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Comparative NMR study of incommensurate helix magnetic order in quasi-1D chain cuprates LiCu2O2 and NaCu2O2
ARTICLE IN PRESS
Journal of Magnetism and Magnetic Materials 316 (2007) 298–301 www.elsevier.com/locate/jmmm
Comparative NMR study of incommensurate helix magnetic order in quasi-1D chain cuprates LiCu2O2 and NaCu2O2 A.A. Gippiusa,b,c,, E.N. Morozovab,c, K.S. Okhotnikovb, A.S. Moskvind, M. Baenitza, S. Drechslere a
Max-Planck-Institute of Chemical Physics of Solids, Dresden D-01187, Germany b Faculty of Physics, Moscow State University, Moscow 119992, Russia c Institute of Crystallography RAS, Moscow 117333, Russia d Ural State University, Ekaterinburg 620083, Russia e Leibnitz-Institut for Solid State Research, Dresden D-01171, Germany Available online 6 March 2007
Abstract NMR and NQR investigations on the complex magnetic structure in the ordered state as well as phase transitions in two isostructural quasi-1D edge-shared cuprates LiCu2O2 and NaCu2O2 have been performed. While LiCu2O2 exhibits a magnetic phase transition at Tc ¼ 24 K, NaCu2O2 orders magnetically at around 13 K. 6,7Li and 23Na NMR spectra in LiCu2O2 and NaCu2O2, respectively, provide an unambiguous experimental evidence that below Tc an incommensurate in-chain helical spin structure is established in both compounds. However, the features of the observed low-temperature NMR and NQR spectra are different pointing to different properties of the helical magnetic structure. r 2007 Elsevier B.V. All rights reserved. PACS: 76.60.Jx; 76.60.k Keywords: 1D spin chain; Incommensurate magnetic order; Helix spin structure; NMR; NQR
1. Introduction Low-dimensional frustrated quantum spin system attracted much attention during the last years (see e.g. Ref. [1]). A particular case of interest are the spin 12 chains with strong in-chain frustration caused by different signs of the nearest neighbor (NN) and next-nearest-neighbor (NNN) in-chain exchange integrals. One of the recently discovered examples of such system are the isostructural quasi-1D cuprates LiCu2O2 and NaCu2O2 with ferromagnetic (FM) NN and strong antiferromagnetic (AFM) NNN in-chain interaction [2–5]. Both compounds are isolators with orthorhombic crystal structure containing bilayers of Corresponding author. Max-Planck-Institute of Chemical Physics of Solids, Dresden D-01187, Germany. E-mail address: [email protected] (A.A. Gippius).
0304-8853/$ - see front matter r 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2007.02.139
edge-shared CuO2 chains running parallel to the b-axis (Fig. 1). Li atoms are situated in between two neighboring CuO2 chains in the (ab)-plane also forming LiO2 chains along b-axis (not shown in Fig. 1). LiCu2O2 exhibits magnetic phase transition at Tc ¼ 24 K when the incommensurate (IC) helical magnetic spin structure is established as evidenced by NMR [4] and neutron scattering [6,7]. The larger ionic radius of Na1+ (0.97 A˚ against 0.68 A˚ of 1+ Li ) favors the higher degree of in-chain crystallographic order and hence increasing one dimensionality of the magnetic properties in NaCu2O2. This results in a lower magnetic ordering temperature Tc ¼ 12.6 K [5] and lower values of local magnetic fields in the ordered state. In this paper, we report the results of 23Na NMR and 63,65Cu NQR measurements in NaCu2O2 and compare them with 63,65Cu NQR and our previous results on 6,7Li NMR in LiCu2O2 [4,8].
ARTICLE IN PRESS A.A. Gippius et al. / Journal of Magnetism and Magnetic Materials 316 (2007) 298–301
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crystal shows no twinning and has no deviation from the ideal stoichiometry as confirmed by X-ray and TGA analysis. 23Na and 7Li NMR measurements were performed at several temperatures in the paramagnetic and in the ordered phases of both compounds. All three principal orientations of the external magnetic field with respect to the crystallographic axes: HJa, b and c were used. The standard pulsed field-sweep NMR technique was applied at fixed frequency of 33.7 MHz for LiCu2O2 and 46.0 MHz for NaCu2O2.
