Low-temperature magnetic properties of horse spleen ferritin

Article Geophysics

September 2010

Vol.55 No.27-28: 3174–3180 doi: 10.1007/s11434-010-4025-3

SPECIAL TOPICS:

Low-temperature magnetic properties of horse spleen ferritin TIAN LanXiang1,2, CAO ChangQian1,2, LIU QingSong1,2 & PAN YongXin1,2* 1 2

Key Laboratory of the Earth’s Deep Interior, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing 100029, China; Franco-Chinese Biomineralization and Nano-structures Laboratory, Beijing 100029, China

Received February 8, 2010; accepted May 13, 2010

The magnetic properties of the antiferromagnetic cores in ferritin are of importance in the construction and improvement of ferritin-based magnetic resonance imaging systems and their application to environmental magnetism. In this study, we carry out integrated magnetic and transmission electron microscopy analyses of horse spleen ferritin (HoSF) to understand the relationships between the magnetic behavior of HoSF and temperature, applied field and grain-size distributions. The R-value from the Wohlfarth-Cisowski test for the investigated sample at 5 K was 0.46, indicating very weak magnetostatic interactions among the nanoparticles of HoSF. The nanoparticles of HoSF show superparamagnetic properties at room temperature, while below the blocking temperature of Tb ≈ 12 K it has a net magnetic moment that comes from the uncompensated spins of the nanoparticle surface or spin-canting. The thermal relaxation process of HoSF follows the Néel-Arrhenius expression. From low-temperature AC susceptibility data, we calculated the effective magnetic anisotropy energy Ea=(5.52±0.16)×10–21 J; the effective magnetic anisotropy energy constant Keff =(4.65±0.14)×104 J/m3 and the pre-exponential frequency factor ƒ0=(4.52±2.93)×1011 Hz. These values are useful in understanding the magnetic behavior of the antiferromagnetic nanoparticles and their potential application in biomedical technology. horse spleen ferritin, superparamagnetic, low temperature magnetic properties, pre-exponential frequency factor Citation:

Tian L X, Cao C Q, Liu Q S, et al. Low-temperature magnetic properties of horse spleen ferritin. Chinese Sci Bull, 2010, 55: 3174−3180, doi: 10.1007/ s11434-010-4025-3

Iron is one of the most important essential elements for all living organisms. Most iron is found in enzymes and proteins and it plays a fundamental role in maintaining the normal growth and metabolism of cells. However, excess free iron together with superoxide and hydrogen peroxide by the Fenton reaction will produce reactive hydroxyl radicals, which results in lipid peroxidation, DNA strand breaks and the degradation of other biomacromolecules. Ferritin may play a key role in iron storage and this will reduce the potential toxic effects of free iron. Toxic Fe (II) is transformed into Fe(III) as ferrihydrite and is sequestered within the ferritin cavity. Iron can thus be released and recycled when cells need Fe (II). Therefore, ferritin has two functional roles: iron detoxification and iron storage [1,2]. Recent studies indicated that neurodegenerative diseases *Corresponding author (email: [email protected])

© Science China Press and Springer-Verlag Berlin Heidelberg 2010

(ND) and cancers are closely associated with iron dyshomeostasis. Abnormal iron depositions were found in the brain tissue of patients that suffered from Alzheimer’s disease (AD), Parkinson’s disease (PD) and Huntington’s disease (HD) [3,4]. Apart from heme iron, many ferrimagnetic minerals less than 20 nm were also found in these pathological brain tissues [5,6]. It is believed that these abnormal iron depositions are related to the dysfunction of ferritin [7]. Therefore, in these pathological tissues the level of ferritin and the rate of ferrimagnetic ferritin cores both increased [8–10]. An increase in ferritin content is probably the consequence of neuron protection from free radicals and redox stress in organisms [11,12]. In addition, the abnormal expression of ferritin has also been tested in several different types of cancer cells. Ferritin is regarded as a prognostic indicator and target for the immune therapy of neuroblastoma and other cancers [13]. More importantly, magnetic csb.scichina.com

www.springerlink.com

TIAN LanXiang, et al.

