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Negative magnetization behavior in Co1−xCuxCr2O4 ceramics
Materials Letters 182 (2016) 155–158
Contents lists available at ScienceDirect
Materials Letters journal homepage: www.elsevier.com/locate/matlet
Negative magnetization behavior in Co1 xCuxCr2O4 ceramics C.M. Zhu 1, L.G. Wang 1, L. Chen, C.L. Li, Z.M. Tian, S.L. Yuan n School of Physics, Huazhong University of Science and Technology, Wuhan 430074, People's Republic of China
art ic l e i nf o
a b s t r a c t
Article history: Received 24 February 2016 Received in revised form 7 June 2016 Accepted 26 June 2016 Available online 27 June 2016
Co1 xCuxCr2O4 (0.1 r x r 0.275) ceramics have been synthesized and identified as having the cubic structure. Doping Cu has the distinct influence on magnetic properties of the samples. Negative magnetization is discovered when content of Cu increases from x ¼0.125 to 0.25. As doping content increases, the maximum of magnetization in field-cooled curves shows a monotonous decreasing tendency. Whereas, the relative intensity of negative magnetization and the magnetization reversal temperature increase and then decrease presenting the maximums at x ¼ 0.225. Especially for x ¼0.225, negative magnetization behavior is also affected by cooling field and the negative value finally turns to positive at 12 kOe. & 2016 Elsevier B.V. All rights reserved.
Keywords: Ceramics Magnetic materials Sol-gel preparation
1. Introduction Transition metal oxides are important materials with numerous technological applications [1]. However, chromite spinels have been a little studied. CoCr2O4 is appealing since it presents magnetic transition and spontaneous electric polarization simultaneously. It is also interesting that coupling interactions among various cations give rise to different competing exchange pathways. Magnetization reversal has been frequently observed in many magnetic materials. Different from ordinary reversal by field direction, some materials can display this behavior only through temperature [2]. Due to potential applications, this unusual phenomenon has attracted much attention. Nevertheless, magnetization reversal in ACr2O4 is rarely reported. In this research, we investigate negative magnetization in Co1 xCuxCr2O4. With increasing Cu, negative value appears at 0.125 rx r0.25. For Co0.775Cu0.225Cr2O4, negative magnetization is also influenced by cooling field (abbreviated as H).
2. Experimental procedure Co1 xCuxCr2O4 (0.1 rx r0.275) ceramics were fabricated by sol-gel method [3]. Firstly, Co(NO3)2 6H2O, Cu(NO3)2 3H2O, Cr (NO3)3 9H2O and citric acid were dissolved in distilled water with stirring. pH 7 was adjusted by adding ammonia. Then, the n
Corresponding author. E-mail address: [email protected] (S.L. Yuan). 1 These two authors contributed equally to this work.
http://dx.doi.org/10.1016/j.matlet.2016.06.116 0167-577X/& 2016 Elsevier B.V. All rights reserved.
solutions were thoroughly homogenized to form sols. Subsequently, the sols were heated to get gels and dried to form the precursor powders. Finally, the powders were ground and annealed at 750 °C for 3 h to obtain Co1 xCuxCr2O4. Crystal structures were investigated by X-ray diffraction (XRD, Philips X′pert pro). Magnetic measurements were measured through Physical Property Measurement System (PPMS, Quantum Design).
3. Results and discussion Fig. 1 shows the XRD patterns of Co1 xCuxCr2O4. All samples are pure without observable impurities. Compared with PDF card numbered 00-022-1084, the ceramics are identified as single phase having a cubic crystal structure with space group Fd-3m. The calculated values of average lattice parameter are 0.8325 nm with 0.1 rx r0.275. So, it can be neglectful of the influence on crystal structure by doped Cu. Temperature dependent magnetization in zero-field cooled (ZFC) and field cooled (FC) processes has been measured with H¼100 Oe in Fig. 2. For all samples, ferrimagnetic transition (TC) at 91 K is clearly manifested. In Fig. 2(a), it is defined as the temperature at which FC magnetization rises sharply from 0 with decreasing temperature. As temperature decreases, FC and ZFC curves display obvious irreversibility indicating the strong magnetocrystalline anisotropy, which is attributed to the random distribution of net moments in polycrystalline ceramics. Compared with the magnetization of CoCr2O4 in Fig. 2(a), which displays the similar change tendency between ZFC and FC curves, Co1 xCuxCr2O4 samples present apparent differences in ZFC and FC curves. This behavior can be well explained by the presence of non-collinear moments with doping Cu. Those moments are under
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C.M. Zhu et al. / Materials Letters 182 (2016) 155–158
the influence of strong magnetocrystalline anisotropic field. So, low cooling field is not strong enough to completely orient the moments to spin configuration with the lowest energy. Except for
Co0.725Cu0.275Cr2O4, with lowering temperature from ferrimagnetic transition, FC magnetization rises sharply, goes through a maximum (Mmax) at 75 K and then drops down. Especially at
Fig. 1. XRD patterns of Co1 xCuxCr2O4 ceramics.
