Asymmetric Magnetization Reversal in Exchange-Biased Hysteresis Loops

Polarized neutron reflectometry is used to probe the in-plane projection of the net-magnetization vector M of polycrystalline Fe films exchange coupled to twinned (110) MnF2 or FeF2 antiferromagnetic (AF) layers. The magnetization reversal mechanism depends upon the orientation of the cooling field with respect to the twinned microstructure of the AF, and whether the applied field is increased to (or decreased from) a positive saturating field; i.e., the magnetization reversal is asymmetric. The reversal of the sample magnetization from one saturated state to the other occurs via either domain wall motion or magnetization rotation on opposite sides of the same hysteresis loop.

With conventional magnetometry, the projection of the net sample magnetization vector, M, onto the direction of the applied field is measured; i.e., the measured quantity is M ?
H a ͞H a .The condition M ?H a 0 can be obtained when the magnetic film breaks up into differently aligned domains with net magnetization equal to zero.Alternatively, the net sample magnetization can remain unchanged in magnitude, but rotate away from the applied field, so M ?H a 0. Domain observations in some AF͞F systems seem to indicate that the locations of domain nucleation in the increasing or decreasing branches of the loop are different [16].This is consistent with the frequent observation of asymmetrically shaped hysteresis loops as seen by many experimenters [12][13][14][15].In this paper, we use polarized neutron reflectometry to investigate this phenomenon beyond the scope of conventional magnetometry.
We report on neutron scattering measurements of M for two kinds of exchange coupled bilayer systems, i.e., Fe deposited onto antiferromagnets with very different anisotropy fields, H k , FeF 2 ͑H k 149 kOe͒ and MnF 2 ͑H k 7 kOe͒ [17].We find the reversal of the sample magnetization from one saturated state to the other can occur via both mechanisms, i.e., the nucleation and propagation of domain walls or the rotation of the net sample magnetization away from the applied field.In fact, we observe both mechanisms on opposite sides of the same hysteresis loop.The particular mechanism observed depends upon the orientation of the cooling field with respect to the crystallographic directions of the AF twins, and whether the measurement is made on the increasing or decreasing branch of the loop [18].
Three bilayer samples (one with MnF 2 and two with FeF 2 ) were prepared by sequential electron beam evaporation of Fe ͑ϳ0.1 nm͞s͒ onto the AF ͑ϳ0.2 nm͞s͒ [4,19].The AF's were deposited on 20 mm 3 20 mm polished single crystal (100) MgO substrates.In the case of the Fe-MnF 2 sample, a buffer layer of ZnF 2 (25 nm) was first deposited onto the MgO in order to improve the epitaxy of MnF 2 [4].The nominal thicknesses were MnF 2 (50 nm), FeF 2 (90 nm), Fe (11 nm), and Al or Ag (3 nm).The base pressure of the deposition chamber was 4 3 10 26 Pa, while the pressure during deposition of the fluorides was approximately 8 3 10 25 Pa.The deposition temperatures were ZnF 2 ͑473 6 2 K͒, MnF 2 ͑573 6 2 K͒, FeF 2 ͑473 6 2 K͒, Fe ͑423 6 2 K͒, and Al or Ag ͑423 6 2 K͒.The Al or Ag acts as a capping layer to prevent oxidation of the Fe.Using x-ray reflectometry [20], the thicknesses of the Fe films were determined to range from 9.5 nm to 12 nm for the different samples, and the roughness of the F-AF interface (root-mean-square deviation about its mean) to be 1.9 6 0.2 nm and 1.0 6 0.2 nm for the Fe-MnF 2 and Fe-FeF 2 interfaces, respectively.In-plane glancing x-ray diffraction [21] and reflection high-energy electron diffraction confirmed that the AF layers grow as twinned quasiepitaxial thin films.One AF crystal domain is oriented such that ͓110͔ MnF 2 (or FeF 2 ͒ k ͓110͔ MgO, while the other domain is oriented with [001] MnF 2 (or FeF 2 ͒ k ͓110͔ MgO. To confirm that the Fe overlayer is exchange coupled to the AF after field cooling through the Néel point of MnF 2 ͑T N 67 K͒ or FeF 2 ͑T N 78 K͒, the ferromagnetic hysteresis loops of the samples were measured with a SQUID magnetometer.The hysteresis loop for the Fe-MnF 2 sample cooled in a field of H FC 6.40 6 0.01 kOe ͑ 509 kA͞m͒ is shown in Fig. 1(a).The exchange bias and coercivity ͑H c ͒ were determined to be H e 230 6 1 Oe and H c 148 6 1 Oe.H e and H c are consistent with previous measurements on similarly grown bilayers [4,19].
For the neutron scattering experiment, two cooling field orientations were used.The first orientation involved applying a cooling field H FC 6.40 6 0.05 kOe along a direction bisecting the anisotropy (easy) axes (the [001] axes) of the two AF domains [see Fig. 1(a), inset] as the sample was cooled from room temperature to 10 6 1 K.The second orientation involved applying the same cooling field along a direction parallel to the anisotropy axis of one AF domain, and thus perpendicular to the easy axis of the other domain [see Fig. 2 The magnitude and orientation of the net sample magnetization relative to the cooling field were determined from measurements of the sample reflectivities with polarized neutrons.Polarized neutron reflectometry involves specular reflection of a polarized neutron beam from a flat sample onto a polarization analyzer [22,23].Four neutron cross sections were measured.Two cross sections correspond to the non-spin-flip (NSF) reflectivity profiles, where the intensities of the reflected radiation for spin-up ͑11͒ [and alternatively spin-down ͑22͒] neutrons illuminating and reflecting from the sample were measured.The difference between the NSF reflectivity profiles, DNSF, is related to the projection on to the direction of the applied field of the net (ferromagnetic) sample magnetization averaged over the lateral dimensions of the sample, i.e., DNSF ~ M ?H a ͞H a M k .The remaining two cross sections are the spin-flip (SF) reflectivities, which are nonzero if the sample changes the neutron beam polarization from spin-up to spin-down ͑12͒, and vice versa.For example, the beam polarization will change and SF scattering will be observed, if the magnetic induction vector is perpendicular to the neutron spin, so SF ~͑ M 3 n͒ ?H a ͞H a M Ќ , where n is the normal to the film surface.
