Effects of configurational anisotropy on exchange bias and coercivity in Co-Cr2O3 nanodots

Accepted Manuscript Effects of Configurational Anisotropy on Exchange Bias and Coercivity in CoCr2O3 Nanodots Muhammad Farooq Nasir, Sadia Manzoor PII: DOI: Reference:

S0304-8853(18)30967-3 https://doi.org/10.1016/j.jmmm.2018.07.067 MAGMA 64173

To appear in:

Journal of Magnetism and Magnetic Materials

Received Date: Revised Date: Accepted Date:

3 April 2018 2 July 2018 23 July 2018

Please cite this article as: M. Farooq Nasir, S. Manzoor, Effects of Configurational Anisotropy on Exchange Bias and Coercivity in Co-Cr2O3 Nanodots, Journal of Magnetism and Magnetic Materials (2018), doi: https://doi.org/ 10.1016/j.jmmm.2018.07.067

This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Effects of Configurational Anisotropy on Exchange Bias and Coercivity in Co-Cr2O3 Nanodots Muhammad Farooq Nasira, Sadia Manzoorb.* a b

Department of Physics, Riphah International University, Islamabad 44000, Pakistan

Magnetism Laboratory Department of Physics, COMSATS University Islamabad, Park Toad, Islamabad 44000, Pakistan *

Corresponding author +92 300 2208523

Email address: [email protected] ABSTRACT Exchange bias and coercivity of two dimensional (2-D) Co-Cr2O3 nanodots of different lateral sizes (120 nm and 240 nm) have been measured to investigate the effects of nanostructuring in exchange coupled systems. Triangular nanodots were prepared using polystyrene nanosphere lithography in conjunction with magnetron sputtering. The thickness of Co in the nanodots has been varied from 5 to 12 nm, while the thickness of Cr2O3 has been kept constant (23 nm) for all samples. Continuous films with the same thicknesses have also been investigated and compared with purely ferromagnetic (Co) and exchange biased (Co/Cr2O3) nanodots in order to study the effect of discretization on the magnetic properties. The coercivity of Co nanodots was found to be larger than that of both Co and Co/Cr2O3 continuous thin films. The Co/Cr2O3 nanodots showed a very large increase in exchange bias and coercivity over that of the continuous exchange biased films. The results have been used to estimate the effective interfacial coupling constant of the Co/Cr2O3 system, which is found to increase due to nanostructuring. These effects have been explained in terms of interfacial and configurational anisotropy of the nanostructures. Keywords: Exchange bias; Nanostructures; Thin films

1.

Introduction The phenomenon of exchange bias is the shift of the magnetization hysteresis loop along

the field axis and occurs due to exchange coupling of interfacial ferromagnetic (FM) and antiferromagnetic (AFM) spins. Although this effect has been widely studied in FM/AFM bilayers, it is still not completely understood, much less so in nanostructures, where there are additional sources of anisotropy as well as surface spin disorder that contribute to both exchange bias and coercivity. These magnetic nanostructures are important due to their potential applications in high density data storage devices [1], magnetic field sensors [2] and magnetic random access memories MRAMS [3]. Coercivity and exchange bias in nanostructures of different sizes and shapes (for example square, rectangle, triangle, diamond [4],[5], elliptical [6], rings, circular [7] and elongated nanorings [8]) have been studied in an effort to understand the role of different types of anisotropies and flux configurations in producing exchange bias. However, so far there is no general agreement on the intrinsic effects of nanostructuring on exchange bias and coercivity in ferromagnetic-antiferromagnetic nanodots. The widely conflicting reports in the literature regarding the effect of nanostructuring on exchange bias are attributed mainly to the measurement procedure as well as to sample composition and nanodot fabrication techniques. The choice of the antiferromagnet Cr2O3 used in our work helps to eliminate some of these extraneous effects as we explain below. It has been reported in detail by many authors (see for example O’Grady et al. [9], [10]) that the measurement of the maximum and reproducible value of exchange bias Hex for any granular ferromagnetic/antiferromagnetic (FM/AFM) system requires that the entire grain volume distribution in the AFM is ‘set’, i.e exchange coupled to the interfacial FM spins during the field cooling process. This ensures that the AFM contributes maximally to pinning the FM. This can be achieved by heating the FM/AFM bilayer to T > TN (where TN is the Néel temperature of the AFM), and then cooling it in a magnetic field that is large enough to saturate the FM, to a temperature at which the AFM is thermally stable [9] [10]. The Néel temperature of bimetallic AFM’s is very high, e.g. for Ir20Mn80, TN = 520 K [11] and for Fe50Mn50, TN = 500 K [12]. Field cooling the AFM from T > TN in these systems can produce crystallographic and morphological changes in the FM/AFM bilayers as well as interfacial alloying and interdiffusion

