Volume and Concentration Scaling of Magnetism in Dilute Magnetic

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Volume and Concentration Scaling of Magnetism in Dilute Magnetic Semiconductor Quantum Dots Avijit Saha, and Ranjani Viswanatha J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b08881 • Publication Date (Web): 14 Sep 2017 Downloaded from http://pubs.acs.org on September 20, 2017

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The Journal of Physical Chemistry

Volume and Concentration Scaling of Magnetism in Dilute Magnetic Semiconductor Quantum Dots Avijit Saha,a and Ranjani Viswanatha,a,b,* New Chemistry Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur, Bangalore-560064, India. International Centre for Materials Science, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur, Bangalore - 560064, India.

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ABSTRACT. Investigation of the magnetism of dilute magnetic semiconductors (DMSs) by changing particle dimensionality and doping concentration and its complete understanding is a major step towards their application in multifunctional devices. The importance of effects, such as magnetization reversal with size, magnetic invariance with respect to doping concentration for an appropriate functioning of DMS system are empirically well known. However, explicit demonstration of these effects, specifically in nanomaterials have so far not been studied mainly due to the lack of synthetic handle. In this work, we have demonstrated the pre-requisites of DMS materials by isolating origins of magnetism arising due to clustering of magnetic dopant ions as well as sp-d exchange interaction with the host. We have studied magnetism with varying concentrations of dopant ions and have shown that the magnetism arising due to exchange interaction with the host is invariant up to 10% doping concentration demonstrating the concentration scaling in DMS systems. Additionally, the study of size dependent magnetic behavior revealed the effect of domain size and disordered spin on the surface leading to a change in magnetization/ion as well as magnetization reversal.

INTRODUCTION Nanoscale magnetism has received enormous attention in the last decade, especially in the case of DMSs1-4 due to their unique magnetic properties as well as magneto-optical3, 5-8 and magnetoelectrical effects9-10 leading to the formation of building blocks for future sensors, data storage and communication technology. This remarkable phenomenon is a result of subtle interplay between intrinsic properties and inter-particle interactions. Fundamental understanding of this field as well as potential applications like magnetic storage devices,11-12 magnetic resonance imaging,13-16 requires an understanding of the effect of domain sizes, role of particle volume, finite size and surface effects. In addition to that, reviewing the issues of localization of magnetic states


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due to secondary phase formation and the implication of quantum confinement on these states is also an important aspect. Finite size effects in DMS quantum dots (QDs) has largely been unexplored except for a few theoretical studies,17-18 primarily due to the lack of appropriate synthesis methods to control the size and dopant concentrations in these QDs. In spite of the tremendous scope to engineer QDs using wet chemical synthesis of colloidal QDs with minute control of size, shape, internal structure and doping, there are often a multitude of microscopic forces that exert the fine control over these systems. Normally, while an extensive post-synthetic study may reveal the forces responsible for the final size and shape of QDs, it is non-trivial to tailor-make DMS QDs with required size and dopant concentration. Moreover, synthesis of larger QDs with dopant ion retention is not well studied. It is well known that though the quantum confinement effects related to optical properties are most prominent below 10 nm, the surface effects and domain size effect on magnetism are applicable up to much larger sizes, typically up to about 100 nm. For the nano-sized particles, increase of surface to volume ratio results in substantial surface contribution to the overall magnetic properties. For example, changes in inter-particle interaction and increase of canted surface spins are the common well-known effects with the decrease of particle dimension. In addition, below a material specific critical size (Dc), multidomian ferromagnetic particle becomes a single domain superparamagnetic particle. Particles below this transition size, due to decrease in typical domain sizes, can lead to substantially different magnetic properties compared to their bulk counterparts. One such example of the characteristic properties is the variation of blocking temperature (Tb) with particle size. This temperature provides the minimum required thermal energy to overcome the magnetic spin relaxation energy arising out of the magnetic anisotropy (Size, shape, strain and magnetocystalline anisotropy) in nanocrystals. Tb is found to be highly


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sensitive parameter as a function of size of the nanocrystals and is often used to characterize the size of the magnetic domain in the nanocrystals. Furthermore, the study of magnetism in nanoscale systems is further complicated by the likely presence of small magnetic clusters within a nonmagnetic matrix.

