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Magnetic anisotropy in ilmenite–hematite solid solution thin films grown by pulsed laser ablation
ARTICLE IN PRESS Journal of Magnetism and Magnetic Materials 320 (2008) 3238– 3241
Contents lists available at ScienceDirect
Journal of Magnetism and Magnetic Materials journal homepage: www.elsevier.com/locate/jmmm
Magnetic anisotropy in ilmenite– hematite solid solution thin films grown by pulsed laser ablation K. Rode , R.D. Gunning, R.G.S. Sofin, M. Venkatesan, J.G. Lunney, J.M.D. Coey, I.V. Shvets CRANN and School of Physics, Trinity College, Dublin 2, Ireland
a r t i c l e in f o
a b s t r a c t
Article history: Received 4 February 2008 Received in revised form 11 June 2008 Available online 14 June 2008
Ferromagnetic thin films of the ilmenite–hematite solid solution Fe2xTixO3 with x ¼ 0.6 and x ¼ 0.8 have been grown on (0 0 1) sapphire substrates. X-ray diffraction analysis reveals that the films are ¯ crystal structure. Strong easy-plane anisotropy is observed for single phase with the ilmenite ðR3Þ the two films, which are nominally n or p type with K1 ¼ 8 106 J m3 for x ¼ 0.6 and 11 106 J m3 for x ¼ 0.8 at T ¼ 4 K. The trigonal splitting of the 5T2g energy level of Fe2+ is inferred to be 0.11 eV, and the zero-field splitting parameter D to be equal to 15 K. & 2008 Elsevier B.V. All rights reserved.
PACS: 71.70.d 75.10.Dg 75.30.Gw 75.50.Gg 75.50.Pp 75.70.Ak 91.60.Pn Keywords: Epitaxial film Ferrimagnetics Hematite Ilmenite Magnetic semiconductors Magnetic anisotropy Pulsed laser ablation Spin electronics
The emerging field of spin electronics aims to integrate new functionalities in semiconductor micro-electronic components and devices by using the spin of the electron in addition to its charge as an information carrier. It is a challenge to efficiently inject and detect a spin-polarized current in a semiconductor such as Si or GaAS. A possible way to avoid these problems is to use a ferromagnetic (FM) semiconductor as ‘‘source’’ and ‘‘drain’’ in a future device. Up to now, most research has been focused on creating such a material by doping a semiconductor with magnetic ions from the 3d series. Although progress has been made the last decade, the dilute magnetic semiconductor route has so far failed to deliver usable room-temperature magnetic semiconductors. Another possible approach is to take a material that is FM or ferrrimagnetic and make it semiconducting. The solid solution of ilmenite (FeTiO3) and hematite (Fe2O3; IHSS), is
Corresponding author. Tel.: +353 18963165.
E-mail address: [email protected] (K. Rode). 0304-8853/$ - see front matter & 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2008.06.010
such a material [1] with the unit formula xFeTiO3+(1x)Fe2O3, usually written as Fe2xTixO3. The solid solution is ferrimagnetic for 0.5oxo0.85 due to preferred ordering of Ti on alternate c-planes in an ilmenite-type structure. Furthermore, the majority carriers change from p type to n type at x0.73 [2]. In order to be FM, IHSS thin films must crystallize in the R3¯ space group of ¯ space group of hematite. This change of ilmenite and not the R3c space group corresponds to the ordering of Ti on every second layer perpendicular to the hexagonal c-axis of IHSS. Although extensively studied in bulk [3] due to its importance in rock magnetism [4–10], the magnetic and electrical properties of thin films of IHSS have been much less investigated. Recently, several groups have reported on the successful growth of IHSS by pulsed laser ablation (PLD) and also demonstrated interaction between carriers and the magnetization of the sample by measurements of the anomalous Hall effect [11–13]. We have grown IHSS with x ¼ 0.8 and x ¼ 0.6 on c-cut sapphire (0 0 0 1) substrates by PLD using a KrF excimer laser at a fluence of 2–3 J cm2 and a repetition rate of 10 Hz. Ceramic targets were
ARTICLE IN PRESS K. Rode et al. / Journal of Magnetism and Magnetic Materials 320 (2008) 3238–3241
10000
0.5
Ilmenite-Hematite sol. solu.
