- Email: [email protected]
Compensation temperatures of mixed ferro-ferrimagnetic ternary alloys
ARTICLE IN PRESS
Journal of Magnetism and Magnetic Materials 310 (2007) e495–e497 www.elsevier.com/locate/jmmm
Compensation temperatures of mixed ferro-ferrimagnetic ternary alloys G.M. Buendı´ a, J.E. Villarroel Department of Physics, Universidad Simo´n Bolı´var, Caracas 1080, Venezuela Available online 7 November 2006
Abstract We present a Monte Carlo study of a mixed Ising model of the type ABP C1P , in a square lattice, were spins SA ¼ 3=2; 1=2 of one sublattice are in alternating sites with spins SB ¼ 52; 32; 12 or spins S C ¼ 1; 0, located on the other sublattice with concentrations P and 1 P, respectively. The SA interact ferromagnetically with the S B and antiferromagnetically with the SC . The results indicate that this simple model can reproduce several aspects of the behavior of a class of molecular compounds called Prussian blue analogs such as a critical temperature that it is independent on the concentration of different types of spins, and the appearance of compensation temperatures in a certain range of values of the concentration of the different species. r 2006 Elsevier B.V. All rights reserved. PACS: 75.10.Hk; 75.30.Kz; 75.50.Gg Keywords: Ferrimagnetic ternary alloys; Compensation temperatures
The objective of the present study is to gain understanding of a type of molecule-based magnets, which have both ferromagnetic and ferrimagnetic interactions. A class of these materials, the so-called Prussian blue analogs, have interesting properties such as: photo induced magnetic pole inversion at the compensation temperature ðT comp Þ, high critical temperatures ðT crit Þ, high coercive fields, etc. [1]. In this work we are going to simulate the properties of ternary III II molecular magnets of the type ðNiII P Mn1P Þ1:5 ½Cr ðCNÞ6 :zH2 O, whose properties can be controlled by changing the relative concentration of the different species, P [2]. The CrIII ion has three unpaired electrons, the Ni has two, and the Mn has five, so depending on how the spins are aligned, their total magnetic moments can take four values ð32; 12Þ, three values ð1; 0Þ, or six values ð52; 32; 12Þ, respectively. In our simulation we are going to include all the possible values. The coupling Cr–Ni is ferromagnetic and the Mn–Cr is antiferromagnetic. These compounds are going to be simulated by a mixed Ising system of the type ABP C1P , where A, B and C represent the atoms of Cr, Ni and Mn, respectively, and P gives the relative concentration of atoms B and C in the compound.
Previous studies indicate that mixed Ising systems can present T comp : temperatures below the critical point at which the magnetization vanishes [3], and a mean field study indicates that this particular system can be a useful tool to explore the general behavior of ternary allows [4]. Experimentally it has been shown that the coercivity of a material increases dramatically at T comp ; at this point only a small driving field is required to reverse the sign of the magnetization [5]. This temperature dependence of the coercivity near the T comp has interesting applications in many fields, particularly for thermomagnetic recording. In this work we are focusing on studying the behavior of the T comp of these ternary compounds. The mixed Ising ABP C1P model consists of two interpenetrating square sublattices, each one of L2 =2 sites. One sublattice only have spins S A ¼ 32; 12. The other sublattice can have spins S B ¼ 1; 0 or S C ¼ 52; 32; 12. The Hamiltonian of the model is the following: X X H ¼ J AB S iA SjB Ai Bj J AC S iA SjC Ai Cj hnni
J AA
X
hnni
S iA SkA Ai Ak ,
ð1Þ
hnnni
Corresponding author. Tel.: +58 212 9063 900; fax: +58 212 9063 903.
E-mail address: [email protected] (G.M. Buendı´ a). 0304-8853/$ - see front matter r 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2006.10.461
where Xi is 1 if there is a spin X (A,B, or C) at the site i, if not it is zero. We choose the interactions between nearest
ARTICLE IN PRESS G.M. Buendı´a, J.E. Villarroel / Journal of Magnetism and Magnetic Materials 310 (2007) e495–e497
P = 0.00 P = 0.25 P = 0.50 P = 0.75 P = 1.00
kTc /Jab
4
0.1 0 -0.1 P = 0.300 P = 0.250 P = 0.200 P = 0.150 P = 0.100
-0.2 -0.3 0
10
20
30
40
50
kT Fig. 2. Magnetization vs temperature for different values of P (J AA ¼ 7:5, J AB ¼ 5 and J AC ¼ 5, all in energy units). Notice that for this set of parameters the system presents T comp for 0:1oPo0:3.
