Evolution of magnetic anisotropy and thermal stability during nanocrystal-chain growth M. Charilaou, 1,a) K. K. Sahu, 2 D. Faivre, 3 A. Fischer, 3,b) I. Garcı ´a-Rubio, 4 and A. U. Gehring 1 1 Earth and Planetary Magnetism, Department of Earth Sciences, ETH Zurich, CH-8092 Zurich, Switzerland 2 Laboratory of Metal Physics and Technology, Department of Materials, ETH Zurich, CH-8093 Zurich, Switzerland 3 Department of Biomaterials, Max Planck Institute of Colloids and Interfaces, D-14476 Potsdam, Germany 4 Laboratory 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. V C 2011 American Institute of Physics. [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 (Fe 3 O 4 ) 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 Fe 3 O 4 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 H cub ¼ K 1 /M, where K 1 is the first-order anisotropy con- stant of magnetite (K 1 ¼1.1 10 5 erg/cm 3 ), 23 and M is the magnetization and (ii) the uniaxial anisotropy field H uni ¼ 4pMN eff , where N eff is the effective demagnetizing factor. In the context of the ellipsoid model, H cub describes the magnetocrystalline field of the individual Fe 3 O 4 crystalli- tes and H uni 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 Ne ´el-Brown-type activation mechanisms: the magnetic moment stability-lifetime is s ¼ s 0 exp(K 1 V/k B T), where s 0 is an intrinsic fluctuation attempt time (taken to be 10 10 s), 24 V ¼ 4pR 3 /3 the particle volume (assuming a spherical sym- metry, R ¼ D/2), k B the Boltzmann constant, and T ¼ 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: [email protected]. b) Present address: Institute of Chemistry, Technische Universita ¨t Berlin, D-10623 Berlin, Germany. 0003-6951/2011/99(18)/182504/3/$30.00 V C 2011 American Institute of Physics 99, 182504-1 APPLIED PHYSICS LETTERS 99, 182504 (2011) Author complimentary copy. Redistribution subject to AIP license or copyright, see http://apl.aip.org/apl/copyright.jsp
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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
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