稀有金属(英文版) 2019,38(01),14-19

Magnetic properties of α-Fe₂O₃ nanopallets

Ying-Ying Xu Long Wang Tong Wu Rong-Ming Wang

作者简介：*Long Wang e-mail:kingkingv@126.com;

收稿日期：5 May 2017

基金：financially supported by the National Natural Science Foundation of China (Nos. 11674023, 51371015,51331002, and 51501004);Beijing Municipal Science and Technology Project (No. 217111000220000);

Magnetic properties of α-Fe₂O₃ nanopallets

Ying-Ying Xu Long Wang Tong Wu Rong-Ming Wang

Beijing Key Laboratory for Magneto-Photoelectrical Composite and Interface Science, School of Mathematics and Physics,University of Science and Technology Beijing

Department of Equipment Manufacture,Zhongshan Torch Polytechnic

Division of Energy and Environmental Measurement, National Institute of Metrology

Abstract：

It is the result of a systemic study about uniform hematite nanopallets with length of about 100 nm, width of about 30 nm, and thickness of less than 10 nm. The sample has superparamagnetic(SPM) properties above the blocking temperature of ～16 K. The temperature dependence of magnetization was well fitted by Bloch T^3/2 law considering the dipolar interaction of the particles. The field dependence of magnetization was fitted with revised Langevin equation.The magnetization of the weak ferromagnetic(WF) canted spins contributes to the linear portion in the high field region;the surface uncompensated spins and the parasitic ferromagnetic moments due to the canted spins both contribute to the particle moments and the superparamagnetic behavior.

Keyword：

α-Fe₂O₃ nanopallets; Magnetic property; Superparamagnetic behavior; Canted spins;

Received： 5 May 2017

1 Introduction

Recently,nanomaterials are drawing intense attention due to their enhanced size and morphology-dependent physchemical properties [ 1, 2, 3, 4, 5, 6, 7, 8] .Among which,iron oxides accomplish wide applications in the fields of semiconductor [ 9] ,recording material,sensor [ 10] ,biological and medical applications [ 11, 12, 13] ,catalyst [ 14, 15] ,etc.As the most stable one under ambient conditions,α-Fe₂O₃ (hematite) attracted much attention due to its unique magnetic properties and has been extensively studied both in bulk form and in the form of nanostructures [ 16] such as ultrafine particles [ 17, 18] ,nanowires [ 19, 20] ,and nanoleaves [ 21] .Bulk hematite has the corundum crystal structure and orders antiferromagnetic ally (AFM) under its Neel temperature (T_N) which is about 950 K.At the Morin temperature of T_M～260 K [ 22] ,hematite undergoes a spin-reorientation transition known as the“Morin transition” [ 23] .Above T_M,the moments lie in the basal plane(111) with a slight canting angle resulting in a weak ferromagnetic (WF) state with a weak net magnetic moment in the plane,which is referred as parasitic ferromagnetism.Below T_M,the two magnetic sublattices are oriented along the rhombohedral[111]axis and are exactly antiparallel [ 24] .

With the size of hematite reducing,it reveals more interesting properties due to the finite size effect.For example,the Morin transition temperature (T_M) decreases with the particle size of hematite decreasing [ 22] .For magnetically ordered particles,the magnetic anisotropy energy is given by E(θ)=KV sin²θ,whereθis the angle between the easy direction of magnetization and the magnetization vector,K is the uniaxial magnetic anisotropy constant,and V is the particle volume.In the system consisting of magnetic nanostructure,if the particles are small enough to ensure the magnetic energy barrier comparable to the thermal energy,there will be the fluctuations of the magnetization direction among the energy minima of each magnetic unit.Such phenomenon is called superparamagnetic (SPM) relaxation.For AFM systems,different models have been proposed to predict the existence of uncompensated spins under their Neel temperature (T_N) [ 25] .The SPM relaxation may come from the uncompensated spins of each unit in AFM nanosystem.As to the hematite,the situation is more complex.Theα-Fe₂O₃ nanosystem has three critical temperatures:T_N,blocking temperature (T_B),and T_M.If T_M<T_B<T_N,the magnetization of each unit would be attributed to both the WF canted spins and other uncompensated spins (mainly coming from surface or interface) when the system behaves SPM between T_B and T_N.

In this paper,it was present a systemic study about uniform hematite nanopallets.The sample was investigated by electron microscopy,X-ray diffraction (XRD),and magnetization measurements.The temperature dependence of inverse susceptibility can be well described by using the Curie-Weiss formula considering the dipolar interaction of the particles.The sample behaves SPM above the blocking temperature of-16 K.The magnetic switching volume is obtained by fitting magnetization field curves to the Langevin equation.It is estimated that the Morin temperature of the sample is lower than 5 K from the magnetic measurement,which is consistent with the results reported in Refs [ 16, 19, 21, 22] .

