## Introduction

After the discovery of the giant magnetoresistance1,2, the exchange bias (EB) effect has become an integral part of spintronics with implications for basic research and for numerous device applications like random access magnetic storage units and spin valves. Although its observation has been made only 60 years ago by Meiklejohn and Bean3 when studying Co particles embedded in their natural oxide (CoO) matrix, the first EB system was engineered by nature long before, a few billion years ago, in grains of titanohaematite4. The origin of the EB effect is related to the magnetic coupling across the common interface shared by a ferromagnetic (FM) and an antiferromagnetic (AF) layer, when the system is cooled through the Néel temperature of the AF layer. The magnetic properties of the AF layer and the interface are crucial for understanding the magnetic properties of the EB systems5. Yet, these two magnetic components are difficult to access experimentally with laboratory tools because of a virtually vanishing magnetization of AF layers and a small volume of the magnetic interface. Important progress has been made by involving neutron and X-ray techniques to study the bulk part of the pinning layer and the interfacial magnetism6,7,8,9,10,11,12,13. For instance, in an archetypal CoO/FM bilayer, neutron scattering has revealed the origin of reduced EB. It was shown to be related to the anisotropic domain state of the AF system12. Using soft X-ray techniques, the frozen and rotatable spins12,14,15 were observed in several systems, leading to a deeper understanding of the enhanced coercivity and the origin of the EB for systems with uncompensated AF interfaces.

Larger efforts were dedicated to the understanding of the FM/AF EB systems with in-plane anisotropy of the ferromagnet16. Notably, Mangin and colleagues17,18,19,20 have performed significant work on GdFe/TbFe ferrimagnetic soft/hard bilayers with in-plane anisotropy in which EB effects occur. EB was also studied in all coupled FM films with in-plane magnetized ferromagnets acting as pinning layers21,22. However, for applications, perpendicular uniaxial and unidirectional anisotropies are more desirable owing to a larger thermal stability of encoded information23. For instance, antiferromagnets in contact to ferromagnets with perpendicular anisotropy like Co/Pt multilayers and CoPt3 layers have been shown to exhibit EB and all other macroscopic behaviour of EB systems, like training effect, enhanced coercivity and blocking temperature for the onset of the EB23,24,25,26. More recently, the perpendicular EB (PEB) was demonstrated in a novel exchange-coupled system Sm1−0.028Gd0.028Al2/SmAl2 based on the zero magnetization ferromagnet Sm1−0.028Gd0.028Al2 as the pinning layer27. The latter exhibits a compensation temperature where the antiparallel oriented spin and orbital moments cancel one another leading to a vanishing macroscopic magnetization of the ferromagnet28. In nearly all cases, the PEB is set through field-cooling or by in situ field growth procedures, similar to the AF/FM systems with in-plane anisotropy.

In this article, we demonstrate that PEB can be set, controlled and reversed at room temperature in exchange-coupled ferrimagnetic systems, by making use of an interlayer exchange decoupling mechanism. As a prototype system, we have chosen artificial DyCo5/Ta(x)/Fe76Gd24 spin-valve (SV) trilayers, where the hard ferrimagnet (HFi) DyCo5 serves as a single magnetic domain pinning layer. In bulk form29 and in thin films30, it has a magnetization compensation temperature and a spin reorientation temperature. As the orbital moment of Dy is nearly as large as the spin moment31, it is expected that DyCo5 exhibits a large perpendicular anisotropy32, which qualifies it as a robust pinning layer. Owing to the vanishing orbital moment of Gd, the perpendicular magnetic anisotropy of Fe76Gd24 (FeGd) is weak. Therefore, it acts as a soft ferrimagnetic layer (SFi). To induce a perpendicular unidirectional anisotropy, in a first step the soft and the hard ferrimagnets are partially decoupled by a Ta interlayer spacer, and in a second step hysteresis loops are measured, reversing the SFi magnetization while keeping the HFi magnetically saturated. In this way, the PEB can be set and even reversed without involving a field-cooling procedure.

## Results

### Perpendicular anisotropy with ferrimagnetic pinning layer

The origin of EB in FM/AF and X/HFi (with X=FM or SFi) bilayers is related to the coupling across the interface shared by two adjacent magnetic layers. The magnetic state of the pinning layer interface has a crucial role in establishing a robust EB5. We exemplify below that, as a prerequisite for the occurrence of a strong PEB, the magnetic state of the interface of HFi pinning layer must be compensated. This contrasts the case of an AF pinning layer, where the magnetic state of the interface has to be uncompensated to establish a finite EB5.