Chinese Sci Bull

resonance imaging (MRI) is primarily a non-invasive medical imaging technique used to test for progressive neurodegenerative diseases and tumors and can be used for the quantitative estimation of iron content in tissue, and the degree of injury to physiological tissue may be assessed [14,15]. Because the level of iron-contained magnetic materials in tested tissue is a key factor which affects the proton relaxation rates and image contrast in MRI testing [16–18], ferritin is also an important early diagnostic marker in tumors and neurodegenerative diseases [5,19]. Therefore, characterizing the magnetic properties of nanoparticles of ferritin is the basis of constructing and improving the ferritin-based MRI reporting system for the early diagnosis of tumors and neurodegenerative diseases [20,21]. In addition, an understanding of the magnetic properties of ferritin is valuable for application in environmental magnetism and rock magnetism. Thanks to protein shells, there is nearly no interaction among the ferrihydrite ferritin cores, which offers an ideal material for the study of superparamagnetism [22–24]. The aim of this study is to use low-temperature magnetic methods in conjunction with transmission electron microscopy (TEM) to investigate the magnetic properties of HoSF and also the effects of variations in temperature, applied field, particle size distribution and experimental timescale.

1 Materials and methods HoSF was purchased from Sigma-Aldrich (85 mg/mL, 0.15 mol/L NaCl background electrolyte). For TEM analysis, a drop consisting of 10 μL HoSF (1.0 mg/mL) was deposited onto Formvar-covered copper grids after dialysis in distilled water. Excess solution was removed with filter paper. For low-temperature magnetic measurements, the sample was freeze-dried in a vacuum freezer dryer to prevent possible biochemical alterations. The dried HoSF (8 mg) was then packed into a small non-magnetic plastic capsule for magnetic measurements. Grain size analysis and selected area electron diffraction (SAED) of HoSF were performed on a JEM2010 transmission electron microscope (JEOL, Japan) operated at 200 kV. For the grain size of irregular particles, the largest diameter was measured. Low-temperature magnetic measurements were performed using a Quantum Design MPMS SQUID magnetometer (Model XP-5, magnetic moment sensitivity was 5.0×10–10 Am2). The following measurements were carried out: (1) Low-field DC susceptibilities were measured between 5 and 300 K in a field of 5 mT after the sample was cooled to 5 K in zero field (zero-field cooling, ZFC) and in the presence of a 5 mT field (field-cooling, FC). (2) To evaluate magnetostatic interactions, the isothermal remanent magnetization (IRM) was acquired and DC field demagnetization (DCD) curves were measured at 5 K up to ±3 T.

September (2010) Vol.55 No.27-28

3175

Once a constant magnetic field was applied for 600 s, the remanent moment was measured after the removal of the field with a delay of 600 s. (3) Hysteresis loops were measured at temperatures between 2 K and 21 K as well as at 300 K in a field of ±5 T. (4) Alternating current (AC) susceptibility measurements were obtained at frequencies of 30, 100, 330, 1000, and 1400 Hz in a weak field of 0.4 mT between 5 K and 300 K. (5) The thermal decay of the isothermal remanence was acquired at 5 K in a field of 5 T after cooling in ZFC and a 5 T FC was measured between 5 and 300 K.

2 Results 2.1

TEM analyses

Bright field TEM shows monodispersed electron-dense cores (Figure 1). The grain sizes of those cores fit a negative skew distribution with a highly uniform size, a mean diameter of 6.1 nm and a standard deviation σV = 1.0. Most particles range within 6–7 nm (Figure 2). The average iron content per HoSF is 1527, as determined by inductivelycoupled plasma mass spectroscopy. Selected area electron diffraction (SAED) shows d-spacings of 0.253, 0.228, 0.205, 0.178, 0.154 and 0.108 nm, which are characteristic of 6-line ferrihydrite, as shown in Table 1. The 0.253 nm and 0.154 nm lattice spacings define the two most intense rings. 2.2

Low-field magnetization curves

Thermal agitation weakened as the temperature decreased in the zero field, so some particles were progressively blocked

Figure 1

Bright field TEM image of unstained HoSF cores.