of metallic species, which are all extrinsic effects that can influence the values of exchange bias and coercivity as has been reported by Li et al. [13]. Alternatively, bimetallic AFM’s may be set by magnetic field annealing at T < TN for an extended period of time making use of thermally activated reversal of interfacial AFM moments in the exchange field of the FM. This process is time consuming and one can never ensure that the entire grain volume distribution in the AFM has been set. The largest AFM grains may have anisotropy energies that are too large to allow their AFM moments to align in the exchange field of the FM even at extended annealing at T < TN. Also, the smallest AFM grains may be thermally unstable at the temperature at which the M(H) loop is measured, and so not contribute to pinning the FM. Thus only the part of the AFM grain volume distribution that lies between the volumes VSET and VC contributes to exchange bias, where VSET is the largest AFM grain volume that can be set in the exchange field of the FM and VC is the smallest AFM grain volume that remains thermally stable during the measurement of the M(H) loop [14]. The advantage of using Cr2O3 as the AFM layer is that it has a low TN = 308 K, so that the whole AFM layer can be field cooled from the paramagnetic state, ensuring that the entire AFM has been set in the exchange field of the ferromagnet. We measure the M(H) loops at T = 60 K, at which we have determined the AFM to be free of thermal activation effects. (Details regarding thermal activation free measurement of M(H) loops can be found in ref. [10]). This ensures that all measurements are conducted from the same initial state, thus ensuring reproducibility and maximizing the exchange bias. Also, using an AFM with low TN eliminates any extrinsic effects related to the high temperature treatment of samples. Some authors report that the technique by which the nanodots are fabricated may also influence their exchange bias and coercivity. For example, Vallejo-Fernandez et al. [14] show that nanodots fabricated using electron beam lithography, show a larger exchange bias than a continuous thin film for AFM layers  10 nm in thickness. The explanation given by them is as follows: continuous thin films can have large AFM grains with volumes V > VSET, and these grains cannot be set during the field cooling procedure due to their large anisotropy energies. The process of electron beam lithography and subsequent lift-off disturbs the lateral coherence of the grains, so that they are reduced in size. The lower anisotropy energies of these smaller grains allows them to be set in the exchange field of the FM and so contribute to increased exchange bias. Baltz et al. [15] have obtained very similar identical results on pre-patterned Si substrates, so that no grain cutting effects are involved. They explain their results in terms of the nanodots

being single domain structures. Our experiments attempt to explain such discrepancies in several reported results eliminating all extraneous effects that may influence the interpretation of the data. This is possible due to the following reasons: i) The low TN of Cr2O3 allows us to field cool our samples from T > TN ensuring that the entire grain volume distribution in the AFM is set. By measuring the M(H) loop in thermal activation free conditions, we ensure that we always measure the maximum value of Hex and not one that is dependent upon the thermomagnetic history of the sample. A further advantage of using a low TN oxide AFM is that one can safely avoid extraneous effects of inter diffusion and interfacial alloying often reported in high TN bimetallic AFM’s like Ir20Mn80 and Fe50Mn50 [13]. ii) By using nanosphere lithography instead of electron beam lithography, we avoid effects of grain size reduction during etching and lift-off processes in nanodot fabrication. iii) By investigating nanodots that are smaller or larger than the theoretical AFM domain size, we are able to explore the effect of the AFM domain size on Hex and distinguish it from effects of discretization on the interfacial coupling between the FM and AFM. In this manner, we are able to demonstrate that the interfacial coupling constant between the FM and AFM, int. increases in nanodots as compared to continuous thin films and is independent of dot size. We think that this change in the interfacial coupling constant may have its source in an additional configurational anisotropy as has been reported for ferromagnetic nanodots. In a series of interesting papers on magnetization studies of purely ferromagnetic nanodots [4],[16], the authors have elaborated upon the effects of so-called ‘configurational anisotropy’ on the coercivity and magnetization reversal behavior of FM nanodots of different shapes and sizes. This additional anisotropy arises due to the constraint imposed by the shape of a nanodot on the spins at the edges of the structure and gives rise to shape specific flux configurations.

2.