However since, unlike other ferromagnetic systems, magnetism in DMS

materials arises due to long-range sp-d exchange interaction19-21 between paramagnetic dopant ions and the electronic states of the host semiconductor,22 the presence of secondary magnetic phases makes it difficult to distinguish the effect of the magnetic interaction due to the doped magnetic ions with the non-magnetic host and the effect due to magnetically active clustered phase. Thus, the wish list of properties required for successful study of size effects in DMS QDs include (a) proven methodology for the formation of cluster free doped QDs, (b) ability to control size and shape with required dopant percentage upto the critical domain size and (c) dopant concentration control to study the origin of magnetism. Recently, it has been observed that it is possible to obtain magnetic cluster free QDs using the diffusion of magnetic core into the semiconducting matrix within a particular size and dopant range.23-24 Extensive local structure studies using X-ray absorption fine structure (XAFS) spectroscopy25 and element specific Energy-Dispersive X-ray (EDX) Spectroscopy 23 have shown the uniformity of the dopant ions within the QDs and their dominant nearest neighbor interactions with the host matrix for any given size within the low doping concentrations ruling out the possibility of aggregation of Fe3O4 or metallic Fe or the formation of any other secondary phase. Further studies have shown that by appropriately modifying the thermodynamic parameters such as bond strength and diffusion constant, it is possible to vary the size and dopant percentages. 26 Based on these prior studies, we have obtained DMS QDs with required sizes and dopant concentration meeting all the three conditions specified above by modifying the core size,


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annealing conditions as well as the choice of appropriate core material. We have obtained Fedoped CdS QDs having various sizes (12-55 nm) and various Fe percentage (up to 14.5 %) to study nanoscale magnetism in QDs. The samples were characterized using transmission electron microscopy (TEM) and inductively coupled plasma optical emission spectroscopy (ICP-OES) measurements. The amount of ligands were estimated using thermo-gravimetric analysis (TGA). Variation of magnetic property of Fe doped CdS quantum dot has been studied using standard magnetization measurements using superconducting quantum interference device (SQUID) vibrating sample magnetometer (VSM). Magnetic parameters such as the variation of coercivity (Hc), saturation magnetization (Ms), remanent magnetization (Mr) with particles dimensionality have been analyzed. Moreover, the magnetic scaling per dopant ion as a function of concentration of magnetic ions has been established. Finite size and surface effects such as canted spin have been identified and systematically quantified as a function of particle size. EXPERIMENTAL SECTION Synthesis. Various Fe doped CdS have been synthesized by diffusing Fe3O4 magnetic core inside a thick CdS semiconducting matrix following the synthesis technique described elsewhere. 23 In brief, Fe3O4 QDs having different sizes 4.5 nm, 5.6 nm, 6.2 nm and 7.3 nm have been synthesized by following literature methods.23, 27 Briefly, iron (II) acetate along with oleic acid and oleylamine are heated to 300 °C in Ar atmosphere and maintained at that temperature for different time periods for QDs growth. Samples were annealed for longer period at high temperature (300 °C) to achieve larger nanocrystals. Successive ionic layer absorption and reaction (SILAR) technique28 was used to overcoat CdS at high temperature (240-260 °C). All the samples were annealed for required amount of time to obtain the required thickness of CdS shell growth as well as close to complete diffusion of Fe3O4 core. Samples were collected at different stages of CdS growth to monitor the reaction and to arrest growth when the required sizes and concentration of Fe ions are obtained.


