- Email: [email protected]
Geometrically frustrated Kagome staircase lattice with chemical disorder
Journal of Non-Crystalline Solids 354 (2008) 4186–4188
Contents lists available at ScienceDirect
Journal of Non-Crystalline Solids journal homepage: www.elsevier.com/locate/jnoncrysol
Geometrically frustrated Kagome staircase lattice with chemical disorder R. Szymczak a, M. Baran a, J. Fink-Finowicki a, B. Krzymanska a, P. Aleshkevych a, H. Szymczak a,*, S.N. Barilo b, G.L. Bychkov b, S.V. Shiryaev b a b
Institute of Physics, Polish Academy of Sciences, 02-668 Warsaw, Poland Institute of Solid State and Semiconductor Physics, NAS, P. Brovki 17, 220072 Minsk, Belarus
a r t i c l e
i n f o
Article history: Available online 18 August 2008 PACS: 75.24.+z 75.30.Kz 75.50.Dd
a b s t r a c t The effect of nonmagnetic Mg2+ and magnetic Co2+ doping in Kagome staircase compounds was investigated using DC magnetic susceptibility. The main effect of doping is to change effective anisotropy of the Ni3V2O8 and Co3V2O8 crystals. It has a considerable effect on magnetic field induced phase transitions in both kinds of crystals. The doping has also an effect on the Dzyaloshinskii–Moriya exchange interactions. In some cases the doping enhances this interaction while in another it suppresses it completely. Ó 2008 Elsevier B.V. All rights reserved.
Keyword: Magnetic properties
1. Introduction Magnetic materials with magnetic interactions that cannot be satisfied simultaneously owing to the topology of the lattice display a variety of interesting properties. Such geometrically frustrated magnetic systems can display various exciting low-temperature phenomena such as spin-liquid, spin-glass and spin-ice states [1– 3]. Recently, a new class of frustrated magnetic materials, Kagome staircase M3V2O8 oxides (M = Ni, Co, Cu, Mn), have attracted considerable attention [4–19]. These materials consist of two inequivalent M2+ sites: the cross-tie sites, which form the apices of the nearly equilateral triangles, and the spine sites, which form the bases of triangles. The magnetic ions are subject to different crystal fields and consequently have different magnetic properties. In the presence of isotropic antiferromagnetic exchange interactions only the cross-tie spins are frustrated [10]. To gain insights into the magnetic interactions in Kagome staircase M3V2O8 oxides, we decided to investigate the impurity effect on their magnetic properties, with a focus on the magnetic anisotropy of this group of materials. Here, we study the effect of chemical disorder due to Co impurities in geometrically frustrated Ni3V2O8 single crystals and Mg impurities in Co3V2O8 single crystals. The Co3V2O8 and Ni3V2O8 crystals have very similar orthorhombic (space group Cmca) crystal structures but different magnetic structures at low temperatures. In the low-temperature region the Co3V2O8 phases are nonfrustrated ferromagnets (unimportant frustration effects are responsible for small noncollinearity of magnetic moments) while the Ni3V2O8 phases are highly frustrated antiferromag* Corresponding author. E-mail address: [email protected] (H. Szymczak). 0022-3093/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.jnoncrysol.2008.06.082
nets (weak ferromagnets). In both cases the easy direction of magnetization is parallel to the a-axis. The differences between the Co3V2O8 and Ni3V2O8 crystals should be related to the different ground states of Ni2+and Co2+; while the ground state of the Ni2+ ion is an orbital singlet; the ground state of the Co2+ ion is an orbital triplet. Thus in the case of the Co2+ ion one should expect a strong ion–lattice coupling and possibly also crystal lattice deformations due to the Jahn–Teller effect, which influences the character and magnitude of exchange interactions and magnetocrystalline anisotropy. Some correlations between measurements performed on both groups of compounds should be observed, since doping of Mg2+ ions is equivalent to removing of Co2+ ions from the lattice, while Co doping means inserting additional Co2+ ions into Kagome lattice. 2. Experimental results The Ni3V2O8 and Ni3(1x)Co3xV2O8 single crystals were grown by a method of spontaneous crystallization while Co33xMg3xV2O8 crystals with x = 0, 0.05 and x = 0.1 were grown by floating zone technique using an optical image furnace. All the samples were found to be single phase by X-ray diffraction measurements with the crystal structures in the orthorhombic space group Cmca. Doping had little influence on the lattice constants. Magnetic measurements were performed using a commercial SQUID magnetometer (MPMS-5, Quantum Design). 2.1. Co33xMg3xV2O8 Neutron diffraction experiments [11,14,16] indicate ferromagnetic ordering of Co3V2O8 crystals at low temperatures with spin
4187
R. Szymczak et al. / Journal of Non-Crystalline Solids 354 (2008) 4186–4188
Fig. 1. The longitudinal magnetization measured at 2 K as a function of magnetic field applied along the a-axis for x = 0, 0.05 and 0.1.
