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Magnetic structure of a spinel system Cu0.3Zn0.7Cr2Se4
ARTICLE IN PRESS
Journal of Magnetism and Magnetic Materials 272–276 (2004) 473–474
Magnetic structure of a spinel system Cu0.3Zn0.7Cr2Se4 Satoshi Iikuboa,*, Yukio Yasuia, Yoshiaki Kobayashia, Youhei Ohnoa, Masafumi Itoa, Minoru Sodaa, Masatoshi Satoa, Kazuhisa Kakuraib a
Department of Physics, Nagoya University, Furocho, Chikusa-ku, Nagoya, Japan b Advanced Science Reserch Center, JAERI, Tokai, Ibaraki, Japan
Abstract Neutron diffraction and NMR studies have been carried out on single crystal samples of a spinel system Cu0.3Zn0.7Cr2Se4, which exhibits unusual behavior of the anomalous Hall resistivity. It is confirmed that the structure is conical and the detailed values of the parameters to characterize the structure are given. r 2003 Elsevier B.V. All rights reserved. PACS: 61.12.q; 61.12.q; 75.25.+z; 76.60.k Keywords: Spinel-type system Cu1xZnxCr2Se4; Conical spin structure; Neutron diffraction; NMR
1. Introduction
2. Results and discussion
There exists much interest in anomalous Hall effect of systems with non-trivial magnetic structure [1–6,8]. The spinel compound Cu1xZnxCr2Se4 is one of such systems. At x=0, it is a collinear ferromagnet with Curie temperature TCB450 K, and at x=1 it has a helical structure with the Ne! el temperature TN=20 K. In the intermediate region of x, the structure seems to be conical [7,8]. The anomalous Hall coefficient Rs observed in this intermediate region changes its sign at around TmB100 K, where magnetic superlattice peaks become appreciable and their intensities gradually grow with decreasing T, indicating the growth of the conical magnetic order [5,8]. The behavior of the Hall resistivity rH of this system has been discussed in relation to the order of the spin chirality w, which is locally defined as wS1 (S2 S3) for three spins S1, S2 and S3 [5,6,8]. In order to accumulate further information on the relationship between w and the behavior of rH, neutron diffraction and NMR have been carried out on single crystal specimens of Cu0.3Zn0.7Cr2Se4. In the present report, its magnetic structure is clarified in detail, based on results of above two kinds of experimental data.
Neutron measurements were carried out on the triple axis spectrometer at T1-1 at JRR-3 M of JAERI in Tokai. The double axis configuration was utilized. The effective collimations were 170 –400 –600 . The Curie temperature TC of the single crystal is B350 K. Data of the integrated intensities of the nuclear reflections were collected at 450 K. Intensity data of the magnetic reflections at (0,0,Q0), (1,1,1Q0) and (1,1,1+Q0), for example, in the reciprocal space, were collected at 3.5 K and used in the present analyses, where Q0 has the incommensurate (IC) value of B0.4282 in the reciprocal lattice unit. The intensity of the 111 magnetic reflection at 3.5 K, estimated by subtracting the weak nuclear intensity at 450 K has also been used. Zero field NMR spectra of Cr nuclei have also been taken at 4.2 K by measuring the spin echo intensity by changing the frequency stepwise and the result are shown in Fig. 1. To clarify detailed characteristics of the magnetic structure, we have to consistently explain these neutron- and NMR-data. We adopt the conical spin structure with the tilting angle y from the conical axis (conical angle) and the difference df of the azimuthal angles between the neighboring planes perpendicular to the propagation vector Q0. (All spins within a plane perpendicular to Q0 are assumed to be parallel. Note that Q0 is not necessarily parallel, as shown later, but can be perpendicular to the conical axis.) The value of
*Corresponding author. Tel.: +81-52-789-2853; fax: +8152-789-2953. E-mail addresses: [email protected] (S. Iikubo), [email protected] (M. Sato).