3176


Chinese Sci Bull


Ir (H) and Id (H) follow the Wohlfarth equation: Id (H)=1−2Ir (H) [32]. The crossover point (R) for the IRM and DCD curves should be equal to 0.5. The R-value obtained in the Wohlfarth-Cisowski test for HoSF was 0.46, as shown in Figure 4. This value indicates very weak interactions between the measured nanoparticles. The median destructive field (MDF) is high at 836 mT, which suggests that the ferrihydrite cores of HoSF are hard magnetic minerals, and this is consistent with the SAED analyses. 2.4

Figure 2

Size distribution histogram of the HoSF cores.

Table 1 d-spacings from the selected area electron diffraction (SAED) patterns of the HoSF cores compared with standard 6-line ferrihydrite mineralsa) d-spacings (nm) of d-spacings (nm) of d-spacings (nm) of HoSF (from SAED, 6-line ferrihydrite 6-line ferrihydrite (from XRD) this study) (from SAED) – 0.456 – 0.30–0.32 0.321 0.253 0.25–0.26 0.252 0.228 0.227 0.222 0.205 0.202 0.196 0.178 0.176 0.170 0.154 0.145–0.158 0.147, 0.149 0.108 0.107 – a) Data in the 2nd and 3rd columns are from [25–27].

and transformed into a single domain (SD) state. As shown in Figure 3, the susceptibility peaks at 12 K and this is associated with the average blocking temperature, Tb. In contrast, the FC curve decays continuously with increasing temperature because the magnetization was already aligned with the field direction during cooling to below the blocking temperature [28]. The ZFC and FC curves of the measured HoSF merge at about 24 K, which corresponds to the maximum unblocking temperature. The difference between the FC and ZFC curves equals the thermal remanent magnetization (TRM) [29]. Above the maximum unblocking temperature (24 K in our case), the reciprocal susceptibilities can be plotted as a function of temperature and should fit the Curie-Weiss law [30]. 2.3

Low-temperature hysteresis loops

Figure 5 shows the hysteresis loops of HoSF measured at 2, 3, 4, 5, 10, 21 and 300 K. All loops are non-saturated up to 5 T and are closed at approximately 3 T. This is probably due to the surface uncompensated moments of ferrihydrite nanoparticles. The remanence moment (Mr), coercivity (Hc) and the magnetization under a 5 T field (M5T) all decreased as the temperature increased and is due to the SD particles gradually unblocking into superparamagnetic (SP) particles as the temperature increases. This is also shown by the hysteresis loops becoming more constricted (wasp-waisted) (Figure 5(a)–(e)). At 5 K, the loop is a typical wasp-waisted shape. All particles are almost unblocked to SP and the hysteresis disappears above 21 K, which is typical SP unblocking behavior (Figure 5(f)). At room temperature, the loop shows typical paramagnetic behavior and this nearly fits a straight line that crosses the original point. 2.5

AC susceptibility

AC magnetic susceptibility measurements give an in-phase or real component, χ′ and an out-of-phase or imaginary component χ′′. The real component χ′ is just the slope of the

Magnetic interactions

Below the blocking temperature, the HoSF core particles behave the same as SD particles. The magnetic interactions among particles can be quantified by IRM (Ir (H)) and DCD (Id (H)) curves [31]. In the absence of magnetic interactions,

Figure 3 Low-field (5 mT) magnetization curves as a function of temperature. These were measured after zero-field-cooling (ZFC) and field-cooling (FC) treatment. The inset represented an enlarged low temperature region (0–30 K).


Chinese Sci Bull


3177

Figure 4 Remanence data for nanoparticles of HoSF measured at 5 K. (a) Normalized IRM acquisition and DC demagnetization (DCD). The DCD curve was rescaled by 0.5 (1+IRM(–H))/SIRM. (b) Henkel plot [33], (Ir (H)) vs. (Id (H)) normalized by SIRM. The straight solid line is the theoretical Wohlfarth equation for non-interaction systems. MDF: median destructive field. R-value: the crossover of IRM and DCD.