2. Experiment Single crystals of LiCu2O2 and NaCu2O2 were synthesized according to the procedure described in Ref. [4]. The quality of the new NaCu2O2 crystal was much better than that used in our preliminary NMR measurements reported in Ref. [8]. In contrast to LiCu2O2, the NaCu2O2 single
3. Results and discussion In Fig. 2, we present the characteristic NMR spectra of Li in LiCu2O2 and 23Na in NaCu2O2 measured both above and below magnetic ordering temperature Tc for orientation of the external magnetic field HJc. To make the comparison more convenient, we use the same scaling of magnetic field in both panels. Above Tc in LiCu2O2 and NaCu2O2 typical first-order quadrupole perturbed NMR spectra for spin I ¼ 32 nuclei are observed. The quadrupole splitting between the satellites in NaCu2O2 is about 200 mT, while in LiCu2O2 it is about 10 mT. Since the ratio of quadrupole moments Q(23Na)/Q(7Li) ¼ 2.7, this large quadrupole splitting ratio means that the electric field gradient (EFG) at Na site in NaCu2O2 is almost an order of magnitude higher than the EFG at Li sites in LiCu2O2. This result reflects an enhanced role of EFG polarization effect on Na1+ as compared with Li1+, which has only weakly polarizable 1s2 shell. 7
Fig. 1. Schematic presentation of the double CuO2 chain structure in LiCu2O2.
1.8 T = 4.2 K
1.6
T = 12.6 K
1.2 1.0 0.8
-3/2 - 1/2
0.4 0.2 0.0
1.8
1.9
2.0 H (T)
2.1
2.2
3.9
4.0
4.1 H (T)
1/2 - 3/2
T = 13.5 K
T = 45 K
0.6
-1/2 - 1/2
Intensity (arb. units)
1.4
4.2
4.3
Fig. 2. 7Li (a) and 23Na (b) NMR spectra measured above Tc (bottom spectra) and below Tc (upper spectra) for HJc in LiCu2O2 and NaCu2O2 single crystals at 33.7 and 46.0 MHz, respectively. The 23Na transitions are labeled near the corresponding lines.
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Below magnetic ordering temperature Tc, the spectra of both compounds exhibit a dramatic change. The spectra are characteristic of IC static modulation of the local magnetic field caused by helical spin structure of Cu moments [4,8,9]. It is worth mentioning that the phase transition at Tc is much narrower in NaCu2O2 than in LiCu2O2. As seen in Fig. 1(b), the formation of IC field modulation in NaCu2O2 occurs within 0.6 K while in LiCu2O2 it takes more than 2 K [4]. The asymmetric van Hove singularities of 23Na NMR central transition line are very sharp and are clearly visible also on satellite transitions, which in contrast to LiCu2O2 are well separated due to the larger EFG. The lineshape of the satellite transitions follows the distribution of the Larmor frequency caused by IC local field modulation. Therefore, in the first-order quadrupole perturbation the satellite lineshape is almost the exact copy of the central transition profile. The most striking difference between 7Li and 23Na spectra is that in NaCu2O2 the doublets (or degenerated quartets) are observed for all three principal orientations of external magnetic field in the magnetically ordered state. For HJa the intensities of both parts of the doublets are equal while for HJc the high-field component of the doublet is more intensive. This anisotropy becomes more significant with decreasing temperature. The splitting is almost symmetric with respect to the central field determined as the resonance field of the central transition above Tc. These results are completely unlike the situation in LiCu2O2 where the 7Li NMR quartet and sextet are observed for HJc (Fig. 2a) and HJ(a, b) [4]. The possible reason for such dissimilar behavior could be the influence of non-magnetic Li defects in CuO2 chains of LiCu2O2. Due to AF character of NNN interaction both the helix phase angles, y and j, exhibit a step-like change on p in the vicinity of Li defect. This phenomenon will be analyzed in more detail elsewhere. It is worth noting that the value of the local magnetic field on Na site estimated as the linewidth at the base of the central transition for HJc is only 80 mT, which is a factor of 3 less than that for Li (250 mT). This is quite reasonable since the transition temperature in NaCu2O2 is lower than in LiCu2O2 pointing to a weaker inter-chain interaction in NaCu2O2. The difference in crystal structure peculiarities of the two compounds is reflected in their NQR properties. Fig. 3 shows the NQR spectra of NaCu2O2 and LiCu2O2 measured above Tc on 63,65Cu nuclei in Cu(2) site. The right and left lines of each pair are assigned to the 63Cu and the 65Cu isotopes, respectively. The observed frequency and intensity ratios correspond to ratios of isotope quadrupole moments and natural abundancies, respectively. In the following, we will concentrate only on 63Cu isotope NQR lines for convenience. From Fig. 3 it is clearly seen that in NaCu2O2 the NQR linewidth is a factor of 3 smaller than that in LiCu2O2. This result reflects more homogeneous EFG distribution as a consequence of higher degree of structural
1.0 LiCuO2 T2=30 K NaCu2O2 T=77 K
0.8
0.6
0.4
0.2
0.0 24
25
26
27
28
29
F (MHz) Fig. 3. NQR spectra of NaCu2O2 (black open circles) and LiCu2O2 (red filled squares) measured above Tc on 63,65Cu nuclei in Cu(2) site.