0304-8853/$ - see front matter r 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2003.12.443
ARTICLE IN PRESS S. Iikubo et al. / Journal of Magnetism and Magnetic Materials 272–276 (2004) 473–474
474
105
Cu0.3Zn0.7Cr2Se4 0.2
Cu0.3Zn0.7Cr2Se4 3.5K
aligned crystals 4.8 K 104
0.15
|F
exp.
|2
0=50degree 0=30degree
0.1
1000
µ =1.43µ
0.05
µ =1.76µ
53
Cr-NMR spin-echo intensity/f 2 (a.u)
0.25
f
δφ=38
0 34
36
38
40
42
f (MHz)
Fig. 1. 53Cr-NMR spectrum taken at 4.2 K for a single crystal sample with x=0.7. Observed data (dots) and calculated data with the conical angle y=50 (solid line) and y=30 (dashed line) are shown.
df is determined to be 38 by the observed value of Q0. The NMR spectra shown in Fig. 1 are found to be roughly fitted within the model by using the y value of B50 (solid line in Fig. 1), if only we consider the uniaxial anisotropy of hyperfine field about the principal (or [1 1 1]) direction at Cr sites. The ferromagnetic component of the Cr moment, mfmCr cos y can be estimated to be B1.76 mB from the ratio of the intensity of the 1 1 1 magnetic reflection to those of the nuclear reflections and mCr(D1.76 mB/cos 50 )D2.74 mB is also obtained. The value of mCr is in rather good agreement with that (B2.85 mB) expected from the valence analysis. In the estimation of the intensities of the IC reflections, we have to consider that there exist two kinds of conical structures with the same propagation vector Q0 and equal values of y and df, but different directions of the conical axes: For one of them, the conical axis is parallel to Q0 and for another, it is perpendicular to Q0. Assuming the equal distribution of these structures, the intensities, which are proportional to the square of m>mCr sin y are deduced and from these ratios to the intensities of the nuclear reflections, m> is obtained to be B1.43 mB, which should be compared with the value 2.74 mB sin 50 =2.1 mB expected from the values of mCr and y. Before discussing this discrepancy, we plot the observed and calculated magnetic structure factors Fexp and Fcal, respectively, in the form of 9Fexp.92 9Fcal.92, where Fcal are obtained for m>=1.43 mB. The points for the IC reflections are roughly on the straight line, indicating that the conical model adopted here is appropriate Fig. 2. As the origin of the discrepancy between the values of m> independently estimated by two different data, the
100 100
104
1000
B
B
o
105
2
|Fcal.|
Fig. 2. 9Fexp.92 of the IC reflections (solid circles) obtained from the integrated intensities are plotted against 9Fcal.92 calculated by the conical model with the parameters m>=1.43 mB. The value of df=38 , respectively. The open circle shows the Value for the 111 magnetic reflection, where 9Fcal.92 is calculated with mf=1.76 mB. See text for details.
random distribution of df around 38 is plausible, because distribution with very small width (of the order 3 ) is enough to bring about the observed reduction of the intensities of the IC reflections. Detailed magnetic structure of Cu0.3Zn0.7Cr2Se4 has been presented. The magnetic field dependence of the spin structure is also being studied. We hope that results of these studies give detailed clues to understand the relationship between the non-trivial magnetic structure and the unusual behavior of the Hall resistivity.
References [1] S. Yoshii, S. Iikubo, T. Kageyama, K. Oda, Y. Kondo, K. Murata, M. Sato, J. Phys. Soc. Jpn. 69 (2000) 3777. [2] S. Iikubo, S. Yoshii, T. Kageyama, K. Oda, Y. Kondo, K. Murata, M. Sato, J. Phys. Soc. Jpn. 70 (2001) 212. [3] Y. Taguchi, Y. Oohara, H. Yoshizawa, N. Nagaosa, Y. Tokura, Science 291 (2001) 2573. [4] Y. Yasui, Y. Kondo, M. Kanada, M. Ito, H. Harashina, M. Sato, K. Kakurai, J. Phys. Soc. Jpn. 69 (2000) 284. [5] K. Oda, S. Yoshii, Y. Yasui, M. Ito, T. Ido, Y. Ohno, Y. Kobayashi, M. Sato, J. Phys. Soc. Jpn. 70 (2001) 2999. [6] K. Ohgushi, S. Murakami, N. Nagaosa, Phys. Rev. B 62 (2000) R6065. [7] J. Krok, S. Juszczyk, J. Warczewski, T. Mydlarz, W. Szamraj, A. Bombik, P. Byszewski, J. Spalek, Phase Transit 4 (1983) 1. [8] S. Iikubo, Y. Yasui, K. Oda, Y. Ohno, Y. Kobayashi, M. Sato, K. Kakurai, J. Phys. Soc. Jpn. 71 (2002) 2792.