2 Experimental

2.1 Material synthesis

In a typical reaction,0.250 mmol FeCl₂·4H₂O and0.125 mmol citric acid were dissolved in 30 ml water and2 mmol NaOH dissolved in 10 ml water,and then the two solutions were mixed at room temperature under stirring.The resulting mixture was thus transferred to a 50-ml autoclave and maintained at 120℃for 12 h.The brown production was separated by centrifugation and cleaned with ethanol.The powder samples were thus used without any further size selection.

2.2 Characterization

XRD pattern of as-prepared products was collected by an X-ray diffractometer (Rigaku Goniometer PMG-A2,CN2155D2,wavelength of 0.15147 nm) with Pb Kαradiation.Scanning electron microscopy (SEM) images were obtained by employing a Hitachi S4800 cold field emission scanning electron microscope (CFE-SEM).Transmission electron microscopy (TEM) measurements ware conducted on a JEOL 21 00FS TEM with field emission gun and accelerating voltage of 200 kV.The magnetic measurements on the hematite sample were performed using the superconducting quantum interference device(SQUID) magnetometer (Quantum Design).The M(T) curves were recorded in an applied field of H_app=9×10^-3 T,in a temperature range of 5-350 K by the field-cooled (FC) and zero-field-cooled (ZFC) modes.For the FC measurement,the sample was cooled down to T=5 K under the applied field of 9×10^-3 T and measured in the same process,whereas for the ZFC,it was cooled down with zero field and then recorded under the field of 9×10^-3 T in the warming process.In addition,a series of hysteresis loops were measured at T=5,30,100,150 and 300 K by a sweeping field from-5 to 5 T,respectively.

3 Results and discussion

3.1 Morphology

SEM images (Fig.1a-c) shows that the as-prepared iron oxide consists of uniform nanopallets with length of about100 nm,width of about 30 nm,and thickness of less than10 nm.Figure 1d shows the high-resolution TEM(HRTEM) image with clearly lattice fringes.The insets are the low-magnified TEM image and the fast Fourier transformation (FFT) pattern corresponding to the zone marked in red square.The controlled synthesis of hematite nanostructures with certain surficial planes such as{110},{104},{012},{102},and{112}facets [ 26, 27] has been reported.The tuning of the aspect ratio and fine shape control are mainly concerned to the synthesis route in the solvothermal method.In our case,using simple hydrothermal method,theα-Fe₂O₃ nanopallets with specific shape and uniform sizes were synthesized.In the nanopallet,the two facet groups both have the interplanar distance of about 0.36 nm at an angle of～80℃,which can be indexed to (012) and ( ) planes,respectively,with zone axis of .Then the surface plane of the pallet can be inferred as (112) plane.

Fig.1 a-c SEM images,d TEM image and e XRD pattern of as-preparedα-Fe₂O₃ nanopallets (inset being FFT pattern corresponding to zone marked in red square)

To confirm the composition of the nanopallets,a representative XRD pattern of the nanowire is shown in Fig.1e.All the reflection peaks of the products can be well indexed to the pure corundum structure of hematite(JCPDS No.33-0664).The grain sizes are estimated to be～20 nm by Scherrer’s equation.

3.2 Magnetic characterization

To generally study the basic magnetic behavior in a large temperature region,the temperature dependences of the magnetization both after FC and ZFC processes were measured.Figure 2 shows M_ZFC(T) and M_FC(T) curves.The absence of the peak of susceptibility in FC curve from5 to 300 K indicates that there is no Morin transition at temperature as low as 5 K.Amin and Arajs [ 22] have proposed a formula to express the size dependence of Morin temperature (T_M),which could be written as:

Fig.2 Temperature dependence of ZFC and FC magnetization for an applied field of 9×10^-3 T.Inset showing fitting of inverse susceptibility (1/χ) using formula considering dipolar interaction and temperature dependence of M_s [29]

where d is the size of the particles.For the sample in this study,d=20 nm by Eq.(1),the Morin temperature is estimated to be about 155 K.However,such result is not observed in our measurements.Such conclusion is not surprising,and the absence of Morin transition in the particle which is about 20 nm has been already reported in Refs. [ 16, 19, 21, 22] .As far as we know,there are two reasons about the differences.At first,such formula is used to describe the annealed particles but not useful for our sample.In the second place,the strain and the defects are also important for Morin transition.As reported in Ref. [ 28] ,the absence of Morin temperature from 300 to 5 K could be quite possible.