Experimental methods

2.1

Mask fabrication

Nanosphere lithography has been used to produce a mask for the fabrication of arrays of triangular nanodots on 4 mm × 5 mm silicon substrates. Polystyrene nanospheres (PNS) of two different diameters (500 nm and 1 µm) have been used to prepare masks for two different sets of nanodot arrays. In order to obtain a clean and hydrophilic surface, the substrates were first cleaned in piranha solution (1:3 solution of H2O2 and H2SO4). Each substrate was then thoroughly rinsed in deionized water. It was further cleaned by sonication in the standard cleaning solution RCA-1 (NH4OH, H2O2 and deionized water in the ratio 1:1:4 respectively). After this, the substrate was sonicated in deionized water and stored in the same until further use. In order to form a monolayer of nanospheres on the Si substrate, first Triton-X was mixed in ethanol in the ratio 1:400. This diluted Triton-X solution was mixed with the original solution of nanospheres in the ratio 1:1. Triton-X was used in order to improve the packing of the polystyrene nanospheres. The cleaned substrate was placed in deionized water in a vertical position inside a small flat bottomed dish that had been previously cleaned with ethanol and deionized water. The prepared solution of polystyrene nanospheres was then spread on the surface of the water using a small syringe where the nanospheres automatically form a monolayer. The water was allowed to slowly evaporate at room temperature allowing the monolayer of nanospheres to transfer onto the Si substrate. Figure 1 shows SEM images of the masks obtained using a scanning electron microscope Hitachi SU-1500. All samples showed good hexagonal packing and long range order of the polystyrene nanospheres.

(a)

Figure 1

(b)

SEM images of masks obtained using nanosphere lithography with (a) 500 nm and (b) 1µm polystyrene nanospheres.

2.2

Sample synthesis and morphology Thin films of Cr2O3 (23 nm), Co(tFM nm) and Ta (10 nm) were deposited in this order on

the 500 nm, 1µm nanosphere masks using a six-target magnetron sputtering system (Alliance Concept DSP650) without breaking the vacuum. Continuous films (without using masks) were also prepared with the same compositions in order to study the effects of nanostructuring on exchange bias and coercivity. Ferromagnetic nanodots and continuous thin films with the composition Si/Co(tFM nm)/Ta(10 nm) were also prepared to study the effects of nanostructuring on the FM alone. The base pressure and argon process pressure during deposition were 2.0  10-6 mbar and 10-3 mbar respectively. The thickness of the ferromagnetic Co layer was tFM = 5 nm, 7 nm, 9 nm and 12 nm. The two categories of samples described above are summarized below, using the abbreviations EB (exchange biased), ND (nanodots) and CF (continuous films). i) Exchange biased samples with composition Si/Cr2O3(23 nm)/Co(tFM)/Ta(10 nm) labeled as: a) EB-ND-120 with dot size of 120 nm, b) EB-ND-240 having dot size 240 nm and c) EB-CF continuous films deposited without using a mask. ii) Ferromagnetic samples with composition Si/Co(tFM)/Ta(10 nm) labeled as: a) FMND-120 with dot size 120 nm, b) FM-ND-240 with dot size 240 nm and c) FM-CF continuous films deposited without using a mask. Samples in the first set are exchange biased, having antiferromagnetic (Cr2O3) and ferromagnetic (Co) layers. By comparing the magnetic properties of these samples, we can obtain information on the effects of nanostructuring on exchange bias. The second set of samples (in category ii)) is purely ferromagnetic. The purpose of investigating these samples is to be able to study the effects of shape and configurational anisotropy in coercivity enhancement of the nanostructures. Comparing coercivities of ferromagnetic nanodots with those of exchange biased nanodots of the same size (e.g. 120 nm or 240 nm), should enable us to estimate the relative

effects of configurational anisotropy and exchange anisotropy in coercivity enhancement of these nanostructures.

After sputter deposition of the desired material, the sample was put in absolute ethanol for 10 minutes and then ultrasonicated for 1minute to remove the nanospheres. This leaves behind a regular array of triangular nanodots arranged over the whole substrate. Figure 2 shows a typical atomic force microscopy (AFM) image of sample FM-ND-120. All samples show a regular and uniform array of triangular nanodots covering the entire substrate. It is also clear from these images that the nanodots are well-isolated from each other. The lateral dimension of the nanodots prepared using nanospheres with diameters 500 nm and 1 m are 120 nm and 240 nm respectively which is in very good agreement with the calculated value of 116 nm and 232 nm respectively obtained using the formula [17] given below:

where D is diameter of nanosphere used for the mask. Before performing magnetic measurements, all samples were annealed at 373 K for 2 hours in an inert atmosphere.