When the AF surface is fully uncompensated, one expects the largest EB to occur. In the opposite case, when the AF interface is fully compensated, the EB is expected to be zero33. The last situation is depicted in Fig. 1a. The magnetic moments in the AF layers are coupled antiferromagnetically. Across the interface, the coupling between neighbouring spins is assumed to be ferromagnetic. One can analyse the impact of this compensated magnetic state on the EB in terms of interfacial energy. The interfacial energy is calculated as Ekl=−JiSkSl per pair of nearest neighbour spins at the interface33. Then, the EB field is proportional to 2*σ/A, where σ is the available energy and A is the unit area33. One observes in Fig. 1a that the first and the third (from the left) spin pair exhibits a parallel orientation; therefore they contribute negatively to the interface energy. However, the second and the fourth spin pairs contribute positively to the interface energy because the spins in the AF are oppositely oriented with respect to the FM spin. As a result, the interfacial energy vanishes for a compensated AF interface leading to a forbidden EB effect.

An opposite situation occurs for bilayers with ferrimagnetic pinning layers. This is depicted in Fig. 1b–d. For the sake of simplicity, we consider the HFi layer to be magnetically compensated. For instance, this can be achieved at the magnetization compensation temperature, where the magnetizations of the two sublattices are equal, leading to a vanishing total magnetization, just as in antiferromagnets. In Fig. 1b, the HFi layer is coupled to a FM layer. For this compensated HFi interface, the interfacial energy does not vanish. The first and third spin pairs contribute negatively to the total energy. The coupling between the transition metal and the rare-earth metal is AF across the interface (and within the HFi layer). Therefore, the second and the fourth spin pairs contribute also negatively to the interfacial energy. As a result, a compensated interface of a HFi layer leads to a maximum EB. When the pinned layer is a SFi, a similar situation occurs as shown in Fig. 1c,d. All the spin pairs contribute negatively to the interface; therefore the compensated nature of HFi leads to maximum interfacial energy for both FM and SFi pinned layers.

The occurrence of a highest available interfacial energy for a compensated interface of a HFi layer does not necessarily lead to a shift of the hysteresis loop for the pinned layer. A critical condition has to be obeyed for the EB to occur5, namely Kt/J>1, where K is the HFi anisotropy, t is the thickness of the HFi layer and J is the interfacial coupling constant. Therefore, when the coupling is large, the above condition prevents the EB to occur. Our approach here is to make use of an interlayer spacer for tuning down the coupling strength to values that fulfills the critical condition for EB.

### Magnetic properties of the ferrimagnetic films

The magnetic properties of the individual HFi and SFi ferrimagnetic layers prepared as separate samples were studied by soft X-ray magnetic circular dichroism (XMCD). In Fig. 2a, we show the temperature dependence of the coercive field and the normalized remanent magnetization for the single DyCo5(250 Å) layer. These data have been extracted from the hysteresis loop measurements at the L3 resonant energy of Co. The DyCo5 layer exhibits two magnetic transition temperatures, a magnetization compensation temperature and a spin reorientation temperature. The magnetization compensation temperature occurs at about Tcomp=120 K where the sum of the orbital and spin moments of the Co layer equals the magnetic moment of Dy, leading to a vanishing net magnetization of the film. For systems with uniaxial magnetic anisotropy, the coercive field is proportional to the magnetic anisotropy of the film and inversely proportional to the total magnetization5. Therefore, at the magnetization compensation temperature, the coercive field diverges as the net magnetization approaches towards zero, as shown in Fig. 2a. The compensation temperature can also be identified by the inverted hysteresis loop below Tcomp as compared with the one measured above Tcomp as shown in the insets of Fig. 2a. Below Tcomp, the Dy magnetic moment becomes dominant and therefore the Co moment is oriented antiparallel with respect to the applied magnetic field. Above Tcomp, the magnetic moment of Co is larger than the one of Dy and therefore, it is oriented parallel to the external field. At higher temperatures, the DyCo5 film exhibits a spin reorientation temperature (TR=350 K). We observe that the uniaxial magnetic anisotropy rotates from out-of-plane, below TR to in-plane, above TR as clearly verified by the different shapes of the hysteresis loops in both regions shown in the insets of Fig. 2a. Below TR, the hysteresis loops of the DyCo5 remain squared as exemplified in the inset of Fig. 2a, and exhibit high remanent magnetization equal to the saturation magnetization. These square loops with their high remanence at room temperature are nearly ideal properties of films with uniaxial perpendicular anisotropy. The hysteresis loop above TR has a very low remanent magnetization, and is characteristic for a hysteresis loop measured along the hard axis of a thin magnetic film with uniaxial anisotropy.