order in NaCu2O2. Probably for the same reason, we succeeded to find another 63Cu line at 26.8 MHz originated from the Cu(1) position. It should be noted that the 63Cu line at around 27 MHz has been observed earlier on the polycrystalline LiCu2O2 sample in Ref. [10], but it was falsely assigned to the Cu(1) position. In this case, the line should exist also below Tc which contradicts with our experimental findings described below. All lines shown in Fig. 3 completely disappear below Tc. Instead, in LiCu2O2 we observed very complicated 63,65Cu antiferromagnetic resonance (AFMR) spectrum at 4.2 K. This effect is caused by the space modulated internal magnetic field at the Cu(2) site in the ordered state of LiCu2O2. For yet unknown reason we did not find any copper AFMR spectrum in NaCu2O2. At the same time, the Cu(1) NQR line at 26.8 MHz exists even below Tc, as expected for non-magnetic Cu+ ion at the Cu(1) site which is symmetric with respect to magnetic Cu2+ ions in the CuO2 chains. Therefore, the complete cancellation of local magnetic field occurs at Cu(1) site in the ordered state of NaCu2O2. In conclusion, 7Li and 23Na NMR spectra measured in the magnetically ordered state of the isostructural quasi-1D oxides LiCu2O2 and NaCu2O2 give unambiguous evidence for static IC modulation of local magnetic fields at the Li and the Na sites, respectively. This modulation is caused by a helical spin structure of Cu moments below Tc. Due to the crystal structure peculiarities, the character of the magnetic helix is dissimilar in both compounds reflecting both in NMR and NQR spectra. Acknowledgments We appreciate support by the Grants RFBR 05-0217719-a, MK-1212.2005.2 and CRDF RU-P1-2599MO-04.
ARTICLE IN PRESS A.A. Gippius et al. / Journal of Magnetism and Magnetic Materials 316 (2007) 298–301
References [1] U. Schollwo¨ck, J. Richter, D.J.J. Farnell, R.F. Bishop (Eds.), Quantum Magnetism, Lecture Notes on Physics, vol. 645, Springer, Berlin, 2004. [2] R. Berger, P. O¨nnerud, R. Tellgren, J. Alloys Compds. 184 (1992) 315. [3] D.A. Zatsepin, V.R. Galakhov, M.A. Korotin, V.V. Fedorenko, E.Z. Kurmaev, S. Bartkowski, M. Neumann, R. Berger, Phys. Rev. B 57 (1998) 4377. [4] A.A. Gippius, E.N. Morosova, A.S. Moskvin, A.V. Zalessky, A.A. Bush, M. Baenitz, H. Rosner, S.-L. Drechsler, Phys. Rev. B 70 (2004) 020406. [5] L. Capogna, M. Mayr, P. Horsch, M. Raichle, R.K. Kremer, M. Sofin, A. Maljuk, M. Jansen, B. Keimer, Phys. Rev. B 71 (2005) 140402(R).
301
[6] T. Masuda, A. Zheludev, A. Bush, M. Markina, A. Vasiliev, Phys. Rev. Lett. 92 (2004) 177201. [7] T. Masuda, A. Zheludev, B. Roessli, A. Bush, M. Markina, A. Vasiliev, Phys. Rev. B 72 (2005) 014405. [8] A.A. Gippius, E.N. Morozova, A.S. Moskvin, S.-L. Drechsler, M. Baenitz, J. Magn. Magn. Mater. 300 (2006) e335. [9] S.-L. Drechsler, J. Richter, A.A. Gippius, A.N. Vasiliev, A.A. Bush, A.S. Moskvin, J. Malek, Yu. Protz, W. Shnelle, H. Rosner, Europhys. Lett. 73 (2006) 83. [10] F.C. Fritschij, H.B. Brom, R. Berger, Solid State Commun. 107 (1998) 719.
