Overcoming inherent magnetic instability, preventing spin

canting and magnetic coding in an assembly of

ferrimagnetic nanoparticles

S. Dey,1 S. K. Dey,1, 2 K. Bagani,3 S. Majumder,1, 3 A. Roychowdhury,4

S. Banerjee,3 V. R. Reddy,5 D. Das,4 and S. Kumar,1,a)

1 Department of Physics, Jadavpur University, Kolkata 700032, India

2Department of Physics, NITMAS, 24 Paragana(s) 743368, India

3Saha Institute of Nuclear Physics, 1/AF Bidhannagar, Kolkata 700064, India

4 UGC-DAE CSR, Kolkata Centre, III/LB-8, Bidhannagar, Kolkata 700098, India

5 UGC-DAE CSR, University Campus, Khandwa Road, Indore 452001, India

EXPERIMENTAL AND METHOD

Sample Preparation

To synthesize at first Ni0.5Zn0.5Fe2O4 in polycrystalline form the powdered oxides of α-Fe2O3

(Aldrich,99.99%), ZnO (Aldrich, 99.99%) and NiO (Aldrich, 99.99%) were mixed together in

stoichiometric ratio and then grounded thoroughly for few hours. The mixture was then

pelletized at a pressure of 15 tons/cm2.The pellets were sintered at 900º C for 12 hours and then

cooled down to room temperature at a rate of 3º C/min.The pellets were then grounded and then

passed through the same process for sintering at temperature 950º C. Finally samples were

annealed at 600º C for 10 hours and slowly cooled down (at a rate of 2º C/min) to the room

temperature. The formation of single phase spinel oxide has been confirmed by recording

powder X-ray diffraction (PXRD) data of the sample.

The nanosized Ni0.5Zn0.5Fe2O4 (MM) was produced by high energy ball milling of the

coarse powders of bulk sample. The high energy mechanical milling was carried out in a Fritsch

Planetarry Mono Mill “pulverisette 6" using Tungsten Carbide vials and balls with ball to mass

ratio 20:1. The grinding experiment was conducted at room temperature setting rotational speed

of the mill at 350 rpm and time 60 hours.

Experimental techniques

The PXRD pattern were recorded in Bruker D8 advanced diffractometer using Cu Kα (λ

= 1.54184 Ả) radiation. The generator settings were 40 kV and 40 mA.The diffraction patterns

were recorded at room temperature (21º C) with step size of 0.0199º and a counting time of 3

s/step over the range of 2θ = 15–80º.

The high resolution transmission electron (HRTEM) micrograph and selected area

electron diffraction (SAED) pattern of MM were recorded by JEOL 2100 HRTEM. In order to

prevent the inherent tendency of agglomeration of ferrite nanoparticles, a special technique was

adopted here for HRTEM sample preparation. Before the HRTEM investigation, the sample was

thoroughly crushed in an agate mortar, dispersed in propanol, fixed on a carbon coated Cu grid

with the help of a spin coater and dried up in vacuum.

The Mössbauer spectra of MM [Fig. S5] were recorded in transmission geometry using

constant acceleration drive (CMTE-250) with a 25 mCi 57Co source in Rh matrix. The

Mössbauer measurement at 10 K in presence of 5T external magnetic field applied parallel to the

Gamma rays was carried out using superconducting magnet (JANIS SuperOptiMag). The

velocity calibration of the spectrometer was done with natural iron absorber at room temperature.

The Mössbauer spectrum was fitted with Recoil program.1 In all the spectra, the solid lines

represent the simulated curves and the solid circles represent the experimental data points.

The dc magnetization (M) as a function of temperature (T) and magnetic field (H) were

measured using a SQUID magnetometer (MPMS XL 7, Quantum Design, USA). The M(T) data

were recorded under zero field cooled (ZFC) and field cooled (FC) modes respectively. The

sample was cooled from 310 K to 5 K in absence of dc magnetic field in ZFC mode and in the

presence of magnetic field in FC mode. In the FC mode the cooling and the measurement fields

were the same. The M(T) data were recorded in the presence of measurement field while

increasing the temperature from 5 to 310 K. The data for magnetic field dependence of

magnetization (M vs B hysteresis loops) at 300 and 10 K were recorded under ZFC mode [Fig.