directions along the a-axis. According to [14] the cobalt ions on the cross-tie sites deviate from the a-axis towards the c-axis by an angle 10° probably due to frustration. Fig. 1 presents the M(H) dependences measured at 2 K for various levels of doping. One can notice that the character of magnetization curves does not depend on x – in each case M(H) dependence is typical of a ferromagnetic phase. The level of doping affects only the value of saturation magnetization, which decreases with x. Such behavior is as expected because doping with nonmagnetic ions decreases the number of magnetic Co2+ ions. Moreover, the value of saturation magnetization (close to 3lB/Co, the value expected for spin-only contribution for high-spin octahedral Co2+) suggests collinear ferromagnetic ordering along the a-axis. Lack of full saturation is due to the noncollinearity of ferromagnetic moments (evidenced for x = 0 by [14]). This noncollinearity is not seen for x = 0.05 and appears again for x = 0.1 Fig. 2 displays the low-temperature magnetization dependence, M(H), measured as a function of magnetic field applied parallel to the b-axis. In agreement with our previous measurements [9], the magnetization induced along the b-axis, Mb, for x = 0 is very small. This magnetization increases with x due to a decrease of the number of Co2+ ions. Fig. 3 indicates that this Mb component of magnetization is characterized by hysteretic behavior suggesting the presence of a domain structure. The analysis of the experimental results leads to the conclusion that the magnetocrystalline anisot-
Fig. 3. The hysteresis loop measured at 2 K in magnetic field applied along the baxis for Co2.9Mg0.1V2O8.
Fig. 4. The longitudinal magnetization measured at 2 K as a function of magnetic field applied along the c-axis for x = 0, 0.05 and 0.1.
ropy of the system decreases with x. The most important result is the observation that doping enhances the Dzyaloshinskii–Moriya interaction that is responsible for a weak ferromagnetic moment along the b-axis for x = 0.1. This interaction causes the deviation
2
Ni3V2O8 + Co
M [ μΒ /f.u.]
H || a T=2K 1
Ni3V2O8
0 0
Fig. 2. The longitudinal magnetization measured at 2 K as a function of magnetic field applied along the b-axis for x = 0, 0.05 and 0.1.
1
2
H[T]
3
4
5
Fig. 5. Magnetization curves at 2 K for Ni3V2O8 and Ni3V2O8:3%Co crystals for magnetic field Hka.
4188
R. Szymczak et al. / Journal of Non-Crystalline Solids 354 (2008) 4186–4188
Ni3V2O8 + Co 3
M [μΒ /f.u.]
H || c T=2K
2
Ni3V2O8 1
0 0
1
2
3
4
5
tion. No such transition is seen in doped samples, probably due to higher anisotropy from the presence of highly anisotropic Co2+ ions. Fig. 6 shows the presence of a weak ferromagnetic moment due to Dzyaloshinskii–Moriya exchange interactions in undoped crystals and the absence of this moment for doped crystals. It suggests that doping suppresses this interaction strongly. At the same time, doped crystals show an unusual M(H) dependence (Figs. 6 and 7) with non-zero ferromagnetic moment seen on extrapolation of M(H) to H = 0. The transition observed near H 2.5 T is not of the spin-flop type but rather similar to that reported for Co33xMg3xV2O8 for Hkc (Fig. 4). This means that the magnetic field Hkc induces a rotation of antiferromagnetic vector from the a-axis towards the c-axis which near H 2.5 T has first-order like character.
H [T] Fig. 6. Magnetization curves at 2 K for Ni3V2O8 and Ni3V2O8:3%Co crystals for magnetic field Hkc.
3. Conclusions It was shown for the first time that the chemical disorder introduced by low level doping has a strong influence on magnetocrystalline effects in Kagome systems. This is because Co2+ ions are strongly connected with lattice. These ions also change the Dzyaloshinskii–Moriya exchange interactions responsible for the noncollinearity of magnetic moments in these Kagome crystals.