It is essential that the SFi exhibits a low coercive field and a high magnetic remanence characteristic for a well-defined perpendicular uniaxial anisotropy. These magnetic properties of the SFi layer were tuned by means of stoichiometry variation. The characterization of a single Fe76Gd24 (500 Å) layer that fulfils the required magnetic behaviour is shown in Fig. 2b. The hysteresis loops were measured at the L3 resonant energy of Fe. The compensation temperature of the FeGd film was tuned34 to lower temperatures in order to obtain a square hysteresis loop with a high remanent magnetization at room temperature. This ideal squareness with a low coercive field of about 60 Oe as well as the compensation nature of the FeGd alloy are clearly demonstrated in the insets of Fig. 2b.

### Decoupling the ferrimagnetic layers

When the SFi (FeGd) and the HFi (DyCo5) layers are set in direct contact, the exchange coupling between them is so strong that the magnetization of the SFi layer follows the one of the HFi layer. Therefore, in order to observe PEB, it is essential to partially decouple the ferrimagnetic layers as presented further on. In Fig. 3, we show the hysteresis loops of the Si3N4/Ta(50 Å)/DyCo5(250 Å)/Ta(x Å)/FeGd(500 Å) trilayers for several Ta thicknesses. The 50 Å Ta layer next to the Si3N4 substrate serves as an adhesion layer and has no role in our further discussion. When the FeGd and DyCo5 films are in direct contact, the coercive field is the same for both layers, Hc=350 Oe as observed in Fig. 3a. Fe and Co are aligned parallel to the field and exhibit a parallel interfacial exchange coupling. Dy and Gd magnetic moments are also parallel exchange coupled but antiparallel oriented with respect to the external field. This is the most favourable configuration leading to a strong coupling between these layers. The other situation, when measuring in between the compensation temperatures of the two ferrimagnets, would lead to frustrated magnetic moments at the interface because of competing interactions between a rare earth dominated ferrimagnet and a transition metal dominated one. In order to allow EB to occur, one needs to partially decouple these two layers. This is achieved by introducing a Ta interlayer of suitable thickness. We observe that for 1, 2 and 3 Å thick Ta interlayer, the DyCo5 and FeGd films are still reversing together as shown in Fig. 3b. A sizeable decoupling appears only when Ta is about 5 Å thick (Fig. 3c). When the Ta thickness is further increased to 10 Å, the interlayer exchange coupling strength diminishes and therefore the coercive field of the FeGd layer further decreases (Fig. 3d). For fully decoupled layers, the coercive field of the SFi layer is Hc=60 Oe (Fig. 3e). Note that the coercive field of the DyCo5 layer does not vary considerably as a function of the spacer layer thickness, which is in strong contrast with the large variation of the coercive field of the FeGd layer. This further confirms the hard and soft nature of the magnetic properties of these two films, in agreement with their much different values for the orbital moments. Given that the total magnetizations of the SFi and HFi layers do have finite values at room temperature, a SV configuration can be induced for the partially decoupled trilayers. Reversing the net magnetization of FeGd in a saturated state of DyCo5 layer leads to an antiparallel orientation of the net magnetizations of both ferrimagnetic films, just like in classical FM SV systems35. One conceptual difference between our perpendicular ferrimagnetic SV and the FM SV systems is that the interlayer is used here to decouple only partially the ferrimagnetic layers, while for the classical case (AF/FM/spacer/FM) an interlayer spacer is used to fully decouple the FM-free layer from the FM pinned layer.