.

Figure 2

Atomic force microscopy images of sample FM-ND-120 with Co thickness tFM = 5 nm, showing a regular array of triangular Co nanodots. The colour coding on the right hand side depicts the height measured by AFM, so that yellow patches correspond to the nanodots (height ~ 15 nm, including the 10 nm Ta capping layer), while the brown background represents the Si substrate.

3.

Results and Discussion In order to measure magnetic properties, the sample was heated in a VSM (Quantun

Design VersaLab) to 340 K, i.e. above the Néel temperatute of Cr2O3. After 10 min., it was field cooled to T = 60 K in the presence of a magnetic field H = 25 kÔe in order to set the direction of exchange bias and all M(H) loops were measured at this temperature. It had been previously determined that at T = 60 K, the AFM is free of thermal activation effects (for details of thermal activation free measurements, please see ref. [10]). Figure 3 shows the M(H) loops of some selected samples. One sees that the thin films have narrow symmetric loops while those for the nanodots are sheared and asymmetric due to domain nucleation and annihilation effects as discussed by Dumas et al. [18].

1.0

0.5

Hc = 130 Oe

0.5

0.0

-0.5

-1.0

-400

-200

0

200

-20k

-10k

0

10k

20k

FM-ND-120 nm tCo = 9 nm

-1.0

400

-400

-30k

30k

-20k

-10k

(c)

0

M / MS

1.0

(d)

0.5

Hex = 24 Oe Hc = 90 Oe

M / MS

Hex = 75 Oe Hc = 140 Oe

0.5

0

0.0

10k

20k

-0.5

-400

-200

0

200

EB-CF tCo = 9 nm

-1.0

400

-400

-200

-20k

-10k

0

10k

20k

30k

-30k

H (Oe)

0.5

Hex= 145 Oe Hc = 345 Oe

-20k

-10k

0

10k

M / Ms

-1.0

1.0

(f)

0.5

Hex = 40 Oe Hc = 198 Oe

-0.5

-1000

-500

0

500

EB-ND-240nm tCo = 9 nm

-1.0

1000

-400

-200

15k

-30k

30k

M / MS

EB-ND-120nm tCo = 5 nm

-0.5

-1.0

-15k

0

2000

0

15k

Hex = 130 Oe Hc = 280 Oe

4000

EB-ND-120nm tCo = 9 nm

-1.0

-1000

-500

-20k

-10k

0

H (Oe)

10k

20k

30k

0

500

1000

H (Oe)

H (Oe)

-30k

30k

0.0

-0.5

-4000 -2000

400

(h)

0.5

M /Ms

M / MS

1.0

Hex = 230 Oe Hc = 556 Oe

0.0

200

H (Oe)

(g)

0.5

0

M / MS

0

H (Oe) 1.0

30k

H (Oe)

H (Oe)

-15k

20k

0.0

EB-ND-240nm tCo = 5 nm

-30k

400

H (Oe)

M / MS

(e)

M / MS

1.0

200

M /MS

-30k

0

H (Oe)

H (Oe)

Figure 3

30k

M / MS

M / MS

EB-CF tCo = 5 nm

-1.0

-0.5

400

0.0

-0.5

0.0

200

H (Oe)

H (Oe) 1.0

-200

H (Oe)

H (Oe)

-30k

Hc = 103 Oe

0.0

-0.5

M / MS

FM-ND-120 tCo = 7 nm

(b)

M / MS

M / MS

(a)

M / MS

1.0

-30k

-20k

-10k

0

10k

20k

30k

H (Oe)

Magnetization hysteresis M(H) loops of nanodots and continuous films shown for selected samples measured at 60 K after field cooling from 340 K in H = 25 kÔe. The inset shows the low field region.

The coercivities (HC) of ferromagnetic continuous films (FM-CF), exchange biased continuous films (EB-CF), ferromagnetic nanodots (FM-ND) and exchange biased nanodots (EB-ND) measured at 60 K as extracted from the M(H) loops shown above are displayed in figures 4a) and 4b). 250

700

a)

FM-CF FM-ND-240 nm

200

b)

EB-CF EB-ND-240 nm EB-ND-120 nm

600

HC (Oe)

HC (Oe)

500 150 100

400 300 200

50 0

100 4

5

6

7

8

9

10

11

12

tFM (nm)

Figure 4

0

4

5

6

7

8

9

10

11

12

tFM (nm)

a) Coercivity of ferromagnetic continuous films (FM-CF) and ferromagnetic nanodots of size 240 nm (FM-ND-240) and b) exchange bias in continuous films (EB-CF) and exchange biased nanodots of size 120 nm (EB-ND-120) and 240 nm (EB-ND-240) as a function of the thickness of the ferromagnetic (Co) layer. These values have been obtained from M(H) loops measured at 60 K (Fig. 3).