S3]. We have calculated the saturation magnetization from M vs 1/H plot using the law of

approach to saturation.

The positron annihilation lifetime measurement [Fig. S4] has been carried out using a

fast-fast coincidence system consisting of two 1 in. tapered of BaF2 scintillators coupled to XP

2020Q photo multiplier tubes.

Method of PXRD data analysis

The Rietveld powder x-ray structure refinement analysis has been employed to determine

the structural (atomic coordinates and lattice etc) and microstructural (crystallite size, r. m. s.

lattice strain) parameters. It may be noted that the Rietveld refinement method is a well

established tool for structural and microstructural characterization of powder sample.2-4 The x-ray

diffraction lines of nanosized samples are neither ideal Gaussian nor purely Lorentzian.5

Moreover, for the nanometric samples the line broadening of x-ray diffraction profile is mainly

determined by the crystallite size and microstrain.5 In our analysis we have assumed the peak

shape to be a pseudo-voigt (pV) function with asymmetry because it takes individual care for

both particle size and the strain broadening of the experimental profile since the function is a

linear combination of Gaussian and Cauchyan (Lorentzian) functions.3,5 According to Wertheim

et al.3 the pseudo-voigt function is defined as

pV (x )=I p[η C ( x )+(1−η )G ( x )]

where C ( x )=(1+x2)−1 and G ( x )=exp[−( ln2 ) x2] with x=(2θ−2θ0)/ω.

2θ0 is the Cu-Kα1 peak maximum position, 2ω is the full width at half maxima (FWHM) of the

total Kα1 or Kα2 profile, FWHM=(U tan2θ+V tanθ+W )1/2, where U, V and W are the

coefficients of the quadratic polynomial, η is the Cauchyan content of the function and Ip is the

intensity at the Kα1 peak maximum (scale factor). Several methods have been proposed by

different groups to calculate the crystallite size and lattice strain by Rietveld refinement of

PXRD data.2-5 Here we have used Rietveld based software package MAUD2.33 6 as it can

precisely determine the structural and microstructural parameters.

The Marquardt least-squares procedures were adopted to minimize the difference

between the observed and simulated powder diffraction patterns. The minimization was carried

out using the reliability index parameters Rwp (weighted profile factor) and RB (Bragg factor)

defined as,

RWP=100[ ∑i=1 , n

wii|y i− yC , i|2

∑i=1, n

w i yi2 ]

1 /2

and RB=100

∑i=1, n

|y i− yC ,i|

∑i=1 , n

y i

where

yi and yc,i are the observed and calculated profile intensities, respectively, and wi is a

suitable weight.

Expected Weighted Profile Factor is given by

Rexp = 100 [ n−p∑

iwi y

i2 ]1 /2

n – p is the number of degrees of freedom.

Goodness of fit indicator: GOF =

Rwp

Rexp

To compute the theoretical pattern it is customary to provide the structural information and some

starting values of the microstructural parameters. Initially, the positions of the peaks were

corrected by successive refinements of zero-shift error. In every step of the refinement cycle the

values of the structural and the microstructural parameters get modified and the refinement

continues until the simulated pattern converge with the experimental pattern with the value of the

quality factor, GOF very closed to 1, which confirms the goodness of fitting.7

The significant broadening of the PXRD peaks of MM with respect to its bulk

counterpart 8 clearly indicates that the particles in the sample are nanometric in size and internal

strain exists among the lattice planes. It is well known that the deviation from ideal crystallinity

due to finite crystallite size, lattice strain (crystallographic imperfection) and instrumental effects

lead to broadening of x-ray diffraction peaks.9,10 Thus the microstructural parameters (crystallite

size and microstrain) of the material can be easily extracted by means of PXRD line profile

analysis. The broadening of PXRD peaks is given by the formula

Br cosθ= kλL

+4 ηsin θ

Br is the width of the diffraction peak due to crystallite sizes and strains, θ is the Bragg angle, L

is the average crystallite size, k is a constant and η is the slope which is related to microstrain.

