Evolution of magnetic anisotropy and thermal stability duringnanocrystal-chain growth

M. Charilaou,1,a) K. K. Sahu,2 D. Faivre,3 A. Fischer,3,b) I. Garcıa-Rubio,4 and A. U. Gehring1

1Earth and Planetary Magnetism, Department of Earth Sciences, ETH Zurich, CH-8092 Zurich, Switzerland2Laboratory of Metal Physics and Technology, Department of Materials, ETH Zurich, CH-8093 Zurich,Switzerland3Department of Biomaterials, Max Planck Institute of Colloids and Interfaces, D-14476 Potsdam, Germany4Laboratory of Physical Chemistry, Department of Chemistry and Applied Biosciences, ETH Zurich,CH-8093 Zurich, Switzerland

(Received 26 August 2011; accepted 13 October 2011; published online 1 November 2011)

We compare measurements and simulations of ferromagnetic resonance spectra of magnetite

nanocrystal-chains at different growth-stages. By fitting the spectra, we extracted the cubic

magnetocrystalline anisotropy field and the uniaxial dipole field at each stage. During the growth of

the nanoparticle-chain assembly, the magnetocrystalline anisotropy grows linearly with increasing

particle diameter. Above a threshold average diameter of D� 23 nm, a dipole field is generated,

which then increases with particle size and the ensemble becomes thermally stable. These findings

demonstrate the anisotropy evolution on going from nano to mesoscopic scales and the dominance of

dipole fields over crystalline fields in one-dimensional assemblies. VC 2011 American Institute ofPhysics. [doi:10.1063/1.3658387]

The properties of magnetic nanoparticle-assemblies are

attracting increasing interest in various scientific commun-

ities, such as solid-state magnetism, earth sciences, biology,

materials science, and medicine.1–10 Gaining deeper insight

into the functionality of such systems allows a better physi-

cal understanding of magnetostatic interactions in the nano-

scale and also promotes new ideas for technological imple-

mentation. In the context of basic physical understanding, an

excellent model-system is the linear nanocrystal-chain. Such

configuration is found in magnetotactic bacteria (MTB).

In MTB cells, one-dimensional chain assemblies of sta-

ble single-domain magnetite (Fe3O4) nanocrystals are ori-

ented along the [111]-axis of the cubic crystal, which is also

the easy-axis of magnetization.11–14 This setup exhibits char-

acteristic anisotropy traits, which result from the combina-

tion of cubic magnetocrystalline anisotropy, of each

individual crystallite, and dipole uniaxial fields generated by

the interactions between the nanocrystals along the chain. In

an ensemble with randomly oriented assemblies, these ani-

sotropy features are readily detectable in ferromagnetic reso-

nance (FMR) experiments, which produce characteristic

spectra with two or three low-field peaks and one strong

high-field peak.15–19 Therefore, we have investigated the

evolution of magnetic anisotropy in growing MTB assem-

blies by FMR spectroscopy at a frequency of 9.8 GHz at am-

bient conditions.

For the simulations, we used FMR data from the MSR-1

strain, which generates equidimensional particles.20 The

time-resolved formation of Fe3O4 particles and their assem-

bly in chains is analyzed. The building of magnetite chains is

a mainly genetically driven process,21 supported by magnetic

docking mechanisms.20 The particle sizes were estimated by

transmission electron microscopy,20 and for the FMR experi-

ments, samples with average particle diameters of D� 5

(T1), 18 (T3), 19 (T4), 23 (T6), 29 (T8), 34 (T10), and

41 nm (T12) were used. The MTB cells were embedded in

paraffin, in order to avoid physical re-orientation during field

exposure in the FMR experiments.

