Coercivity Enhancement in Exchange Biased Systems Driven by Interfacial Magnetic Frustration

We report the temperature and cooling field dependence of the coercivity of exchange biased MnF2 Fe bilayers. When the antiferromagnetic surface is in a state of maximum magnetic frustration and the net exchange bias is zero, we observe a strong enhancement of the coercivity, which is proportional to the exchange coupling between the layers. Hence, the coercivity can be tuned in a reproducible and repeatable fashion in the same sample. We propose that a frustrated interface provides local energy minima which effectively pin the propagating domain walls in the ferromagnet, leading to an enhanced coercivity.

The magnetic coercivity H C (i.e., the half-width of the magnetic hysteresis loop) is an important parameter used to characterize magnetic materials.Control over the coercivity is desirable to tune the behavior of magnetic devices.In spite of this, the issue of controlling the magnetic coercivity has received little attention from physicists as it is supposed to be an extrinsic quantity often determined by such parameters as defect density.As such it is difficult to control in a reproducible fashion by changing an external parameter.Exchange bias H E (the shift of the hysteresis loop along the field axis) has been extensively studied in antiferromagnetic (AF)/ferromagnetic (F) bilayers, although a quantitative understanding is still unavailable [1].Despite this, some intriguing correlations exist between H E and H C .Moreover, recent theoretical work [2,3] claims that the behavior of H C and the correlations between H E and H C provide important clues as to the microscopic origin of exchange anisotropy.However, experimental investigations of H C , as well as H E , in systems with well controlled and characterized microstructure are rare ( [4][5][6][7] are examples).
Here we present measurements on an exchange biased system in which the coercivity can be tuned by the field applied ͑H FC ͒ when cooling through the AF Néel temperature T N .In this fashion, the AF surface spin structure can be varied and its effect on the behavior of H E and H C observed.The crossover from negative to positive H E , with increasing H FC , is accompanied by an additional increase in the coercivity.This increase is in addition to that which occurs on cooling below T N and increases with the exchange coupling between the AF and F layers.The dependence of the exchange bias on cooling field and temperature can be analyzed using a simple model in which the AF surface spin structure is modified by the applied H FC , in the presence of an antiferromagnetic coupling between the F and AF layers [7][8][9].We show that this enhancement is brought about by magnetic frustration at the AF͞F interface, a result that has important implications for the physics of exchange biased systems.ZnF 2 ͑25 nm͒͞MnF 2 ͑60 nm͒͞Fe͑12 nm͒͞Al͑3 nm͒ layers were deposited by electron beam evaporation.The nonmagnetic ZnF 2 layer serves as a buffer between the MgO(100) substrate and the AF MnF 2 layer (T N 67 K [8]), while the Al capping layer prevents oxidation.ZnF 2 , Fe, and Al were deposited at 200 ± C, 150 ± C, and 150 ± C, respectively, whereas MnF 2 was deposited at several temperatures in the 275-375 ± C range.Varying the substrate temperature during deposition of the MnF 2 layer affords control over the roughness ͑s͒ of the MnF 2 ͞Fe interface [8] which in turn changes H E .The pressure during fluoride deposition is around 6 3 10 27 Torr.X-ray diffraction, grazing incidence reflectivity, and reflection high energy electron diffraction were used for structural characterization, while magnetic measurements were made with a SQUID magnetometer between 4.2 and 100 K and in fields up to 70 kOe.Remnant fields were minimized by heating the superconducting magnet above its transition temperature after application of large fields.They were then measured and accounted for by measuring the hysteresis loops of single Fe films.It is noted that it has been suggested that hysteresis loops may provide a lower bound for H E [10].However, the absence of training effects, the reproducibility of the data, and earlier reversible measurements [11] all indicate that hysteresis loops provide a good measure of H E .
ZnF 2 and MnF 2 layers have a body centered tetragonal structure with a (110) orientation perpendicular to the substrate surface, while the Fe overlayers are polycrystalline.The (110) fluoride reflection peak widths give a grain size equivalent to the thickness of the film.The roughness ͑s͒ determined from refinement of the grazing incidence reflectivity [12] is identified as the rms thickness fluctuation at the fluoride-Fe interface over the relatively long length scale probed by grazing incidence reflectivity.This can be controlled from 0.6 nm up to *4 5 nm without significantly varying the full width at half maximum of the MnF 2 (110) reflection or the rocking curve peak width, thus proving that the crystalline quality is not affected.As shown previously, MnF 2 ͞Fe layers with "smooth" interfaces ͑s , 1.5 nm͒ show positive H E (i.e., in the same direction as H FC ) for cooling fields *10 kOe while layers with "rough" interfaces show only negative H E (i.e., in the opposite direction to H FC ) [8].
