Exchange bias in ferromagnetic bilayers with orthogonal anisotropies: the case of GaMnAsP/GaMnAs combination

We report the observation of exchange bias in a ferromagnetic Ga0.94Mn0.06As0.77P0.23/ Ga0.94Mn0.06As bilayer, in which the easy axis in one layer is oriented out-of-plane, and in the other in-plane. Magnetization reversal in this system is explored using planar Hall effect (PHE) measurements under various initial conditions and with various field-cooling orientations. Our results show that the two magnetic layers are ferromagnetically exchange-coupled, and that such coupling results in pronounced exchange-bias-like shifts of magnetic hysteresis loops during reversal of in-plane magnetization. The presence of exchange bias in this system can be understood on the basis of magnetic closure domains formed in the layer with the out-of-plane easy axis.


experiment
The growth of Ga 0.94 Mn 0.06 As 0.77 P 0.23 /Ga 0.94 Mn 0.06 As bilayers was carried out as follows. The Ga 1-x Mn x As layer was grown first to a thickness of 12 nm with the phosphorus cracker cell closed. The phosphorus cell was then opened, and a ~21 nm Ga 0.94 Mn 0.06 As 0.77 P 0.23 layer was deposited directly on Ga 0.94 Mn 0.06 As. The thicknesses of 12 nm and 21 nm for Ga 0.94 Mn 0.06 As and Ga 0.94 Mn 0.06 As 0.77 P 0.23 layers, respectively, were selected in order to have well-defined in-plane easy axes in Ga 1-x Mn x As and out-of-plane easy axes in Ga 0.94 Mn 0.06 As 0.77 P 0. 23 17 , so that we can investigate the interaction between orthogonal magnetic configuration in Ga 0.94 Mn 0.06 As 0.77 P 0.23 / Ga 0.94 Mn 0.06 As 0.77 bilayers. During the growth the Mn content was kept constant in both layers at ~0.06. The P content in the Ga 0.94 Mn 0.06 As 0.77 P 0.23 layer was selected in order to achieve a large tensile strain, to make certain that the easy axis in that layer was normal to the layer plane 5,16 . The growth was monitored by reflection high energy electron diffraction (RHEED), which showed a streaky (1 × 2) RHEED pattern throughout the growth of both layers, indicating high crystalline quality of the samples.
Temperature dependences of in-plane and out-of-plane magnetizations on the Ga 0.94 Mn 0.06 As 0.77 P 0.23 / Ga 0.94 Mn 0.06 As bilayer were carried out using a magnetometer; the Curie temperatures T c of the Ga 0.94 Mn 0.06 As and the Ga 0.94 Mn 0.06 As 0.77 P 0.23 were identified as 70 K and 45 K, respectively. Measurement of the planar Hall resistance (PHR) in magnetic fields whose direction can be applied along arbitrary in-plane direction provides a particularly convenient tool for investigating the details of magnetization reversal in the layer plane 18,19 , and we have adapted this approach for investigating the effects of exchange bias in the Ga 0.94 Mn 0.06 As layer 20 . For this purpose the sample was patterned by photolithography and by chemical wet etching into 100 μm × 1500 μm Hall bars with the long dimension lying along the [110] direction, as shown in Fig. 1(c). Measurements of the planar Hall resistance R xy were performed by using a sample holder and experimental arrangement such that a magnetic field could be applied in the plane of the sample at an arbitrary angle. The experiments consisted of measuring the dependence of the planar Hall resistance (PHR) on the external field swept in several selected field directions, after cooling fields of various strengths and orientations were applied to the bilayer. The angles of magnetization φ M , of the applied magnetic field φ H , and of the cooling field φ H FC are measured counterclockwise from the [110] crystallographic direction in the (001) plane.

Results
The in-plane anisotropy of the Ga 0.94 Mn 0.06 As layer were determined by measuring the angular dependence of PHR and by analyzing the results based on conditions that minimize magnetic free energy during the rotation of magnetization, as described by Son et al. 21 . This method is now well established as a tool for investigating magnetic anisotropy of ferromagnetic films. The obtained magnetic anisotropy energy density for the Ga 0.94 Mn 0.06 As layer is plotted in Fig. 1(b), showing the in-plane easy axes near the <100> directions.