### Room temperature control of PEB

Taking advantage of the partial decoupling of the FeGd and DyCo5, we demonstrate in Fig. 4 that the hysteresis loops of FeGd can be shifted and the shift's sign even reversed without involving a field-cooling procedure. In the left column, we show the measured data corresponding to the sample with a Ta interlayer thickness of 5 Å. When the hysteresis loop is measured between −900 Oe to +900 Oe and backwards, both element-specific hysteresis loops of the DyCo5 and FeGd layers are centred with respect to the external field as shown in Fig. 4a. However, after saturating the system in a positive field higher than the coercive field of HFi and measuring the hysteresis loop of the FeGd layer from 300 to −300 Oe and backwards, a shift of the hysteresis loop occurs (Fig. 4b), revealing the presence of a unidirectional anisotropy. The EB and the coercive fields are HEB=−80 Oe and Hc=112 Oe, respectively. Note that the coercive field of the biased FeGd is higher than the coercive field when unbiased, as expected (compare Fig. 4b with Fig. 3e). Please also note that the hysteresis loops in Fig. 4a, although centred with respect to the field axis, are not unbiased. They are centred because we reverse the unidirectional anisotropy by reversing the DyCo5 layer during the field cycle. As a result, the EB field adds to the coercivity in the Fig. 4a. For the scenario in Fig. 4b, the DyCo5 film remains saturated in a single magnetic domain state, and through interlayer exchange coupling a unidirectional anisotropy is mediated in the FeGd layer, according to the coupling mechanism described at the beginning of this section. When the system is saturated in a negative field smaller than the coercive field of the HFi layer and a subsequent hysteresis loop is measured from −300 to +300 Oe and backwards, the magnetization curve of FeGd is shifted to the opposite side, as shown in Fig. 4c. This demonstrates that the unidirectional anisotropy can be reversed in relatively low fields and without involving any field-cooling procedure. The single magnetic domain state of the pinning layer is of crucial importance also for the stability of the EB field. In Supplementary Fig. S1, we show that the coercive and EB fields remain stable as a function of the loop index, demonstrating that a training effect is essentially absent. A magnetic multi-domain state in the pinning layer not only diminishes drastically the absolute value of the EB field but it also mediates a strong EB reduction upon consecutive cycling (training effect)12,21.

To further demonstrate that the absolute value of the PEB field can also be controlled, we show in the right column of Fig. 4 the magnetization for a sample with 10 Å Ta interlayer thickness. The same procedure (as for the sample with 5 Å Ta) was applied to reveal the occurrence of the unidirectional anisotropy in FeGd. The characteristic hysteresis loops shown here are measured by probing the rare earth elements (at the M5 resonant energy), which demonstrates also their intrinsic AF orientation with respect to the transition metal. The coercive field and the EB for the SFi layer are clearly smaller as compared with the sample with thinner Ta thickness. Therefore, by varying the interlayer thickness one can tune in a controlled manner the absolute value of the EB and coercive fields.

## Discussion

The coupling mechanism with HFi pinning layers is fundamentally different as compared with the established mechanism of EB with AF pinning layers. While for the latter one it is required that the AF exhibits a magnetically uncompensated interface for EB to be established, in the former case a compensated HFi interface is required for the largest EB effect to occur. Moreover, for FM/AF EB systems with in-plane anisotropy, the thickness of the interlayer does not exhibit a cutoff behaviour. Submonolayer dusting of the interface is sufficient to dramatically reduce the absolute values of the EB and coercive fields36. This is different for our system, where a much larger thickness of Ta, equal to 5 Å, was needed to allow EB to occur. The critical thickness for the interlayer can be understood based on models for EB5. For instance, in AF/FM bilayers, the onset of EB occurs for a critical AF thickness, which is given by the condition R=(KAF tAF)/JEB≥1, where the KAF and tAF are the anisotropy and the thickness of the AF, respectively, and JEB is the interfacial coupling constant. This implies that the AF thickness needs to be increased until the AF layer can resist the interfacial torque that acts during the rotation of the ferromagnet15. In our case, the thickness and the anisotropy of the HFi layer are held constant; therefore the interfacial coupling has to be decreased by increasing the thickness of the interlayer until the condition above is satisfied. The dipolar coupling between the macroscopic magnetization of the two ferrimagnetic layers also has a role, contributing, however, minimally to the absolute critical thickness of the interlayer. In fact, the enhanced coercive fields of the SFi hysteresis loops in Fig. 4 can be partially attributed to dipolar coupling. For instance, when the FeGd magnetization reverses first, the net magnetizations of the HFi and SFi layers are in an unfavourable antiparallel situation, therefore an enhanced coercive field is observed. This is different with respect to the EB with in-plane anisotropy where the stray fields are not present leading to a vanishing dipolar coupling.