From Fig.2,it is also found that the ZFC curve shows a peak around 16 K,below which the ZFC and FC curves separate widely from each other.It indicates the presence of a magnetic anisotropy potential barrier which causes the blocking of the magnetic moment of the hematite below16 K.Additionally,the peak of ZFC curve is quite narrow,indicating a narrow size distribution of the sample,which is consistent with the observation through SEM.Furthermore,the ZFC and FC curves overlap above the blocking temperature,suggesting the SPM behavior.For further analysis of such behavior,it is addressed the temperature dependence of the inverse susceptibility above 50 K,as shown in the inset of Fig.2,which does not follow the classical Curie-Weiss law.The origin of such discrepancy from the Curie-Weiss law can be attributed to the dipolar interaction between the particles and the temperature dependence of the magnetization (M_s).Owing to the presence of dipolar interactions,the temperature dependence of M_s,the magnetic susceptibility (x) in the SPM for a system with particle volume (V) should be expressed as:

whereθis an effective temperature deriving from the dipolar interactions [ 29] ,T is temperature,k_B is the Boltzmann constant,and magnetization (M_s(T)) can be roughly deduced by Bloch T^3/2 law [ 29] at high temperature s:

where M_s(0) andαare Bloch’s parameters.Then,the inverse susceptibilityχcan be well fitted on T with parameter M_s(0),αandθby Eqs.(2) and (3).From the fitting,θ=-11 K is obtained,which indicates the existence of dipolar interaction.It is believed that the fitted value of-11 K is reasonable,representing the dipolar interaction,which is much weaker than the exchange interaction in ferromagnet with Curie temperature (T_C) of several hundreds Kelvins.It is also got the Bloch’s parameter ofα=2×10^-5 K^-3/2,indicating the temperature dependence of magnetization,which has the same magnitude as the parameters in Ref. [ 29] .

On the other hand,the anisotropic constant could be estimated using the blocking temperature.For SPM system,using Néel-Brown expression and considering the dipolar interaction which could be expressed by an effective temperature (θ),we could get

where V_s is the magnetic volume and K_an is the effective anisotropy constant.For the sample in this study,whose blocking temperature is 16.4 K,the volume derived from XRD (D=20 nm) can be used,which is about4.19×10³ nm³ according to a sphere model for each particle andθ=-11 K obtained from the fitting of inverse susceptibility to estimate the anisotropy constant.It is estimated to be 2.25×10³ J·m^-3,quite close to the bulk hematite’s anisotropy constant which is about2×10³ J.m^-3 [ 30] .The evidence of a slightly large anisotropy for such nanostructures compared to the bulk material is not so surprising.For these systems,the large anisotropy could be explained by several intrinsic factors of the samples,including magnetocrystalline,surface,and shape anisotropy [ 30] .

To understand the properties of the blocking state,it was measured the hysteresis loop at 5 K,which is below the blocking temperature 16 K.Figure 3 shows M(H) curve measured at T=5 K.The magnetization does not saturate even the field reaches 5 T but follows a linear behavior with the field instead,which is mainly because of the magnetization of the WF canted spins.The inset in Fig.3shows the open loop in the low field region,which indicates the blocking of magnetization.The coercivity determined from the hysteresis is about 7.4×10^-3 T,and the remnant magnetization is about 0.1 mA·m².g^-1.This is consistent with the result of ZFC and FC curves,which are widely separated at such temperature.

Fig.3 Hysteresis loop measured at 5 K (inset showing low field region)

Figure 4 shows M(H) curves measured at T=30,100,150,and 300 K.The hysteresis loops could be viewed as the combination of the low filed saturation part and the high field linear part.Very small coercivity and remanence are found in these loops,which is the typical characteristic of SPM.A large magnetic moment (μ_p) is expected for each particle,mainly contributed by the surface uncompensated spins and the parasitic ferromagnetic moments due to the canted spins,which are perpendicular to each other.The SPM relaxation from the fluctuations of the particle magnetization may be responsible for the low filed saturation part,while the magnetizations still present linear behaviors in high field region due to the further magnetization of the WF canted spins.

For further proof,considering the temperature region in which the data were obtained,the hysteresis loops could be viewed as the combination of two parts:the linear portion contributed by the magnetization of WF canted spins,and the SPM part coming from the magnetic fluctuations of the particle moments.Taking the dipolar interaction expressed byθ,the revised Langevin equation to fit the data.The revised Langevin equation could be expressed as:

whereχ_WF is the susceptibility for the magnetization of the WF canted spins and H is the applied field.The inset in Fig.4 shows the hysteresis loop measured at 30 K,which could be well fitted using Eq.(5) as the other loops.Through the fitting,it is noted that the saturation magnetization of M_s=1.18 mA·m²·g^-1 andμ_p to be about2800μ_B per particle.