0.4
1.5
0.3
1000
0.1
0.5
0.0
0.0
-0.1
-0.5
-0.2 -1.0
-0.3
1
-1.5
-0.4 -0.5
0.1
-4 20
30
40
50 60 Angle 2θ
70
80
90
-2
100
0 H (MA/m)
2
4
Fig. 3. Magnetization as a function of applied magnetic field at T ¼ 4 K (full symbols) and T ¼ 300 K (empty symbols) for samples with x ¼ 0.8 and x ¼ 0.6.
Fig. 1. X-ray diffraction pattern for a film of IHSS with x ¼ 0.8 and (multiplied by 10 for clarity) x ¼ 0.6. Black squares indicate the position of peaks for the ordered IHSS. No secondary phase is detected in the scans and the presence of peaks from (0 0 3) and (0 0 9) planes confirms that the solid solution is ordered.
0.5 2.5 2.0 1.5 1.0 0.5 0.0 -0.5 -1.0 -1.5 -2.0 -2.5
0.4 0.3
2.5
0.2 M (MA/m)
x = 0.8 x = 0.6 2.0
1.5
0.1 0.0 -0.1 -0.2 -0.3 -0.4
1.0
μB/f.u.
10
M (105 A /m)
μB/f.u.
(009)
(0012)
M (MA/m)
(006)
10
1.0
0.2
(003)
100 Cps (1/s)
3239
-0.5 -4 0.5
0.0 0
50
100
150
200 T (K)
250
300
350
400
Fig. 2. Scans of the magnetization of thin films with two different compositions as a function of temperature in a field of m0H ¼ 50 mT applied parallel to the film surface. A linear extrapolation of the region with the steepest slope yields TC (x ¼ 0.8) ¼ 161 K and TC (x ¼ 0.6) ¼ 383 K.
prepared by mixing the correct amounts of Fe2O3 and TiO2 sintered in Ar flow at 1100 1C for 12 h. The distance between the target and the substrate was 3 cm. The sample substrate was kept at 700 1C during deposition and cooled at the highest rate possible in our system, approximately 10 1C min1 down to 300 1C. We found the optimal oxygen pressures to obtain this ordering to be 8 106 mbar for x ¼ 0.6 and 1.2 105 mbar for x ¼ 0.8. Fig. 1 shows the X-ray diffraction (XRD) diagrams for a film of each composition. No secondary phases are detected in either scan. The presence of peaks from the (0 0 3) and (0 0 9) family of ¯ but allowed in R3) ¯ confirms that both planes (forbidden in R3c films are ordered. In both cases the growth is oriented with the hexagonal [0 0 1] axis of IHSS parallel to sapphire [0 0 0 1]. We find the epitaxial relation to be ð0 0 0 1Þ½1 1¯ 0 0IHSS ==ð0 0 0 1Þ½1 1¯ 0 0Al2 O3 by reciprocal space mapping (not shown) in agreement with literature [12]. No twinning of either sample is observed in a phi scan. We measured the magnetic properties of the films using a Quantum Design SQUID magnetometer in the RSO detection
-2
0 H (MA/m)
2
4
Fig. 4. Hysteresis loops recorded at 4 K with the applied field parallel and perpendicular to the sample surface of two thin films with x ¼ 0.6 and x ¼ 0.8. Strikingly, the difference of magnetization between the two directions of applied field is almost one order of magnitude, even at m0H ¼ 5.5 T.