Figure 1 shows the temperature dependence of H E and H C [defined as the half loop width at magnetic moment ͑m͒ 0] for two H FC values for a sample with a smooth MnF 2 ͞Fe interface ͑s 0.6 nm͒.
For low cooling field ͑H FC 2 kOe͒ typical behavior is observed: The negative H E switches on close to T N eventually saturating below 30 K [Fig. 1 1(c)] and H C [Fig.1(d)] is similar to the H FC 2 kOe case.It is interesting that in both cases the H C enhancement below T N does not saturate at low temperatures, despite the fact that H E reaches a temperature independent value (presumably this reflects the saturation of the AF sublattice magnetization and anisotropy [13]).Such behavior in H E and H C has been observed in several systems (e.g., [4][5][6][14][15][16]) and appears to be a common phenomenon.It seems clear that this behavior warrants further study.We note that the theoretical work mentioned earlier [2] suggests that H E and H C are of fundamentally different origins (H C is due to the uniaxial anisotropy resulting from spin-flop coupling while H E is created via a different mechanism, such as interfacial defects), suggesting that the temperature dependences should not necessarily be expected to be similar.However, we also note that identical mechanisms may give dissimilar temperature dependencies as coercivity is dependent upon thermally activated processes and is therefore expected to have a temperature dependence in the whole range of temperature measured here.
The cooling field dependence of H E and H C is shown in Fig. 2 for two representative samples: one with a smooth MnF 2 ͞Fe interface (s 0.6 nm, shown in Fig. 1) and one with a rougher interface ͑s ഠ 3 nm͒.The smooth sample shows a crossover from negative to positive H E at H FC 10 kOe, while the rough sample shows only negative exchange bias which is weakly dependent on H FC .This behavior was found to be due to a crossover from AF exchange coupling to F exchange coupling with increasing roughness [8].The coercivity behavior is intriguing; the rough sample (which shows only negative H E ) exhibits a very weak dependence of H C on H FC [Figs.2(c the sample, or the crystallinity, with the consequent difficulties with interpretation. We define the size of the "peak" in H C ͑H FC ͒ [see Fig. 2(b)] as the increase of H C from H FC 0 to the maximum value of H C , labeled DH C -the "coercivity enhancement."The percentage value can then be defined as DH C ͞H C ͑0͒, where H C ͑0͒ is the coercivity at zero cooling field.Figure 3 shows this percentage coercivity enhancement plotted against the exchange bias measured at low (2 kOe) cooling field ͑H 0 E ͒, for a total of seven samples.The variation in H 0 E is achieved by varying the interfacial roughness via the substrate temperature during growth [7,8].These seven samples exhibit AF coupling between the AF and F layers and the low cooling field exchange bias is indicative of the coupling strength across the interface [8].Hence the data of Fig. 3 show that the coercivity enhancement is more pronounced for strong coupling between layers and approaches zero as the AF coupling strength falls to zero.
Since in exchange biased systems the H C enhancement is thought to originate from a finite H E , the naive expectation is that H C should reach a minimum close to H E ͑H FC ͒ 0. However, Fig. 2 clearly shows that the maximum in H C occurs very close to the point at which H E ͑H FC ͒ 0. We first note that such coercivity maxima can generally be observed at magnetic phase transitions [17].However, the AF surface or bulk spin flop can be ruled out as a possible mechanism as the fields involved are an order of magnitude larger than measured here [18].The coercivity enhancement can be understood qualitatively and quantitatively as described below.Within the simple model for positive H E [7][8][9], the AF exchange coupling across the interface ͑J F͞AF ͒ is being frustrated by the coupling of the AF surface spins to H FC .At low cooling FIG. 3. DH C (the percentage increase in coercivity over the H FC !0 value) as a function of H 0 E , the low cooling field exchange bias (measured at H FC 2 kOe) for seven samples.The rms roughnesses as determined by low angle reflectivity are 0.60, 0.72, 0.80, 0.92, 1.00, 1.13, and 1.2 nm.The dotted line is a least squares linear fit through the origin.DH C and H 0 E are labeled in Fig. 2.
fields the AF coupling dominates and a low energy state is "frozen in" at T N , but for high cooling fields the coupling of the AF surface spins to H FC dominates and leads to an unstable state being frozen at T N .This leads to the positive exchange bias.It is in the intermediate region where H E is close to zero that we observe the enhancement of the coercivity.Here some fraction of the spins are aligned with the cooling field and are therefore frustrating the AF exchange coupling, while others remain in the low potential energy, AF-coupled, state.It is at this point of maximum frustration that we observe the largest H C .In other words, the AF surface splits into regions or "domains" [19], which are aligned either with H FC or in the original AF-coupled configuration.Given that H C in these Fe films is dominated by domain wall pinning, an enhancement of H C can be understood in terms of increased pinning of the Fe domain walls at the edges of the AF domains.This explanation is also consistent with the data of Fig. 3 where it is seen that the coercivity enhancement becomes more pronounced with increasing exchange coupling.Essentially, the effectiveness of the AF domain walls as pinning sites for the propagating F domain wall increases as the exchange coupling between the layers is increased.
