First of all, we have analyzed the possibility of Fe72Ga28 oxidation because of its growth on top of Cr2O3 (Fig. 1). XRD measurements do not show evidences of oxidation within the resolution technique. The diffraction patterns are similar to what we have previously reported about sputtered Fe72Ga28 being the (110) the main Fe72Ga28 diffraction peak [16–19]. On the other hand, the diffraction peaks of Cr2O3 show no variations upon the deposition of Fe72Ga28 on top of it (Fig. 1).

Sputtered Fe72Ga28 layers deposited in the ballistic regime develop in-plane magnetic anisotropy above 100 nm [16, 18]. Nevertheless, the coupling with Cr2O3 completely eliminate this in-plane anisotropy even for thicknesses well above 100 nm (Fig. 2a). This can be understood considering that a sample will show PMA if two conditions are fulfilled: i) it is magnetically isotropic in the sample plane, and ii) the OOP direction is an easy axis in comparison to any direction in the sample plane. Therefore, the absence of in-plane magnetic anisotropy is a necessary condition for the PMA to be developed.

The VSM hysteresis loops also reveal the change of the magnetization direction from in-plane to OOP as the Fe72Ga28 thickness is reduced (Fig. 2b). We can quantitively monitor this evolution by means of the OOP squareness (*M**r*/*M**max*) defined as the ratio between the remanence (*M**r*) and the maximum magnetization (*M**max*) obtained in the perpendicular hysteresis loops. In table 1 we can observe how the squareness increases as the Fe72Ga28 thickness is reduced, mostly for a thickness below 80 nm.

MFM images can also be used to monitor the influence of the Cr2O3 on the Fe72Ga28 magnetic behavior (Fig. 3). When Fe72Ga28 is no coupled (Fig. 3a), it is observed the magnetic contrast known as magnetic ripple in agreement with previous works [24–26]. However, due to the interfacial coupling with Cr2O3, the OOP component of the magnetization of Fe72Ga28 is enhanced, and stripe domains start to be visible in the MFM images (Fig. 3b-d).

In ferromagnetic materials with PMA, the quality factor *Q* is defined as:

$$Q={K}_{FM}/2\pi {M}_{FM}^{2}$$

1

where *K**FM* is the perpendicular magnetic anisotropy, and \({M}_{FM}\) is the magnetization saturation [9, 39]. For materials with moderate or low PMA, *Q* < 1, and stripe domains appear above a critical thickness (\({t}_{cr})\):

$${t}_{cr}=2\pi \sqrt{{A}_{ex}/{K}_{FM}}$$

2

where *A*ex is the exchange energy per unit length. When *Q* > 0.1, stripe domains are wider than the layer thickness, whereas they exhibit a periodicity equals to the layer thickness if *Q* < 0.1.

We have inferred *K**FM* from the comparison of in-plane and OOP hysteresis loops following the work of Garnier *et al*. [9]. In average, we have obtained a *K**FM* of 3.4·106 erg/cm3. Taking \({M}_{FM}\) as 1100 emu·cm− 3 [26], it is inferred a *Q* of 0.3 in our samples and therefore, stripes are expected above a critical thickness. Considering *A**ex* = 1.7·10− 6 erg·cm− 1 from the literature [22–23, 40], and using Eq. (2), it is obtained an experimental *t**cr* of 44 nm. This is in agreement with our experimental findings in which stripes have only been observed for Fe72Ga28 thickness ≥ 40 nm. In fact, if we take this experimental value as *t**cr*, a *K**FM* of 4·106 erg·cm− 3 is calculated, pretty close to the value inferred from experimental hysteresis loops. Finally, from the MFM images we have obtained a stripe period of 125 nm by means of the power spectral density. This stripe periodicity higher than the layer thickness is consistent with the quality factor *Q* higher than 0.1 calculated in our samples.

In addition to the rotation of the Fe72Ga28 direction magnetization towards the perpendicular direction, we have observed an exchange-bias effect related to the Cr2O3/ Fe72Ga28 interfacial coupling as indicated by the shift of the hysteresis loop in the horizontal axis (*H*E) at 5 K after a FC process at 1 kOe (Fig. 4). This exchange-bias phenomenon in the perpendicular direction is related to the exchange-coupling between the antiferromagnetic Cr2O3, and the ferromagnetic Fe72Ga28 [41]. For a Fe72Ga28 thickness of 20 nm, *H*E is -17 Oe, and -9 Oe for a thickness of 40 nm.

Since the perpendicular magnetic anisotropy inferred in this work for Fe72Ga28 (\({K}_{FM}\) = 3.4·106 erg·cm− 3) is higher than the theoretical value of Cr2O3 (\({K}_{AF}\) = 2·105 erg·cm− 3) [42], and some chemical roughness is expected at the Fe72Ga28/Cr2O3 interface, we have used the random field model proposed by Malozemoff [35–37] to calculate the theoretical *H**E* values. In this random field model, the AF layer breaks into domains, and the exchange-bias field is obtained thanks to the expression:

$${H}_{E}=\frac{2z\sqrt{{A}_{AF}{K}_{AF}}}{{\pi }^{2}{M}_{FM}{t}_{FM}}$$

3

where \(z\) is generally taken as the unity, and \({A}_{AF}\) is the exchange stiffness of the antiferromagnet that takes a value of 4·107 erg/cm [42]. With this expression (3) we obtain \({H}_{E}\) equals to -26 Oe and − 13 Oe for Fe72Ga28 thickness of 20 and 40 nm, respectively, that are pretty close to the experimental − 17 Oe and − 9 Oe, respectively. This well agreement confirms the possibility of using this model in Cr2O3-based exchange-biased systems as also previously reported [42].

Finally, from \({H}_{E}\) experimental values the interfacial exchange energy \(\varDelta E\) can be calculated:

$$\varDelta E={H}_{E}2{M}_{FM}{t}_{FM}$$

4

For Fe72Ga28 of 20 nm and 40 nm, it is obtained a \(\varDelta E\) of 0.08 erg·cm− 2 that is higher than in previous works in which Cr2O3 has been coupled with other ferromagnets with reported values of 0.05 erg·cm− 2 at 5 K [30, 41].