Anomalous properties of magnetic nanoparticles

~ Journalof mngneusm ad magnetic ELSEVIER

Journal of Magnetism and Magnetic Materials 196-197 (1999) 591-594

~

materials

Invited paper

Anomalous properties of magnetic nanoparticles A.E. Berkowitz a'b'*, R.H. Kodama a'b, Salah A. Makhlouf °'~, F.T. Parker b, F.E. Spada b, E.J. M c N i f f Jr. d, S. F o n e r a aphysics Department, University of California, San Diego, La Jolla, CA 92093, USA bCenterfor Magnetic Recording Research, University of California, San Diego, La Jolla, CA 92093, USA CAssuit University, Egypt dFrancis Bitter National Magnet Laborato~, MIT, Cambridge, MA 02139, USA

Abstract Nanoparticles of ferrimagnetic NiFe204 and antiferromagnetic NiO exhibit a variety of anomalous magnetic properties. The lower coordination of surface spins is responsible in both cases for the observed behavior. This conclusion is supported by calculations of field-dependent spin distributions in these nanoparticles. © 1999 Elsevier Science B.V. All rights reserved. Keywords: Ferrimagnetic nanoparticles; Antiferromagnetic nanoparticles; Spin distributions

1. Introduction

2. NiFeeO4 nanoparticles

Magnetic surface properties can differ significantly from those in the bulk. This is principally a result of the lower coordination of the surface atoms, but it is also influenced by surface roughness, and by modified exchange bonds when surface impurity atoms are present. These effects are most clearly evident for magnetic oxides with localized exchange interactions, such as are found in ferrimagnetic and antiferromagnetic systems in which superexchange via an oxygen atom occurs. When these materials are prepared as nanoparticles (NP), with large surface/volume ratios, surface magnetic properties or surface-driven spin rearrangements can dominate the net magnetic behavior, with some remarkable results. Two such examples of magnetic nanoparticles will be discussed: ferrimagnetic NiFe204 (nickel ferrite) and antiferromagnetic NiO.

Samples were produced by prolonged grinding of high-purity NiFe204 in a stainless-steel ball mill with hardened steel mill balls using kerosene as the carrier fluid, with and without addition of surfactants such as oleic acid [1,2]. The average particle size as determined from X-ray diffraction line widths was ~ 65 ~,, consistent with electron micrographs. High-resolution TEM studies on an identically prepared CoFe204 sample showed that the cubic spinel structure was preserved, and that the particles are equiaxed single crystals [3]. These ball-milled samples contained an amorphous contaminant from the wear of the steel mill and balls. All data have been corrected for this contaminant and for the surfactant, when present. In addition, a sample was prepared by grinding NiFe204 in a NiFe204 mortar and pestle to avoid contamination. There were no qualitative differences in the anomalies observed among the three types of NiFe204 nanoparticles (ball-milled with and without surfactant, and ground in a NiFe204 mortar and pestle) [4,5]. High field magnetization measurements (0-200kOe) were made using a water-cooled Bitter

*Corresponding author. Fax: + 1 19 534-2720; e-mail: [email protected].

0304-8853/99/$ - see front matter © 1999 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 8 8 5 3 ( 9 8 ) 0 0 8 4 5 - 2

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A.E. Berkowitz et al. :Journal o/Magnetism atul Magnelic Materials 196-197 (1999) 591-594