40 JAA JAB -JAC
30
20
10
0 2
4
6 J
8
10
Fig. 3. Dependence of the T comp on the parameters of the Hamiltonian. The dependence on J AA ðJ AB Þ was obtained for J AB ¼ 5ðJ AA ¼ 7:5Þ and J AC ¼ 5. In all the cases P ¼ 0:25. The lines are guides to the eye.
reproduce qualitatively interesting properties of ferrimagnetic ternary compounds, such as T crit that depend very weakly on the concentration of the different compounds, and the existence of T comp that can be tuned by adjusting the proportion of compounds that interact ferromagnetically and antiferromagnetically, properties that can be very useful for designing molecular magnets.
6 5
0.2
Magnetization
neighbors, J AB 40 and J AC o0, in correspondence with the experimental systems. The fraction of SB in the second sublattice is given by P ¼ N B 2=L2 , where N B is the number of sites occupied by SB . The fraction of S C is 1 P. When P ¼ 1ð0Þ the system consists in S A alternating with SB ðS C Þ. Our results indicate that when there is no interaction between the A spins (next-nearest neighbors in the lattice), J AA ¼ 0, the system does not have T comp , and that its T crit has a linear dependence on the parameter R ¼ J AC =J AB . When R ¼ 0:49 01 the T crit is independent of P, as seen in Fig. 1. This behavior was already reported in studies based on a mean field approximation [4]. Experimental measurements indicate that there are Prussian blue analogs that at R ¼ 0:45 (a value curiously close to our numerical result) have a T crit that is almost independent of P [6]. Our results show that a T comp is induced by the presence of a ferromagnetic interaction, J AA 40, between the S A . There is a minimum value of J AA above which a T comp appears, this minimum depends on the other parameters in the hamiltonian. For J AA above this minimum, the system presents T comp in a certain range of values of P, as can be seen in Fig. 2, where we plot the total magnetization of the system vs the temperature. For the particular choice of parameters of Fig. 2 there are T comp in the range 0:1oPo0:3. This behavior has been observed experimentally in several ternary compounds whose T comp can be changed by modifying the relative concentration of ferromagnetic and antiferromagnetic components of the material [7]. Notice that, while the T comp depends strongly on P, the T crit is almost independent of it. The dependence of the T comp on the parameters of the hamiltonian is shown in Fig. 3. Once the T comp appears its dependence on J AB and J AA is relatively weak: it decreases slowly as the strength of the interaction increases, reaching a value that seems to be constant at high values of the interactions. Quite the contrary, the T comp has a strong dependence on the parameter J AC , it increases rapidly as jJ AC j increases. These results indicate that this mixed Ising model can
kTcomp
e496
3
References
2 Rc
1 0 0.2
0.3
0.4
0.5 Rc
0.6
0.7
0.8
0.9
1
R
Fig. 1. T crit as a function of R ¼ J AC =J AB , J AA ¼ 0, for different values of P. The straight lines are linear fitting of the data.
[1] S. Ferlay, T. Mallah, R. Ouahs, P. Veillet, M. Verdaguer, Nature 378 (1995) 701; O. Hatlevik, W.E. Bushmann, J. Zhang, J.L. Mason, J.S. Miller, Adv. Mater. 11 (1999) 914; S.M. Holmes, G.S. Girolami, J. Am. Chem. Soc. 121 (1999) 5593; S. Ohkoshi, S. Yorozu, O. Sato, T. Iyoda, A. Fujishima, K. Hashimoto, Appl. Phys. Lett. 70 (1997) 1040. [2] S. Ohkoshi, T. Iyoda, A. Fujishima, K. Hashimoto, Phys. Rev. B 56 (1997) 11642.
ARTICLE IN PRESS G.M. Buendı´a, J.E. Villarroel / Journal of Magnetism and Magnetic Materials 310 (2007) e495–e497 [3] G.M. Buendı´ a, M.A. Novotny, J. Phys. Condens.: Matter 9 (1997) 5951; G.M. Buendı´ a, E. Machado, Phys. Rev. B 61 (2000) 14686. [4] A. Bobak, F.O. Abubrig, T. Balcerzak, Phys. Rev. B 68 (2003) 224405.
e497
[5] M. Masuripur, J. Appl. Phys. 61 (1987) 1580; S. Ohkoshi, Phys. Rev. Lett. 82 (1999) 1285. [6] P. Zhoug, D. Xue, H. Lou, X. Chen, Nanoletters 2 (2002) 845. [7] S. Ohkoshi, Y. Abe, A. Fujishima, K. Hashimoto, Phys. Rev. Lett. 82 (1999) 0031.
