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Investigation of anisotropy in cadmium ferrite-based ionic magnetic fluid using magnetic resonance
ARTICLE IN PRESS
Journal of Magnetism and Magnetic Materials 289 (2005) 136–138 www.elsevier.com/locate/jmmm
Investigation of anisotropy in cadmium ferrite-based ionic magnetic fluid using magnetic resonance O. Silvaa,, P.C. Moraisb a Instituto de Fı´sica, Universidade Federal de Goia´s, 74001-970 Goiaˆnia-GO, Brazil Instituto de Fı´sica, Fı´sica Aplicada, Universidade de Brası´lia, 70919-970 Brası´lia-DF, Brazil
b
Available online 25 November 2004
Abstract Magnetic resonance was used to investigate a magnetic fluid sample containing a bimodal particle size distribution of CdFe2O4. The angular variation data was explained considering the external, the exchange, and the anisotropy fields. The isotropic structure around g ¼ 2 was associated to the 7.4 nm particles whereas the signal around g ¼ 4; assigned to the 4.8 nm particles, is highly anisotropic. The resonance field versus temperature of the anisotropic component indicates that the anisotropy surface component dominates the magnetic behavior of very small particles. r 2004 Elsevier B.V. All rights reserved. PACS: 75.50.Mm; 75.30.Gw; 76.50.+g Keywords: Magnetic fluid; Magnetic anisotropy; Magnetic resonance
Though nanometer-sized cadmium ferrite particles have been synthesized and characterized in the past few years [1,2], only recently the preparation of stable aqueous-based [3] and hydrocarbon-based [4] magnetic fluids containing cadmium ferrite nanoparticles have been reported in the literature. Bulk cadmium ferrite has been described as a normal spinel structure with Cd(II) and Fe(III) ions occupying the tetrahedral A-sites and octahedral B-sites, respectively. Previous investigations indicated that bulk cadmium ferrite samples presented antiferromagnetic behavior due to B–B magnetic coupling [5]. In contrast to the bulk samples, however, it has been reported that cadmium ferrite-based nanoparticles exhibits spontaneous magnetization [1,2]. The onset of the spontaneous magnetization in nanometer-sized cadmium ferrite particles has been discussed in terms of the occupancy of the A-sites by Fe(III) [6]. A more Corresponding author. Tel.:/fax: +55 62 5211029.
E-mail address: osni@fis.ufg.br (O. Silva).
detailed investigation of the magnetic properties of both bulk and nanometer-sized cadmium ferrite-based samples suggested two distinct spin structures [1]. In the first one a core-shell spin structure with a ferrimagnetic core and a magnetically inactive shell was proposed. The second one suggests a non-collinear spin arrangement over the particle volume. Which spin arrangement may explain the magnetic behavior of the nanometer-sized cadmium ferrite-based particles is still an open question. Magnetic resonance experiments, however, may help to throw some light upon this question once angular variation measurements has been successfully used to investigate the bulk and surface components of the magnetic anisotropy [7,8]. In this study we report on the temperature dependence of the effective magnetic anisotropy field obtained from angular variation measurements (magnetic resonance) of a field-frozen (FF) cobalt ferrite-based ionic magnetic fluid (MF) sample. The ionic MF sample containing nanometer-sized cadmium ferrite (CdFe2O4) particles was prepared
0304-8853/$ - see front matter r 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2004.11.040
ARTICLE IN PRESS O. Silva, P.C. Morais / Journal of Magnetism and Magnetic Materials 289 (2005) 136–138