magnet with a vibrating sample magnetometer; lower field measurements were made with a commercial S Q U I D magnetometer ( 0 - 7 0 kOe, 5-300 K). Samples were dry powders, immobilized in paraffin. The unusual properties observed in the N i F e 2 0 4 sampies arc as follows [1,2,4,5]: (a) The magnetizations at 4.2 K in 2 0 0 k O e were < 85'!/o of bulk values and were not saturated. (b) M6ssbauer measurements at 23 K in 68.5 kOe showed that all Fe spins were magnetically ordered (i.e., no dead layer), but that a significant fraction of spins were canted, i.e., not collinear with the direction of the applied field. (el Hysteresis loops were still open at 4.2 K in fields as high as 150 kOe. This indicates irreversible magnetization in fields ~ t w o orders of magnitude larger than the magnetocrystalline anisotropy field of bulk NiFe20,,. This feature persisted to ~ 50 K. (d) The hysteresis loops at 4.2 K were shifted hundreds of Oe after cooling in high fields (FC}. (e) The magnetization increased with time at 5 K in 70 kOe after cooling in zero field (ZFC). If) FC and Z F C cur ves taken in 70 kOe were bifurcated (i.e. showed a non-equilibrium state for the ZFC) below ~ 50 K. This is consistent with (c) above. {g) The rate of relaxation of the remanence was finite at 400 m K and temperature independent below 2 K [6], a feature often taken to indicate macroscopic quantum tunneling of the magnetization. We have accounted for the features (al-(fl with a model in which the lower coordination of the surface atoms, together with surface roughness and bonding to surface impurity atoms, produces a spin-glass-like state of spatially disordered (canted) spins in the surface cations. This surface spin state freezes at ~ 50 K and is strongly exchange coupled to the core spins. The spin-frustrationdriven origin of these surface states is satisfied by a number of different spin configurations which can be accessed by various combinations of applied field and temperature. With such a model, the low magnetization in high fields at 4.2 K is due to the canting of a significant fraction of the surface spins, as indicated by the M6ssbauer data. The open hysteresis loops below - 5 0 K indicate the progressive thermally assisted, field-driven occupation of surface spin states with a net moment in the field direction. The hysteresis loop shifts are a consequence of the strong coupling of surface states with a net moment in the field direction to the core spins. The bifurcation of the F C and Z F C 70 kOe susceptibility curves below ~ 50 K are consistent with the non-equilibrium nature of the Z F C surface spin states in high fields. This non-equilibrium nature also explains why the magnetization of Z F C samples increases with time in high fields below ~ 50 K. This model was developed by numerical atomic calculations of spin configurations in N i F e 2 0 ¢ N P and the

energy barriers between surface spin states [4,5]. The assumptions were: (1) exchange constants derived from a mean field analysis of magnetization and M6ssbauer data: (2) classical spins in an inverse spinel structure: (3) no dipolar interactions: (4) a fraction of broken exchange bonds between surface spins (80% for the example below), with exchange bonds between surface and core spins unaffected; (5) anisotropy of surface cations taken from EPR data on Ni 2 " and Fe 3 + ions in low symmetry sites in non-magnetic oxides [7,8]. Surface roughness and bonding of impurity atoms were included by calculations for particles with different surface vacancy densities and broken bond densities, respectively. The algorithm used to calculate the equilibrium spin configurations was a three-dimensional generalization of one developed by Hughes [9]. Details of the calculations can be found in Refs. [4,5]. Fig. 1 shows a calculated spin configuration for a (1 1 0) cross-section of a 40 ,~ NIFe204 NP. We note the non-collinear orientations of some of the surface spins. Spin distributions, hysteresis loops, order parameters, etc., were calculated for thousands of particles, and established the lnodel discussed above with very satisfactory quantitative agreement with the experimental results discussed in (a)-(f}. The behavior model noted in (g) above, a finite relaxation of the remanence at very low temperatures, seems to be associated with the shape of the distribution of energy barriers in the N i F e 2 0 4 - N P , rather than indicating M Q T . This conclusion was reached by calculations of distributions of activation energies for irreversible changes of the particle's spin states. These states are found by perturbing an initial spin configuration with random rotations. The "'activation energy" is the perturbation required for the particle's spin distribution to converge to a different state. Fig. 2 shows a distribution of activation energies associated with the spin configurations of a 25 A particle. We find a hierarchy of states in the

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Fig. 1. Calculated spin configuration in zero field for a cross section of a 40 A. NiFezO4 particle, with surface w/cancy density SVD = 0.1/0.1/0.1, broken bond density BBD 0.8. The three SVD parameters are applied iteratively. A surface anisotropy of 4 kB/spin is included.