M(H) curve. The imaginary component, χ′′, indicates dissipative processes in the sample [34]. Figure 6 shows the in-phase (χ′) and out-of-phase (χ′′) susceptibility data of HoSF. The peak temperatures (Tmax) in the χ′ and χ′′ curves are related to the Tb and particle size distribution of the sample [35]. Tmax in the χ′ curves range from 17–22 K. χ′ shows frequency-dependence below 30 K. The peak values of χ′ decrease and the peak temperatures (Tmax) increase with increasing frequencies (see inset in Figure 6(a)). Above 30 K, χ′ shows nearly no frequency dependence and this corresponds to the maximum unblocking temperature. Above this temperature, all nanoparticles are completely unblocked. The nonzero out-of-phase susceptibility (χ′′) data indicates that the magnetization of the sample may lag behind the drive field. The lag time is consistent with the reciprocal of the frequency (Figure 6(b)). For a non-interacting SD particle with uniaxial anisotropy, the superparamagnetic thermal relaxation time fits the Néel-Arrhenius expression [36], (1) τ =1/f0 exp (Ea/kT), where τ is the relaxation time of the magnetic moment of the particles, ƒ0 is the pre-exponential frequency factor, Ea is the average effective energy barrier to be overcome for the magnetic moment of a grain to switch direction, k is Boltzmann’s constant and T is the temperature. For uniaxial anisotropic particles, Ea = Keff V, where Keff is the effective magnetic anisotropy energy constant and V is the particle volume [37]. Thus, according to eq. (1) and the Néel-Arrhenius plot (Figure 6(a)), we calculate that the average value of Ea is (5.52±0.16)×10–21 J; Keff is (4.65±0.14)×104 J/m3 and ƒ0 is (4.52±2.93)×1011 Hz from the in-phase susceptibility data. 2.6

Low-temperature remanence curves

The thermal demagnetization curves of IRM5T_5K that were

acquired in a 5 T applied field at 5 K showed a rapid decrease in remanence with increasing temperature, as shown in Figure 7. The ZFC and FC curves bifurcate below 20 K, which suggests the ferrihydrite cores are not saturated in the 5 T applied field. The HoSF sample acquires TRM when cooled below the blocking temperature, which results in higher initial remanences in the FC curve than that in the ZFC curve. Above 30 K, the remanence falls to zero (Figure 7). The first derivative curves of the ZFC and FC curves reflect the Tb distribution. For pure HoSF, the Tb distribution is directly related to the particle size distribution. The peaks of the first derivative curves are consistent with the average Tb, i.e. most SP particles transform into SD particles at that temperature. However, Tb was different because of the change in experimental timescales for the different magnetic measurements.

3 Discussion TEM indicated that the diameters of the ferrihydrite cores range from 2 to 8 nm with an average diameter of 6.1±1.0 nm. This suggests that the growth of ferrihydrite cores is constrained by the outer protein shells. Meanwhile, growth of the cores is also regulated by the iron concentration and by apo-ferritin expression at the levels of transcription and translation so the grain size distribution is slightly wider than that for reconstituted ferritin in vitro [23]. The main mineral phase is 6-line ferrihydrite, as determined by the SAED patterns. Magnetic measurements show that there is a very weak magnetic interaction among the HoSF cores, which allows for the calculation of the other magnetic parameters [22,23]. The calculated f0, Ea and Keff of HoSF offers crucial reference values for the iron-based MRI technique and for Mössbauer spectroscopy.

3178

Figure 5


Chinese Sci Bull

Hysteresis loops of HoSF measured at 2, 3, 4, 5, 10, 21 and 300 K.