following the three-step route described in literature [9]. The nanoparticle polydispersity profile was obtained from the transmission electron microscopy (TEM) micrographs. A bimodal particle size distribution function characterized by the mean particle diameters of 4.8 nm (93 wt%) and 7.4 nm (7 wt%) was obtained from the TEM data. The magnetic resonance spectra were recorded using a commercial X-band spectrometer (Bruker ESP300). In order to promote a magnetic texture the MF sample containing 1016 particle/cm3 was frozen from room temperature down to the liquid nitrogen temperature under a steady applied field of 1.5 T. In our experiment the sample holder was attached to a goniometer and allowed to rotate around the vertical axis while the resonance spectra were recorded in steps of 101. Magnetic resonance spectra as a function of the temperature (T) and angular orientation (y) were recorded in the range of 100–200 K and 0–1801, respectively. Fig. 1 shows typical resonance spectra (y ¼ 901) at T ¼ 100 and 200 K. The magnetic resonance structures near g ¼ 2 (around 3 kG) and g ¼ 4 (around 1.3 kG) were curve-fitted using one (quoted as L3) and two (quoted as L2 and L1) resonance lines, respectively. Whereas line L3 is a welldefined resonance line near g ¼ 2; lines L2 (weak signal) and L1 (strong signal) occurs very close together at the higher and lower field side of the g ¼ 4 structure, respectively. Note that the resonance features around g ¼ 2 and 4 have been assigned to the 7.4 and 4.8 nm sized nanoparticles, respectively [3]. No significant angular dependence was observed for the resonance lines L2 and L3 in the temperature range of our investigation. In contrast, a strong angular dependence was observed for the resonance line L1 in the whole range of temperature of our investigation. Symbols in Fig. 2 represent the resonance field of line L1 as a
Fig. 1. Typical magnetic resonance spectra of the FR cadmium ferrite-based MF sample at different temperatures (T) and at y ¼ 901:
137
Fig. 2. Angular dependence of the resonance field. The solid lines represent the best fit of the data according to the model described in this study.
function of sample orientation, at different temperatures in the range of 100–200 K. The model used to fit the data shown in Fig. 2 starts by writing the relationship between the resonance frequency (or ) and the effective field (Heff) as or ¼ gH eff ; where g is the gyromagnetic ratio [7]. The effective field acting on a given nanometer-sized particle will be taken as a result of three components: the external sweeping field (He), the exchange anisotropy field (Hx), and the effective uniaxial anisotropy field (Hek). Therefore, the effective field reads H eff ¼ H e þ H x þ H ek : At the resonance condition the resonance field is given by H r ¼ or =g H x H ek : For field-frozen samples Hek depends upon y whereas Hx is angular independent. The effective uniaxial anisotropy field can be expanded in terms of spherical harmonics as H ek ¼ P P H Plm ðcos yÞ expðimjÞ; where Plm(cos y) are Kl I m Legendre polynomials and HKl effective anisotropy field coefficients. For spherical ðm ¼ 0Þ and uniaxial ðl ¼ 2Þ nanoparticles, however, the Hek expansion can be simplified to H ek ¼ 12H K2 ð3 cos2 y 1Þ: In addition, HK2 can be written as a linear combination of a volume component (HV) plus a surface component (HS) as HK2 ¼ HV+HS. Whereas HV is related to the bulk anisotropy field and therefore only temperature dependent, HS is dependent upon both parameters size and temperature. The surface component (HS) is described in terms of a surface anisotropy field (hS) times the surfaceto-volume ratio (S/V). Therefore, for spherical nanoparticles H S ¼ ð6=DÞhS ; where D is the nanoparticle diameter. As a result HK2 is now re-written as H K2 ¼ H V þ ð6=DÞhS : The exchange anisotropy field, on the other hand, is written as H x ¼ 4Cn2 =M S Db ; where C is the exchange constant, n are eigenvalues of the differential equation involving the spherical Bessel
ARTICLE IN PRESS 138
O. Silva, P.C. Morais / Journal of Magnetism and Magnetic Materials 289 (2005) 136–138
Fig. 3. Temperature dependence of the angular-independent (Hr1) and angular-dependent (Hr2) components of the resonance field (Hr) associated to the L1 line.