Journal of Magnetism and Magnetic Materials 272–276 (2004) 473–474
Magnetic structure of a spinel system Cu0.3Zn0.7Cr2Se4 Satoshi Iikuboa,*, Yukio Yasuia, Yoshiaki Kobayashia, Youhei Ohnoa, Masafumi Itoa, Minoru Sodaa, Masatoshi Satoa, Kazuhisa Kakuraib a
Department of Physics, Nagoya University, Furocho, Chikusa-ku, Nagoya, Japan b Advanced Science Reserch Center, JAERI, Tokai, Ibaraki, Japan
Abstract Neutron diffraction and NMR studies have been carried out on single crystal samples of a spinel system Cu0.3Zn0.7Cr2Se4, which exhibits unusual behavior of the anomalous Hall resistivity. It is confirmed that the structure is conical and the detailed values of the parameters to characterize the structure are given. r 2003 Elsevier B.V. All rights reserved. PACS: 61.12.q; 61.12.q; 75.25.+z; 76.60.k Keywords: Spinel-type system Cu1xZnxCr2Se4; Conical spin structure; Neutron diffraction; NMR
1. Introduction
2. Results and discussion
There exists much interest in anomalous Hall effect of systems with non-trivial magnetic structure [1–6,8]. The spinel compound Cu1xZnxCr2Se4 is one of such systems. At x=0, it is a collinear ferromagnet with Curie temperature TCB450 K, and at x=1 it has a helical structure with the Ne! el temperature TN=20 K. In the intermediate region of x, the structure seems to be conical [7,8]. The anomalous Hall coefficient Rs observed in this intermediate region changes its sign at around TmB100 K, where magnetic superlattice peaks become appreciable and their intensities gradually grow with decreasing T, indicating the growth of the conical magnetic order [5,8]. The behavior of the Hall resistivity rH of this system has been discussed in relation to the order of the spin chirality w, which is locally defined as wS1 (S2 S3) for three spins S1, S2 and S3 [5,6,8]. In order to accumulate further information on the relationship between w and the behavior of rH, neutron diffraction and NMR have been carried out on single crystal specimens of Cu0.3Zn0.7Cr2Se4. In the present report, its magnetic structure is clarified in detail, based on results of above two kinds of experimental data.
Neutron measurements were carried out on the triple axis spectrometer at T1-1 at JRR-3 M of JAERI in Tokai. The double axis configuration was utilized. The effective collimations were 170 –400 –600 . The Curie temperature TC of the single crystal is B350 K. Data of the integrated intensities of the nuclear reflections were collected at 450 K. Intensity data of the magnetic reflections at (0,0,Q0), (1,1,1Q0) and (1,1,1+Q0), for example, in the reciprocal space, were collected at 3.5 K and used in the present analyses, where Q0 has the incommensurate (IC) value of B0.4282 in the reciprocal lattice unit. The intensity of the 111 magnetic reflection at 3.5 K, estimated by subtracting the weak nuclear intensity at 450 K has also been used. Zero field NMR spectra of Cr nuclei have also been taken at 4.2 K by measuring the spin echo intensity by changing the frequency stepwise and the result are shown in Fig. 1. To clarify detailed characteristics of the magnetic structure, we have to consistently explain these neutron- and NMR-data. We adopt the conical spin structure with the tilting angle y from the conical axis (conical angle) and the difference df of the azimuthal angles between the neighboring planes perpendicular to the propagation vector Q0. (All spins within a plane perpendicular to Q0 are assumed to be parallel. Note that Q0 is not necessarily parallel, as shown later, but can be perpendicular to the conical axis.) The value of
*Corresponding author. Tel.: +81-52-789-2853; fax: +8152-789-2953. E-mail addresses: [email protected] (S. Iikubo), [email protected] (M. Sato).