The lattice strain and crystalline size can be easily calculated by the so called Williamson-Hall

plot (Br cosθ vs sinθ plot).9,10 This traditional single peak method of analyzing X-ray powder

diffraction patterns uses only selective parts of X-ray data, whereas the Rietveld based methods

utilize the entire diffraction profile during analysis. Therefore any Rietveld based method will

provide more accurate results than the conventional single peak method. Here, we have used

Rietveld based software package MAUD2.33 to determine the structural (atomic coordinates and

lattice) and microstructural (crystalline size, r. m. s. lattice strain) parameters of the sample as

this package is capable of extracting these parameters simultaneously and accurately through the

successive refinement of calculated pattern. It is noteworthy that in addition to structural

parameters which must be refined to ensure the best fit between the observed and calculated X-

ray patterns, other parameters related to micro-structural features, such as crystallite size and

strain, can also be refined during the Rietveld refinement through MAUD2.33 package.

The PXRD pattern of MM has been indexed by NTREOR90 of EXPO2009 package11 and

tthe results were crosschecked by DICVOL06 and TREOR90 of Fullprof.2k package.12,13 The

results obtained through different methods match with each other and have been presented in

Fig. 1. The space group of the sample has been determined by using FINDSPACE of EXPO2009

package14 through statistical analysis of the PXRD data. The results indicate that MM has been

crystallized in fd-3m space group. The nanometric size, structural disorder, large internal

microstrain and very high structural deformation (even amorphousness) at surface region are

characteristic features of the mechano-synthesized samples.

Moreover, the possibility of the presence of impurity phases cannot be totally ruled out

for these samples. So, we have performed simultaneous structural, microstructural refinement as

well as phase analysis by considering Ni-Zn ferrite as the major phase and NiO, ZnO and α-

Fe2O3 as possible impurity phases in the samples. Again, the Bragg peaks of NiO (JCPDS No.78-

0643), ZnO (JCPDS No.80-0075), α-Fe2O3 (JCPDS No.33-0664) and Ni-Zn ferrite (JCPDS

No.08-0234) overlap partially or completely. Therefore, the simultaneous structural,

microstructural refinement and the analysis of phase abundance have been carried out by

providing all necessary structural information and some starting values of microstructural

parameters of the individual phases using the Rietveld based software package MAUD2.33 6 as

this package is capable of extracting the structural, microstructural (crystalline sizes, r.m.s strain)

parameters along with quantitative abundance of different phases successfully. To analyze the

PXRD pattern by MAUD2.33 software package, it is necessary to provide some initial guess

values of different structural and microstructural parameters. For having the initial values of

microstructural parameters we have fitted the individual lines of the PXRD pattern by the

Lorentzian profile and determined the average crystallite size and residual strain using the

Williamson-Hall plots. The initial positions of tetrahedral (A) site metal ions, octahedral [B] site

metal ions and O atoms have been assigned in the special Wyckoff positions 8(b), 16(c) and

32(e) respectively. The Rietveld structure refinement has been performed by providing the

occupancies of Zn, Ni, Fe and O atoms of Ni-Zn ferrite phase in accordance with the result of

cation distribution obtained by infield Mössbauer study. After a few successful refinement

cycles, we have obtained the refined lattice parameters, crystalline size and r.m.s strain [Fig. S1].

The Rietveld refinement of PXRD data has also been carried out using GSAS15 program

with EXPGUI16 interface to determine the crystal structure more precisely. Before refining the

position coordinates of the oxygen atom, refinement of lattice parameters, background

coefficients and profile parameters were performed. The background was described by the

shifted Chebyshev function of first kind with 36 points regularly distributed over the entire 2θ

range. In the final stages of refinement, the preferred orientation correction was performed using

the generalized spherical harmonic (order 14) model. The final Rietveld refinement of 63

parameters (3 coordinates, 1 lattice parameter, 36 background points, 15 profile parameters, 7

orientation distribution function coefficients and 1 scale factor) converged with an excellent

agreement between the observed and calculated patterns [Fig. S2].