functions dj n ðnÞ=dn ¼ 0; M S is the saturation magnetization, and b ¼ 2 for zero surface anisotropy. Indeed, the description of the angular dependence of the resonance field reads H r ¼ ðor =g 4Cv2 =M S Db Þ 1 2 2H K2 ð3 cos y 1Þ: As quoted above the resonance field can be written as a combination of an angular independent component plus an angular dependent one, i.e. H r ¼ H r1 ðD; TÞ þ H r2 ðD; T; yÞ; both components depending upon D and T. Solid lines in Fig. 2 represent the best curve-fitting of the angular variation of the resonance field according to H r ¼ ðor =g 4Cv2 =M S Db Þ 12H K2 ð3 cos2 y 1Þ: The temperature dependence of Hr1 and Hr2 components obtained from this fitting procedure is plotted in Fig. 3. The temperature dependence of the Hr1 component is mainly due to the exchange anisotropy field (Hx) contribution. In particular, it is due to the temperature dependence of the saturation magnetization (MS). The solid line running over the Hr1 versus T data (solid squares) is the best fit of the experimental results assuming M S ¼ M 0 ð1 T=T 0 ÞZ ; with T 0 ¼ ð491 4Þ K and Z ¼ 0:335 0:003: Note that Yokoyama et al. [1] have found the Curie temperature of 540 K for CdFe2O4 nanoparticles of about 8 nm in diameter. As previously reported [3], HK2 scales linearly with the temperature. The dashed line running over the HK2 versus T data (open squares) is the best fit of the experimental results assuming H K2 ¼ A þ BT; with A ¼ ð60:0 0:4Þ G and B ¼ ð0:099 0:003Þ G=K: In conclusion, the magnetic resonance measurements of FR cadmium ferrite-based MFs revealed two distinct structures around g ¼ 2 and 4. The two structures at g ¼ 2 and 4 have been already identified with the bimodal particle size distribution peaking at D ¼ 7:4 and 4.8 nm, respectively. The angular variation measure-
ments showed the nearly isotropic behavior of the resonance feature peaking around g ¼ 2: However, the angular variation measurements of the resonance structure around g ¼ 4 revealed two distinct resonance lines. The strong resonance peak at the lower field side of the g ¼ 4 structure is highly anisotropic whereas the weak resonance peak at the higher field side of the g ¼ 4 structure is nearly isotropic under the angular rotation of the frozen sample. The Hr1 versus T data related to the strong and anisotropic resonance peak component of the g ¼ 4 structure follows the expected behavior (see Fig. 3), whereas the HK2 versus T data reveals important details related to the spin arrangement in nanometersized cadmium ferrite particles. The relatively small variation of HK2 in the temperature range of 100–200 K indicates the dominant contribution of the surface anisotropy. In other words, the strong resonance peak around g ¼ 4 is more likely related to the surface material of the smallest ðD ¼ 4:8 nmÞ component of the bimodal particle size distribution. Indeed, the findings of the present study indicate a different spin structure for nanometer-sized cadmium ferrite particles, namely a core–shell structure with an antiferromagnetic core and a shell characterized by a canting-like spin structure responsible for the spontaneous magnetization. The antiferromagnetic core may extend its volume fraction as the nanoparticle size increases, probably due to the recovering of the translational symmetry and/or crystal structure. The Brazilian agencies CNPq, FINEP, and FINATEC have supported this work.
References [1] M. Yokoyama, E. Ohta, T. Sato, T. Sato, J. Magn. Magn. Mater. 183 (1998) 173. [2] M.H. Mahmoud, A.M. Abdallas, H.H. Hamdeh, W.M. Hikal, S.M. Taher, H.C. Ho, J. Magn. Magn. Mater. 263 (2003) 269. [3] O. Silva, E.C.D. Lima, P.C. Morais, J. Appl. Phys. 93 (2003) 8456. [4] P.C. Morais, O. Silva, P.P. Gravina, L.C. Figueiredo, E.C.D. Lima, L.P. Silva, R.B. Azevedo, K. Skeff Neto, IEEE Trans. Magn. 39 (2003) 2639. [5] J.M. Hastings, L.M. Corliss, Phys. Rev. 102 (1956) 1460. [6] F.K. Lotgering, J. Phys. Chem. Solids 27 (1966) 139. [7] A.F. Bakuzis, P.C. Morais, F. Pelegrini, J. Appl. Phys. 85 (1999) 7480. [8] R.V. Upadhyay, K. Parekh, R.V. Mehta, Phys. Rev. B 68 (2003) 224434. [9] P.C. Morais, V.K. Garg, A.C. Oliveira, L.P. Silva, R.B. Azevedo, A.M.L. Silva, E.C.D. Lima, J. Magn. Magn. Mater. 225 (2001) 37.