mode. Fig. 2 shows the magnetization as a function of temperature for a 50 mT field applied parallel to the film surface. The x ¼ 0.6 film has a magnetic-ordering temperature of 380 K, whereas that of the film with x ¼ 0.8 is 160 K. The hysteresis loops of both films at 300 and 4 K are shown in Fig. 3. The saturation moments are 1.8 and 2.5 mB per formula unit, in reasonably good agreement with literature values [3]. The sample with x ¼ 0.8 is weakly ferrimagnetic even above the estimated Curie point. We believe that this may be due to an inhomogenous distribution of Ti ions in the sample as no secondary phase is detected by XRD. If this is the case, there will be regions, presumably towards the sample surface, where the Ti concentration is low enough to allow for a ferrimagnetic ordering even at room temperature. Another possible origin of this weak moment is the presence of about 5% of magnetite inclusions in the sample. Such inclusions cannot be entirely ruled out, in particular as the samples are grown at a low oxygen pressure. From the relative (0 0 0 3) peak intensity in Fig. 1 we infer the cation order parameter to be 0.4, in reasonable agreement with the order parameter deduced from the magnetization data (0.5). A value of 1 corresponds to ideal Ti order on alternate c-planes. We believe the disorder is not due to exosolutions as pure hematite or ilmenite grains would be easily detectable by XRD,
ARTICLE IN PRESS 3240
K. Rode et al. / Journal of Magnetism and Magnetic Materials 320 (2008) 3238–3241
but rather to stoichiometric variations and general disorder, i.e. the Ti atoms are not strictly confined to alternate (0 0 0 1) planes. The contribution to the magnetic properties due to the disorder is intermediate between hematite and ilmenite. A more striking observation is shown in Fig. 4, where we plot the magnetization for both a sample with x ¼ 0.6 and for a sample with x ¼ 0.8 at 4 K, with the applied magnetic field parallel and perpendicular to the sample surface. The magnetization is almost an order of magnitude lower when the field is applied out of plane compared to the in-plane configuration. To our knowledge, this magnetocrystalline anisotropy has never been reported before in thin film samples of IHSS, although pure ilmenite is known, from measurements of the metamagnetic transition, to exhibit strong anisotropy, with an anisotropy field above 10 T [14]. Furthermore, the magnitude of the anisotropy field at low temperature, estimated by the intercept of the linear extrapolations of the high field magnetization data with the applied magnetic field in the easy plane and along the hard axis, respectively, of almost 30 and 50 T for x ¼ 0.6 and x ¼ 0.8, respectively, is surprisingly large. The corresponding anisotropy constant K1 ¼ (1/2)m0HaMs is 8 106 J m3 for x ¼ 0.6 and K1 ¼ 11 106 J m3 for x ¼ 0.8. It should be noted that the estimations of the anisotropy field magnitude are made under the assumption that the magnetization is linearly increasing above our experimental range. The relative error bar of the estimates if this is the case is 30%. The origin of such large magnetocrystalline anisotropy is the single-ion anisotropy of the ferrous ion in the noncubic crystal field at octahedral sites in the structure. Shape can at best contribute to the anisotropy field equal to the polarization of the film, JS ¼ m0MS0.5 T. The ground state of free Fe2+ ions is 5D4. In octahedral sites, the degeneracy of the ground state is removed by the cubic crystal field, which splits the state into an orbital doublet 5Eg and a lower-lying orbital triplet 5T2g separated in energy by the cubic crystal field energy parameter 10Dq. The trigonal component of the crystal field further splits the triplet into the ground singlet 5A1g and a higher doublet 5Eg (we suppose the crystal field parameter B02 40) [15] separated in energy by d. The spin-dependent part of the Hamiltonian can then be written in the following form: 2 2 ^ ¼ gm m H ~ ~ H B 0 ex S þ D Sa 1=3S where Hex is the exchange field, g the spectroscopic splitting, mB the Bohr magneton and Sa the spin operator projection in the a direction. The zero-field splitting constant D reflects the spin–orbit and spin–spin coupling energy, as well as the trigonal crystal field d. By treating the second part of this equation as a perturbation we obtain the following energy spectrum (to second order): ! 9D2 3D E2 ¼ 2g mB m0 Hex þ 2D þ g mB m0 Hex sin2 y
33D2 sin4 y 4g mB m0 Hex 2
E1 ¼ g mB m0 Hex D þ sin2 y
3D 15D 2 2g mB m0 Hex
!