Neutron reflectivity profiles for several fields, H a , applied parallel and antiparallel to H FC , were measured.Examples, typical of the profiles observed from the Fe-MnF 2 sample, are shown in Fig. 1(b).The net sample magnetizations deduced from the neutron measurements H a adjacent to the letters A 1 D 1 and symbols "ᮀ" in Fig. 1(a).
The large splitting between the NSF profiles requires DNSF ¿ 0, for H a 26.4 kOe [curves A 1 in Fig. 1(b)], and the lack of SF scattering above background [ϳ10 23  for the measurements shown in Fig. 1(b)] requires SF ϳ 0 and indicates that the sample was saturated for this applied field.For point B 1 in Fig. 1  were nearly superimposed, DNSF ϳ 0, and no SF scattering above background was observed, SF ϳ 0. DNSF ϳ 0 indicates the net sample magnetization parallel to the applied field was zero.SF ϳ 0 further indicates that the film did not contain domains with components of magnetization perpendicular to the applied field [24].Together, the conditions DNSF ϳ 0 and SF ϳ 0 mean that the Fe film is composed of nearly equal populations of domains with magnetization aligned parallel or antiparallel to the applied field [25].The NSF profiles (not shown) corresponding to C 1 (at H a 16.4 kOe) in Fig. 1(a) were similar to those shown in Fig. 1(b) corresponding to A 1 , thus, indicating saturation of the sample at C 1 .Reduction of the applied field from C 1 to D 1 (Fig. 1) resulted in SF scattering nearly an order of magnitude above background, SF ¿ 0. In contrast to observations at point B 1 ͑H a H e 1 H c ͒, where SF ϳ 0, the presence of significant SF scattering at point D 1 ͑H a ϳ H e 2 H c ͒ indicates rotation of the sample magnetization away from the applied field.In other words, we observe a different magnetization reversal mechanism on increasing the field to saturation than decreasing the field from saturation.Explicitly, we have domain wall nucleation and propagation at B 1 , in contrast to magnetization rotation at D 1 [26].This asymmetry in reversal mechanisms was also observed in the Fe-FeF 2 system under identical cooling conditions.The results obtained for the first cooling field orientation [see Fig. 1(a), inset] and their implications for the magnitude of M k and M Ќ are summarized in Table I.Detailed quantitative fitting of model magnetic structures, whose calculated reflectivity profiles are shown in Fig. 1(b) as the solid curves, to the neutron data confirms the qualitative picture described previously.
The reflectivity profiles measured from the sample after field cooling in the second orientation field applied parallel to the easy axis of one MnF 2 domain (and perpendicular to the other [see Fig. 2(a) inset]) are shown in Fig. 2(b).These profiles correspond to point D 2 ͑H a H e 2 H c ͒ in Fig. 2(a).As was the case for the first cooling field orientation at a similar field ͑D 1 ͒, significant SF scattering, SF ¿ 0, was observed indicating a rotation of the sample magnetization as the field was changed to H a H e 2 H c .However, in stark contrast to the first cooling field orientation, the profile recorded for point B 2 was no different than that recorded for point D 2 .In other words, after the sample is cooled in a field corresponding to the second orientation [see Fig. 2(a), inset], the reversal of the sample magnetization from one saturated state to the other involved rotation of the sample magnetization regardless of whether the applied field was increased or decreased.The reversal of the sample magnetization is symmetric.The magnetization reversal field with the cooling field applied in the second configuration for the Fe-FeF 2 sample was qualitatively the same as that observed for the Fe-MnF 2 sample.Note that since the anisotropy fields of MnF 2 and FeF 2 are so different, and the mechanisms through which the Fe film magnetization was reversed were identical for both AFs, we conclude that the anisotropy field plays little role in the magnetization reversal in these systems.The results for the second cooling field orientation are summarized in Table I.
For the first cooling field condition [see Fig. 1(a), inset] and at H a ϳ H e 1 H c , the Fe magnetization was at 45 ± to the anisotropy axes of both AF domains.We propose that this direction constitutes an "easy axis" for the magnetization direction due to the frustration of the perpendicular coupling [5,6,27,28] in a twinned system.
The "45 ± coupling" is energetically favorable as each AF domain independently tends to perpendicular coupling.(N.B. twin-driven frustration of collinear coupling also results in 45 ± coupling.)An added factor is that the field cooling provides an additional unidirectional asymmetry.Therefore, for the first cooling condition [Fig.1(a), inset], field reduction from saturation results in magnetization rotation rather than domain nucleation.This is due to the intrinsic unidirectionality that hinders formation of domains with magnetization antiparallel to the cooling field direction.Gradual rotation is energetically favorable.As the field is reduced from negative saturation, formation of domains with magnetization parallel to the initial cooling direction is favored.Hence reversal occurs by domain nucleation and propagation.On the other hand, in the second cooling field condition [Fig.2(a), inset] the situation is essentially different in that rotation towards the "45 ± easy axis" is always favored.The initial reduction of the field from saturation results in rotation towards a direction 45 ± to both anisotropy axes of the AF domains on both sides of the loop.
In conclusion, the magnetization reversal process of an Fe overlayer exchange coupled to MnF 2 or FeF 2 depends upon (1) the cooling field direction relative to the AF anisotropy axis, and (2) whether the applied field was increased from negative to positive values (relative to the direction of the cooling field) vice versa.A simple model is capable of explaining the observed reversal symmetry when the cooling field is at 45 ± with respect to both twin anisotropy axes, as well as the symmetric reversal found when the field is parallel to the anisotropy axis of one of the twins.This model is based upon the existence of a unidirectional anisotropy in conjunction with the "45 ± coupling" intuitively expected in a twinned system.As was observed for exchange coupled Fe-MnF 2 and Fe-FeF 2 films, the presence of complex microstructures, e.g., twins, may be a determining factor in the magnetization reversal process and exchange bias in many other F-AF exchange coupled systems.