There is large increase in the coercivity of the ferromagnetic nanodots (FM-ND) of size 240 nm over that of continuous Co films. This increase in the coercivity occurs because of nonuniformity of magnetization reversal in these triangular nanostructures that gives rise to an additional source of anisotropy. The effects of this so-called configurational anisotropy have been extensively investigated by Cowburn et al. [4] in 2D Permalloy nanostructures of different shapes and sizes. They found that the coercivity depends sensitively on the symmetry of the nanostructure, which itself is defined by its shape. They have plotted the coercivity as a function of

and obtain a maximum coercivity of about 60 Ôe for triangular permalloy nanodots. In

our work, the 240 nm Co nanodots have

. We have varied the Co thickness

from 5 nm to 12 nm, which gives a variation in coercivity from 183 Ôe to 63 Ôe. Imperia et al. [16] have used micromagnetic simulations in triangular Co nanostructures having side ~ 400 nm and thickness 32 nm to show that the spins follow the edges of the triangular nanostructures and are pinned at corners during field reversal, giving rise to configurational anisotropy. Comparing the coercivity of the FM nanodots (Fig. 4a) with that of the exchange bias continuous films (Fig. 4b) one sees that configurational anisotropy of the Co nanodots is interestingly more effective as

a means of coercivity enhancement than the exchange anisotropy produced in the continuous CoCr2O3 bilayer. For the exchange biased nanodots there is further enhancement of coercivity, which is very large at low values of tFM (Fig. 4b). Exchange biased nanodots having size of 240 nm have larger values of coercivity compared to the purely ferromagnetic nanodots or exchange biased thin films. For the case of exchange biased nanodots of side 120 nm the coercivity enhancement is even more pronounced. The values of the exchange bias (Hex) for continuous films (EB-CF), 240 nm nanodots (EB-ND-240) and 120 nm nanodots (EB-ND-120) are shown in figure 5, where they have been plotted as a function of

.

300 EB-CF EB-ND-120 EB-ND-240

250

Hex (Oe)

200 150 100 50 0

0.8

1.0

1.2

1.4

1.6

1.8

2.0

1/tFM ( x 106 cm-1)

Figure 5

Exchange bias of continuous films (EB-CF), 240 nm sized nanodots (EB-ND-240) and 120 nm sized nanodots (EB-ND-120) having composition Si/Cr2O3/Co(tFM) as a function of measured at 60 K. Straight lines represent linear fits.

As seen earlier in case of the coercivity, there is a remarkable increase in the magnitude of exchange bias in the nanodots as compared to the continuous films and a further large increase with reduction in dot size from 240 nm to 120 nm. The exchange bias in 240 nm nanodots increases by a factor of 1.6 - 2.5 as compared to continuous films with the same thickness of Co.

This increase is by a factor of ~ 3 - 5.5 for 120 nm nanodots compared to the thin films. Similar results have been reported by Baltz [15] and Vallejo-Fernandez [14] on lithographically fabricated exchange biased nanodots. Both observe that, for sufficiently thick AFM layers, nanodots have larger values of Hex compared to continuous thin films. Baltz et al. [15] argue that for sufficiently thick AFM layers, the domain size in the AFM becomes larger than the size of the nanostructure and the constraint imposed by the lateral dimension of the nanodot restricts the AFM to a single domain state, so increasing the exchange bias. Vallejo-Fernandez et al. [15] on the other hand are of the view that grain cutting during lift-off in the fabrication of lithographically deposited nanodots is responsible for the increase in Hex over that of continuous thin films. In this work, we have used a bottom-up technique and since there is no lithography and lift-off involved, grain cutting can be safely eliminated as being a reason for the increase in exchange bias. Also, as opposed to the simulations presented in ref. [15], we find a strong increase in Hex as the nanostructure becomes smaller. As has been mentioned by the authors, the simulations in that reference give only the contributions to the exchange bias that arise from the bulk of the AFM. We show that while the large increase in Hex in the 120 nm nanodots over that of the 240 nm nanodots is related to the AFM domain size, the increase in Hex of the 240 nm dots over that of the continuous films points to the dominance of interfacial and edge spin states rather than bulk states in the AFM in determining the magnitude of exchange bias in these nanostructures. It is well established that exchange bias is inversely proportional to the thickness of the ferromagnet in FM/AFM bilayer systems through the relation [19]: (1) where  int is an effective interfacial exchange coupling constant which gives the interfacial coupling energy per unit area, and MS is the saturation magnetization. Figure 5 shows that the exchange biased continuous films as well as the nanodots show the typical with a gradient equal to

 int MS

. Values of

linear fits are shown in Table 1 below.