Journal of Magnetism and Magnetic Materials 310 (2007) e495–e497 www.elsevier.com/locate/jmmm
Compensation temperatures of mixed ferro-ferrimagnetic ternary alloys G.M. Buendı´ a, J.E. Villarroel Department of Physics, Universidad Simo´n Bolı´var, Caracas 1080, Venezuela Available online 7 November 2006
Abstract We present a Monte Carlo study of a mixed Ising model of the type ABP C1P , in a square lattice, were spins SA ¼ 3=2; 1=2 of one sublattice are in alternating sites with spins SB ¼ 52; 32; 12 or spins S C ¼ 1; 0, located on the other sublattice with concentrations P and 1 P, respectively. The SA interact ferromagnetically with the S B and antiferromagnetically with the SC . The results indicate that this simple model can reproduce several aspects of the behavior of a class of molecular compounds called Prussian blue analogs such as a critical temperature that it is independent on the concentration of different types of spins, and the appearance of compensation temperatures in a certain range of values of the concentration of the different species. r 2006 Elsevier B.V. All rights reserved. PACS: 75.10.Hk; 75.30.Kz; 75.50.Gg Keywords: Ferrimagnetic ternary alloys; Compensation temperatures
The objective of the present study is to gain understanding of a type of molecule-based magnets, which have both ferromagnetic and ferrimagnetic interactions. A class of these materials, the so-called Prussian blue analogs, have interesting properties such as: photo induced magnetic pole inversion at the compensation temperature ðT comp Þ, high critical temperatures ðT crit Þ, high coercive fields, etc. [1]. In this work we are going to simulate the properties of ternary III II molecular magnets of the type ðNiII P Mn1P Þ1:5 ½Cr ðCNÞ6 :zH2 O, whose properties can be controlled by changing the relative concentration of the different species, P [2]. The CrIII ion has three unpaired electrons, the Ni has two, and the Mn has five, so depending on how the spins are aligned, their total magnetic moments can take four values ð32; 12Þ, three values ð1; 0Þ, or six values ð52; 32; 12Þ, respectively. In our simulation we are going to include all the possible values. The coupling Cr–Ni is ferromagnetic and the Mn–Cr is antiferromagnetic. These compounds are going to be simulated by a mixed Ising system of the type ABP C1P , where A, B and C represent the atoms of Cr, Ni and Mn, respectively, and P gives the relative concentration of atoms B and C in the compound.
Previous studies indicate that mixed Ising systems can present T comp : temperatures below the critical point at which the magnetization vanishes [3], and a mean field study indicates that this particular system can be a useful tool to explore the general behavior of ternary allows [4]. Experimentally it has been shown that the coercivity of a material increases dramatically at T comp ; at this point only a small driving field is required to reverse the sign of the magnetization [5]. This temperature dependence of the coercivity near the T comp has interesting applications in many fields, particularly for thermomagnetic recording. In this work we are focusing on studying the behavior of the T comp of these ternary compounds. The mixed Ising ABP C1P model consists of two interpenetrating square sublattices, each one of L2 =2 sites. One sublattice only have spins S A ¼ 32; 12. The other sublattice can have spins S B ¼ 1; 0 or S C ¼ 52; 32; 12. The Hamiltonian of the model is the following: X X H ¼ J AB S iA SjB Ai Bj J AC S iA SjC Ai Cj hnni
J AA
X
hnni
S iA SkA Ai Ak ,
ð1Þ
hnnni
Corresponding author. Tel.: +58 212 9063 900; fax: +58 212 9063 903.
E-mail address: [email protected] (G.M. Buendı´ a). 0304-8853/$ - see front matter r 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2006.10.461
where Xi is 1 if there is a spin X (A,B, or C) at the site i, if not it is zero. We choose the interactions between nearest
ARTICLE IN PRESS G.M. Buendı´a, J.E. Villarroel / Journal of Magnetism and Magnetic Materials 310 (2007) e495–e497
P = 0.00 P = 0.25 P = 0.50 P = 0.75 P = 1.00
kTc /Jab
4
0.1 0 -0.1 P = 0.300 P = 0.250 P = 0.200 P = 0.150 P = 0.100
-0.2 -0.3 0
10
20
30
40
50
kT Fig. 2. Magnetization vs temperature for different values of P (J AA ¼ 7:5, J AB ¼ 5 and J AC ¼ 5, all in energy units). Notice that for this set of parameters the system presents T comp for 0:1oPo0:3.