FIG. 1 .
FIG. 1.(a) Hysteresis loop ͑≤͒ for the Fe-MnF 2 sample and the orientation of the cooling field, H FC 6.4 kOe, relative to the MnF 2 domains (inset).The net magnetization M ͑!͒ relative to H FC deduced from the neutron data corresponding to H a ͑ᮀ͒ is superimposed.(b) Polarized neutron reflectivity profiles measured for the same sample and cooling field.A 1 : negative saturation H a 26.4 kOe (note the break in the figure scale); B 1 : H a H e 1 H c , and D 1 : H a H e 2 H c .A representative error bar is shown for the spin-flip scattering.Solid curves are fits of a model to the data.
(a), corresponding to H a ϳ H c 2 H e , the NSF profiles [curves B 1 in Fig. 1(b)]

FIG. 2 .
FIG. 2. (a) Hysteresis loop ͑≤͒ for the Fe-MnF 2 sample and the orientation of the cooling field, H FC 6.4 kOe, relative to the MnF 2 domains (inset).The net magnetization M ͑!͒ relative to H FC deduced from the neutron data corresponding to H a ͑ᮀ͒ is superimposed.(b) Polarized neutron reflectivity profiles measured for the same sample and cooling field.D 1 : H a H e 2 H c .

TABLE I .
Summary of observations for Fe-MnF 2 and Fe-FeF 2 bilayers for the first (subscript 1) and second (subscript 2) H FC conditions.