Journal of Magnetism and Magnetic Materials 316 (2007) 298–301 www.elsevier.com/locate/jmmm
Comparative NMR study of incommensurate helix magnetic order in quasi-1D chain cuprates LiCu2O2 and NaCu2O2 A.A. Gippiusa,b,c,, E.N. Morozovab,c, K.S. Okhotnikovb, A.S. Moskvind, M. Baenitza, S. Drechslere a
Max-Planck-Institute of Chemical Physics of Solids, Dresden D-01187, Germany b Faculty of Physics, Moscow State University, Moscow 119992, Russia c Institute of Crystallography RAS, Moscow 117333, Russia d Ural State University, Ekaterinburg 620083, Russia e Leibnitz-Institut for Solid State Research, Dresden D-01171, Germany Available online 6 March 2007
Abstract NMR and NQR investigations on the complex magnetic structure in the ordered state as well as phase transitions in two isostructural quasi-1D edge-shared cuprates LiCu2O2 and NaCu2O2 have been performed. While LiCu2O2 exhibits a magnetic phase transition at Tc ¼ 24 K, NaCu2O2 orders magnetically at around 13 K. 6,7Li and 23Na NMR spectra in LiCu2O2 and NaCu2O2, respectively, provide an unambiguous experimental evidence that below Tc an incommensurate in-chain helical spin structure is established in both compounds. However, the features of the observed low-temperature NMR and NQR spectra are different pointing to different properties of the helical magnetic structure. r 2007 Elsevier B.V. All rights reserved. PACS: 76.60.Jx; 76.60.k Keywords: 1D spin chain; Incommensurate magnetic order; Helix spin structure; NMR; NQR
1. Introduction Low-dimensional frustrated quantum spin system attracted much attention during the last years (see e.g. Ref. [1]). A particular case of interest are the spin 12 chains with strong in-chain frustration caused by different signs of the nearest neighbor (NN) and next-nearest-neighbor (NNN) in-chain exchange integrals. One of the recently discovered examples of such system are the isostructural quasi-1D cuprates LiCu2O2 and NaCu2O2 with ferromagnetic (FM) NN and strong antiferromagnetic (AFM) NNN in-chain interaction [2–5]. Both compounds are isolators with orthorhombic crystal structure containing bilayers of Corresponding author. Max-Planck-Institute of Chemical Physics of Solids, Dresden D-01187, Germany. E-mail address: [email protected] (A.A. Gippius).
0304-8853/$ - see front matter r 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2007.02.139
edge-shared CuO2 chains running parallel to the b-axis (Fig. 1). Li atoms are situated in between two neighboring CuO2 chains in the (ab)-plane also forming LiO2 chains along b-axis (not shown in Fig. 1). LiCu2O2 exhibits magnetic phase transition at Tc ¼ 24 K when the incommensurate (IC) helical magnetic spin structure is established as evidenced by NMR [4] and neutron scattering [6,7]. The larger ionic radius of Na1+ (0.97 A˚ against 0.68 A˚ of 1+ Li ) favors the higher degree of in-chain crystallographic order and hence increasing one dimensionality of the magnetic properties in NaCu2O2. This results in a lower magnetic ordering temperature Tc ¼ 12.6 K [5] and lower values of local magnetic fields in the ordered state. In this paper, we report the results of 23Na NMR and 63,65Cu NQR measurements in NaCu2O2 and compare them with 63,65Cu NQR and our previous results on 6,7Li NMR in LiCu2O2 [4,8].
ARTICLE IN PRESS A.A. Gippius et al. / Journal of Magnetism and Magnetic Materials 316 (2007) 298–301
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crystal shows no twinning and has no deviation from the ideal stoichiometry as confirmed by X-ray and TGA analysis. 23Na and 7Li NMR measurements were performed at several temperatures in the paramagnetic and in the ordered phases of both compounds. All three principal orientations of the external magnetic field with respect to the crystallographic axes: HJa, b and c were used. The standard pulsed field-sweep NMR technique was applied at fixed frequency of 33.7 MHz for LiCu2O2 and 46.0 MHz for NaCu2O2.