Fig.4 Hysteresis loops measured at 30,100,150 and 300 K (inset showing fitting of hysteresis loop at 30 K by using revised Langevin equation)

According to Eq.(5),the linear portion was reduced and then the reduced data at different temperatures were used to draw the M/M_s versusμ_pH/(T-θ) curves,respectively,and these curves should be coincident.Figure 5 shows M/M_s versusμ_pH/(T-θ) curves.As shown,it can be found that these curves are basically coincident.Such coincidence suggests that the hysteresis behavior at different temperatures could all be well described by Eq.(5).

Moreover,the susceptibilityχWF for the magnetization of the WF canted spins can be also obtained from fitting the loops.The inset in Fig.5 shows the temperature dependence of this susceptibility.χ_WF decreases steadily with increase in temperature.

3.3 Discussion about surface uncompensated spins

Antiferromagnetic nanostructures are expected to have a magnetic moment due to uncompensated spins.Neel [ 31] has proposed different models which predict surface uncompensated magnetic moments(μ_uc) given by:

whereμ_atom is the atomic moment,z is the model parameter,and n is the number of magnetic atoms per particle (in hematite,each Fe³⁺contributes about 4.9μ_B).Depending on the model,z may have values of 1/3,1/2,or 2/3.For the sample in this study,because the Morin temperature is expected to be lower than 5 K,therefore,the moment of each particle would consist of the contribution from both uncompensated spins and canted spins.However,the uncompensated spins are expected to be parallel to the sublattice magnetization directions,whereas the contribution of canted spins is perpendicular to the sublattice magnetization directions.So,the contribution of the uncompensated spins can be approximately calculated.For the sample in this study,the average particle diameter is D=20 nm and the average volume per particle is about4.19×10³ nm³.At 300 K where M_s is about the0.78 mA·m²·g^-1,the moment per particle is estimated to be 2130μ_B,and the net magnetic moment of the parasitic ferromagnetism derived from canted spins is about 920μ_B;therefore,the moment that came from uncompensated spin is about 1920μ_B per particle (take the perpendicular configuration).Consequently,the parameter z is estimated to be 0.497,which is almost 1/2.In Néel’s model [ 31] ,z=1/2 corresponds to a completely random distribution of the magnetic atoms between the two sublattices,and z=1/3corresponds to a structure where alternating compensated planes have incomplete top and bottom planes,i.e.,where randomness in the distribution of magnetic ions occurs only on the particle surface.Additionally,similar result of z value,smaller than 1/2,has already been reported [ 32] .When z=1/2 was used,the moment derived from uncompensated spins per particle would be about 2000μ_B.The small value for the experiment data (1920μ_B) might be attributed to the disorder spins on the surface of particle,whose directions are randomly distributed,contributing nearly zero moment.

Fig.5 M/M_s versusμ_pH/(T-θ) curves at 30,100,150 and 300 K,whose coincidence indicates SPM relaxation (inset showing temper-ature dependence of parasite ferromagnetism susceptibility)

3.4 Estimation of particle size using SPM model

Estimation about the upper limit of the particle size could be accomplished through SPM model.In M(H) loops,the major contribution to the slope near zero field for SPM structures with a size distribution comes from the largest pieces.Therefore,the upper limit for the magnetic size(D_max) could be estimated using the formula below [ 33] :

whereρis the density ofα-Fe₂O₃ (5.256 g·cm^-3) and(dM/dH)_H=0 was determined to be 2.06×10^-3A.m²·g^-1·T^-1 from Fig.4.So,the average magnetic size could be obtained from the slope of the magnetization near the zero field.Consideringθto be-11 K,D_max=24.9 nm is obtained.Although it is larger than the result obtained from XRD result,which is about 20 nm,it is still quite sensible considering that it is the upper bound of the size.

4 Conclusion

In this study,a systemic study about one type of hematite nanopallets with specific shape and uniform sizes was carried out.The sample behaves SPM above the blocking temperature of～16 K.The absence of the peak of susceptibility from 5 to 300 K indicates that there is no Morin transition at temperature as low as 5 K.Owing to the dipolar interaction of the particles,the temperature dependence of magnetization can be fitted by Bloch T^3/2law with the Bloch’s parameter ofα=2×10^-5 K^-3/2and effective temperature ofθ=-11 K.The anisotropy constant is estimated to be 2.25×10³ J.m^-3.The hysteresis loops at different temperatures of about 5-300 K were measured and fitted with revised Langevin equation.The magnetization of the WF cants contributes to the linear portion in the high field region;the surface uncompensated spins and the parasitic ferromagnetic moments due to the canted spins both contribute to the particle moments and the SPM behavior.

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