 int MS

behavior,

for continuous films and nanodots obtained from

  int    M   S

Sample

( 10-4 Ôe.cm)

EB-CF EB-ND-240

0.5 1.0

EB-ND-120

1.1

 int for continuous films and nanodots obtained from linear fits of data MS shown in figure 5.

Table 1 Values of

From this one can see a clear increase in the gradient of the linear fit of the Hex vs.

plot

between the continuous thin films and the 240 nm sized dots, while there is no significant change in slope upon size reduction of the nanodots, i.e. between the 240 nm sized and 120 nm sized dots. An obvious reason for the increase in the value of

 int MS

could be a reduction in MS due to

effects of size and shape of the nanodots. Ferromagnetic spins along the edges of the nanostructure may not follow the field due to configurational anisotropy or may be disordered much as the surface spins of nanoparticles. The other (less obvious) reason could be an increase in the effective interfacial coupling constant int in the nanostructures over that of the continuous film. The value of the interfacial coupling constant for the continuous film, from the slope of the linear fit of the corresponding Hex vs.

, was extracted

plot using the measured value of

MS for the continuous Co films. In order to investigate whether nanostructuring has any influence on

* in the nanodot samples, we have calculated the value of exchange bias H ex by using the

interfacial coupling constant of continuous film

ND and the actual value of M S for the

nanodot samples obtained from the M(H) loops for all samples of nanodots, i.e. H ex* 

CF  int

M SND t FM

The calculated value ( H ex* ) is a hypothetical value of exchange bias that would result if only the saturation magnetization changed due to nanostructuring and the interfacial coupling constant remained the same as that of continuous FM/AFM bilayers.

was estimated by measuring

the area covered by nanodots using images similar to those shown in Fig. 2. These calculated

values of

have been plotted as a function of 1/tFM in figure 6 below; the measured values of

Hex are also shown for comparison. 300 EB-ND-120 (exp.) EB-ND-120 (calc.) EB-ND-240 (exp.) EB-ND-240 (calc.)

*

Hex , Hex (Oe)

250 200 150 100 50 0

0.8

1.0

1.2

1.4

1.6

1.8

2.0

-1 1/tFM ( x 106 cm )

Figure 6

Measured (Hex) and calculated values of the exchange bias in Cr2O3/Co(tFM) 120 nm sized nanodots (EB-ND-120) and 240 nm sized nanodots (EB-ND-240) as a function of 1/tFM.. values have been calculated using the interfacial coupling constant for the continuous thin film . Straight lines represent linear fits.

These results show that calculated values

are generally smaller than the actual measured

values for the nanodot samples. The difference between the values of

and

is more

pronounced for smaller dot sizes and thinner ferromagnetic layers. This difference indicates that the reduced values of magnetization in the nanodots cannot be the only reason behind the increase in the slope of the linear fit of the Hex vs.

curves shown in Fig. 6 above and that int

must also increase between the continuous film and the nanodots, but it is approximately the same for both nanodots irrespective of their size. This implies that there are qualitatively different mechanisms at work, which are responsible for the increase in Hex in the two cases, namely (i) continuous film vs. nanostructures and (ii) larger and smaller nanostructures. Using the slopes of the linear fits shown in Fig. 5 and the estimated values of

, int. has been

estimated for samples having the thinnest FM layer (5 nm) since interfacial effects are expected to dominate in samples with thin FM layers. For the sample EB-CF-5nm, int. = 5.3  10-2 erg

cm-2, and it increases to 9.5  10-2 erg cm-2 for the 240 nm dots and further to 11.7  10-2 erg cm2

for the 120 nm dots of corresponding thickness of the ferromagnet. It appears that the configurational anisotropy produced as a result of nanostructuring the