2. Experiment Single crystals of LiCu2O2 and NaCu2O2 were synthesized according to the procedure described in Ref. [4]. The quality of the new NaCu2O2 crystal was much better than that used in our preliminary NMR measurements reported in Ref. [8]. In contrast to LiCu2O2, the NaCu2O2 single
3. Results and discussion In Fig. 2, we present the characteristic NMR spectra of Li in LiCu2O2 and 23Na in NaCu2O2 measured both above and below magnetic ordering temperature Tc for orientation of the external magnetic field HJc. To make the comparison more convenient, we use the same scaling of magnetic field in both panels. Above Tc in LiCu2O2 and NaCu2O2 typical first-order quadrupole perturbed NMR spectra for spin I ¼ 32 nuclei are observed. The quadrupole splitting between the satellites in NaCu2O2 is about 200 mT, while in LiCu2O2 it is about 10 mT. Since the ratio of quadrupole moments Q(23Na)/Q(7Li) ¼ 2.7, this large quadrupole splitting ratio means that the electric field gradient (EFG) at Na site in NaCu2O2 is almost an order of magnitude higher than the EFG at Li sites in LiCu2O2. This result reflects an enhanced role of EFG polarization effect on Na1+ as compared with Li1+, which has only weakly polarizable 1s2 shell. 7
Fig. 1. Schematic presentation of the double CuO2 chain structure in LiCu2O2.
1.8 T = 4.2 K
1.6
T = 12.6 K
1.2 1.0 0.8
-3/2 - 1/2
0.4 0.2 0.0
1.8
1.9
2.0 H (T)
2.1
2.2
3.9
4.0
4.1 H (T)
1/2 - 3/2
T = 13.5 K
T = 45 K
0.6
-1/2 - 1/2
Intensity (arb. units)
1.4
4.2
4.3
Fig. 2. 7Li (a) and 23Na (b) NMR spectra measured above Tc (bottom spectra) and below Tc (upper spectra) for HJc in LiCu2O2 and NaCu2O2 single crystals at 33.7 and 46.0 MHz, respectively. The 23Na transitions are labeled near the corresponding lines.
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Below magnetic ordering temperature Tc, the spectra of both compounds exhibit a dramatic change. The spectra are characteristic of IC static modulation of the local magnetic field caused by helical spin structure of Cu moments [4,8,9]. It is worth mentioning that the phase transition at Tc is much narrower in NaCu2O2 than in LiCu2O2. As seen in Fig. 1(b), the formation of IC field modulation in NaCu2O2 occurs within 0.6 K while in LiCu2O2 it takes more than 2 K [4]. The asymmetric van Hove singularities of 23Na NMR central transition line are very sharp and are clearly visible also on satellite transitions, which in contrast to LiCu2O2 are well separated due to the larger EFG. The lineshape of the satellite transitions follows the distribution of the Larmor frequency caused by IC local field modulation. Therefore, in the first-order quadrupole perturbation the satellite lineshape is almost the exact copy of the central transition profile. The most striking difference between 7Li and 23Na spectra is that in NaCu2O2 the doublets (or degenerated quartets) are observed for all three principal orientations of external magnetic field in the magnetically ordered state. For HJa the intensities of both parts of the doublets are equal while for HJc the high-field component of the doublet is more intensive. This anisotropy becomes more significant with decreasing temperature. The splitting is almost symmetric with respect to the central field determined as the resonance field of the central transition above Tc. These results are completely unlike the situation in LiCu2O2 where the 7Li NMR quartet and sextet are observed for HJc (Fig. 2a) and HJ(a, b) [4]. The possible reason for such dissimilar behavior could be the influence of non-magnetic Li defects in CuO2 chains of LiCu2O2. Due to AF character of NNN interaction both the helix phase angles, y and j, exhibit a step-like change on p in the vicinity of Li defect. This phenomenon will be analyzed in more detail elsewhere. It is worth noting that the value of the local magnetic field on Na site estimated as the linewidth at the base of the central transition for HJc is only 80 mT, which is a factor of 3 less than that for Li (250 mT). This is quite reasonable since the transition temperature in NaCu2O2 is lower than in LiCu2O2 pointing to a weaker inter-chain interaction in NaCu2O2. The difference in crystal structure peculiarities of the two compounds is reflected in their NQR properties. Fig. 3 shows the NQR spectra of NaCu2O2 and LiCu2O2 measured above Tc on 63,65Cu nuclei in Cu(2) site. The right and left lines of each pair are assigned to the 63Cu and the 65Cu isotopes, respectively. The observed frequency and intensity ratios correspond to ratios of isotope quadrupole moments and natural abundancies, respectively. In the following, we will concentrate only on 63Cu isotope NQR lines for convenience. From Fig. 3 it is clearly seen that in NaCu2O2 the NQR linewidth is a factor of 3 smaller than that in LiCu2O2. This result reflects more homogeneous EFG distribution as a consequence of higher degree of structural
1.0 LiCuO2 T2=30 K NaCu2O2 T=77 K
0.8
0.6
0.4
0.2
0.0 24
25
26
27
28
29
F (MHz) Fig. 3. NQR spectra of NaCu2O2 (black open circles) and LiCu2O2 (red filled squares) measured above Tc on 63,65Cu nuclei in Cu(2) site.