In order to extract the anisotropy parameters from the

FMR data, we used the ellipsoid model described in Ref. 22,

which can be used to simulate FMR spectra of randomly ori-

ented linear-chains. The ellipsoid model approximates the

whole linear chain as a rigid rotation ellipsoid and assumes a

uniform spatial distribution of identical non-interacting ellip-

soids. In this model, two parameters are needed to describe

the anisotropy: (1) the cubic magnetocrystalline anisotropy

field Hcub¼K1/M, where K1 is the first-order anisotropy con-

stant of magnetite (K1¼�1.1� 105 erg/cm3),23 and M is the

magnetization and (ii) the uniaxial anisotropy field

Huni¼ 4pMNeff, where Neff is the effective demagnetizing

factor. In the context of the ellipsoid model, Hcub describes

the magnetocrystalline field of the individual Fe3O4 crystalli-

tes and Huni the total effective dipole field of the chain which

requires that the nanocrystals are thermally stable and inter-

acting with each other. The criterion for thermal stability can

be assessed from the anisotropy energy of magnetite, assum-

ing Neel-Brown-type activation mechanisms: the magnetic

moment stability-lifetime is s¼ s0exp(K1V/kBT), where s0 is

an intrinsic fluctuation attempt time (taken to be 10�10 s),24

V¼ 4pR3/3 the particle volume (assuming a spherical sym-

metry, R¼D/2), kB the Boltzmann constant, and T¼ 300 K

the temperature. In this context, any particle with size

D> 12 nm, yielding a lifetime of 10�9 s, will be virtually

blocked at 9.8 GHz and its anisotropy will be “visible” to

FMR, whereas the anisotropy of particles with D< 12 nm,

having a lifetime smaller than that of the microwave,

remains undetected by FMR. For the development of an

a)Author to whom correspondence should be addressed. Electronic mail:

michalis.charilaou@erdw.ethz.ch.b)Present address: Institute of Chemistry, Technische Universitat Berlin,

D-10623 Berlin, Germany.

0003-6951/2011/99(18)/182504/3/$30.00 VC 2011 American Institute of Physics99, 182504-1

APPLIED PHYSICS LETTERS 99, 182504 (2011)

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effective dipole moment, i.e., thermal stability over a long

time-range, a size of D> 30 nm is necessary (s� 2� 106 s).

With this in mind, the intrinsic (magnetocrystalline) anisot-

ropy can be determined from FMR data for all samples

(except at D� 5 nm), and the interaction-induced extrinsic

anisotropy (dipole uniaxiality) can be detected as soon as

thermal stability is established. In principle, the dipolar inter-

actions contribute towards thermal stability as well, but the

dipolar fields fluctuate with the particle moments. Therefore,

the dipolar interaction is both the cause and the effect of

thermal stability and requires a more explicit approach, as

shown in Refs. 25 and 26. Thus, the consideration of only K1

for the thermal stability is a simplified approach, used as a

guide.

We fitted the FMR spectra and extracted the two anisot-

ropy fields with an accuracy of 610 Oe for Hcub and 65 Oe

for Huni. The simulated spectra agree well with the data, with

some intensity discrepancies. The deviation between meas-

ured and simulated intensities is justified considering the

assumption of the model that all particles and chains are

evenly oriented in space and that the volume distribution is

uniform.22

Figure 1 shows all seven FMR spectra of the time series.

At the first recordable growth-stage (T1, D� 5 nm), a weak

paramagnetic signal is recorded, which can be attributed to

Fe(III) in an octahedral configuration. For T3 and T4, the

magnetic moment stability lifetime is s> 3.3� 10�7 s and

s> 1.4� 10�6 s, respectively, and the moment is virtually

blocked at 9.8 GHz. Thus, their anisotropy is detectable, as

seen by the asymmetric signals of T3 and T4. At stage T6,

where the particles have an average diameter of 23 nm, the

first signs of dipole uniaxiality can be seen in the spectrum:

the low-field tail corresponds to uniaxial anisotropy contribu-

tions, which require lower resonance fields along the easy

axis. Upon going from T8 to T12, we see an evolution of the

FMR signal into that of a typical uniaxial symmetry, which

in a random distribution exhibits two low-field peaks and

one strong high-field peak, with a shoulder at 3.5–3.7

kOe.15–19,22

Figure 2 summarizes the evolution of anisotropy fields

during particle-chain growth. The cubic anisotropy becomes

evident as soon as the particles are formed, i.e., at T3 with

D� 18 nm. At the early stages, Hcub¼�100(10) Oe for T3

and �120(10) Oe for T4 (the value in the parenthesis corre-

sponds to the error bar). With increasing average particle di-

ameter, Hcub increases almost linearly and reaches �250(10)