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Characterization. Transmission electron microscopy (TEM) was performed on Technai F30 UHR version electron microscope, using a field emission gun (FEG) operating at an accelerating voltage of 200 kV in bright field mode using Cu coated holey carbon TEM grids. Elemental analysis, to determine the Cd and Fe ratio, was carried out using inductively coupled plasma optical emission spectroscopy (ICP-OES). It was performed by dissolving the samples in millipore water with 25% of HNO3 solution, and the Fe and Cd concentrations were measured against known Fe and Cd standards (high purity). XAFS spectroscopy has been employed to probe the local environment around undoped and Fe-doped CdS. Fe K-edge (7112 eV) and Cd K-edge (26,711 eV) for the samples were measured at beamline 2-2 at Stanford Synchrotron Radiation Lightsource, SLAC National Accelerator Laboratory. Athena29 software was used for data collection and processing while theoretical model consistent with other characterization technique and corresponding paths has been generated using FEEF630 and fitted in Artemis31 program. SQUID VSM, Quantum Design was used for DC magnetic susceptibility and magnetization measurements (M vs H) at 2 K and at room temperature (300 K). Magnetization values were first obtained in emu/g that was inclusive of the quantum dots as well as the ligands. In order to exclude the effect of ligand weight we performed thermo-gravimetric analysis (TGA) to estimate the amount of ligand attached with the QDs surface and estimate the molecular weight of the QDs. After subtracting the ligand weight, approximate Ms values obtained for different QDs are reported here. TGA was carried out using a TGA/DSC 2 STAR instrument in the temperature range of 300–1073 K under nitrogen atmosphere with a ramp rate of 5 K/min. RESULTS AND DISCUSSION Figure 1a shows the magnetization (M) vs magnetic field (H) curves at 2 K for Fe-CdS during the formation of the thick shell of CdS for Fe-nCdS with varying values of n, the number of


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monolayers of CdS and with a core size of 4.5 nm. The magnetic core is expected to diffuse into the CdS matrix by self-purification process32-33 within about 5 monolayers of CdS at the given annealing temperature with no signatures of magnetic clustering. It is important to elucidate the radial position of Fe ions and its clustering effect giving rise to secondary phases like metallic Fe and/or magnetic clusters of Fe3O4 with annealing time and nanocrystal growth before we attempt to understand the origin as well as the nature of magnetism of these QDs. However, that has been established in literature for a similar synthesis method by studying the evolution of internal structure by element specific XAFS spectroscopy25 and EDX23 in earlier reports. A typical XAFS data of Fe (5.5%) doped CdS along with the corresponding fits to the theoretical model is shown in supporting information (SI) Figure S1 (a) demonstrating similar environment as that observed in literature25 proving the presence of uniform dopant concentration. Moreover, Fe K-edge and Cd K-edge χ (K) data for Fe (5.5%) doped CdS and Cd K-edge data for undoped CdS (wurtzite) has been compared in Figure S1(b). Data from all the three samples looks very similar to each other. This suggests that CdS retains its wurtzite crystal structure even after Fe doping similar to the undoped counterpart as indicated by the similar local structure around Cd atoms in the undoped CdS and doped CdS. In addition to that, the similarity between the Cd K-edge and Fe K-edge χ (K) oscillations in Fe-doped CdS, confirm the Fe ions have distributed uniformly replacing few of the Cd atoms inside CdS matrix. Herein, in this work, we have studied the evolution of magnetic property with the diffusion of the magnetic core. From the Figure 1a, it is observed that, at low temperature all these QDs showed ferromagnetic behavior with significant coercivity (Hc). However, at room temperature (SI Figure S2) these particles show superparamagnetic behavior with zero coercivity. The increase in coercivity at 2K (Figure 1a) is well known due to spin blocking,34-35 as thermal energy is not sufficient at that low temperature for spin relaxation and


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require higher magnetic field to flip the magnetic spins. Secondly, it is observed that in spite of the correction from the ligand weight, there is a significant reduction of absolute magnetization from the bulk value (Figure 1a), possibly due to decrease of domain size and increase of canted surface spins. Magnetic Field (kOe)

(a)

-8

-4

0

Magnetization (B/Fe )

0.8

4

8

2K

0.4

0.0 Fe-0CdS Fe-5CdS Fe-10CdS Fe-14CdS

-0.4

-0.8

(b) Saturation Magnetization (B/Fe )

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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Fe (%) 100

80

60

40

20

0.9

0 2K 300 K

0.6

0.3

0.0 4

8

12

16

Size (nm)

Figure. 1 (a) A comparison of M vs H hysteresis loop (2K) for different Fe-CdS QDs (b) variation of magnetization/Fe with increasing size (black symbols) and percentage of Fe (red symbols) measured at 2 K and 300K. Solid lines are guide to the eye. The variation of saturation magnetization (Ms) as a function of size as well as Fe concentration is shown in Figure 1b. From the figure, it can be observed that the Ms decreases upto about 7.2 nm, followed by a slow increase. Therefore, it is evident from the experimental observation that there are two significant origins controlling the magnetization of these QDs. In the first part, magnetism is dominated by the magnetic core that is well known to contribute to the