2
Ni3V2O8 + Co
H || b
M [μ Β/f.u.]
Acknowledgement
T=2K
1
The work was supported in part by the Ministry of Science under the Project N202 057 32/1201.
Ni3V2O8
References
0 0
1
2
3
4
5
H[T] Fig. 7. Magnetization curves at 2 K for Ni3V2O8 and Ni3V2O8:3%Co crystals for magnetic field Hkb.
of magnetic moments from the c-axis towards b-axis. This effect is seen also on Fig. 1 for x = 0.1. The Dzyaloshinskii–Moriya vector in this case is directed along the c-axis. In Fig. 4 the M(H) dependences are shown measured at 2 K for magnetic field Hkc. The magnetic field induces a rotation of magnetization from the a-axis towards the c-axis. At low magnetic fields this rotation has continuous character. For x = 0, a jump of the magnetization is observed with magnetic field increase. This first-order phase transition becomes smoothed for x 6¼ 0 due to disorder resulting from the doping. 2.2. Ni3(1x)Co3xV2O8 Neutron diffraction experiments [7,8] indicate an commensurate antiferromagnetic structure of Ni3V2O8 crystals at low temperatures, with the staggered magnetization primarily along the aaxis and a weak ferromagnetic moment along the c-axis. Results presented here confirm the antiferromagnetic ground state of Ni3V2O8 crystals. The M(H) dependence measured for Hkc in undoped Ni3V2O8 (Fig. 5) has typical antiferromagnetic character, confirmed by the presence of the spin-flop first-order phase transi-
[1] A.P. Ramirez, in: K.J.H. Buschow (Ed.), Handbook on Magnetic Materials, vol. 15, Elsevier, Amsterdam, 2001, p. 423. [2] S.T. Bramwell, M.J.P. Gingras, Science 294 (2001) 1495. [3] S.-H. Lee, C. Broholm, W. Ratcliff, G. Gasparovic, Q. Huang, T. Kim, S.W. Cheong, Nature 418 (2002) 856. [4] N. Rogado, G. Laves, D.A. Huse, A.P. Ramirez, R.J. Cava, Solid State Commun. 124 (2002) 229. [5] N. Rogado, M.K. Haas, G. Laves, D.A. Huse, A.P. Ramirez, R.J. Cava, J. Phys.: Condens. Matter 15 (2003) 907. [6] G. Balakrishnan, O.A. Petrenko, M.R. Lees, D.M.K. Paul, J. Phys.: Condens. Matter 16 (2004) L347. [7] G. Laves, A.B. Harris, T. Kimura, N. Rogado, R.J. Cava, A. Aharony, O. EntinWohlman, T. Yildirim, M. Kenzelmann, C. Broholm, A.P. Ramirez, Phys. Rev. Lett. 95 (2005) 097205. [8] G. Lawes, M. Kenzelmann, N. Rogado, K.H. Kim, G.A. Jorge, R.J. Cava, A. Aharony, O. Entin-Wohlman, A.B. Harris, T. Yildirim, Q.Z. Huang, S. Park, C. Broholm, A.P. Ramirez, Phys. Rev. Lett. 93 (2004) 247201. [9] R. Szymczak, M. Baran, R. Diduszko, J. Fink-Finowicki, M. Gutowska, A. Szewczyk, H. Szymczak, Phys. Rev. B 73 (2006) 094425. [10] M. Kenzelmann, A.B. Harris, A. Aharony, O. Entin-Wohlman, T. Yildirim, Q. Huang, S. Park, G. Lawes, C. Broholm, N. Rogado, R.J. Cava, K.H. Kim, G. Jorge, A.P. Ramirez, Phys. Rev. B 74 (2006) 014429. [11] Y. Chen, J.W. Lynn, Q. Huang, F.M. Woodward, T. Yildirim, G. Lawes, A.P. Ramirez, N. Rogado, R.J. Cava, A. Aharony, O. Entin-Wohlman, A.B. Harris, Phys. Rev. B 74 (2006) 014430. [12] N. Qureshi, H. Fuess, H. Ehrenberg, T.C. Hansen, C. Ritter, K. Prokes, A. Podlesnyak, G. Schwabe, Phys. Rev. B 74 (2006) 212407. [13] N. Qureshi, H. Fuess, H. Ehrenberg, T.C. Hansen, C. Ritter, G. Schwabe, Solid State Commun., 142 (2007) 169. [14] Y. Yasui, Y. Kobayashi, M. Soda, T. Moyoshi, M. Sato, N. Igawa, J. Phys. Soc. Jpn. 76 (2007) 034706. [15] A.B. Harris, T. Yildirim, A. Aharony, O. Entin-Wohlman, Phys. Rev. B 73 (2006) 184433. [16] N.R. Wilson, O.A. Petrenko, L.C. Chapon, Phys. Rev. B 75 (2007) 094432. [17] N.R. Wilson, O.A. Petrenko, L.C. Chapon, J. Phys.: Condens. Matter 19 (2007) 145257. [18] H. Szymczak, M. Baran, R. Szymczak, S.N. Barilo, G.L. Bychkov, S.V. Shiryaev, Acta Phys. Polon. A 111 (2007) 71. [19] N. Bellido, Ch. Martin, Ch. Simon, A. Maignan, J. Phys.: Condens. Matter 19 (2007) 056001.