Oe at D> 35 nm. The threshold value of 35 nm is slightly

above the theoretical superparamagnetic/stable-single-do-

main threshold, which means that at this size, the bulk single

crystal properties are accomplished and the effect of the sur-

face is diminished; surface strains do not dominate over bulk

crystal symmetries. In addition, for particles with an average

diameter of 23 nm (T6), Huni appears at 300(5) Oe (circles in

Fig. 2). This suggests that some particles are assembled in

chains and are weakly interacting. With a diameter of 23 nm,

however, the lifetime of the magnetic moment is 2.2 ms,

which does not suggest stable magnetization. One possibility

is that the apparent early blocking is induced by inter-

particle interactions.25,26 In addition, considering the rela-

tively broad particle-volume distribution,20 the observed

dipole fields are most probably due to particles with larger

sizes. Therefore, we can safely assume that larger particles

promote magnetic docking,20 generating stable assemblies.

The effect of interaction-induced dipole fields becomes more

pronounced with increasing average particle diameter and

Huni increases, due to the addition of more particles to the

chain, and the growth of the particles already in the chain. At

the final stage (T12), Huni is 870(5) Oe, giving an effective

demagnetization factor of 0.147(1), which suggests an effec-

tive elongation of (length/width) 1.42(1) of the ellipsoid, i.e.,

of the chain. This elongation does not correspond to the

physical dimensions of the chain but to the inter-particle

dipole interactions along the assembly which generate the

apparent total dipole field.

We now use the extracted anisotropy fields to visualize

the evolution of magnetocrystalline and dipole fields in this

system. Figure 3 shows the evolution at four critical stages:

(a) no anisotropy, (b) only cubic anisotropy, (c) balance

between cubic and dipole fields, and (d) dominant dipole

fields. Under the influence of the external field, such as in

FIG. 1. (Color online) Measured (solid lines) and simulated (dashed lines)

FMR spectra of cultured MTB during particle-chain growth.

FIG. 2. (Color online) Evolution of cubic magnetocrystalline anisotropy

Hcub (squares) and dipole uniaxial field Huni (circles) with increasing particle

diameter. The size of the symbols corresponds to the error-range.

182504-2 Charilaou et al. Appl. Phys. Lett. 99, 182504 (2011)

Author complimentary copy. Redistribution subject to AIP license or copyright, see http://apl.aip.org/apl/copyright.jsp

FMR or static magnetization measurements, the changing

symmetries during growth are smeared out. However, know-

ing the anisotropy fields of the system allows us to visualize

the true energetic symmetries. This is seen by the compari-

son between resonance field Hres (left in Fig. 3) and the

energy density Ftot(H) (right in Fig. 3), showing the differ-

ence between field-induced equilibrium (Hres) and the state

of the system at the absence of external fields [Ftot(H¼ 0)].

The transition from nano-scopic, i.e., only crystalline effects,

to meso-scopic scale, i.e., extrinsic dipole fields, is abrupt.

The uniaxial energy dominates over cubic as soon as it

appears. Therefore, although in the FMR spectra no abrupt

change is seen, the energetic change upon the onset of ther-

mal stability is striking.

Finally, our findings clearly show that in one-

dimensional nanocrystal-assemblies, the nano-scopic crystal-

line symmetries develop gradually with increasing particle

diameter and that inter-particle interaction, i.e., thermal sta-

bility of magnetic moments occurs abruptly and dominates

over crystalline anisotropy.

M.C. acknowledges financial support from the Swiss

National Science Foundation Grant No. 200021-121844.

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FIG. 3. (Color online) 3-dimensional anisotropy maps of the linear assem-

blies for average diameter of (a) D� 5 nm, (b) 18 nm, (c) 23 nm, and (d)

41 nm, normalized to (left) the resonance field and (right) the free energy

density. The coordinate system is illustrated in (a).

182504-3 Charilaou et al. Appl. Phys. Lett. 99, 182504 (2011)

Author complimentary copy. Redistribution subject to AIP license or copyright, see http://apl.aip.org/apl/copyright.jsp