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ferrimagnetism due to strong short-range ferrimagnetic coupling between magnetic spins.36 With the increase in annealing time, this cluster slowly diffuses into the lattice decreasing the core size and hence resulting in a decrease of Ms. After the core diffuses completely, magnetization of these QDs solely depends on percentage of magnetic ions and the size of the entire QD rather than just the core. Hence, with increasing CdS overcoating and thereby with increasing size of the QDs, we observe a small increase in magnetization. In such condition, transition metal (TM) impurity ions exist as dopants inside semiconductor host and the magnetization is dominated by the sp-d exchange interaction between magnetic ions and the electronic states of the semiconductor host. Apart from these two factors, defects induced magnetism is also well known in these kind of small QDs as has been reported earlier.37-38 However, we can rule out this effect here as the magnitude of the magnetization arising from defects is several orders of magnitude smaller as observed from almost zero line graph of CdS shown in SI Figure. S3. However, it is interesting to note that even though there is high percentage (18%) of Fe in Fe5CdS (size-8.5 nm), Ms is lower than with lesser percentage (2.3 %) of Fe ions in Fe-14CdS (15.4 nm). This could arise due to two different origins of magnetism, i.e., magnetism from ferrimagnetic clusters of Fe and magnetism arising due to the sp-d interactions of the dopant with that of the host semiconductor. From these results, it is evident that this set of samples cannot isolate the effects arising due to increase in overall size of the QDs and decreasing size of the magnetic core as both these variables change simultaneously. Hence, in order to investigate the effect of magnetic ion concentration and size individually on the magnetic property, we used different core sizes to obtain two sets of samples. The first set was obtained with varying sizes and uniformly diffused dopant concentration of 5.5 % and the second set differing magnetic ion concentrations with similar sizes (~12 nm) and the magnetism of these two sets were then studied.


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Effect of particle size We proceed to study the size dependence in both magnetic core/shell materials as well as the uniformly distributed magnetically doped semiconductors. Figure 2a and 2b shows the magnetic properties of two different sizes 30% Fe-CdS QDs. From the figure, it is evident that even though the magnetism is largely contributed by the magnetic core, the smaller core/shell system of 6 nm has lower Ms (0.3 µB/Fe) and Tb (32 K) compared to the 8.5 nm core/shell system with values of 0.5 µB/Fe and 48 K respectively. This suggests that even though there exists a magnetic core, the non-magnetic CdS matrix also contributes substantially to the magnetism possibly due to the dopant ions diffused into the CdS lattice. 0.6

(a)

2K

0.3

0.0

-0.3

6 nm (Fe- 30%) 8.4 nm (Fe- 30%)

-0.6 -10

-5

0

5

10

Magnetic Field (kOe) 0.16

ZFC FC

Tb=32 K

0.40

0.14 0.35

Tb=48 K

0.12 0.10

0.30

0.08

(b) 0

Magnetization (/Fe)

Magnetization (/Fe)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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0.25 100

200

300

400

Temperature (K)

Figure. 2 M vs H hysteresis loop at 2K Fe-CdS (Fe-30%) samples having size 6 nm and 8.4 nm and (b) their corresponding variation of FC/ZFC curves using a field of 200 Oe.