The results of dc magnetic measurements clearly indicate that the sample is in blocked state at

300 K. The blocking temperatures of unstrained counterparts of MM synthesized by chemical

route are presented in the table below:

Synthesis technique Blocking Temperature (TB)

(K)

Particle Size

(nm)

References

Hydrothermal 80, 100, 150 6, 11, 19 17

Sol-gel 42, 62, 84 9, 24, 50 18

Sol-gel autocombustion 30 70 19

It is clear from the literature review that the sample (MM) exhibits enhancement of blocking

temperature compared to its unstrained counterparts synthesized by chemical methods.

Enhancement of blocking temperature and coercivity of the sample under investigation

compared to its counterparts synthesized by chemical methods indicates that the anisotropy

energy of this system is higher than that of its unstrained counterparts.17-19 It may be noted that,

mechanical milling produces grain boundary defects and lattice strain. Thus the strain in the

sample has evolved by the mechanical stress applied during sample preparation through ball

milling and high energy mechanical milling has also produced grain boundary defects.20-22 In

case of mechanically milled samples, there are several reports on enhancement of anisotropy

energy due to microstrain and grain boundary defect but not to the extent we have obtained in

present case. The experimental results suggest the presence of good amount of grain boundary

defect and large microstrain in the sample induces high amount of stress and surface anisotropy

which enhances the total anisotropy and magnetization of the sample.

Reference:

1 K. Lagarec and D. G. Rancourt, Recoil-Mössbauer Spectral Analysis Software for Windows,

University of Ottawa Press; Ottawa, 1998.

2 R. A. Young, D. B. Wiles, J. Appl. Cryst. 15, 430 (1982).

3 S. Enzo, G. Fagherazzi, A. Benedetti, S. Polizzi, J. Appl. Cryst. 21, 536 (1988).

4 H. De Keijser, E. J. Mittemeijer, H. C. F. Rozendaal, J. Appl. Cryst. 16, 309 (1983).

5 S. Bid, S. K. Pradhan, Mater. Chem. Phys. 84, 291 (2004).

6 L. Lutterotti, Nucl. Instrum. Methods Phys. Res., Sect. B 268, 334 (2010).

7 S. Dey, S. K. Dey, B. Ghosh, P. Dasgupta, A. Poddar, V. R. Reddy, S. Kumar, J. Appl. Phys.

114, 0933901-1 (2013).

8 S. Dey, S. K. Dey, B. Ghosh, V. R. Reddy, S. Kumar, Mater. Chem. Phys., 138, 833 (2013).

9 K. Venkateswarlu, A. Chandra Bose, N. Rameshbabu, Physica B 405, 4256 (2010).

10 A. Khorsand Zak, W. H. Abd. Majid, M. E. Abrishami, R. Yousefi, Solid State Sci. 13, 251

(2011).

11 A. Altomare, C. Giacovazzo, A. Guagliardi, A. G. G. Moliterni, R. Rizzi and E. J. Werner, J.

Appl. Crystallogr. 33, 1180 (2000).

12 P. E. Werner, L. Eriksson and M. J. Westdahl; J. Appl. Crystallogr. 18, 367 (1985).

13 A. Boultif and D. Louer, J. Appl. Crystallogr. 37, 724 (2004).

14 A. Altomare, R. Caliandro, M. Camalli, C. Cuocci, C. Giacovazzo, A. G. G. Moliterni and R.

Rizzi, J. Appl. Crystallogr. 37, 1025 (2004).

15 A. C. Larson and R. B. Von Dreele, General structure analysis system (GSAS), Los Alamos

National Laboratory, Report LAUR, 86-748 (2000).

16 B. H. Toby, J. Appl. Crystallogr. 34, 210 (2001).

17 X. Li and G. Wang, J. Magn. Magn. Mater. 321, 1276 (2009).

18 J. J. Thomas, A.B. Shinde, P.S.R. Krishna, N. Kalarikkal, J. Alloys Compd. 546, 77 (2013).

19 K. H. Wu, Y. M. Shin, C. C. Yang, W. D. Ho, J. S. Hsu, J. Polym. Sci., Part A: Polym. Chem.

44, 2657 (2006).