Below the Tb of HoSF (~12 K), both hysteresis loops and isothermal remanence acquisition curves indicate that the magnetization and remanence acquired by HoSF increases with the external field. For a perfect antiferromagnetic particle, the macroscopic magnetization should be zero because the two opposing sublattices cancel each other out [38]. However, the number of uncompensated spins at the surfaces of the nanoparticles or impurity phases could both result in parasitic, weakly ferrimagnetic moments especially for the ferritin nanoparticles with particle sizes less than 10 nm [39,40]. Therefore, the antiferromagnetic nanoparticles of HoSF spontaneously magnetize in an external field. Furthermore, because of the high coercivities of the ferrihydrite cores, the HoSF cores saturate with difficulty, even in applied fields higher than 5 T [41,42]. In general, the wasp-waisted hysteresis loop can be caused by two mechanisms: (1) a mixture of grain sizes (SD+SP) and (2) two magnetic mineral phases with distinct coercivity spectra [43,44]. The low-field ZFC and FC curves do not superimpose onto each other at the low temperatures 5–24 K. This clearly suggests that the nanoparticles of HoSF gradually transform from SD to SP (see Figure 3). At T < 5 K, most nanoparticles are blocked for the SD states so the shape of the hysteresis loop is similar to that of pure SD samples. At T = 5 K, more particles are unblocked and become SP particles which contributes to the magnetic signals of the SD particles and a typical wasp-waisted hysteresis loop results. In the range of 5 K < T < 21 K, the hysteresis loops become increasingly constricted. When the temperature is increased further, all the particles are unblocked into SP or paramagnetic particles. These temperature variations are also shown by the low-temperature remanence curves of IRM5T_5K. For such ultrafine nanoparticles, it is very difficult to determine the precise mineral phases. It is, therefore, uncertain if there are any other magnetic minerals in the HoSF cores at this stage. However, from our magnetic data the contribution

Figure 6 (a) In-phase susceptibility (χ′) of HoSF. Inset is the Néel-Arrhenius plot, lnτ vs. 1/Tmax. The dashed line is the best fit to the Néel-Arrhenius equation. (b) Out-of-phase susceptibility (χ′′).


Chinese Sci Bull


3

4

5

6 7

8 Figure 7 Decay curves of the remanent magnetization acquired in a 5 T applied field and the corresponding first derivative curves after zerofield-cooling (ZFC) and field-cooling (FC) treatments.

of the low-coercivity minerals (e.g. magnetite and/or maghemite) can be ignored. If low-coercivity minerals were present, they would show dominant magnetic signals in the sample because of their strong magnetization capacity. Based on both TEM and magnetic data, we interpreted the observed wasp-waisted loops as effects of grain size distribution.

4

9

10

11

12

Conclusions 13

The studied HoSF sample was monodispersed and showed nearly no interaction between ferrihydrite nanoparticle cores. This is an ideal material to study superparamagnetism and antiferromagnetism in nanoparticles. The average particle size of the measured HoSF sample was 6.1±1.0 nm. It has an average blocking temperature of about 12 K as determined by low-field DC susceptibility measurements. The effective magnetic anisotropy energy Ea is (5.52±0.16)×10–21 J, the effective magnetic anisotropy energy constant Keff is (4.65±0.14)×104 J/m3 and the pre-exponential frequency factor ƒ0 is (4.52±2.93)×1011 Hz. Furthermore, the low temperature magnetic measurement techniques were found to be very important approaches to investigate magnetic nanoparticles in biological and geological samples.

14

15

16

17

18

19 The authors thank Yang Xinan, Li Jinhua and Sun Lei for their kind help with the TEM observations. They also thank two anonymous reviewers for their constructive suggestions to improve the manuscript. This work was supported by the National Natural Science Foundation of China (40821091 and 40904017) and the CAS/SAFEA International Partnership Program for Creative Research Teams (KZCXZ-YW-T10).

1

2

Harrison P M, Arosio P. The ferritins: Molecular properties, iron storage function and cellular regulation. Biochim Biophys Acta, 1996, 1275: 161–203 Schneider B D, Leibold E A. Regulation of mammalian iron homeostasis. Curr Opin Clin Nutr Metab Care, 2000, 3: 267–273