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Hence, in order to obtain contributions only from the DMS material as a function of size, we prepare different sizes of 5.5 % Fe doped CdS and the corresponding magnetic properties are shown in Figure 3. The sizes of the QDs are obtained from TEM images shown in SI Figure S4 and range from 12 to 60 nm. The Ms values range from 0.44 µB/Fe to 1.65 µB/Fe as the size increase from 12 nm to 55 nm as shown in Figure 3a at 2K and SI Figure S5 at 300K. The variation of saturation magnetization/ion obtained from M vs H hysteresis curve shown in Figure 3b demonstrates an increase of magnetization/ion as particle size increases and saturates for large size (55 nm) particles. It is notable that the Ms values for all these QDs are quite significant, in spite of their small size. Due to their small size, DMS QDs exist as single domain magnet in which spins of free electrons within the QDs are aligned in one direction. Moreover, at this size regime, physical properties of QDs are strongly influenced by the high surface to volume ratio that changes drastically with the size.39 As the particle size decreases, the percentage of disordered surface atoms in a QD increases, which demonstrates the importance of surface and interface effects. These disordered surface atoms have spins in random direction, which effectively reduce the overall magnetization of the particle as observed from the results. In multidomain particles, magnetization reversal is proportional to both the anisotropy energy given by the product of anisotropy constant, K and the volume of the domain, V as well as the energy for the domain wall motion. However, in a single domain particle the magnetization reversal follows the Stoner-Wohlfarth (SW) model.40 It is the simplest model for ferromagnetic QDs, which explains the dynamics of magnetization reversal under external temperature or magnetic field. According to the SW model energy for magnetization reversal or the magnetic anisotropy (EA) of the QDs is proportional to its volume (V) as EA = KV sin2 θ

(1)


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Where, K is the anisotropy constant and θ is the angle between easy axis and the direction of applied magnetic field. With the decrease of particle size in a single domain QDs KV decreases, thus leading to a decrease in EA. This, in turn decreases Tb as it requires lesser thermal energy given by kBT (kB is the Boltzmann constant) to flip into a superparamagnetic state with spontaneous magnetization reversal leading to significant Ms value but no coercivity. Magnetic Field (kOe) -5

0

5

10

Size (nm) 10

20

30

40

50

60

(b)

1.6 (a)

Fe- 5.5%

2K 300 K

0.0 55 nm 17 nm 14 nm 12 nm

-0.8 -1.6

1.0

Ms (B/Fe)

1.5 0.8

0.5 0.0

(c)

2K 300 K

0.15

400

(d)

300

100 0.10

Tb (K)

Magnetization (B/Fe)

-10


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50 0.05

0 0

100

200

300

Temperature (K)

0

3

6

9 80 85 3

3

Volume (10 nm )

Figure. 3 (a) M vs H hysteresis loop (2 K) and (b) variation of Ms of Fe-doped CdS QDs having various size. (c) Field cooled (solid line) and zero field cooled (dotted line) magnetization (field 200 Oe) for 12 nm, 14 nm 17 nm and 55 nm Fe-doped CdS QDs having same Fe percentage (5.5%) and (d) variation of blocking temperature with particles volume. Further confirmation of the size effect is obtained by studying the effect of particle size on magnetization reversal dynamics by measuring temperature dependence of magnetization. Variation of magnetization reversal has been studied DC susceptibility from FC/ZFC


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magnetization as demonstrated in Figure 3c and the variation of Tb as a function of volume is shown in Figure 3d. It is evident from the result that the variation of Tb is consistent with the Stoner-Wohlfarth model and it increases with increase in volume and saturates for the large size close to the bulk value of about 370 K similar to the Ms value further confirming the origin of magnetism in these DMS materials. The relevant values for varying sizes are tabulated in Table 1. Table 1. Variation of Tb and saturation magnetization of 5.5 % Fe-doped CdS QDs having different size. Size (Fe=5.5%)

Tb

Ms (µB/Fe) 2K

300 K

12 nm

~2 K

0.44

0.09

14 nm

25 K

0.51

0.13

17 nm

44 K

1.12

0.30

55 nm

370 K

1.65

0.60

It is also important to note that the overall magnetization arising out of smaller magnetic clusters is much smaller than the bulk value of 4 µB/Fe (for Fe2+ ion). It is to be noted here that though the magnetic moment of a Fe atom in metallic iron is 2.2 μB and average value in case of Fe3O4 is 1.3 μB this includes the presence of Fe3+ and Fe2+ in antiferromagnetic ferrimagnetic ordering between octahedral and tetrahedral spins specific to the spinel structure. However, in uniformly doped CdS QDs Fe exists as Fe2+ state and there is no existence of ferrimagnetic ordering, as the inverse spinel structure breaks down, instead the magnetization arises via long range sp-d exchange interaction between Fe2+ ions and the semiconductor host. Hence, an atomic saturation moment of 4 μB is considered for comparison in this case. Additionally it should be noted that the magnetization, possibly arising out of sp-d exchange interactions is a long range interaction and is hence weaker