69D2 sin4 y 8g mB m0 Hex
E0 ¼ Dð3sin2 y 2Þ where y is the angle between the trigonal axis and the exchange field. At sufficiently low temperatures, only the lowest-lying energy level will be populated, and we can therefore deduce the first- and second-order single-ion anisotropy constants K1 and K2
(J m3) at T0 K from E2: K 1 ¼ k1 N ¼
K 2 ¼ k2 N ¼ þ
! 9D2 3D N g mB Hex
33D2 N 4g mB Hex
where k is the anisotropy energy per ferrous ion and N the number of Fe2+ ions per unit volume. From Ref. [15] we have ! ! D 3r þ
l2 l2 þ2 d 10Dq
where r is the spin–spin coupling constant and l the spin–orbit coupling constant. Free ion values of r and l are 0.12 and 12.3 meV, respectively [16]. From the magnetic-ordering temperature of the sample we can estimate the exchange field m0Hex to be of the order of 285 T for x ¼ 0.6 and 120 T for x ¼ 0.8 [16]. From X-ray absorption measurements on the iron L edges, Ref. [17] has estimated 10Dq to be 1.8 eV in hematite. Inserting these values into the expression for the first-order anisotropy constant we derive the magnitude of the trigonal splitting d and find 0.10 and 0.11 eV for the x ¼ 0.6 and x ¼ 0.8 samples, respectively. The corresponding value of D, the zero-field splitting parameter is 15 K. The trigonal field is of the same order of magnitude as the splittings found in other Fe2+-bearing minerals, where values range from 0.13 to 0.69 eV [18]. As outlined above, magnetocrystalline anisotropy depends on the exchange field as well as the magnitude of the cubic and trigonal crystal field components. The electric field gradient depends among others on the c/a ratio. In our case, this ratio is 2.70 for the x ¼ 0.6 sample compared to 2.75 expected for bulk IHSS based on Vegard’s law [2] (the ratio is 2.73 for hematite and 2.77 for ilmenite), meaning that the unit cell is compressed along c and dilated in the hexagonal basal plane. This implies that the trigonal distortion of the crystal field is more important in thin film IHSS than in the end members. The energy splitting between the lowest-lying multiplets is therefore enhanced. An investigation of the temperature dependence of the optical absorption spectra of IHSS, in the infra-red or in the X-ray region, would allow more precise determination of this crystal field splitting. In conclusion, the ilmenite–hematite solid solution thin films grown on sapphire (0 0 0 1) substrates by pulsed laser deposition are under compressive strain along the hexagonal c-axis. The samples of composition x ¼ 0.6 and x ¼ 0.8 (n and p type according to Ref. [2]) are both ferrimagnetic with a Ne´el temperature of, respectively, 380 and 160 K. The large anisotropy fields of 30 and 50 T are related to a small trigonal distortion of the crystal field in these samples. The calculation of the spindependent energy spectrum using standard perturbation methods allows us to deduce the zero-field splitting parameter D ¼ 15 K as well as the magnitude of the trigonal splitting d ¼ 0.11 eV. References [1] W.H. Butler, et al., J. Appl. Phys. 93 (10) (2003) 7882; A. Bandyopadhyay, et al., Phys. Rev. B 69 (2004) 174429. [2] Y. Ishikawa, S. Akimoto, J. Phys. Soc. Japan 12 (1957) 1083; Y. Ishikawa, J. Phys. Soc. Japan 13 (1958) 37. [3] L. Navarette, et al., J. Am. Ceram. Soc. 89 (5) (2006) 1601 and references therein. [4] N.E. Brown, et al., Am. Mineral. 78 (1993) 941. [5] N.E. Brown, A. Navrotsky, Am. Mineral. 79 (1994) 485. [6] R.J. Harrison, et al., Am. Mineral. 85 (2000) 194. [7] R.J. Harrison, Am. Mineral. 91 (2006) 1006. [8] P. Robinson, et al., Nature 418 (2002) 517. [9] G.L. Nord, et al., Am. Mineral. 74 (1989) 160. [10] P. Robinson, et al., Am. Mineral. 89 (2004) 725.
ARTICLE IN PRESS K. Rode et al. / Journal of Magnetism and Magnetic Materials 320 (2008) 3238–3241
[11] [12] [13] [14] [15]
F. Zhou, et al., Mater. Lett. 57 (2003) 2104. H. Hojo, et al., Appl. Phys. Lett. 89 (2006) 082509. H. Hojo, et al., J. Mag. Magn. Mater. 310 (2007) 2105. H. Kato, et al., J. Phys. Soc. Japan 51 (1982) 1769. F. Varret, J. Phys. Colloq. C6 (sup. au no. 12) 37 (1976) C6-437.
3241
[16] In a mean field model the exchange field (Hex) can be written as a function of the magnetic ordering temperature TC: m0 Hex ¼ ð3kB T C Þ=ðg mB ðS þ 1ÞÞ. [17] T. Droubay, S.A. Chambers, Phys. Rev. B 64 (2001) 205414. [18] R.G. Burns, Mineralogical applications of crystal field theory, second ed., Cambridge University Press, Cambridge, 1993, p. 229.