Journal of Magnetism and Magnetic Materials 289 (2005) 136–138 www.elsevier.com/locate/jmmm
Investigation of anisotropy in cadmium ferrite-based ionic magnetic fluid using magnetic resonance O. Silvaa,, P.C. Moraisb a Instituto de Fı´sica, Universidade Federal de Goia´s, 74001-970 Goiaˆnia-GO, Brazil Instituto de Fı´sica, Fı´sica Aplicada, Universidade de Brası´lia, 70919-970 Brası´lia-DF, Brazil
b
Available online 25 November 2004
Abstract Magnetic resonance was used to investigate a magnetic fluid sample containing a bimodal particle size distribution of CdFe2O4. The angular variation data was explained considering the external, the exchange, and the anisotropy fields. The isotropic structure around g ¼ 2 was associated to the 7.4 nm particles whereas the signal around g ¼ 4; assigned to the 4.8 nm particles, is highly anisotropic. The resonance field versus temperature of the anisotropic component indicates that the anisotropy surface component dominates the magnetic behavior of very small particles. r 2004 Elsevier B.V. All rights reserved. PACS: 75.50.Mm; 75.30.Gw; 76.50.+g Keywords: Magnetic fluid; Magnetic anisotropy; Magnetic resonance
Though nanometer-sized cadmium ferrite particles have been synthesized and characterized in the past few years [1,2], only recently the preparation of stable aqueous-based [3] and hydrocarbon-based [4] magnetic fluids containing cadmium ferrite nanoparticles have been reported in the literature. Bulk cadmium ferrite has been described as a normal spinel structure with Cd(II) and Fe(III) ions occupying the tetrahedral A-sites and octahedral B-sites, respectively. Previous investigations indicated that bulk cadmium ferrite samples presented antiferromagnetic behavior due to B–B magnetic coupling [5]. In contrast to the bulk samples, however, it has been reported that cadmium ferrite-based nanoparticles exhibits spontaneous magnetization [1,2]. The onset of the spontaneous magnetization in nanometer-sized cadmium ferrite particles has been discussed in terms of the occupancy of the A-sites by Fe(III) [6]. A more Corresponding author. Tel.:/fax: +55 62 5211029.
E-mail address: osni@fis.ufg.br (O. Silva).
detailed investigation of the magnetic properties of both bulk and nanometer-sized cadmium ferrite-based samples suggested two distinct spin structures [1]. In the first one a core-shell spin structure with a ferrimagnetic core and a magnetically inactive shell was proposed. The second one suggests a non-collinear spin arrangement over the particle volume. Which spin arrangement may explain the magnetic behavior of the nanometer-sized cadmium ferrite-based particles is still an open question. Magnetic resonance experiments, however, may help to throw some light upon this question once angular variation measurements has been successfully used to investigate the bulk and surface components of the magnetic anisotropy [7,8]. In this study we report on the temperature dependence of the effective magnetic anisotropy field obtained from angular variation measurements (magnetic resonance) of a field-frozen (FF) cobalt ferrite-based ionic magnetic fluid (MF) sample. The ionic MF sample containing nanometer-sized cadmium ferrite (CdFe2O4) particles was prepared
0304-8853/$ - see front matter r 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2004.11.040
ARTICLE IN PRESS O. Silva, P.C. Morais / Journal of Magnetism and Magnetic Materials 289 (2005) 136–138