A simple modeling of this scenario can be realized by considering a domain wall in an F layer (in the x-y plane) of thickness t, domain wall width W, and length L, propagating over a semi-infinite AF block split into N square shaped domains aligned parallel or antiparallel to H FC .Balancing the energy due to an applied field H with the energy change of the domain wall on propagating a distance dy gives the following integral [20]: where M S is the saturation magnetization and g is the domain wall energy.g can be written g͑x, y͒ 2M S a 0 m͑x, y͒h͑x, y͒, where m͑x, y͒ is a unit vector in the direction of the local magnetization, h͑x, y͒ is the local field, and a 0 is the interfacial atomic separation.
We then define h͑x, y͒ as a series of delta functions at each domain edge which crudely models the real situation where the domain walls in the AF provide a local energy perturbation for the propagating F domain wall.
Evaluating the integral we obtain DH C a 0 h 0 L͞td AF , where DH C is the enhancement of H C , d AF is the AF domain size, and the field h 0 is the delta function weight.
To evaluate DH C a suitable value for h 0 is required.As a first approximation, for an order of magnitude estimate we simply use the amplitude of the Malozemoff random field [21], h 0 J AF͞F ͞M S a 3 0 , giving DH C J AF͞F L͞d AF tM S a 2 0 . ( At low H FC and high H FC the AF is aligned antiparallel or parallel to H FC , there are no AF domains, d AF approaches the sample size, and DH C is minimized.At the point H E 0 the number of AF domains reaches a maximum, hence d AF reaches a minimum value and there is a consequent maximum enhancement in H C .Taking literature values [22] for the parameters involved we obtain the reasonable value d AF ϳ 1000 nm, required to reproduce our observed DH C of 30%.In addition to this, Eq. ( 2) implies that if the AF domain size (d AF ) is constant at the H C peak, the H C enhancement is directly proportional to J AF͞F .Given that H E is proportional to J AF͞F [23] this dependence is exactly that observed in Fig. 3, where the H C enhancement increases linearly with the low field H 0 E .In summary, we have measured the temperature and cooling field dependence of the coercivity of MnF 2 ͞Fe exchange biased bilayers.In this system the surface spin structure of the AF layer can be varied by the cooling field which systematically varies the exchange bias and coercivity.A strong coercivity enhancement is observed in the region where the AF surface spin structure exhibits maximal frustration.The coercivity enhancement is shown to be proportional to the exchange coupling between the layers.Simple modeling shows that the increased coercivity is due to enhanced pinning of the propagating domain wall in the (a)], while H C increases monotonically with decreasing temperature below T N [Fig.1(b)].The temperature dependence of H C for ZnF 2 ͞Fe͞Al, also in Fig. 1(b), shows a rather low H C ͑,15 Oe͒ with a weak temperature dependence.These data clearly indicate that the large coercivities at T , T N in the MnF 2 ͞Fe bilayers are due to exchange coupling across the AF͞F interface.For H FC 70 kOe the temperature dependence of the positive H E [Fig.

FIG. 1 .
FIG. 1. H E and H C as a function of T for H FC 2 kOe and H FC 70 kOe [the sample has a smooth MnF 2 ͞Fe interface ͑s 0.6 nm͒].(a) H E ͑T ͒ for H FC 2 kOe, (b) H C ͑T͒ for H FC 2 kOe, (c) H E ͑T͒ for H FC 70 kOe, and (d) H C ͑T͒ for H FC 70 kOe.Note the sign reversal in H E from (a) to (c).Open symbols are for ZnF 2 ͞Fe.The lines are guides to the eye.
FIG. 2. H E and H C as a function of H FC for a sample with a smooth MnF 2 ͞Fe interface (s 0.6 nm; see Fig. 1) and a sample with a rougher interface ͑s ഠ 3 nm͒; (a) H E ͑H FC ͒ for the smooth interface, (b) H C ͑H FC ͒ for the smooth interface, (c) H E ͑H FC ͒ for the rough interface, and (d) H C ͑H FC ͒ for the rough interface.T 10.0 K.The lines are guides to the eye.