2 L$_{2}$$_{,}$$_{3}$ absorption edges in order to determine the magnetic response of the individual elements. In L$_{2}$$_{,}$$_{3}$ XMCD, elec- trons are excited from a 2 p core level to the unoccupied 3 d valence states of the element of interest by circularly polarized x-rays at the resonance energies of the transi- tions. The difference in absorption for opposite polariza- tions gives a direct and element-specific measurement of the projection of the 3 d magnetic moment along the x- ray polarization vector. The absorption cross-section is conventionally obtained by measuring the decay products – either fluorescent x-rays or electrons – of the photoex- cited core hole. The type of decay product measured determines the probing depth of the technique. For Mn L$_{2}$$_{,}$$_{3}$ absorption, the probing depths for FY and TEY de- tection are λ$_{FY}$ ≈ 100 nm and λ$_{TEY}$ ≈ 3 nm. In the current experiment, the Mn XMCD measured using FY and TEY are thus sensitive to the bulk of the (Ga,Mn)As film and the near-interface layers, respectively. measurements were performed on beamline I06 at the Diamond Light Source, and on beamline 4.0.2 at the Ad- vanced Light Source. Total-electron yield (TEY) and fluorescence yield (FY) were monitored simultaneously using the sample drain current and the photocurrent of a diode mounted at 90 ◦ to the incident beam, respectively. SQUID magnetometry measurements were first performed on control Fe/GaAs(001) and (Ga,Mn)As/GaAs(001) samples, grown under the same conditions as the bilayers, to determine the magnetic anisotropies of the individual layers and the Curie temperature of the (Ga,Mn)As layer. The Fe film has a uniaxial magnetic anisotropy with easy axis along the [110] orientation, similar to previous studies $^{6}$. For the (Ga,Mn)As control sample, there is a competition between cubic and uniaxial magnetic anisotropies, with the former dominant at low temperatures and favoring easy axes along the in-plane 〈 100 〉 orientations, and the latter dominant close to T$_{C}$ ( ∼ 35 K) giving an easy axis along the [1 ¯ 10] orientation. Figure 1 shows [110] magne- tization versus temperature curves and low temperature hysteresis loops for a bilayer film containing a 20 nm thick (Ga,Mn)As layer. The total remnant moment of the bilayer film decreases on cooling under zero magnetic field below the T$_{C}$ of the (Ga,Mn)As, indicating that this layer aligns antiparallel to the Fe magnetization at zero field. The hysteresis curve shows a two-step magnetization reversal, indicating different behavior of the Fe and (Ga,Mn)As layers, with the smaller loop attributed to the dilute moment (Ga,Mn)As film. The minor hysteresis loop shown in Fig. 1 clearly shows a shift from zero field by a bias field H$_{E}$ , indicating that the Fe layer induces an exchange bias in the magnetic semiconductor. The shape and size of the minor loop is in agreement with the hysteresis loop for the control (Ga,Mn)As sample, also shown in Fig. 1. This strongly indicates that the exchange bias affects the whole of the (Ga,Mn)As layer in the bilayer sample. Figure 2(a)-(c) shows the magnetic field dependence of XMCD asymmetry, defined as ( I$_{l}$ − I$_{r}$ ) / ( I$_{l}$ + I$_{r}$ ) where I$_{l}$$_{(}$$_{r}$$_{)}$ is the absorption for left- (right-) circularly polarized x-rays. This is measured at the Fe and Mn L$_{3}$ absorption peaks for a Fe(2 nm)/(Ga,Mn)As(10 nm) sample at 2 K. The external field is applied along the photon incidence direction, which is at 70 ◦ to the surface normal with an in-plane projection along the [110] axis. The XMCD data show that the Fe film displays a square hysteresis loop with a single magnetization switch, as expected for a monocrystalline Fe film with strong uniaxial magnetic anisotropy. The Mn XMCD shows a more complicated loop due to the effect of the interlayer coupling. The pro- jected Mn moment aligns antiparallel to the Fe moment at remanence, and undergoes a magnetization reversal of opposite sign to the Fe. With further increase of the ex- ternal magnetic field, the Mn moment gradually rotates away from antiparallel alignment with the Fe layer, and into the field direction. Qualitatively similar behavior is observed for the Fe(2 nm)/(Ga,Mn)As(20 nm) sam- ple: the (Ga,Mn)As layer is aligned antiparallel to the Fe layer at zero field, although the bias field is lower by approximately a factor of two. Similar behavior is observed for bilayer samples con- taining a 10 nm or 50 nm (Ga,Mn)As layer, with a bias field which is approximately inversely proportional to the thickness d of the ferromagnetic semiconductor layer (Fig. 1, inset). This 1/ d dependence of H$_{E}$ was found previously for MnAs/(Ga,Mn)As bilayers $^{4}$, and is generally observed in exchanged-biased thin films $^{12}$. From this dependence it is possible to describe the ex- change bias in terms of an interface energy per unit area, Δ E = M$_{FS}$H$_{E}$d = 0 . 003 erg/cm $^{2}$. This value is rather small compared to typical exchange bias systems $^{12}$, re- flecting the low moment density M$_{FS}$ of the diluted FM semiconductor layer. However, the bias field for a given (Ga,Mn)As thickness is larger than is observed for MnO/(Ga,Mn)As structures $^{13}$, while the reproducibility and flexibility of the present structures is much higher due to the single-crystalline ferromagnetic nature of the Fe layer. Clear differences are observed between the Mn XMCD hysteresis loops obtained using TEY and FY detection modes. For FY the magnitude of the XMCD is similar (but of opposite sign) at remanence and at high mag- netic fields, whereas for TEY at remanence it is approx- imately a factor of two larger than at 1000 Oe. The Mn L$_{2}$$_{,}$$_{3}$ XMCD spectra recorded at remanence and at 1000 Oe, shown in Fig. 3, confirm this result. At re- manence the FY and TEY detected XMCD have similar magnitudes. However, under a large external field the XMCD is substantially smaller in TEY than in FY, con- firming that the net magnetization of the Mn ions near the interface is significantly less than in the bulk of the (Ga,Mn)As film. This is the case even up to the high- est field applied (20 kOe). By applying the XMCD sum rules 14 to the TEY data, and by comparing the spectra to previous measurements on well-characterized (Ga,Mn)As To confirm the presence of AFM interlayer coupling, we performed XMCD measurements at the Mn and Fe