Fig. 3. Evolution of Tcomp with x. Upper inset is Mmax variation with x. Lower inset is the relative intensity change of negative magnetization as Cu increases.
Fig. 2. Temperature dependent magnetization in ZFC and FC processes.
C.M. Zhu et al. / Materials Letters 182 (2016) 155–158
157
Fig. 4. Temperature dependent magnetization in ZFC and FC processes with different cooling fields. Inset of Fig. 4(a) is a mirror-like behavior in FC curves. Inset of (c) is Tcomp evolution with cooling field. Inset of (d) is Mmin evolution with cooling field.
0.125 rx r0.25, FC magnetization passes through zero value at compensation temperature (Tcomp). Then, it takes on negative value with the minimum (Mmin) at 25 K. The negative value signifies the direction of moments is antiparallel to that of applied field. That is, negative magnetization can be generated in Co1 xCuxCr2O4. Moreover, negative value in ZFC magnetization is due to the uncompensated spins at grain boundaries of polycrystalline Co1 xCuxCr2O4. In order to see negative magnetization characteristics clearly, we plots the parameter change with increasing Cu in Fig. 3. Upper inset is Mmax variation with x, which presents monotonous decrease with increasing Cu. The main figure shows that Tcomp increases from 33.8 K of x ¼0.125 to 56.9 K of x¼ 0.225 and then decreases to 55.6 K of x ¼0.25. Lower inset is the relative intensity change of negative magnetization (|Mmax/Mmin|), which can act as the index of negative magnetization behavior. Similarly, it is enhanced from x¼0.125 to 0.225 and then weakened at x ¼0.25. That is, negative magnetization starts at x¼ 0.125, obtains the most distinct phenomenon at x ¼0.225 and finally disappears at x¼ 0.275 with increasing Cu. CoCr2O4 does not show negative magnetization. Doping Cu does not induce structure transition, either. So, negative magnetization should be mainly related to the destroyed stability of magnetic structure in Co1 xCuxCr2O4. According to previous studies, it can be explained based on two-sublattice model [4]. Cations occupied A sites with ferromagnetic interaction are formed to AO4 tetrahedral sublattices (A sublattices) and those occupied B sites with antiferromagnetic interaction are formed to BO6 octahedral sublattices (B sublattices). Cu2 þ and Co2 þ are randomly distributed in A sites. Cu2 þ can induce magnetic structure change
from two aspects. On the one hand, the spin-only value of Cu2 þ is lower than that of Co2 þ . The decreased spin-only value in A sites not only weakens the moments parallel to field direction exhibiting the decreasing Mmax, but also makes it possible that antiferromagnetic interaction can have impact on the weakened ferromagnetic interaction. In accordance with the theory about different temperature dependence of sublattices [5], Co2 þ and Cu2 þ spins are oriented along field direction at higher temperature than Cr3 þ spins which order gradually with moments antiparallel to field direction during FC process. So, ferromagnetic interaction is enhanced earlier than antiferromagnetic interaction. Whereas, B sublattice interaction is usually stronger than A sublattices indicating the moments antiparallel to field direction can be dominating with decreasing temperature. Thus, the sum of FC magnetization is positive and then decreases to negative through Tcomp. However, the change of negative magnetization is not consistent with increasing Cu. We speculate that the other reason is the relative angle change. According to bulk configuration of Cr3 þ and Cu2 þ moments [6], the relative angle is between Cr cations. For balance of magnetic structure, Cu2 þ with lower moments will increase the angle in Co1 xCuxCr2O4. So, negative moments in B sublattices are weakened. Co0.9Cu0.1Cr2O4 without negative magnetization means that the decreased negative moments because of increasing angle are much more than decreased positive moments due to lower moments of Cu2 þ . At 0.125 rxr 0.225, relative angle continues to increase but the corresponding decrease in negative moments is slow. Lower moments of Cu2 þ have main influence on sum magnetization. Thus, with decreasing temperature, negative moments are larger than