Contents lists available at ScienceDirect
Journal of Magnetism and Magnetic Materials journal homepage: www.elsevier.com/locate/jmmm
Magnetic anisotropy in ilmenite– hematite solid solution thin films grown by pulsed laser ablation K. Rode , R.D. Gunning, R.G.S. Sofin, M. Venkatesan, J.G. Lunney, J.M.D. Coey, I.V. Shvets CRANN and School of Physics, Trinity College, Dublin 2, Ireland
a r t i c l e in f o
a b s t r a c t
Article history: Received 4 February 2008 Received in revised form 11 June 2008 Available online 14 June 2008
Ferromagnetic thin films of the ilmenite–hematite solid solution Fe2xTixO3 with x ¼ 0.6 and x ¼ 0.8 have been grown on (0 0 1) sapphire substrates. X-ray diffraction analysis reveals that the films are ¯ crystal structure. Strong easy-plane anisotropy is observed for single phase with the ilmenite ðR3Þ the two films, which are nominally n or p type with K1 ¼ 8 106 J m3 for x ¼ 0.6 and 11 106 J m3 for x ¼ 0.8 at T ¼ 4 K. The trigonal splitting of the 5T2g energy level of Fe2+ is inferred to be 0.11 eV, and the zero-field splitting parameter D to be equal to 15 K. & 2008 Elsevier B.V. All rights reserved.
PACS: 71.70.d 75.10.Dg 75.30.Gw 75.50.Gg 75.50.Pp 75.70.Ak 91.60.Pn Keywords: Epitaxial film Ferrimagnetics Hematite Ilmenite Magnetic semiconductors Magnetic anisotropy Pulsed laser ablation Spin electronics
The emerging field of spin electronics aims to integrate new functionalities in semiconductor micro-electronic components and devices by using the spin of the electron in addition to its charge as an information carrier. It is a challenge to efficiently inject and detect a spin-polarized current in a semiconductor such as Si or GaAS. A possible way to avoid these problems is to use a ferromagnetic (FM) semiconductor as ‘‘source’’ and ‘‘drain’’ in a future device. Up to now, most research has been focused on creating such a material by doping a semiconductor with magnetic ions from the 3d series. Although progress has been made the last decade, the dilute magnetic semiconductor route has so far failed to deliver usable room-temperature magnetic semiconductors. Another possible approach is to take a material that is FM or ferrrimagnetic and make it semiconducting. The solid solution of ilmenite (FeTiO3) and hematite (Fe2O3; IHSS), is
Corresponding author. Tel.: +353 18963165.
E-mail address: [email protected] (K. Rode). 0304-8853/$ - see front matter & 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2008.06.010
such a material [1] with the unit formula xFeTiO3+(1x)Fe2O3, usually written as Fe2xTixO3. The solid solution is ferrimagnetic for 0.5oxo0.85 due to preferred ordering of Ti on alternate c-planes in an ilmenite-type structure. Furthermore, the majority carriers change from p type to n type at x0.73 [2]. In order to be FM, IHSS thin films must crystallize in the R3¯ space group of ¯ space group of hematite. This change of ilmenite and not the R3c space group corresponds to the ordering of Ti on every second layer perpendicular to the hexagonal c-axis of IHSS. Although extensively studied in bulk [3] due to its importance in rock magnetism [4–10], the magnetic and electrical properties of thin films of IHSS have been much less investigated. Recently, several groups have reported on the successful growth of IHSS by pulsed laser ablation (PLD) and also demonstrated interaction between carriers and the magnetization of the sample by measurements of the anomalous Hall effect [11–13]. We have grown IHSS with x ¼ 0.8 and x ¼ 0.6 on c-cut sapphire (0 0 0 1) substrates by PLD using a KrF excimer laser at a fluence of 2–3 J cm2 and a repetition rate of 10 Hz. Ceramic targets were
ARTICLE IN PRESS K. Rode et al. / Journal of Magnetism and Magnetic Materials 320 (2008) 3238–3241
10000
0.5
Ilmenite-Hematite sol. solu.