A.E. Berkowitz et al. / Journal of Magnetism and Magnetic Materials 196-197 (1999) 591-594

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Fig. 2. Calculated activation energy distribution for a 30 ~, NiFe204 particle with surface anisotropy of 4 kB/spin, using values of 0.1 and 0.5 for the I~1 threshold. Note the larger energy units of the bottom histogram (K/cation rather than mK/cation).

neighborhood of any starting state. If the perturbation energy is small, the particle can converge to a state where the change in the spin vectors is relatively small (IASil > 0.1), as shown in Fig. 2(a). Higher-energy perturbations are required to produce larger changes in the spin vectors (IASil > 0.5), as shown in Fig. 2(b). The dashed curve is a fit to 1/E. Barbara et al. [10] have shown that such a distribution of activation energies leads to a temperature-independent thermally activated relaxation. Thus, the temperature-independent relaxation of the remanence which we found in these NiFe2Og-NP is not indicative of MQT, but is a thermally activated consequence of the 1/E form of the activation energy distribution, which, in turn, is driven by the existence of the spin-glass-like surface spin states.

3. N i O nanoparticles

The NiO nanoparticles were prepared by first precipitating a Ni(OH)2 gel from a Ni(NOa)2 aqueous solution by adding a NaOH solution at room temperature. Portions of the dried gel were then heaed in air for 3 h at various temperatures to produce NiO nanoparticles of various average sizes. The heating temperatures were 2507700°C, which produced average particle sizes of 53 A- > 600 A. Particle sizes were determined from Xray line broadening and from BET surface area measurements. Agreement between these two methods was excellent [10].

Fig. 3. Hysteresis loops at 5 K of 315 ,~ NiO particles;ZFC and FC from 340 K in 20 kOe. Inset is the coercive field, Hc and exchange field, H+, as functions of particle size.

Bulk NiO is an antiferromagnet with two antiparallel sublattices whose equal moments compensate each other. As such, it has a small, reversible susceptibility in applied fields, and no irreversible hysteresis properties. When NiO is prepared as small particles, the number of magnetic atoms in each sublattice may not be equal. Thus, NiO-NP samples can possess a significant fixed magnetic moment due to the uncompensated spins. The NiO-NP prepared as described above have significant moments which increased with decreasing average particle diameter [11]. This is due to the fact that the uncompensated spin density increases with the density of surface atoms. However, the NiO-NP also exhibited the following unexpected properties [-11,12]: (a) The measured magnetic moments of the N i O - N P over the size range 53-315 ~, were 5-10 times higher than the moments calculated on the basis of a two-sublattice model. A spherical shape was assumed for the calculations, and the center position of the sphere within the unit cell was varied to obtain a statistical average of 104 particles. Thus a two sublattice model seems inconsistent with the measurements. (b) The N i O - N P had very significant coercive forces and (after FC) loop shifts at 5 K. Fig. 3 shows the ZFC and FC hysteresis loops for the 315 A sample - both Hc and the loop shift were ~ 10 kOe. The insert shows the dependence of He and loop shift on the average particle size. In order to account for the properties of the NiO-NP, their spin configurations were calculated in the manner employed for the NiFezO+-NP. Details of the assumptions, exchange and anisotropy constants, spin Hamiltonian, broken bond densities, roughness, etc., are found in Ref. [12]. The principal result of the calculations was that the N i O - N P could have up to eight spin sub

594

,4.E. Berkowitz et al. / Journal o]'Magnetism and Magnetic Materials 196-197 (1999) 591 - 594