FM also influences the magnetic behavior of the exchange biased nanostructures. X-ray magnetic circular dichroism (XMCD) studies of exchange biased films [20], [21] show that only a small fraction of pinned, uncompensated interfacial spins in the antiferromagnet are actually responsible for producing exchange bias. The number of such uncompensated spins is expected to be larger in AFM nanostructures due to contributions from the edges. At the edges, these uncompensated interfacial spins would tend to follow the contours of the nanostructure, creating an additional source of anisotropy. This additional anisotropy barrier to magnetization reversal would manifest itself as an increase in the effective interfacial coupling energy per unit area int. Recently, similar results have been reported by Xi et al. [22] on IrMn/CoFe nanodots deposited on anodic alumina substrates. Using the first-order reversal curve (FORC) method, they show that the nanodots have higher exchange bias and coercivity compared to the continuous thin films. They attribute this to the disordered nature of the FM/AFM material deposited in the ‘valleys’ between the nanodots that impedes domain wall motion and magnetically decouples the nanodots. Reduction in dot size from 240 nm to 120 nm increases the exchange bias by a factor that lies between 1.6 and 3.2 and the coercivity by upto a factor of 1.6. Although there is a large increase in Hex for all thickness of Co, the slope of the Hex vs. 1/tFM remains approximately the same for both sizes of nanodots, and significantly larger than the corresponding value for the continuous thin films. In order to understand the increase in Hex in the 120 nm sized dots, we have calculated the domain size DAFM of the AFM as given by the expression [15] (2)

where tAFM is the thickness of the AFM, JAFM is the exchange coupling constant of AFM spins and is given by [22] (3)

Here kB is the Boltzmann constant, Z is the number of nearest neighbor Cr ions in the AFM and TN is the Néel temperature of the AFM. For Cr2O3, Z = 3 and TN = 308 K. Using eq. 3 gives . Jint is the interfacial coupling energy and its value is given by [22]:

(4) Here ao is the distance between nearest neighbor AFM moments and for Cr2O3 ao = 2.88 Ǻ. We have obtained the value of int. from the gradient of the graphs shown in Figure 6. Equations 2 – 4 were then used to calculate the antiferromagnetic domain sizes for the nanodots and continuous films. The AFM domain size for the continuous film is ~ 400 nm, for 240 nm nanodots is ~ 200 nm and for 120 nm nanodots its values is ~ 180 nm. This shows that the 120 nm nanodots are single domain and therefore more effective in pinning the FM than the 240 nm nanodots and continuous film which can support multidomain structures.

Summary and Conclusions We have measured exchange bias and coercivity in continuous films and triangular nanodots of size 240 nm and 120 nm with composition Si/Cr2O3/Co/Ta fabricated using nanosphere lithography. The coercivity of ferromagnetic Co films and 240 nm sized Co dots was also studied for comparison. We find that configurational anisotropy increases the coercivity of the Co nanodots over that of continuous films, both ferromagnetic and exchange biased. Discretizing the AFM in the exchange biased nanodots produces a much larger increase in the coercivity and exchange bias over that of continuous films of Cr2O3/Co. The exchange bias increases by a factor of about 2.5 and upto 5.5 in comparison to that of the continuous film for the 240 nm and 120 nm nanodots respectively. The exchange bias for nanodots as well as the continuous film depends inversely on the thickness of the ferromagnetic layer. This dependence has been used to extract the effective interfacial coupling energy per unit area int. for the samples with tFM = 5 nm. int. for the 120 nm sized dot is found to be approximately double the value obtained for the continuous film of corresponding thickness. We conclude from these observations that this enhancement in coercivity and exchange bias is not simply due to the cumulative effect of exchange biasing and / or discretizing the

ferromagnet. Nanostructuring the antiferromagnet seems to play an important role in this large increase in Hex and HC. This may be due to the effects of configurational anisotropy on uncompensated edge spins in the antiferromagnet. We have also shown that these effects are distinct from the effects produced due to the AFM domain size which can lead to further enhancement of exchange bias in nanodots that can support single domain structures in the antiferromagnet.

ACKNOWLEDGEMENTS Sadia Manzoor and M. Farooq Nasir are grateful for financial support from the CIIT and the HEC, Government of Pakistan (PIN # 063-112020-Ps3-115). We also thank Dr. U. Manzoor for help with the SEM images.

References [1]

R. L. White, R.M.H. Newt, R.F.W. Pease, Patterned media: a viable route to 50 Gbit/in2 and up for magnetic recording, IEEE Trans. Magn. 33 (1997) 990.

[2]

M. Hehn, K. Ounadjela, J.P. Bucher, F. Rousseaux, D. Decanini, B. Bartenlian, C. Chappert, Nanoscale magnetic domains in mesoscopic magnets, Science. 272 (1996) 1782.