0.4
1.5
0.3
1000
0.1
0.5
0.0
0.0
-0.1
-0.5
-0.2 -1.0
-0.3
1
-1.5
-0.4 -0.5
0.1
-4 20
30
40
50 60 Angle 2θ
70
80
90
-2
100
0 H (MA/m)
2
4
Fig. 3. Magnetization as a function of applied magnetic field at T ¼ 4 K (full symbols) and T ¼ 300 K (empty symbols) for samples with x ¼ 0.8 and x ¼ 0.6.
Fig. 1. X-ray diffraction pattern for a film of IHSS with x ¼ 0.8 and (multiplied by 10 for clarity) x ¼ 0.6. Black squares indicate the position of peaks for the ordered IHSS. No secondary phase is detected in the scans and the presence of peaks from (0 0 3) and (0 0 9) planes confirms that the solid solution is ordered.
0.5 2.5 2.0 1.5 1.0 0.5 0.0 -0.5 -1.0 -1.5 -2.0 -2.5
0.4 0.3
2.5
0.2 M (MA/m)
x = 0.8 x = 0.6 2.0
1.5
0.1 0.0 -0.1 -0.2 -0.3 -0.4
1.0
μB/f.u.
10
M (105 A /m)
μB/f.u.
(009)
(0012)
M (MA/m)
(006)
10
1.0
0.2
(003)
100 Cps (1/s)
3239
-0.5 -4 0.5
0.0 0
50
100
150
200 T (K)
250
300
350
400
Fig. 2. Scans of the magnetization of thin films with two different compositions as a function of temperature in a field of m0H ¼ 50 mT applied parallel to the film surface. A linear extrapolation of the region with the steepest slope yields TC (x ¼ 0.8) ¼ 161 K and TC (x ¼ 0.6) ¼ 383 K.
prepared by mixing the correct amounts of Fe2O3 and TiO2 sintered in Ar flow at 1100 1C for 12 h. The distance between the target and the substrate was 3 cm. The sample substrate was kept at 700 1C during deposition and cooled at the highest rate possible in our system, approximately 10 1C min1 down to 300 1C. We found the optimal oxygen pressures to obtain this ordering to be 8 106 mbar for x ¼ 0.6 and 1.2 105 mbar for x ¼ 0.8. Fig. 1 shows the X-ray diffraction (XRD) diagrams for a film of each composition. No secondary phases are detected in either scan. The presence of peaks from the (0 0 3) and (0 0 9) family of ¯ but allowed in R3) ¯ confirms that both planes (forbidden in R3c films are ordered. In both cases the growth is oriented with the hexagonal [0 0 1] axis of IHSS parallel to sapphire [0 0 0 1]. We find the epitaxial relation to be ð0 0 0 1Þ½1 1¯ 0 0IHSS ==ð0 0 0 1Þ½1 1¯ 0 0Al2 O3 by reciprocal space mapping (not shown) in agreement with literature [12]. No twinning of either sample is observed in a phi scan. We measured the magnetic properties of the films using a Quantum Design SQUID magnetometer in the RSO detection
-2
0 H (MA/m)
2
4
Fig. 4. Hysteresis loops recorded at 4 K with the applied field parallel and perpendicular to the sample surface of two thin films with x ¼ 0.6 and x ¼ 0.8. Strikingly, the difference of magnetization between the two directions of applied field is almost one order of magnitude, even at m0H ¼ 5.5 T.