In conclusion, we have demonstrated that PEB in ferrimagnetic DyCo5/Ta(x)/Fe76Gd24 alloys, where the DyCo5 layer has the role of a single magnetic domain hard ferrimagnet and the FeGd alloy acts as a soft ferrimagnet, can be controlled in a flexible and robust manner. Taking advantage of the tunability of the interlayer exchange coupling, we have shown that PEB can be induced without making use of a field-cooling procedure. This was achieved by carefully engineering the magnetic properties of the soft ferrimagnet and the thickness of the partially decoupling interlayer. Owing to the strong coupling between the DyCo5 and FeGd, the EB occurs above a critical thickness of Ta interlayer, at 5 Å. The absolute value of the EB can be tuned through the thickness of the interlayer spacer and even reversed with relatively low magnetic fields of several hundred Oersteds. This flexibility in controlling a robust PEB at room temperature may be of outmost importance for applications in modern ultrafast storage media37.

## Methods

### Sample preparation

The samples were grown by magnetron sputtering (MAGSSY chamber at HZB) in an ultraclean Argon atmosphere of 1.5×10−3 mbar with a base pressure of <5×10−9 mbar at the deposition temperature of 300 K. The stoichiometry of the ferrimagnetic alloys was controlled by varying the deposition rate of separate chemical elements in a co-evaporation scheme. As substrates, we used Si3N4 membranes.

### XMCD from ferrimagnetic films

XMCD was measured in a transmission geometry38,39 at BESSY II using the ALICE diffractometer40 installed at the PM3 bending magnet beamline. The study of the DyCo5 layer in high fields was performed with the high-field endstation at the beamline UE46-PGM1 installed at the electron storage ring BESSY II. The measurements were performed by detecting the external field-dependent transmitted intensity of the circularly polarized soft X-rays with the energy set to the experimental L3 resonant edges of Co(780.4 eV) and Fe(709.4 eV), and M5 resonant edges of Gd(1,187 eV) and Dy(1,297 eV).

Circularly polarized soft X-rays are impinging at normal incidence on the sample placed in an external magnetic field set parallel to the beam direction. The transmitted intensity is measured by a Si photodiode, which is insensitive to applied magnetic fields. Typical experimental spectra for a DyCo5/Ta/FeGd sample are shown in Fig. 5b–e. By varying the energy of the circularly polarized light and measuring the normalized transmitted intensity for two opposite saturating fields, one observes a strong variation of intensity at the absorption edges. The experimental XMCD curves are then extracted as the logarithm of the ratio of the transmitted intensities for positive and negative field, respectively. Inspecting the polarity of the XMCD signal at the absorption edges, one obtains information about the relative orientation of the sublattice magnetization components. For instance, the XMCD at the Co L3 edge is negative whereas the XMCD at the M5 edge of Dy is positive. This shows that the magnetic moments of Co and Dy are oriented antiparallel with respect to each other. Similarly, the XMCD signals at the L3 edge of Fe and at the M5 edge of Gd have opposite signs, demonstrating the ferrimagnetic nature of the layers. Most important, for the case of interfacial (or interlayer) coupled films, the coupling sign between the magnetic moments of adjacent magnetic layers can be directly extracted owing to the element-specific sensitivity of the XMCD technique. In our case, the transition metal (Fe and Co) are oriented parallel with respect to each other and the rare earth metals (Gd and Dy) are also parallel oriented.

The element-specific hysteresis loops are recorded by setting the photon energy to the experimental L3 absorption edges of the transition metal or to the M5 absorption edges of the rare earth and measuring the transmitted intensity while sweeping the magnetic field. Typical hysteresis loops obtained for Co, Dy, Fe and Gd are shown in Fig. 5f–i. The polarity of the hysteresis loops reflects also the relative orientation of the elemental magnetic moments. Additionally, it provides intrinsic magnetic parameters, that is, the coercive and EB fields for each probed element. In this way, element-specific hysteresis loops can be used to probe the complex magnetic behaviour of exchange-coupled films, demonstrating also the coupling ground state of these layers.