Contents lists available at ScienceDirect
Journal of Non-Crystalline Solids journal homepage: www.elsevier.com/locate/jnoncrysol
Geometrically frustrated Kagome staircase lattice with chemical disorder R. Szymczak a, M. Baran a, J. Fink-Finowicki a, B. Krzymanska a, P. Aleshkevych a, H. Szymczak a,*, S.N. Barilo b, G.L. Bychkov b, S.V. Shiryaev b a b
Institute of Physics, Polish Academy of Sciences, 02-668 Warsaw, Poland Institute of Solid State and Semiconductor Physics, NAS, P. Brovki 17, 220072 Minsk, Belarus
a r t i c l e
i n f o
Article history: Available online 18 August 2008 PACS: 75.24.+z 75.30.Kz 75.50.Dd
a b s t r a c t The effect of nonmagnetic Mg2+ and magnetic Co2+ doping in Kagome staircase compounds was investigated using DC magnetic susceptibility. The main effect of doping is to change effective anisotropy of the Ni3V2O8 and Co3V2O8 crystals. It has a considerable effect on magnetic field induced phase transitions in both kinds of crystals. The doping has also an effect on the Dzyaloshinskii–Moriya exchange interactions. In some cases the doping enhances this interaction while in another it suppresses it completely. Ó 2008 Elsevier B.V. All rights reserved.
Keyword: Magnetic properties
1. Introduction Magnetic materials with magnetic interactions that cannot be satisfied simultaneously owing to the topology of the lattice display a variety of interesting properties. Such geometrically frustrated magnetic systems can display various exciting low-temperature phenomena such as spin-liquid, spin-glass and spin-ice states [1– 3]. Recently, a new class of frustrated magnetic materials, Kagome staircase M3V2O8 oxides (M = Ni, Co, Cu, Mn), have attracted considerable attention [4–19]. These materials consist of two inequivalent M2+ sites: the cross-tie sites, which form the apices of the nearly equilateral triangles, and the spine sites, which form the bases of triangles. The magnetic ions are subject to different crystal fields and consequently have different magnetic properties. In the presence of isotropic antiferromagnetic exchange interactions only the cross-tie spins are frustrated [10]. To gain insights into the magnetic interactions in Kagome staircase M3V2O8 oxides, we decided to investigate the impurity effect on their magnetic properties, with a focus on the magnetic anisotropy of this group of materials. Here, we study the effect of chemical disorder due to Co impurities in geometrically frustrated Ni3V2O8 single crystals and Mg impurities in Co3V2O8 single crystals. The Co3V2O8 and Ni3V2O8 crystals have very similar orthorhombic (space group Cmca) crystal structures but different magnetic structures at low temperatures. In the low-temperature region the Co3V2O8 phases are nonfrustrated ferromagnets (unimportant frustration effects are responsible for small noncollinearity of magnetic moments) while the Ni3V2O8 phases are highly frustrated antiferromag* Corresponding author. E-mail address: [email protected] (H. Szymczak). 0022-3093/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.jnoncrysol.2008.06.082
nets (weak ferromagnets). In both cases the easy direction of magnetization is parallel to the a-axis. The differences between the Co3V2O8 and Ni3V2O8 crystals should be related to the different ground states of Ni2+and Co2+; while the ground state of the Ni2+ ion is an orbital singlet; the ground state of the Co2+ ion is an orbital triplet. Thus in the case of the Co2+ ion one should expect a strong ion–lattice coupling and possibly also crystal lattice deformations due to the Jahn–Teller effect, which influences the character and magnitude of exchange interactions and magnetocrystalline anisotropy. Some correlations between measurements performed on both groups of compounds should be observed, since doping of Mg2+ ions is equivalent to removing of Co2+ ions from the lattice, while Co doping means inserting additional Co2+ ions into Kagome lattice. 