mode. Fig. 2 shows the magnetization as a function of temperature for a 50 mT field applied parallel to the film surface. The x ¼ 0.6 film has a magnetic-ordering temperature of 380 K, whereas that of the film with x ¼ 0.8 is 160 K. The hysteresis loops of both films at 300 and 4 K are shown in Fig. 3. The saturation moments are 1.8 and 2.5 mB per formula unit, in reasonably good agreement with literature values [3]. The sample with x ¼ 0.8 is weakly ferrimagnetic even above the estimated Curie point. We believe that this may be due to an inhomogenous distribution of Ti ions in the sample as no secondary phase is detected by XRD. If this is the case, there will be regions, presumably towards the sample surface, where the Ti concentration is low enough to allow for a ferrimagnetic ordering even at room temperature. Another possible origin of this weak moment is the presence of about 5% of magnetite inclusions in the sample. Such inclusions cannot be entirely ruled out, in particular as the samples are grown at a low oxygen pressure. From the relative (0 0 0 3) peak intensity in Fig. 1 we infer the cation order parameter to be 0.4, in reasonable agreement with the order parameter deduced from the magnetization data (0.5). A value of 1 corresponds to ideal Ti order on alternate c-planes. We believe the disorder is not due to exosolutions as pure hematite or ilmenite grains would be easily detectable by XRD,
ARTICLE IN PRESS 3240
K. Rode et al. / Journal of Magnetism and Magnetic Materials 320 (2008) 3238–3241
but rather to stoichiometric variations and general disorder, i.e. the Ti atoms are not strictly confined to alternate (0 0 0 1) planes. The contribution to the magnetic properties due to the disorder is intermediate between hematite and ilmenite. A more striking observation is shown in Fig. 4, where we plot the magnetization for both a sample with x ¼ 0.6 and for a sample with x ¼ 0.8 at 4 K, with the applied magnetic field parallel and perpendicular to the sample surface. The magnetization is almost an order of magnitude lower when the field is applied out of plane compared to the in-plane configuration. To our knowledge, this magnetocrystalline anisotropy has never been reported before in thin film samples of IHSS, although pure ilmenite is known, from measurements of the metamagnetic transition, to exhibit strong anisotropy, with an anisotropy field above 10 T [14]. Furthermore, the magnitude of the anisotropy field at low temperature, estimated by the intercept of the linear extrapolations of the high field magnetization data with the applied magnetic field in the easy plane and along the hard axis, respectively, of almost 30 and 50 T for x ¼ 0.6 and x ¼ 0.8, respectively, is surprisingly large. The corresponding anisotropy constant K1 ¼ (1/2)m0HaMs is 8 106 J m3 for x ¼ 0.6 and K1 ¼ 11 106 J m3 for x ¼ 0.8. It should be noted that the estimations of the anisotropy field magnitude are made under the assumption that the magnetization is linearly increasing above our experimental range. The relative error bar of the estimates if this is the case is 30%. The origin of such large magnetocrystalline anisotropy is the single-ion anisotropy of the ferrous ion in the noncubic crystal field at octahedral sites in the structure. Shape can at best contribute to the anisotropy field equal to the polarization of the film, JS ¼ m0MS0.5 T. The ground state of free Fe2+ ions is 5D4. In octahedral sites, the degeneracy of the ground state is removed by the cubic crystal field, which splits the state into an orbital doublet 5Eg and a lower-lying orbital triplet 5T2g separated in energy by the cubic crystal field energy parameter 10Dq. The trigonal component of the crystal field further splits the triplet into the ground singlet 5A1g and a higher doublet 5Eg (we suppose the crystal field parameter B02 40) [15] separated in energy by d. The spin-dependent part of the Hamiltonian can then be written in the following form: 2 2 ^ ¼ gm m H ~ ~ H B 0 ex S þ D Sa 1=3S where Hex is the exchange field, g the spectroscopic splitting, mB the Bohr magneton and Sa the spin operator projection in the a direction. The zero-field splitting constant D reflects the spin–orbit and spin–spin coupling energy, as well as the trigonal crystal field d. By treating the second part of this equation as a perturbation we obtain the following energy spectrum (to second order): ! 9D2 3D E2 ¼ 2g mB m0 Hex þ 2D þ g mB m0 Hex sin2 y
33D2 sin4 y 4g mB m0 Hex 2
E1 ¼ g mB m0 Hex D þ sin2 y
3D 15D 2 2g mB m0 Hex
!