~ A particle

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~\*\-\ iN*N,N* \ , \ , \ * \ * \ * N~N*N*N*N*N \ ~ \ , \ * \ * \ * \ * ,N~NiN*N*N* \ ~ \ , \ * \ * \ * \ NtN~N*N*N*N* \ , \ , \ , \ - \ , \ * iNiN*N* N,N* ~ \ , \ , \ , \ , \ , \ * \ , \ , N , \ , \ ,\,\ H=O

sublattices are not fixed, but they can change on cycling the field. This produces a variety of reversal paths for the spins, leading to coercivity. Surface anisotropy and multisublattice states are essential for producing simultaneous coercivities and shifted loops. Therefore. just as for the N i F e 2 O a - N P , the anomalous properties found in the N i O - N P are driven by surface parameters such as lower coordination, roughness, broken bond density and surface anisotropy.

Acknowledgements

*

Fig. 4. Calculated spin configuration in zero field for a cross section of a 44 A diameter, 17 A thick NiO platelet, which has (1 1 1) orientation. Arrow lengths denote the projection of the spin in the cross section plane (i.e. shorter arrows point out of the plane). The surface vacancy density SVD = 0.2 and broken bond density BBD = 0.5. A surface anisotropy of 2 kB/spin is included.

lattices, depending on the particle diameter, surface roughness, and broken bond density. Fi~. 4 shows the spin configuration for a 44 ,~ diameter ! 7 A thick particle with surface vacancy density of 0.2, and broken bond density of 0.5. Generally, it was found that the average number of sublattices is near 8 for the smaller particles and decreases to 2 as the particle size increases [12]. For a given particle size, the transition from one sublattice configuration to another is determined by the nature of the surface. The multisublattices in the N i O - N P result in moments due to uncompensated spins much higher than those calculated for two-sublattices, e.g., 4 times larger for particles 25-50 A diameter with 4 A roughness and a broken bond density = 0.8. Hysteresis loops were calculated with simulated field cooling in 100 kOe, as described in Ref. [12]. The resulting loops were qualitatively similar to those found experimentally in that large coercivities and loop shifts were obtained, and the loops were open to very large fields. It was established that the angles between the

This work was supported in part by the N S F under Grant # DMR-9400439. The F B N M L is also supported by the NSF.

References

[1] A.E. Berkowitz, J.A. Lahut, I.S. Jacobs, L.M. Levmson. D.E. Forester, Phys. Rev. Lett. 34 (1975) 594. [2] A.E. Berkowitz, J.L. Lahut, C.E. VanBuren, IEEE Trans. Magn. 16 (1980} 18. [3] A.C. Nunes, E.L. Hall, A.E. Berkowitz, J. Appl. Phys. 63 (1988) 5181. [4] R.H. Kodama, A.E. Berkowitz. E.J. McNiff Jr.. S. Foner. Phys. Rev. Lett. 77 (1996} 394. [5] R.H. Kodama, A.E. Berkowitz, E.J. McNiff Jr., S. Foner. J. Appl. Phys. 81 (1997) 5552. [6] R.H. Kodama, C.L. Seaman, A.E. Berkowtiz, M.B. Maple. J. Appl. Phys. 75 (1994) 5639. [7] A.K. Petrosyan, A.A. Mirzakhanyan, Phys. Stat. Sol. B. 133 (1986) 315. [8] E.S. Kirkpatrick, K.A. Mfiller, R.S. Rubins. Phys. Rev. A 135 (1964) A86. [9] G.F. Hughes, J. Appl. Phys. 54 (19831 5306. [10] B. Barbara et al., m: J.L. Dormann, D. Fiorani (Eds.). Magnetic Properties of Fine Particles, Elsevier, Amsterdam, t993, p. 235. [11] S.H. Makhlouf, F.T. Parker, F.E. Spada. A.E Berkowitz. J. Appl. Phys. 81 {1997) 5561. [12] R.H. Kodama, S.A. Makhlouf, A.E. Berkowitz, Phys. Rev. kett. 79 (1997) 1393.