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than the short range interaction in ferromagnetic materials and the value of magnetic moment is less from 4μB (for Fe2+) and the highest we observe is 1.65μB. However, this magnetization is of similar order of magnitude compared to the magnetism from the small cluster making it non-trivial to point to the origin of magnetism. Therefore, it is also important to study the magnetic scaling for varying concentrations of the dopant ions. Effect of magnetic ion concentration Magnetic impurity concentration dependence on the magnetic properties (magnetization, Curie temperature) of a DMS material is known to be an important and a direct approach for the understanding of the origin of magnetism. It is well known that Ms scaling proportional to the dopant concentration is important to ensure that the magnetism is not arising out of clusters of magnetic islands but rather from the interaction of magnetic dopant with that of the host. However, so far, this systematic dependence has been established only in very few bulk systems, like Mn doped GaAs41 or InAs42-43 and none in the three dimensionally confined QDs. This shortfall in QDs can be attributed to the inability to obtain the weight of ligands and hence the actual magnetic moment per unit weight of the magnetic material as well as the inability to tune the percentage of dopant ions for a given size. However, with the current technique, wherein we overcome both these shortcomings, we chose five different 12 nm Fe doped CdS QDs with differing Fe ion concentrations ranging from 5-60% to investigate the effect of magnetic ion concentration on Ms and Tb. The sizes of these particles were observed to be uniform (12 ± 1.5 nm) as characterized by TEM and shown in Figure S6 in SI. Figure 4a and SI Figure S7 shows the M vs H hysteresis loop at 2 K and room temperature respectively while the variation of Ms/ Fe ion contribution, after removing the weight contribution by the ligands as obtained from the TGA data, with the increasing Fe ion concentration is demonstrated in Figure 4b. The Ms value remains invariant upto


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~10% of Fe concentration, above which it starts to increase suggesting that the dilute limit is valid only below 10% doping similar to the bulk values of about 5-6%. Further, this increase can be simply explained by the presence of a strong ferrimagnetic interaction, most likely arising from Fe3O4 cluster that has not diffused completely into the semiconducting matrix.

0

5

10

Fe (%) 5

(a)

0.8

10

15 60 62 2.0

(b) 2K 300 K

0.4

1.5

12 nm

0.0

1.0 14.5 % 11 % 9% 5.5 %

-0.4 -0.8

(c)

0.6

0.5 0.0

(d)

ZFC FC

60

0.4

40

0.2

20

0.0

0 0

100

200

Temperature (K)

5

10

Tb (K)


-5

Ms (B/Fe)

Magnetic Field (kOe) -10


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


15 60 62

Fe (%)

Figure. 4 (a) M vs H hysteresis loop (2 K) and (b) variation of saturation magnetization (M s) of Fe-doped CdS QDs having different Fe percentage. (Solid lines are guide to the eye). (c) Field cooled (solid line) and zero field cooled (dotted line) magnetization (field 200 Oe) for 5.5 % 9 % 11 % and 14.5 % Fe-doped CdS QDs having same size (12 nm) (d) Variation of blocking temperature (Tb) with percentage of Fe.


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Table 2. Variation of blocking temperature (Tb) and Ms of 12 nm Fe-doped CdS QDs having different Fe percentage. %Fe (Size=12 nm) 5.5

Tb

Ms (µB/Fe)

~2 K

2K 0.44

300 K 0.09

9

~2 K

0.32

0.07

11

10 K

0.37

0.18

14.5

35 K

0.93

0.46

60

68 K

1.87

1.55

Apart from the Ms, it is also important to further characterize these materials using the Tb as determined from the temperature dependence of DC susceptibility by measuring zero field cooled (ZFC) and field cooled (FC) magnetization measurement as shown in Figure 4c to obtain the magnetic domain size. The blocking temperatures were determined from the peak of ZFC curve and tabulated in Table 2 as well as plotted in Figure 4d as a function of Fe concentration. Constant value of Tb for small percentage of Fe ions (

Volume and Concentration Scaling of Magnetism in Dilute Magnetic

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