1(b)].This asymmetry is evidenced by the appearance of a curved, reversible, central part.The loop curvature and the remanent magnetization increase as H FC is increased.This allows precise tuning of the loop asymmetry.Similar to the ZFC Py-IrMn disks, no transverse Kerr signal is detected.
On the other hand, when H FC is applied in-plane but perpendicular ( FC 90 ) to the measuring direction, then both longitudinal and transverse magnetization components are observed [Fig.1(c)].The asymmetry observed along FC 0 is no longer observed for FC 90 , and the remanence in the longitudinal loop is zero.However, the transverse component is now nonzero, indicating that unlike in the ZFC case the vortex core is not centered but displaced perpendicular to the field-cooling direction.
The simulated hysteresis loop for a Py-IrMn disk after ZFC is shown in Fig. 2(a), together with the simulated loop corresponding to Py only.These loops are remarkably similar to their experimental counterparts in Fig. 1 with the exception of the annihilation field, which is slightly larger in the simulated loops.The measured loops are also a bit more rounded as compared to the simulated ones.This is probably due to the fact that an ensemble of dots, instead of a single dot, are measured by MOKE, and slight inhomogeneities between the different dots can bring about a distribution of nucleation and annihilation fields.For the ZFC case, the remanence is zero because during the cooling a symmetric vortex state is imprinted to the AFM [as shown schematically in Fig. 3(a)].During the hysteresis loop, the vortex core moves along a straight line [Fig.3(e)], perpendicular to the applied field, as revealed by the simulated dependence of the vortex core position as a function of the applied field [Fig.2(d)].This process changes the longitudinal magnetization component, but, due to the disk symmetry, the transverse one remains zero, in agreement with the experimental results.The simulations indicate that the magnetic susceptibility in Py-IrMn is smaller than for Py disks, in agreement with the enhanced stability of the vortex state in ZFC Py-IrMn disks.
In contrast to the ZFC case, the simulated longitudinal loop for Py-IrMn FC in 0 H FC 10 mT, when applying H FC along FC 0 , reveals a nonzero remanent magne-

FIG. 2 (
FIG. 3 (color online).Micromagnetic calculations of the spin configurations imprinted to the AFM when cooling in (a) zero field, (b) FC 0 and 0 H FC 2:5 mT, (c) FC 0 and 0 H FC 10 mT, and (d) FC 90 and 0 H FC 10 mT.(e)-(h) are the spin configurations of the FM at remanence calculated for the imprinted configurations of (a)-(d), respectively.The shading represents the magnitude of the magnetization vector along the perpendicular to the field-cooling direction.The direction of the applied field during the hysteresis loops ( 0 H appl ) is also indicated.The lines illustrate the core trajectories.