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C.M. Zhu et al. / Materials Letters 182 (2016) 155–158
positive moments presenting the stronger negative magnetization. Exceeding this content range, the decreased negative moments are more evident than the decrease in positive moments. So, negative magnetization is weakened again and finally disappears. Tcomp is the temperature at which negative moments are equal to positive ones. The consistent change between Tcomp and |Mmax/Mmin| is in that the enhanced negative magnetization is easier to obtain at higher temperature. The results also prove that x ¼0.225 is a special content with outstanding negative magnetization. Fig. 4 shows ZFC and FC curves under different cooling fields of Co0.775Cu0.225Cr2O4. Magnetization becomes negative below Tcomp. A mirror-like behavior is observed in FC curves under H¼ 7 1000 Oe in inset of Fig. 4(a), which also testifies the sum magnetization is opposite to field direction. With increasing field, Tcomp presents monotonous decrease from H¼1000 Oe to 11 kOe and disappears at 12 kOe in inset of Fig. 4(c). In inset of Fig. 4(d), absolute value of Mmin (|Mmin|) increases at 1000 OerH r3000 Oe and then decreases with further increasing field. Finally, negative value turns to positive at H ¼12 kOe. With Hr3000 Oe, both positive and negative moments are enhanced, but the field is too low to change moment direction in B sublattices. So, difference between the two moments is increased showing an increasing |Mmin|. Further increasing field, it is high enough to reverse parts of negative moments to field direction, thus the sum of negative magnetization is decreased and finally turns to positive. The monotonous relationship between Tcomp and applied field is attributed to the enhanced positive moment in A sublattices with increasing field, which needs more negative moments to offset it. Therefore, negative magnetization appears at lower temperature with increasing applied field.
4. Conclusions Negative magnetization is observed in Co1 xCuxCr2O4 ceramics presenting the evident dependence on the doping content of Cu. It is enhanced from x¼ 0.125 to 0.225 and then decreases with Cu
increasing. At x ¼0.225, Tcomp is monotonously decreased with increasing applied field. |Mmin| is increased at low field, then decreased and finally Mmin turns to positive with field increasing. We explain the negative magnetization through two-sublattice model. With doping Cu, the decreased moments in A sublattices and the changed relative angle in magnetic structure give rise to different dependence on temperature of two kinds of sublattices. These findings accentuate meaningful fundamental physics for information storage. Moreover, negative magnetization behavior can be helpful to Co1 xCuxCr2O4 on the potential applications in spintronics devices with the optional magnetization direction.
Acknowledgments This work was supported by National Natural Science Foundation of China (Grant no. 11474111). We also thank the staff of Analysis Center of HUST for their assistance in various measurements.
References [1] S. More, R. Kadam, A. Kadam, D. Mane, G. Bichile, Structural properties and magnetic interactions in Al3 þ and Cr3 þ co-substituted CoFe2O4 ferrite, Cent. Eur. J. Chem. 8 (2010) 419–425. [2] K. Yoshii, Magnetization reversal in TmCrO3, Mater. Res. Bull. 47 (2012) 3243–3248. [3] L.G. Wang, C.M. Zhu, H. Luo, S.L. Yuan, Studies on room temperature multiferroic properties of xBi0.5Na0.5TiO3-(1 x)NiFe2O4 ceramics, J. Electroceram. 35 (2015) 59–67. [4] Y.J. Choi, J. Okamoto, D.J. Huang, K.S. Chao, H.J. Lin, C.T. Chen, M. van Veenendaal, T.A. Kaplan, S.-W. Cheong, Thermally or magnetically induced polarization reversal in the multiferroic CoCr2O4, Phys. Rev. Lett. 102 (2009) 067601. [5] Y.L. Su, J.C. Zhang, Z.J. Feng, L. Li, B.Z. Li, Y. Zhou, Z.P. Chen, S.X. Cao, Magnetization reversal and Yb3 þ /Cr3 þ spin ordering at low temperature for perovskite YbCrO3 chromites, J. Appl. Phys. 108 (2010) 013905. [6] J.M. Iwata, R.V. Chopdekar, F.J. Wong, B.B. Nelson-Cheeseman, E. Arenholz, Y. Suzuki, Enhanced magnetization of CuCr2O4 thin films by substrate-induced strain, J. Appl. Phys. 105 (2009) 07A905.