following the three-step route described in literature [9]. The nanoparticle polydispersity profile was obtained from the transmission electron microscopy (TEM) micrographs. A bimodal particle size distribution function characterized by the mean particle diameters of 4.8 nm (93 wt%) and 7.4 nm (7 wt%) was obtained from the TEM data. The magnetic resonance spectra were recorded using a commercial X-band spectrometer (Bruker ESP300). In order to promote a magnetic texture the MF sample containing 1016 particle/cm3 was frozen from room temperature down to the liquid nitrogen temperature under a steady applied field of 1.5 T. In our experiment the sample holder was attached to a goniometer and allowed to rotate around the vertical axis while the resonance spectra were recorded in steps of 101. Magnetic resonance spectra as a function of the temperature (T) and angular orientation (y) were recorded in the range of 100–200 K and 0–1801, respectively. Fig. 1 shows typical resonance spectra (y ¼ 901) at T ¼ 100 and 200 K. The magnetic resonance structures near g ¼ 2 (around 3 kG) and g ¼ 4 (around 1.3 kG) were curve-fitted using one (quoted as L3) and two (quoted as L2 and L1) resonance lines, respectively. Whereas line L3 is a welldefined resonance line near g ¼ 2; lines L2 (weak signal) and L1 (strong signal) occurs very close together at the higher and lower field side of the g ¼ 4 structure, respectively. Note that the resonance features around g ¼ 2 and 4 have been assigned to the 7.4 and 4.8 nm sized nanoparticles, respectively [3]. No significant angular dependence was observed for the resonance lines L2 and L3 in the temperature range of our investigation. In contrast, a strong angular dependence was observed for the resonance line L1 in the whole range of temperature of our investigation. Symbols in Fig. 2 represent the resonance field of line L1 as a
Fig. 1. Typical magnetic resonance spectra of the FR cadmium ferrite-based MF sample at different temperatures (T) and at y ¼ 901:
137
Fig. 2. Angular dependence of the resonance field. The solid lines represent the best fit of the data according to the model described in this study.
function of sample orientation, at different temperatures in the range of 100–200 K. The model used to fit the data shown in Fig. 2 starts by writing the relationship between the resonance frequency (or ) and the effective field (Heff) as or ¼ gH eff ; where g is the gyromagnetic ratio [7]. The effective field acting on a given nanometer-sized particle will be taken as a result of three components: the external sweeping field (He), the exchange anisotropy field (Hx), and the effective uniaxial anisotropy field (Hek). Therefore, the effective field reads H eff ¼ H e þ H x þ H ek : At the resonance condition the resonance field is given by H r ¼ or =g H x H ek : For field-frozen samples Hek depends upon y whereas Hx is angular independent. The effective uniaxial anisotropy field can be expanded in terms of spherical harmonics as H ek ¼ P P H Plm ðcos yÞ expðimjÞ; where Plm(cos y) are Kl I m Legendre polynomials and HKl effective anisotropy field coefficients. For spherical ðm ¼ 0Þ and uniaxial ðl ¼ 2Þ nanoparticles, however, the Hek expansion can be simplified to H ek ¼ 12H K2 ð3 cos2 y 1Þ: In addition, HK2 can be written as a linear combination of a volume component (HV) plus a surface component (HS) as HK2 ¼ HV+HS. Whereas HV is related to the bulk anisotropy field and therefore only temperature dependent, HS is dependent upon both parameters size and temperature. The surface component (HS) is described in terms of a surface anisotropy field (hS) times the surfaceto-volume ratio (S/V). Therefore, for spherical nanoparticles H S ¼ ð6=DÞhS ; where D is the nanoparticle diameter. As a result HK2 is now re-written as H K2 ¼ H V þ ð6=DÞhS : The exchange anisotropy field, on the other hand, is written as H x ¼ 4Cn2 =M S Db ; where C is the exchange constant, n are eigenvalues of the differential equation involving the spherical Bessel
ARTICLE IN PRESS 138
O. Silva, P.C. Morais / Journal of Magnetism and Magnetic Materials 289 (2005) 136–138
Fig. 3. Temperature dependence of the angular-independent (Hr1) and angular-dependent (Hr2) components of the resonance field (Hr) associated to the L1 line.