20

21

22

23

3179

Gotz M E, Double K, Gerlach M, et al. The relevance of iron in the pathogenesis of Parkinson’s disease. Ann Ny Acad Sci, 2004, 1012: 193–208 Sofic E, Riederer P, Heinsen H, et al. Increased iron(III) and total iron content in post-mortem substantia nigra of Parkinsonian brain. J Neural Transm, 1988, 74: 199–205 Martin W R W, Wieler M, Gee M. Midbrain iron content in early Parkinson disease–A potential biomarker of disease status. Neurology, 2008, 70: 1411–1417 Snyder A M, Connor J R. Iron, the substantia nigra and related neurological disorders. Biochim Biophys Acta, 2009, 1790: 606–614 Pankhurst Q, Hautot D, Khan N, et al. Increased levels of magnetic iron compounds in Alzheimer’s disease. J Alzheimers Dis, 2008, 13: 49–52 Quintana C, Bellefqih S, Laval J Y, et al. Study of the localization of iron, ferritin, and hemosiderin in Alzheimer’s disease hippocampus by analytical microscopy at the subcellular level. J Struct Biol, 2006, 153: 42–54 Quintana C, Cowley J M, Marhic C. Electron nanodiffraction and high-resolution electron microscopy studies of the structure and composition of physiological and pathological ferritin. J Struct Biol, 2004, 147: 166–178 Quintana C, Lancin M, Marhic C, et al. Initial studies with high resolution TEM and electron energy loss spectroscopy studies of ferritin cores extracted from brains of patients with progressive supranuclear palsy and Alzheimer disease. Cell Mol Biol, 2000, 46: 807–820 Arosio P, Ingrassia R, Cavadini P. Ferritins: A family of molecules for iron storage, antioxidation and more. Biochim Biophys Acta, 2009, 1790: 589–599 Kaur D, Rajagopalan S, Andersen J K. Chronic expression of H-ferritin in dopaminergic midbrain neurons results in an age-related expansion of the labile iron pool and subsequent neurodegeneration: Implications for Parkinson’s disease. Brain Res, 2009, 1297: 17–22 Sabbah E N, Kadouche J, Ellison D, et al. In vitro and in vivo comparison of DTPA- and DOTA-conjugated antiferritin monoclonal antibody for imaging and therapy of pancreatic cancer. Nucl Med Biol, 2007, 34: 293–304 Bartzokis G, Tishler T A. MRI evaluation of basal ganglia ferritin iron and neurotoxicity in Alzheimer’s and Huntingon’s disease. Cell Mol Biol, 2000, 46: 821–833 Hammond K E, Metcalf M, Carvajal L, et al. Quantitative in vivo magnetic resonance imaging of multiple sclerosis at 7 tesla with sensitivity to iron. Ann Neurol, 2008, 64: 707–713 Gossuin Y, Muller R N, Gillis P. Relaxation induced by ferritin: A better understanding for an improved MRI iron quantification. NMR Biomed, 2004, 17: 427–432 Gottesfeld Z, Neeman M. Ferritin effect on the transverse relaxation of water: NMR microscopy at 9.4 T. Magn Reson Med, 1996, 35: 514–520 Zhou J H, Huang L, Wang W W, et al. Prostate cancer targeted MRI nanoprobe based on superparamagnetic iron oxide and copolymer of poly(ethylene glycol) and polyethyleneimin. Chinese Sci Bull, 2009, 54: 3137–3146 Cohen B, Dafni H, Meir G, et al. Ferritin as an endogenous MRI reporter for noninvasive imaging of gene expression in C6 glioma tumors. Neoplasia, 2005, 7: 109–117 Gilad A A, Winnard P T, van Zijl P C M, et al. Developing MRI reporter genes: Promises and pitfalls. NMR Biomed, 2007, 20: 275– 290 House M J, St Pierre T G, Kowdley K V, et al. Correlation of proton transverse relaxation rates (R2) with iron concentrations in postmortem brain tissue from Alzheimer’s disease patients. Magn Reson Med, 2007, 57: 172–180 Allen P D, St Pierre T G, Street R. Magnetic interactions in native horse spleen ferritin below the superparamagnetic blocking temperature. J Magn Magn Mater, 1998, 177: 1459–1460 Cao C, Tian L, Liu Q, et al. Magnetic characterization of non-interacting, randomly oriented, nanometer-scale ferrimagnetic particles. J