order in NaCu2O2. Probably for the same reason, we succeeded to find another 63Cu line at 26.8 MHz originated from the Cu(1) position. It should be noted that the 63Cu line at around 27 MHz has been observed earlier on the polycrystalline LiCu2O2 sample in Ref. [10], but it was falsely assigned to the Cu(1) position. In this case, the line should exist also below Tc which contradicts with our experimental findings described below. All lines shown in Fig. 3 completely disappear below Tc. Instead, in LiCu2O2 we observed very complicated 63,65Cu antiferromagnetic resonance (AFMR) spectrum at 4.2 K. This effect is caused by the space modulated internal magnetic field at the Cu(2) site in the ordered state of LiCu2O2. For yet unknown reason we did not find any copper AFMR spectrum in NaCu2O2. At the same time, the Cu(1) NQR line at 26.8 MHz exists even below Tc, as expected for non-magnetic Cu+ ion at the Cu(1) site which is symmetric with respect to magnetic Cu2+ ions in the CuO2 chains. Therefore, the complete cancellation of local magnetic field occurs at Cu(1) site in the ordered state of NaCu2O2. In conclusion, 7Li and 23Na NMR spectra measured in the magnetically ordered state of the isostructural quasi-1D oxides LiCu2O2 and NaCu2O2 give unambiguous evidence for static IC modulation of local magnetic fields at the Li and the Na sites, respectively. This modulation is caused by a helical spin structure of Cu moments below Tc. Due to the crystal structure peculiarities, the character of the magnetic helix is dissimilar in both compounds reflecting both in NMR and NQR spectra. Acknowledgments We appreciate support by the Grants RFBR 05-0217719-a, MK-1212.2005.2 and CRDF RU-P1-2599MO-04.
ARTICLE IN PRESS A.A. Gippius et al. / Journal of Magnetism and Magnetic Materials 316 (2007) 298–301
References [1] U. Schollwo¨ck, J. Richter, D.J.J. Farnell, R.F. Bishop (Eds.), Quantum Magnetism, Lecture Notes on Physics, vol. 645, Springer, Berlin, 2004. [2] R. Berger, P. O¨nnerud, R. Tellgren, J. Alloys Compds. 184 (1992) 315. [3] D.A. Zatsepin, V.R. Galakhov, M.A. Korotin, V.V. Fedorenko, E.Z. Kurmaev, S. Bartkowski, M. Neumann, R. Berger, Phys. Rev. B 57 (1998) 4377. [4] A.A. Gippius, E.N. Morosova, A.S. Moskvin, A.V. Zalessky, A.A. Bush, M. Baenitz, H. Rosner, S.-L. Drechsler, Phys. Rev. B 70 (2004) 020406. [5] L. Capogna, M. Mayr, P. Horsch, M. Raichle, R.K. Kremer, M. Sofin, A. Maljuk, M. Jansen, B. Keimer, Phys. Rev. B 71 (2005) 140402(R).
301
[6] T. Masuda, A. Zheludev, A. Bush, M. Markina, A. Vasiliev, Phys. Rev. Lett. 92 (2004) 177201. [7] T. Masuda, A. Zheludev, B. Roessli, A. Bush, M. Markina, A. Vasiliev, Phys. Rev. B 72 (2005) 014405. [8] A.A. Gippius, E.N. Morozova, A.S. Moskvin, S.-L. Drechsler, M. Baenitz, J. Magn. Magn. Mater. 300 (2006) e335. [9] S.-L. Drechsler, J. Richter, A.A. Gippius, A.N. Vasiliev, A.A. Bush, A.S. Moskvin, J. Malek, Yu. Protz, W. Shnelle, H. Rosner, Europhys. Lett. 73 (2006) 83. [10] F.C. Fritschij, H.B. Brom, R. Berger, Solid State Commun. 107 (1998) 719.