Cooling field dependence of PHE. Figure 2(a) shows results of PHR measurements at 3 K during magnetization reversal scans for several field orientations. To discuss these results, it is important to describe the sequence of steps used in taking the data. The sample was cooled to 3 K in a field of 1 kOe applied in-plane either at φ H FC = 45° or at 225° with respect to the [110] direction. After reducing the field to zero, the magnet was rotated to φ H = 10°, as indicated in the figure, and the PHR was measured during a field scan between −1000 Oe and 1000 Oe. Qualitatively, the behavior of PHR scan shown in Fig. 2 is typical for Ga 0.94 Mn 0.06 As, showing abrupt changes of sign when magnetization experiences quasi-90° reorientations between the two in-plane easy axes in adjacent quadrants as the field is swept. This behavior can be described by the equation 22 where t is sample thickness, k is a negative constant related to anisotropic magnetoresistance, and φ M is the angle between the current (i.e., the [110] direction) and magnetization. The most interesting feature of the hysteresis shown in Fig. 2(a) is the conspicuous asymmetry of the PHR data obtained after in-plane field cooling, indicating exchange-bias-like behavior. Marking the fields at which magnetization switches from one easy axis to the next during magnetization reversal as H 1 … H 4 , as shown in Fig. 2, the PHR asymmetry is conveniently expressed by the differences of the switching fields |H 1 |-|H 3 | and |H 2 |-|H 4 |.
In Fig. 2(b), the sample was cooled to 3 K in a field of 1 kOe applied normal to the sample plane, either up or down. The field was then brought to zero, and PHR was measured during in-plane field scans between −1000 Oe and 1000 Oe at φ H = 10°, as in Fig. 2(a). In this case the hysteresis loops of PHR are symmetric, but with a vertical shift. The data in Fig. 2 thus reveal that exchange-bias-like shifts are only observed after cooling in an in-plane field.
pHe and exchange bias. In Fig. 3(a,b) we plot the hysteresis loops of PHR for field sweeps along φ H = 10° after applying the cooling field in several in-plane directions. From the data we conclude that the exchange bias of our bilayer film depends on the orientation of the cooling field. The observed behavior of PHR can be readily www.nature.com/scientificreports www.nature.com/scientificreports/ understood by considering the free energy of the (Ga,Mn)As layer that includes the additional bias field H EB oriented at some angle φ EB in the layer plane. This can be written as 19 where H is the external magnetic field; H c and H u are the cubic and uniaxial anisotropy fields; and H EB is the exchange bias field. The angles φ M , φ H , and φ EB are the directions of magnetization M, the applied magnetic field H, and the exchange bias field H EB , respectively, measured counterclockwise from the [110] direction. In our experiment we assume that the cooling field imprints the field H EB along its direction, so that φ EB = φ H FC . The free energy, Eq. (2), determines the four easy magnetization directions of the Ga 0.94 Mn 0.06 As film in the layer plane with respect to the [110] crystal axis, shown at 45° + δ, 135°−δ, 225° + δ, and 315°−δ in Fig. 4(a). Here the δ is a deviation angle of magnetic easy axes from the <100> directions. We have plotted the energy profiles calculated at zero applied field H = 0, using the cubic and uniaxial anisotropy parameters in the absence of exchange bias. Since the energy profile at H = 0 is symmetric with respect to the <110> crystallographic directions, magnetization transitions between the easy axes are also symmetric with respect to the <110> directions. This is seen in Fig. 2(b), obtained when the sample was cooled in a field applied normal to the sample plane, i.e., when there is no exchange bias, as discussed later in the paper. It is readily seen from Eq. (2) that when the field is swept along some direction, the values of the free energy minima change relative to one another. In particular, when the magnetization lies initially along the energy minimum in quadrant, and the energy minimum in the adjacent quadrant is made deeper by the applied field, the magnetization will switch to the lower minimum when the difference between the initial and the final minimum exceeds a domain pinning energy 23,24 . By inserting the switching fields observed for this symmetric results shown in Fig. 2(b), we can then determine the difference between two energy minima required for the magnetization transition to occur in the absence of H EB .
The energy profile is no longer symmetric with respect to the < 110 > directions when H EB is present in the sample plane, as seen in Fig. 4(b) (H EB = 38 Oe and φ EB = 45°). However, for magnetization transitions to occur between adjacent quadrants, the same conditions on the difference between adjacent energy minima are expected to apply as in the symmetric case. By varying the strength of H EB , we can then simulate the behavior of such asymmetric transitions obtained for different field cooling directions. The best results of simulation for several field cooling directions are obtained with H EB = 38 Oe, and are plotted in Fig. 3(c,d). The simulation nicely describes the asymmetric behavior of switching fields that is observed in the experiment (see the corresponding panels in the left column of Fig. 3).