20 B. H. Liu and J. Ding, Appl. Phys. Lett. 88, 042506 (2006).

21 R. N. Bhowmik, R. Ranganathan, S. Sarkar, C. Bansal and R. Nagarajan, Phys. Rev. B, 68,

134433 (2003).

22 R. N. Bhowmik, R. Ranganathan, R. Nagarajan, B. Ghosh, S. Kumar, Phys. Rev. B 72,

094405–1 (2005).

Fig. S1. PXRD pattern of MM with Rietveld refinement plot using MAUD2.33.

Fig. S2. Final Rietveld plot (output of GSAS) of MM showing the difference (pink color

line) between the experimental (orange color symbol) and simulated (green color line)

pattern.

Fig. S3. M-H (hysteresis)loop of MM at 300 and 10 K shown between ± 5 T.

Fig. S4. PAL spectrum of MM with the counts plotted in logarithmic scale.

FIG. S5. Mössbauer spectra of MM at (a) 10K and (b) 10K in an external magnetic field of

5 T fitted by Lorentzian profile of Recoil program. Solid circles represent experimental

data and lines represent fitted curve.

TABLE I. Structural parameters of MA4 obtained by Rietveld refinement method.

Crystal Space Lattice Volume Density Crystalline MicrostrainSystem Group Parameter Size

a (Å) V [Å3] (gcm-3) (nm)

Cubic Fd-3m 8.399(4) 592.45 5.330 10.5 6.7×10-5

TABLE II. Bond distances and bond angles obtained by GSAS program.

Bond Distance (Å) Bond Angle (°)

A−O B−O O−A−O O−B−O

1.823(8) 2.097(8) 109.50(3) 89.90(3)

TABLE III. Fractional coordinates and occupancy of different ions obtained by GSAS program.

Ions x y z Occupancy

(±0.003)

Zn(A) 1/8 1/8 1/8 0.500

Fe(B) 1/2 1/2 1/2 0.750

Fe(A) 1/8 1/8 1/8 0.500

Ni(B) 1/2 1/2 1/2 0.250

O 0.2503(9) 0.2503(9) 0.2503(9) 1.000

Table IV. Values of zero field and infield Mössbauer parameters of MM at 10 K determined by

Lorentzian profile analysis of Recoil program.

Temperature Site Width IS 2ε BHF a HMF A23 θ b Area

/Field (mm s -1) (mm s -1) (mm s -1) (T) (T) (Degree) (%)

(±0.03) (±0.03) (±0.03) (±0.4) (±0.4) (±0.02) (±0.2)

10 K /0 T [ Fe3+A]S 0.34 0.44 0.05 49.7 10.4

[ Fe3+B]S 0.30 0.49 0.07 51.7 31.2

[ Fe3+A]C 0.37 0.45 0.00 50.3 14.1

[ Fe3+B]C 0.35 0.50 0.05 53.4 44.3

10 K /5 T [ Fe3+A]S

d 0.34 0.44 0.05 54.0 49.9c 0.70 33.1 10.4

[ Fe3+B]S 0.30 0.49 0.07 47.5 51.3c 1.10 41.1 31.2

[ Fe3+A]C

e 0.39 0.45 0.08 55.0 50.0 c 0.02 5.7 14.1

[ Fe3+B]C 0.35 0.50 0.01 49 .0 53.9c 0.08 4.0 44.3

a Observed HMF (BHF) is the vector sum of the internal HMF and the external applied magnetic field. b The average canting angle estimated from the ratio of the intensities of lines 2 and 3 from each subspectra, I2/ I3

according to θ = arccos[(4- I2/ I3) / (4+ I2/ I3)]1/2. Where I2/ I3=A23.

c Estimated according to the relationship of BHF, HMF and applied field. d S denotes the surface/shell region of the particles.e C denotes the core region of the particles.