69D2 sin4 y 8g mB m0 Hex
E0 ¼ Dð3sin2 y 2Þ where y is the angle between the trigonal axis and the exchange field. At sufficiently low temperatures, only the lowest-lying energy level will be populated, and we can therefore deduce the first- and second-order single-ion anisotropy constants K1 and K2
(J m3) at T0 K from E2: K 1 ¼ k1 N ¼
K 2 ¼ k2 N ¼ þ
! 9D2 3D N g mB Hex
33D2 N 4g mB Hex
where k is the anisotropy energy per ferrous ion and N the number of Fe2+ ions per unit volume. From Ref. [15] we have ! ! D 3r þ
l2 l2 þ2 d 10Dq
where r is the spin–spin coupling constant and l the spin–orbit coupling constant. Free ion values of r and l are 0.12 and 12.3 meV, respectively [16]. From the magnetic-ordering temperature of the sample we can estimate the exchange field m0Hex to be of the order of 285 T for x ¼ 0.6 and 120 T for x ¼ 0.8 [16]. From X-ray absorption measurements on the iron L edges, Ref. [17] has estimated 10Dq to be 1.8 eV in hematite. Inserting these values into the expression for the first-order anisotropy constant we derive the magnitude of the trigonal splitting d and find 0.10 and 0.11 eV for the x ¼ 0.6 and x ¼ 0.8 samples, respectively. The corresponding value of D, the zero-field splitting parameter is 15 K. The trigonal field is of the same order of magnitude as the splittings found in other Fe2+-bearing minerals, where values range from 0.13 to 0.69 eV [18]. As outlined above, magnetocrystalline anisotropy depends on the exchange field as well as the magnitude of the cubic and trigonal crystal field components. The electric field gradient depends among others on the c/a ratio. In our case, this ratio is 2.70 for the x ¼ 0.6 sample compared to 2.75 expected for bulk IHSS based on Vegard’s law [2] (the ratio is 2.73 for hematite and 2.77 for ilmenite), meaning that the unit cell is compressed along c and dilated in the hexagonal basal plane. This implies that the trigonal distortion of the crystal field is more important in thin film IHSS than in the end members. The energy splitting between the lowest-lying multiplets is therefore enhanced. An investigation of the temperature dependence of the optical absorption spectra of IHSS, in the infra-red or in the X-ray region, would allow more precise determination of this crystal field splitting. In conclusion, the ilmenite–hematite solid solution thin films grown on sapphire (0 0 0 1) substrates by pulsed laser deposition are under compressive strain along the hexagonal c-axis. The samples of composition x ¼ 0.6 and x ¼ 0.8 (n and p type according to Ref. [2]) are both ferrimagnetic with a Ne´el temperature of, respectively, 380 and 160 K. The large anisotropy fields of 30 and 50 T are related to a small trigonal distortion of the crystal field in these samples. The calculation of the spindependent energy spectrum using standard perturbation methods allows us to deduce the zero-field splitting parameter D ¼ 15 K as well as the magnitude of the trigonal splitting d ¼ 0.11 eV. References [1] W.H. Butler, et al., J. Appl. Phys. 93 (10) (2003) 7882; A. Bandyopadhyay, et al., Phys. Rev. B 69 (2004) 174429. [2] Y. Ishikawa, S. Akimoto, J. Phys. Soc. Japan 12 (1957) 1083; Y. Ishikawa, J. Phys. Soc. Japan 13 (1958) 37. [3] L. Navarette, et al., J. Am. Ceram. Soc. 89 (5) (2006) 1601 and references therein. [4] N.E. Brown, et al., Am. Mineral. 78 (1993) 941. [5] N.E. Brown, A. Navrotsky, Am. Mineral. 79 (1994) 485. [6] R.J. Harrison, et al., Am. Mineral. 85 (2000) 194. [7] R.J. Harrison, Am. Mineral. 91 (2006) 1006. [8] P. Robinson, et al., Nature 418 (2002) 517. [9] G.L. Nord, et al., Am. Mineral. 74 (1989) 160. [10] P. Robinson, et al., Am. Mineral. 89 (2004) 725.
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[11] [12] [13] [14] [15]
F. Zhou, et al., Mater. Lett. 57 (2003) 2104. H. Hojo, et al., Appl. Phys. Lett. 89 (2006) 082509. H. Hojo, et al., J. Mag. Magn. Mater. 310 (2007) 2105. H. Kato, et al., J. Phys. Soc. Japan 51 (1982) 1769. F. Varret, J. Phys. Colloq. C6 (sup. au no. 12) 37 (1976) C6-437.
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[16] In a mean field model the exchange field (Hex) can be written as a function of the magnetic ordering temperature TC: m0 Hex ¼ ð3kB T C Þ=ðg mB ðS þ 1ÞÞ. [17] T. Droubay, S.A. Chambers, Phys. Rev. B 64 (2001) 205414. [18] R.G. Burns, Mineralogical applications of crystal field theory, second ed., Cambridge University Press, Cambridge, 1993, p. 229.