Additionally, when a magnetic field is applied along 10°, that further distorts the free energy profile by making the energy of some minima deeper and maxima weaker, and others higher. This is illustrated in Fig. 4(c-f), where we show the energy profile at the four fields corresponding to transitions of magnetization calculated H 1 , H 2 , H 3 and H 4 as the applied field is swept along φ H = 10°.
The specific case illustrated in Fig. 4(c-f) is as follows: the field is initially swept along φ H = 10°, which has a component along the easy axis in the Quadrant 1, and orients the magnetization along that axis (near 45°). The www.nature.com/scientificreports www.nature.com/scientificreports/ field is then reversed. As the field increases in the reverse direction, its projection on the easy axis in Quadrant 2 first "flips" the magnetization to that easy axis as the minimum in Quadrant 2 is deep enough to overcome the intervening barrier, and finally flips it again to the easy axis in Quadrant 3. As the field is then swept in the positive direction, in a similar sequence the magnetization first "flips" to Quadrant 4, and finally back to Quadrant 1. Note, however, that the magnetization transition at H 4 to the easy axis in Quadrant 1 occurs at a lower field than the transition at H 2 , in Quadrant 3 because the projection of the applied field causing the transitions is aided by the bias field in Quadrant 1, while it is opposed by the presence of the bias field in Quadrant 3. This is the cause of the observed asymmetry in PHR. The cases with H EB oriented in other directions, shown in Fig. 3(a,b) can be similarly analyzed.
Cooling field and temperature dependences of exchange bias. For completeness, we carried out PHR measurements at 3 K using cooling fields of different magnitude. Figure 5(a) shows representative PHR hysteresis loops obtained for four different cooling fields. The asymmetry of the PHR hysteresis curves systematically increases as the cooling field strength is increased. In order to quantify this asymmetry, the differences of transition fields |H 1 |-|H 3 |and|H 2 |-|H 4 |are plotted in Fig. 5(b). It is clear from the figure that as the cooling field increases, the exchange bias first increases rapidly, but eventually levels off at fields over ~100 Oe. These results indicate that a moderate cooling field of a few hundred Oe is sufficient to generate an exchange bias in our structure. (c-f) Magnetic free-energy density profile at the moment of rotation of magnetization corresponding to the switching fields H 1 , H 2 , H 3 and H 4 . The relative change of the energy minima and maxima can be clearly seen at each switching field. The energy minima involving each transition are marked with shaded region. Open dots at the minima indicate the orientation of the initial state of magnetization, and solid dots indicate its final state after reorientation occurs.
Additionally, we have also studied the temperature dependence of exchange bias by using a cooling field of the same value (1.0 kOe), and cooling the system to a series of different temperatures. The data of this series of measurements are plotted in Fig. 5(c). Clearly, the asymmetry of PHR gradually decreases with increasing temperature, with the hysteresis becoming symmetric at temperatures over 20 K. In order to see the temperature dependence of the asymmetry, the differences of transition fields|H 1 |-|H 3 |and |H 2 |-|H 4 |obtained at several temperatures are plotted in Fig. 5(d). The asymmetries of the observed PHR scans decrease monotonically at similar rates for both |H 1 |-|H 3 | and |H 2 |-|H 4 |as the temperature increases, indicating that the exchange bias in the Ga 0.94 Mn 0.06 As 0.77 P 0.23 / Ga 0.94 Mn 0.06 As bilayer is strong function of temperature.

Discussion
The observed exchange bias can be explained in terms of closure domains created in the region at the top of the Ga 0.94 Mn 0.06 As 0.77 P 0.23 layer, as suggested schematically in Fig. 1(d,e). Due to its out-of-plane anisotropy, under in-plane field-cooling conditions, the magnetic structure in Ga 0.94 Mn 0.06 As 0.77 P 0.23 layer is expected to occur in multi-domain form comprised of out-of-plane and in-plane configurations that satisfy magnetic flux closure requirements indicated in the figure, similar to that observed in metallic systems involving out-of-plane films 12 .