[3]

G. A. Prinz, Magnetoelectronics, Science 282 (1998) 1660.

[4]

R.P. Cowburn, D.K. Koltsov, A.O. Adeyeye, M.E. Welland, Designing nanostructured magnetic materials by symmetry, Europhys. Lett. 48 (1999) 221.

[5]

S. Goolaup, A.O. Adeyeye, N. Singh, Magnetization reversal mechanisms in diamondshaped Co nanomagnets, Phys. Rev. B. 73 (2006) 104444.

[6]

P. Vavassori, N. Zaluzec, V. Metlushko, V. Novosad, B. Ilic, M. Grimsditch, Magnetization reversal via single and double vortex states in submicron Permalloy ellipses, Phys. Rev. B. 69 (2004) 214404.

[7]

A.O. Adeyeye, N. Singh, Large area patterned magnetic nanostructures, J. Phys. D. Appl. Phys. 41 (2008) 153001.

[8]

D. Tripathy, A.O. Adeyeye, Magnetic properties of exchange biased Co / CoO elongated nanoring arrays, J. Appl. Phys. 105 (2009) 07C110.

[9]

L.E. Fernandez-Outon, G. Vallejo-Fernandez, S. Manzoor, B. Hillebrands, K. O’Grady, Interfacial spin order in exchange biased systems, J. Appl. Phys. 104 (2008) 93907.

[10] M.F. Nasir, H.H. Hng, K. O’Grady, S. Manzoor, Bulk and interfacial effects in Co-Cr2O3 nanocomposites, J. Nanosci. Nanotechnol. 11 (2011) 2700 [11] A. Paul, E. Kentzinger, U. Rücker, Nonuniform and sequential magnetization reversal via domain structure formation for multilayered system with grain size induced enhanced exchange bias, Eur. Phys. J. B - Condens. Matter Complex Syst. 45 (2005) 249. [12] F. Offi, W. Kuch, Structural and magnetic properties of FexMn1-x thin films on Cu (001) and on CoCu(001), Phys. Rev. B. 66 (2002) 64419. [13] X. Li, C.W. Leung, C.C. Chiu, K.W. Lin, M. Chal, Exchange bias study of sub-100 nmdiameter CoFeB/IrMn antidot and nanodot arrays fabricated by nanosphere lithography, Phys. Lett. A. 381 (2017) 2709. [14] G. Vallejo-Fernandez and J. N. Chapmam, Size effects in submicron exchange bias square elements, Appl. Phys. Lett. 94 (2009) 262508. [15] V. Baltz, J. Sort, S. Landis, B. Rodmacq, B. Dieny, Tailoring Size Effects on the Exchange Bias in Ferromagnetic-Antiferromagnetic 100  nm Nanostructures, Phys. Rev. Lett. 94 (2005) 117201. [16] P. Imperia, W. Kandulski, a. Kosiorek, H. Głaczyńska, H. Maletta, M. Giersig, Magnetic anisotropy study of triangular-shaped Co nanostructures, J. Magn. Magn. Mater. 320 (2008) 2682 [17] Haynes, V.C.L. Duyne, No Title, J. Phys. Chem. B. 105 (2001) 5599.

[18]

R. K. Dumas, C. Li, I. V Roshchin, I. K. Schuller and K. Liu, Phys. Rev. B 86, (2012) 144410.

[19] A.H. Morish, The Physical Principles of Magnetism, IEEE Press, 2001. [20] E. Arenholz, K. Liu, Magnetization reversal of uncompensated Fe moments in exchange biased Ni / FeF2 bilayers, Appl. Phys. Lett. 88 (2006) 72503. [21] H. Ohldag, A. Scholl, F. Nolting, E. Arenholz, S. Maat, A.T. Young, M. Carey, J. Stohr, Correlation between exchange bias and pinned interfacial spins, Phys. Rev. Lett. 91 (2003) 17203. [22] H. Xi, J. Rantschler, S. Mao, M.T. Kief, R.M. White, Interface coupling and magnetic properties of exchange-coupled Ni81 Fe19 / Ir22 Mn78 bilayers, J. Phys. D. Appl. Phys. 36 (2003) 1464

 int for continuous films and nanodots obtained from linear fits of data MS shown in figure 5.

Table 1 Values of

Sample EB-CF EB-ND-240 EB-ND-120

  int    M   S

( 10-4 Ôe.cm) 0.5 1.0 1.1