functions dj n ðnÞ=dn ¼ 0; M S is the saturation magnetization, and b ¼ 2 for zero surface anisotropy. Indeed, the description of the angular dependence of the resonance field reads H r ¼ ðor =g 4Cv2 =M S Db Þ 1 2 2H K2 ð3 cos y 1Þ: As quoted above the resonance field can be written as a combination of an angular independent component plus an angular dependent one, i.e. H r ¼ H r1 ðD; TÞ þ H r2 ðD; T; yÞ; both components depending upon D and T. Solid lines in Fig. 2 represent the best curve-fitting of the angular variation of the resonance field according to H r ¼ ðor =g 4Cv2 =M S Db Þ 12H K2 ð3 cos2 y 1Þ: The temperature dependence of Hr1 and Hr2 components obtained from this fitting procedure is plotted in Fig. 3. The temperature dependence of the Hr1 component is mainly due to the exchange anisotropy field (Hx) contribution. In particular, it is due to the temperature dependence of the saturation magnetization (MS). The solid line running over the Hr1 versus T data (solid squares) is the best fit of the experimental results assuming M S ¼ M 0 ð1 T=T 0 ÞZ ; with T 0 ¼ ð491 4Þ K and Z ¼ 0:335 0:003: Note that Yokoyama et al. [1] have found the Curie temperature of 540 K for CdFe2O4 nanoparticles of about 8 nm in diameter. As previously reported [3], HK2 scales linearly with the temperature. The dashed line running over the HK2 versus T data (open squares) is the best fit of the experimental results assuming H K2 ¼ A þ BT; with A ¼ ð60:0 0:4Þ G and B ¼ ð0:099 0:003Þ G=K: In conclusion, the magnetic resonance measurements of FR cadmium ferrite-based MFs revealed two distinct structures around g ¼ 2 and 4. The two structures at g ¼ 2 and 4 have been already identified with the bimodal particle size distribution peaking at D ¼ 7:4 and 4.8 nm, respectively. The angular variation measure-
ments showed the nearly isotropic behavior of the resonance feature peaking around g ¼ 2: However, the angular variation measurements of the resonance structure around g ¼ 4 revealed two distinct resonance lines. The strong resonance peak at the lower field side of the g ¼ 4 structure is highly anisotropic whereas the weak resonance peak at the higher field side of the g ¼ 4 structure is nearly isotropic under the angular rotation of the frozen sample. The Hr1 versus T data related to the strong and anisotropic resonance peak component of the g ¼ 4 structure follows the expected behavior (see Fig. 3), whereas the HK2 versus T data reveals important details related to the spin arrangement in nanometersized cadmium ferrite particles. The relatively small variation of HK2 in the temperature range of 100–200 K indicates the dominant contribution of the surface anisotropy. In other words, the strong resonance peak around g ¼ 4 is more likely related to the surface material of the smallest ðD ¼ 4:8 nmÞ component of the bimodal particle size distribution. Indeed, the findings of the present study indicate a different spin structure for nanometer-sized cadmium ferrite particles, namely a core–shell structure with an antiferromagnetic core and a shell characterized by a canting-like spin structure responsible for the spontaneous magnetization. The antiferromagnetic core may extend its volume fraction as the nanoparticle size increases, probably due to the recovering of the translational symmetry and/or crystal structure. The Brazilian agencies CNPq, FINEP, and FINATEC have supported this work.
References [1] M. Yokoyama, E. Ohta, T. Sato, T. Sato, J. Magn. Magn. Mater. 183 (1998) 173. [2] M.H. Mahmoud, A.M. Abdallas, H.H. Hamdeh, W.M. Hikal, S.M. Taher, H.C. Ho, J. Magn. Magn. Mater. 263 (2003) 269. [3] O. Silva, E.C.D. Lima, P.C. Morais, J. Appl. Phys. 93 (2003) 8456. [4] P.C. Morais, O. Silva, P.P. Gravina, L.C. Figueiredo, E.C.D. Lima, L.P. Silva, R.B. Azevedo, K. Skeff Neto, IEEE Trans. Magn. 39 (2003) 2639. [5] J.M. Hastings, L.M. Corliss, Phys. Rev. 102 (1956) 1460. [6] F.K. Lotgering, J. Phys. Chem. Solids 27 (1966) 139. [7] A.F. Bakuzis, P.C. Morais, F. Pelegrini, J. Appl. Phys. 85 (1999) 7480. [8] R.V. Upadhyay, K. Parekh, R.V. Mehta, Phys. Rev. B 68 (2003) 224434. [9] P.C. Morais, V.K. Garg, A.C. Oliveira, L.P. Silva, R.B. Azevedo, A.M.L. Silva, E.C.D. Lima, J. Magn. Magn. Mater. 225 (2001) 37.