3180

24 25 26

27 28

29

30 31 32

33 34


Chinese Sci Bull

Geophys Res, 2010, doi:10.1029/2009JB006855 Kilcoyne S H, Cywinski R. Ferritin: A model superparamagnet. J Magn Magn Mater, 1995, 140-144: 1466–1467 Drits V A, Sakharov B A, Salyn A L, et al. Structural model for ferrihydrite. Clay Min, 1993, 28: 185–207 Janney D E, Cowley J M, Buseck P R. Transmission electron microscopy of synthetic 2- and 6-line ferrihydrite. Clay Clay Min, 2000, 48: 111–119 Towe K M, Bradley W F. Mineralogical constitution of colloidal “hydrous ferric oxides”. J Colloid Interface Sci, 1967, 24: 384–392 Moskowitz B M, Frankel R B, Walton S A, et al. Determination of the preexponential frequency factor for superparamagnetic maghemite particles in magnetoferritin. J Geophys Res, 1997, 102: 22671– 22680 Liu Q S, Torrent J, Yu Y J, et al. Mechanism of the parasitic remanence of aluminous goethite [alpha-(Fe, Al)OOH]. J Geophys Res, 2004, 109: 0148–0227 Bedanta S, Kleemann W. Supermagnetism. J Phys D: Appl Phys, 2009, 42, doi: 10.1088/0022-3727/42/1/013001 Cisowski S. Interacting vs non-interacting single domain behavior in natural and synthetic samples. Phys Earth Planet Inter, 1981, 26: 56–62 Wohlfarth E P. Relations between different modes of acquisition of the remanent magnetization of ferromagnetic particles. J Appl Phys, 1958, 29: 595–595 Henkel O. Remanenzverhalten und wechselwirkungen in hartmagnetischen teilchenkollektiven. Phys Stat Sol, 1964, 7: 919–929 Liu Q S, Deng C L, Pan Y X. Temperature-dependency and frequencydependency of magnetic susceptibility of magnetite and maghemite and their significance for environmental magnetism (in Chinese). Quat Sci,


35

36

37

38 39

40 41

42

43

44

2007, 27: 955–962 Mørup S, Madsen D E, Frandsen C, et al. Experimental and theoretical studies of nanoparticles of antiferromagnetic materials. J Phys: Condens Matter, 2007, 19, doi: 10.1088/0953-8984/19/21/213202 Néel L. Influence des fluctuations thermiques sur laimantation de grains ferromagnetiques tres fins. Comptes Rendus Hebdomad Seances L Acad Sci, 1949, 228: 664–666 Gittleman J I, Abeles B, Bozowski S. Superparamagnetism and relaxation effects in granular Ni-SiO2 and Ni-Al2O3 films. Phys Rev B, 1974, 9: 3891–3897 Dunlop D J, Özdemir Ö, eds. Rock Magnetism-fundamentals and Frontiers. Cambridge: Cambridge University Press, 1997 Allen P D, St Pierre T G, Chua-anusorn W, et al. Low-frequency low-field magnetic susceptibility of ferritin and hemosiderin. Biochim Biophys Acta-Mol Basis Dis, 2000, 1500: 186–196 Evans M E, Heller F. Environmental Magnetism: Principles and Applications of Enviromagnetics. New York: Academic Press, 2003 Guertin R P, Harrison N, Zhou Z X, et al. Very high field magnetization and ac susceptibility of native horse spleen ferritin. J Magn Magn Mater, 2007, 308: 97–100 Silva N J O, Millán A, Palacio F, et al. Temperature dependence of antiferromagnetic susceptibility in ferritin. Phys Rev B, 2009, 79, doi: 10.1103/PhysRevB.79.104405 Roberts A P, Cui Y, Verosub K L. Wasp-waisted hysteresis loops: Mineral magnetic Characteristics and discrimination of components in mixed magnetic systems. J Geophys Res, 1995, 100: 17909–17924 Tauxe L, Mullender T A T, Pick T. Potbellies, wasp-waists, and superparamagnetism in magnetic hysteresis. J Geophys Res, 1996, 101: 571–583