Contents lists available at ScienceDirect
Materials Letters journal homepage: www.elsevier.com/locate/matlet
Negative magnetization behavior in Co1 xCuxCr2O4 ceramics C.M. Zhu 1, L.G. Wang 1, L. Chen, C.L. Li, Z.M. Tian, S.L. Yuan n School of Physics, Huazhong University of Science and Technology, Wuhan 430074, People's Republic of China
art ic l e i nf o
a b s t r a c t
Article history: Received 24 February 2016 Received in revised form 7 June 2016 Accepted 26 June 2016 Available online 27 June 2016
Co1 xCuxCr2O4 (0.1 r x r 0.275) ceramics have been synthesized and identified as having the cubic structure. Doping Cu has the distinct influence on magnetic properties of the samples. Negative magnetization is discovered when content of Cu increases from x ¼0.125 to 0.25. As doping content increases, the maximum of magnetization in field-cooled curves shows a monotonous decreasing tendency. Whereas, the relative intensity of negative magnetization and the magnetization reversal temperature increase and then decrease presenting the maximums at x ¼ 0.225. Especially for x ¼0.225, negative magnetization behavior is also affected by cooling field and the negative value finally turns to positive at 12 kOe. & 2016 Elsevier B.V. All rights reserved.
Keywords: Ceramics Magnetic materials Sol-gel preparation
1. Introduction Transition metal oxides are important materials with numerous technological applications [1]. However, chromite spinels have been a little studied. CoCr2O4 is appealing since it presents magnetic transition and spontaneous electric polarization simultaneously. It is also interesting that coupling interactions among various cations give rise to different competing exchange pathways. Magnetization reversal has been frequently observed in many magnetic materials. Different from ordinary reversal by field direction, some materials can display this behavior only through temperature [2]. Due to potential applications, this unusual phenomenon has attracted much attention. Nevertheless, magnetization reversal in ACr2O4 is rarely reported. In this research, we investigate negative magnetization in Co1 xCuxCr2O4. With increasing Cu, negative value appears at 0.125 rx r0.25. For Co0.775Cu0.225Cr2O4, negative magnetization is also influenced by cooling field (abbreviated as H).
2. Experimental procedure Co1 xCuxCr2O4 (0.1 rx r0.275) ceramics were fabricated by sol-gel method [3]. Firstly, Co(NO3)2 6H2O, Cu(NO3)2 3H2O, Cr (NO3)3 9H2O and citric acid were dissolved in distilled water with stirring. pH 7 was adjusted by adding ammonia. Then, the n
Corresponding author. E-mail address: [email protected] (S.L. Yuan). 1 These two authors contributed equally to this work.
http://dx.doi.org/10.1016/j.matlet.2016.06.116 0167-577X/& 2016 Elsevier B.V. All rights reserved.
solutions were thoroughly homogenized to form sols. Subsequently, the sols were heated to get gels and dried to form the precursor powders. Finally, the powders were ground and annealed at 750 °C for 3 h to obtain Co1 xCuxCr2O4. Crystal structures were investigated by X-ray diffraction (XRD, Philips X′pert pro). Magnetic measurements were measured through Physical Property Measurement System (PPMS, Quantum Design).
3. Results and discussion Fig. 1 shows the XRD patterns of Co1 xCuxCr2O4. All samples are pure without observable impurities. Compared with PDF card numbered 00-022-1084, the ceramics are identified as single phase having a cubic crystal structure with space group Fd-3m. The calculated values of average lattice parameter are 0.8325 nm with 0.1 rx r0.275. So, it can be neglectful of the influence on crystal structure by doped Cu. Temperature dependent magnetization in zero-field cooled (ZFC) and field cooled (FC) processes has been measured with H¼100 Oe in Fig. 2. For all samples, ferrimagnetic transition (TC) at 91 K is clearly manifested. In Fig. 2(a), it is defined as the temperature at which FC magnetization rises sharply from 0 with decreasing temperature. As temperature decreases, FC and ZFC curves display obvious irreversibility indicating the strong magnetocrystalline anisotropy, which is attributed to the random distribution of net moments in polycrystalline ceramics. Compared with the magnetization of CoCr2O4 in Fig. 2(a), which displays the similar change tendency between ZFC and FC curves, Co1 xCuxCr2O4 samples present apparent differences in ZFC and FC curves. This behavior can be well explained by the presence of non-collinear moments with doping Cu. Those moments are under
156
C.M. Zhu et al. / Materials Letters 182 (2016) 155–158
the influence of strong magnetocrystalline anisotropic field. So, low cooling field is not strong enough to completely orient the moments to spin configuration with the lowest energy. Except for
Co0.725Cu0.275Cr2O4, with lowering temperature from ferrimagnetic transition, FC magnetization rises sharply, goes through a maximum (Mmax) at 75 K and then drops down. Especially at
Fig. 1. XRD patterns of Co1 xCuxCr2O4 ceramics.