40 JAA JAB -JAC
30
20
10
0 2
4
6 J
8
10
Fig. 3. Dependence of the T comp on the parameters of the Hamiltonian. The dependence on J AA ðJ AB Þ was obtained for J AB ¼ 5ðJ AA ¼ 7:5Þ and J AC ¼ 5. In all the cases P ¼ 0:25. The lines are guides to the eye.
reproduce qualitatively interesting properties of ferrimagnetic ternary compounds, such as T crit that depend very weakly on the concentration of the different compounds, and the existence of T comp that can be tuned by adjusting the proportion of compounds that interact ferromagnetically and antiferromagnetically, properties that can be very useful for designing molecular magnets.
6 5
0.2
Magnetization
neighbors, J AB 40 and J AC o0, in correspondence with the experimental systems. The fraction of SB in the second sublattice is given by P ¼ N B 2=L2 , where N B is the number of sites occupied by SB . The fraction of S C is 1 P. When P ¼ 1ð0Þ the system consists in S A alternating with SB ðS C Þ. Our results indicate that when there is no interaction between the A spins (next-nearest neighbors in the lattice), J AA ¼ 0, the system does not have T comp , and that its T crit has a linear dependence on the parameter R ¼ J AC =J AB . When R ¼ 0:49 01 the T crit is independent of P, as seen in Fig. 1. This behavior was already reported in studies based on a mean field approximation [4]. Experimental measurements indicate that there are Prussian blue analogs that at R ¼ 0:45 (a value curiously close to our numerical result) have a T crit that is almost independent of P [6]. Our results show that a T comp is induced by the presence of a ferromagnetic interaction, J AA 40, between the S A . There is a minimum value of J AA above which a T comp appears, this minimum depends on the other parameters in the hamiltonian. For J AA above this minimum, the system presents T comp in a certain range of values of P, as can be seen in Fig. 2, where we plot the total magnetization of the system vs the temperature. For the particular choice of parameters of Fig. 2 there are T comp in the range 0:1oPo0:3. This behavior has been observed experimentally in several ternary compounds whose T comp can be changed by modifying the relative concentration of ferromagnetic and antiferromagnetic components of the material [7]. Notice that, while the T comp depends strongly on P, the T crit is almost independent of it. The dependence of the T comp on the parameters of the hamiltonian is shown in Fig. 3. Once the T comp appears its dependence on J AB and J AA is relatively weak: it decreases slowly as the strength of the interaction increases, reaching a value that seems to be constant at high values of the interactions. Quite the contrary, the T comp has a strong dependence on the parameter J AC , it increases rapidly as jJ AC j increases. These results indicate that this mixed Ising model can
kTcomp
e496
3
References
2 Rc
1 0 0.2
0.3
0.4
0.5 Rc
0.6
0.7
0.8
0.9
1
R
Fig. 1. T crit as a function of R ¼ J AC =J AB , J AA ¼ 0, for different values of P. The straight lines are linear fitting of the data.
[1] S. Ferlay, T. Mallah, R. Ouahs, P. Veillet, M. Verdaguer, Nature 378 (1995) 701; O. Hatlevik, W.E. Bushmann, J. Zhang, J.L. Mason, J.S. Miller, Adv. Mater. 11 (1999) 914; S.M. Holmes, G.S. Girolami, J. Am. Chem. Soc. 121 (1999) 5593; S. Ohkoshi, S. Yorozu, O. Sato, T. Iyoda, A. Fujishima, K. Hashimoto, Appl. Phys. Lett. 70 (1997) 1040. [2] S. Ohkoshi, T. Iyoda, A. Fujishima, K. Hashimoto, Phys. Rev. B 56 (1997) 11642.
ARTICLE IN PRESS G.M. Buendı´a, J.E. Villarroel / Journal of Magnetism and Magnetic Materials 310 (2007) e495–e497 [3] G.M. Buendı´ a, M.A. Novotny, J. Phys. Condens.: Matter 9 (1997) 5951; G.M. Buendı´ a, E. Machado, Phys. Rev. B 61 (2000) 14686. [4] A. Bobak, F.O. Abubrig, T. Balcerzak, Phys. Rev. B 68 (2003) 224405.
e497
[5] M. Masuripur, J. Appl. Phys. 61 (1987) 1580; S. Ohkoshi, Phys. Rev. Lett. 82 (1999) 1285. [6] P. Zhoug, D. Xue, H. Lou, X. Chen, Nanoletters 2 (2002) 845. [7] S. Ohkoshi, Y. Abe, A. Fujishima, K. Hashimoto, Phys. Rev. Lett. 82 (1999) 0031.