Loop Bifurcation and Magnetization Rotation in Exchange Biased Ni/FeF2

Exchange biased Ni/ FeF2 films have been investigated using vector coil vibrating sample magnetometry as a function of the cooling field strength H_FC. In films with epitaxial FeF2, a loop bifurcation develops with increasing H_FC as it divides into two sub-loops shifted oppositely from zero field by the same amount. The positively biased sub-loop grows in size with H_FC until only a single positively shifted loop is found. Throughout this process, the negative/positive (sub)loop shift has maintained the same discrete value. This is in sharp contrast to films with twinned FeF2 where the exchange field gradually changes with increasing H_FC. The transverse magnetization shows clear correlations with the longitudinal sub-loops. Interestingly, over 85% of the Ni reverses its magnetization by rotation, either in one step or through two successive rotations. These results are due to the single crystal nature of the antiferromagnetic FeF2, which breaks down into two opposite regions of large domains.

sizes may also affect the shape of the hysteresis loop. Recent experiments on model systems using synthetic antiferromagnets have shown that larger domain sizes could lead to a loop bifurcation [13,14].
In this work, we demonstrate that a bifurcated hysteresis loop can be realized in field cooled (FC) Ni/epitaxial-FeF 2 bilayers. In comparison, the bifurcation is absent in FC Ni/twinned-FeF 2 and Ni/polycrystalline-FeF 2 , which are expected to have smaller AF domain sizes. Unlike the aforementioned bifurcation seen in ZFC bilayers caused by opposite FM domains [5][6][7], here the FM is a single domain and the bifurcation is due to the opposite AF domains frozen in during cooling and consequently can be tuned by the cooling field. Additionally, the Ni layer reverses its magnetization mostly via rotation. 3 For this study, we have prepared thin films of Al (76 Å) / Ni (210 Å) / FeF 2 (500 Å) simultaneously onto single crystal MgF 2 (110), MgO (100) and Si (100) substrates, to respectively achieve untwinned epitaxial (110), twinned (110), and polycrystalline FeF 2 [15][16][17][18]. All samples have been grown by electron beam evaporation, using conditions similar to those reported in earlier publications [16,18]. The FeF 2 layer was deposited at 200 -300 ºC while the Ni and Al layers were grown at 150 ºC. The crystal structures of FeF 2 and Ni (always polycrystalline) have been confirmed by x-ray diffraction. The FeF 2 (110) rocking curve full-width at half maximum (FWHM) is about 3.9º (using Cu Kα) for twinned FeF 2 and < 1.2º for untwinned epitaxial FeF 2 . This is consistent with x-ray reflectivity measurements by Shi and Lederman where the in-plane coherence length in similarly prepared twinned FeF 2 was determined to be about 60-100 Å and that in untwinned FeF 2 was ~ 280 Å [17].
Field cooling and magnetic measurements have been performed in a vibrating sample magnetometer. The samples were cooled from 150 K (above 78K, the FeF 2 Néel temperature) to 15 K in different cooling fields H FC (2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15) (Fig. 1a) which is larger than that in Ni/twinned-FeF 2 . As H FC is increased (2 kOe < H FC < 15 kOe), a loop bifurcation develops as the loop splits into two oppositely shifted sub-loops separated by a plateau in the middle. The two sub-loops have similar coercivity and symmetric exchange fields, H E ≈ ±1 kOe ( Fig. 1b & 1c). Note that as H FC increases, the sub-loops maintain their discrete exchange fields, at ±1 kOe, only their relative sizes change. For example, the negatively biased sub-loop accounts for ~ 85% of the total Ni magnetization at H FC = 5 kOe, but only ~ 35% at H FC = 7.5 kOe. Finally at H FC = 15 kOe, the loop is completely positively shifted with H E ≈ +1 kOe. Thus an increasing H FC drives the sample from negative to positive bias while the middle plateau moves in a "top-tobottom" fashion. This is in contrast to Ni/twinned-FeF 2 and Fe/twinned-FeF 2 [15] samples where H FC drives the whole loop continuously (for certain samples from negative to positive bias) in a "left-to-right" fashion.
The transverse loops show peaks at the fields corresponding to the switching fields of the longitudinal (sub)loops. We will use "upward" and "downward" to represent directions in the film plane that are perpendicular to the applied field, corresponding to positive and negative transverse moment, respectively. For H FC = 2 kOe, the transverse loop shows two positive peaks at H ≈ -1 kOe -one for each branch of the field cycle ( Fig. 1a). Both peaks have large magnitudes, ~ 82% of the saturation moment, m s . This indicates that most of the sample reverses its magnetization via rotation, as opposed to domain nucleation and motion. In films with twinned and polycrystalline FeF 2 , we 5 usually observe a smaller transverse peak, ~ 10-60% of the total magnetization. As H FC is increased, a pair of peaks at H ≈ ±1 kOe is observed for each field-sweep direction ( where A m // and B m // are the moments associated with the sub-loops, as schematically shown in Fig. 2a. In the transverse direction, the domain fraction can be defined as 6 where A m ⊥ and B m ⊥ are the local maximum (peak) moment value near H = ± 1 kOe, as schematically shown in Fig. 2b [19].
As shown in Fig. 2c Since A E H is in close alignment with +H, as opposed to -H, the reversal from/to positive saturation is always sharper than that from/to negative saturation, as seen in Fig. 1a to rotate upwards, which in turn drag FM-B spins to also rotate upward (rather than downward) at + 1 kOe. Hence, the m ⊥ peaks in general are both negative and both positive for the decreasing-and increasing-field sweep, respectively [20]. where the small twin sizes and the orthogonal twinning encourage the formation of small AF domains with orthogonal anisotropy directions [15,16].
In the opposite limit, i.e., where D FM ≤D AF during switching, each FM domain couples to a large, uniform collection of interfacial AF spins so that the total influence (and consequently the exchange bias) on the FM domain is greater than that for the D FM >> D AF case. Furthermore, when opposite AF domains are present, each FM domain still couples to a uniform AF structure and is discretely biased. The sum of the FM domains results in sub-loops. This is consistent with the findings in synthetic antiferromagnets where it has been shown that a loop bifurcation develops as the domain size becomes larger [13,14]. For the Ni/epitaxial-FeF 2 bilayers studied here, the larger in-plane coherence length and the lack of orthogonal twinning encourage the formation of large domains, leading to a larger D AF than that in twinned-FeF 2 . Although the actual D AF here is yet to be determined, large AF domains (up to ~mm scale) have been seen in bulk single crystal fluorides [21,22]. Additionally, the large AF domains also encourage the FM domains to remain intact during magnetization reversals. This explains the large domain fractions (~85%) seen in the transverse hysteresis loops that reverse by rotation.
Indeed, recent magneto-optical Kerr effect studies have shown the existence of ~mm scale domain structures in similar samples [18], and simulations have reproduced the loop bifurcation for systems with large AF domains [23].
It is interesting to note that the exchange field is larger in Ni/untwinned-FeF 2 than in Ni/twinned-FeF 2 , where the latter is expected to have a smaller AF domain size. This is opposite to some of the theoretical predictions [4] as well as experimental results in Co/LaFeO 3 [9]. The key issue might be whether the exchange field depends most critically on the AF domain size or the interfacial spin density. This is the subject of an ongoing study.   Arrows indicate the field-cycle sequence for the transverse loop.