Fig. 3. Evolution of Tcomp with x. Upper inset is Mmax variation with x. Lower inset is the relative intensity change of negative magnetization as Cu increases.
Fig. 2. Temperature dependent magnetization in ZFC and FC processes.
C.M. Zhu et al. / Materials Letters 182 (2016) 155–158
157
Fig. 4. Temperature dependent magnetization in ZFC and FC processes with different cooling fields. Inset of Fig. 4(a) is a mirror-like behavior in FC curves. Inset of (c) is Tcomp evolution with cooling field. Inset of (d) is Mmin evolution with cooling field.
0.125 rx r0.25, FC magnetization passes through zero value at compensation temperature (Tcomp). Then, it takes on negative value with the minimum (Mmin) at 25 K. The negative value signifies the direction of moments is antiparallel to that of applied field. That is, negative magnetization can be generated in Co1 xCuxCr2O4. Moreover, negative value in ZFC magnetization is due to the uncompensated spins at grain boundaries of polycrystalline Co1 xCuxCr2O4. In order to see negative magnetization characteristics clearly, we plots the parameter change with increasing Cu in Fig. 3. Upper inset is Mmax variation with x, which presents monotonous decrease with increasing Cu. The main figure shows that Tcomp increases from 33.8 K of x ¼0.125 to 56.9 K of x¼ 0.225 and then decreases to 55.6 K of x ¼0.25. Lower inset is the relative intensity change of negative magnetization (|Mmax/Mmin|), which can act as the index of negative magnetization behavior. Similarly, it is enhanced from x¼0.125 to 0.225 and then weakened at x ¼0.25. That is, negative magnetization starts at x¼ 0.125, obtains the most distinct phenomenon at x ¼0.225 and finally disappears at x¼ 0.275 with increasing Cu. CoCr2O4 does not show negative magnetization. Doping Cu does not induce structure transition, either. So, negative magnetization should be mainly related to the destroyed stability of magnetic structure in Co1 xCuxCr2O4. According to previous studies, it can be explained based on two-sublattice model [4]. Cations occupied A sites with ferromagnetic interaction are formed to AO4 tetrahedral sublattices (A sublattices) and those occupied B sites with antiferromagnetic interaction are formed to BO6 octahedral sublattices (B sublattices). Cu2 þ and Co2 þ are randomly distributed in A sites. Cu2 þ can induce magnetic structure change
from two aspects. On the one hand, the spin-only value of Cu2 þ is lower than that of Co2 þ . The decreased spin-only value in A sites not only weakens the moments parallel to field direction exhibiting the decreasing Mmax, but also makes it possible that antiferromagnetic interaction can have impact on the weakened ferromagnetic interaction. In accordance with the theory about different temperature dependence of sublattices [5], Co2 þ and Cu2 þ spins are oriented along field direction at higher temperature than Cr3 þ spins which order gradually with moments antiparallel to field direction during FC process. So, ferromagnetic interaction is enhanced earlier than antiferromagnetic interaction. Whereas, B sublattice interaction is usually stronger than A sublattices indicating the moments antiparallel to field direction can be dominating with decreasing temperature. Thus, the sum of FC magnetization is positive and then decreases to negative through Tcomp. However, the change of negative magnetization is not consistent with increasing Cu. We speculate that the other reason is the relative angle change. According to bulk configuration of Cr3 þ and Cu2 þ moments [6], the relative angle is between Cr cations. For balance of magnetic structure, Cu2 þ with lower moments will increase the angle in Co1 xCuxCr2O4. So, negative moments in B sublattices are weakened. Co0.9Cu0.1Cr2O4 without negative magnetization means that the decreased negative moments because of increasing angle are much more than decreased positive moments due to lower moments of Cu2 þ . At 0.125 rxr 0.225, relative angle continues to increase but the corresponding decrease in negative moments is slow. Lower moments of Cu2 þ have main influence on sum magnetization. Thus, with decreasing temperature, negative moments are larger than