0304-8853/$ - see front matter r 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2003.12.443
ARTICLE IN PRESS S. Iikubo et al. / Journal of Magnetism and Magnetic Materials 272–276 (2004) 473–474
474
105
Cu0.3Zn0.7Cr2Se4 0.2
Cu0.3Zn0.7Cr2Se4 3.5K
aligned crystals 4.8 K 104
0.15
|F
exp.
|2
0=50degree 0=30degree
0.1
1000
µ =1.43µ
0.05
µ =1.76µ
53
Cr-NMR spin-echo intensity/f 2 (a.u)
0.25
f
δφ=38
0 34
36
38
40
42
f (MHz)
Fig. 1. 53Cr-NMR spectrum taken at 4.2 K for a single crystal sample with x=0.7. Observed data (dots) and calculated data with the conical angle y=50 (solid line) and y=30 (dashed line) are shown.
df is determined to be 38 by the observed value of Q0. The NMR spectra shown in Fig. 1 are found to be roughly fitted within the model by using the y value of B50 (solid line in Fig. 1), if only we consider the uniaxial anisotropy of hyperfine field about the principal (or [1 1 1]) direction at Cr sites. The ferromagnetic component of the Cr moment, mfmCr cos y can be estimated to be B1.76 mB from the ratio of the intensity of the 1 1 1 magnetic reflection to those of the nuclear reflections and mCr(D1.76 mB/cos 50 )D2.74 mB is also obtained. The value of mCr is in rather good agreement with that (B2.85 mB) expected from the valence analysis. In the estimation of the intensities of the IC reflections, we have to consider that there exist two kinds of conical structures with the same propagation vector Q0 and equal values of y and df, but different directions of the conical axes: For one of them, the conical axis is parallel to Q0 and for another, it is perpendicular to Q0. Assuming the equal distribution of these structures, the intensities, which are proportional to the square of m>mCr sin y are deduced and from these ratios to the intensities of the nuclear reflections, m> is obtained to be B1.43 mB, which should be compared with the value 2.74 mB sin 50 =2.1 mB expected from the values of mCr and y. Before discussing this discrepancy, we plot the observed and calculated magnetic structure factors Fexp and Fcal, respectively, in the form of 9Fexp.92 9Fcal.92, where Fcal are obtained for m>=1.43 mB. The points for the IC reflections are roughly on the straight line, indicating that the conical model adopted here is appropriate Fig. 2. As the origin of the discrepancy between the values of m> independently estimated by two different data, the
100 100
104
1000
B
B
o
105
2
|Fcal.|
Fig. 2. 9Fexp.92 of the IC reflections (solid circles) obtained from the integrated intensities are plotted against 9Fcal.92 calculated by the conical model with the parameters m>=1.43 mB. The value of df=38 , respectively. The open circle shows the Value for the 111 magnetic reflection, where 9Fcal.92 is calculated with mf=1.76 mB. See text for details.
random distribution of df around 38 is plausible, because distribution with very small width (of the order 3 ) is enough to bring about the observed reduction of the intensities of the IC reflections. Detailed magnetic structure of Cu0.3Zn0.7Cr2Se4 has been presented. The magnetic field dependence of the spin structure is also being studied. We hope that results of these studies give detailed clues to understand the relationship between the non-trivial magnetic structure and the unusual behavior of the Hall resistivity.
References [1] S. Yoshii, S. Iikubo, T. Kageyama, K. Oda, Y. Kondo, K. Murata, M. Sato, J. Phys. Soc. Jpn. 69 (2000) 3777. [2] S. Iikubo, S. Yoshii, T. Kageyama, K. Oda, Y. Kondo, K. Murata, M. Sato, J. Phys. Soc. Jpn. 70 (2001) 212. [3] Y. Taguchi, Y. Oohara, H. Yoshizawa, N. Nagaosa, Y. Tokura, Science 291 (2001) 2573. [4] Y. Yasui, Y. Kondo, M. Kanada, M. Ito, H. Harashina, M. Sato, K. Kakurai, J. Phys. Soc. Jpn. 69 (2000) 284. [5] K. Oda, S. Yoshii, Y. Yasui, M. Ito, T. Ido, Y. Ohno, Y. Kobayashi, M. Sato, J. Phys. Soc. Jpn. 70 (2001) 2999. [6] K. Ohgushi, S. Murakami, N. Nagaosa, Phys. Rev. B 62 (2000) R6065. [7] J. Krok, S. Juszczyk, J. Warczewski, T. Mydlarz, W. Szamraj, A. Bombik, P. Byszewski, J. Spalek, Phase Transit 4 (1983) 1. [8] S. Iikubo, Y. Yasui, K. Oda, Y. Ohno, Y. Kobayashi, M. Sato, K. Kakurai, J. Phys. Soc. Jpn. 71 (2002) 2792.