158
C.M. Zhu et al. / Materials Letters 182 (2016) 155–158
positive moments presenting the stronger negative magnetization. Exceeding this content range, the decreased negative moments are more evident than the decrease in positive moments. So, negative magnetization is weakened again and finally disappears. Tcomp is the temperature at which negative moments are equal to positive ones. The consistent change between Tcomp and |Mmax/Mmin| is in that the enhanced negative magnetization is easier to obtain at higher temperature. The results also prove that x ¼0.225 is a special content with outstanding negative magnetization. Fig. 4 shows ZFC and FC curves under different cooling fields of Co0.775Cu0.225Cr2O4. Magnetization becomes negative below Tcomp. A mirror-like behavior is observed in FC curves under H¼ 7 1000 Oe in inset of Fig. 4(a), which also testifies the sum magnetization is opposite to field direction. With increasing field, Tcomp presents monotonous decrease from H¼1000 Oe to 11 kOe and disappears at 12 kOe in inset of Fig. 4(c). In inset of Fig. 4(d), absolute value of Mmin (|Mmin|) increases at 1000 OerH r3000 Oe and then decreases with further increasing field. Finally, negative value turns to positive at H ¼12 kOe. With Hr3000 Oe, both positive and negative moments are enhanced, but the field is too low to change moment direction in B sublattices. So, difference between the two moments is increased showing an increasing |Mmin|. Further increasing field, it is high enough to reverse parts of negative moments to field direction, thus the sum of negative magnetization is decreased and finally turns to positive. The monotonous relationship between Tcomp and applied field is attributed to the enhanced positive moment in A sublattices with increasing field, which needs more negative moments to offset it. Therefore, negative magnetization appears at lower temperature with increasing applied field.
4. Conclusions Negative magnetization is observed in Co1 xCuxCr2O4 ceramics presenting the evident dependence on the doping content of Cu. It is enhanced from x¼ 0.125 to 0.225 and then decreases with Cu
increasing. At x ¼0.225, Tcomp is monotonously decreased with increasing applied field. |Mmin| is increased at low field, then decreased and finally Mmin turns to positive with field increasing. We explain the negative magnetization through two-sublattice model. With doping Cu, the decreased moments in A sublattices and the changed relative angle in magnetic structure give rise to different dependence on temperature of two kinds of sublattices. These findings accentuate meaningful fundamental physics for information storage. Moreover, negative magnetization behavior can be helpful to Co1 xCuxCr2O4 on the potential applications in spintronics devices with the optional magnetization direction.
Acknowledgments This work was supported by National Natural Science Foundation of China (Grant no. 11474111). We also thank the staff of Analysis Center of HUST for their assistance in various measurements.
References [1] S. More, R. Kadam, A. Kadam, D. Mane, G. Bichile, Structural properties and magnetic interactions in Al3 þ and Cr3 þ co-substituted CoFe2O4 ferrite, Cent. Eur. J. Chem. 8 (2010) 419–425. [2] K. Yoshii, Magnetization reversal in TmCrO3, Mater. Res. Bull. 47 (2012) 3243–3248. [3] L.G. Wang, C.M. Zhu, H. Luo, S.L. Yuan, Studies on room temperature multiferroic properties of xBi0.5Na0.5TiO3-(1 x)NiFe2O4 ceramics, J. Electroceram. 35 (2015) 59–67. [4] Y.J. Choi, J. Okamoto, D.J. Huang, K.S. Chao, H.J. Lin, C.T. Chen, M. van Veenendaal, T.A. Kaplan, S.-W. Cheong, Thermally or magnetically induced polarization reversal in the multiferroic CoCr2O4, Phys. Rev. Lett. 102 (2009) 067601. [5] Y.L. Su, J.C. Zhang, Z.J. Feng, L. Li, B.Z. Li, Y. Zhou, Z.P. Chen, S.X. Cao, Magnetization reversal and Yb3 þ /Cr3 þ spin ordering at low temperature for perovskite YbCrO3 chromites, J. Appl. Phys. 108 (2010) 013905. [6] J.M. Iwata, R.V. Chopdekar, F.J. Wong, B.B. Nelson-Cheeseman, E. Arenholz, Y. Suzuki, Enhanced magnetization of CuCr2O4 thin films by substrate-induced strain, J. Appl. Phys. 105 (2009) 07A905.