2. Experimental results The Ni3V2O8 and Ni3(1x)Co3xV2O8 single crystals were grown by a method of spontaneous crystallization while Co33xMg3xV2O8 crystals with x = 0, 0.05 and x = 0.1 were grown by floating zone technique using an optical image furnace. All the samples were found to be single phase by X-ray diffraction measurements with the crystal structures in the orthorhombic space group Cmca. Doping had little influence on the lattice constants. Magnetic measurements were performed using a commercial SQUID magnetometer (MPMS-5, Quantum Design). 2.1. Co33xMg3xV2O8 Neutron diffraction experiments [11,14,16] indicate ferromagnetic ordering of Co3V2O8 crystals at low temperatures with spin
4187
R. Szymczak et al. / Journal of Non-Crystalline Solids 354 (2008) 4186–4188
Fig. 1. The longitudinal magnetization measured at 2 K as a function of magnetic field applied along the a-axis for x = 0, 0.05 and 0.1.
directions along the a-axis. According to [14] the cobalt ions on the cross-tie sites deviate from the a-axis towards the c-axis by an angle 10° probably due to frustration. Fig. 1 presents the M(H) dependences measured at 2 K for various levels of doping. One can notice that the character of magnetization curves does not depend on x – in each case M(H) dependence is typical of a ferromagnetic phase. The level of doping affects only the value of saturation magnetization, which decreases with x. Such behavior is as expected because doping with nonmagnetic ions decreases the number of magnetic Co2+ ions. Moreover, the value of saturation magnetization (close to 3lB/Co, the value expected for spin-only contribution for high-spin octahedral Co2+) suggests collinear ferromagnetic ordering along the a-axis. Lack of full saturation is due to the noncollinearity of ferromagnetic moments (evidenced for x = 0 by [14]). This noncollinearity is not seen for x = 0.05 and appears again for x = 0.1 Fig. 2 displays the low-temperature magnetization dependence, M(H), measured as a function of magnetic field applied parallel to the b-axis. In agreement with our previous measurements [9], the magnetization induced along the b-axis, Mb, for x = 0 is very small. This magnetization increases with x due to a decrease of the number of Co2+ ions. Fig. 3 indicates that this Mb component of magnetization is characterized by hysteretic behavior suggesting the presence of a domain structure. The analysis of the experimental results leads to the conclusion that the magnetocrystalline anisot-
Fig. 3. The hysteresis loop measured at 2 K in magnetic field applied along the baxis for Co2.9Mg0.1V2O8.
Fig. 4. The longitudinal magnetization measured at 2 K as a function of magnetic field applied along the c-axis for x = 0, 0.05 and 0.1.
ropy of the system decreases with x. The most important result is the observation that doping enhances the Dzyaloshinskii–Moriya interaction that is responsible for a weak ferromagnetic moment along the b-axis for x = 0.1. This interaction causes the deviation
2
Ni3V2O8 + Co
M [ μΒ /f.u.]
H || a T=2K 1
Ni3V2O8
0 0
Fig. 2. The longitudinal magnetization measured at 2 K as a function of magnetic field applied along the b-axis for x = 0, 0.05 and 0.1.
1
2
H[T]
3
4
5
Fig. 5. Magnetization curves at 2 K for Ni3V2O8 and Ni3V2O8:3%Co crystals for magnetic field Hka.
4188
R. Szymczak et al. / Journal of Non-Crystalline Solids 354 (2008) 4186–4188
Ni3V2O8 + Co 3
M [μΒ /f.u.]
H || c T=2K
2
Ni3V2O8 1
0 0
1
2
3
4
5
tion. No such transition is seen in doped samples, probably due to higher anisotropy from the presence of highly anisotropic Co2+ ions. Fig. 6 shows the presence of a weak ferromagnetic moment due to Dzyaloshinskii–Moriya exchange interactions in undoped crystals and the absence of this moment for doped crystals. It suggests that doping suppresses this interaction strongly. At the same time, doped crystals show an unusual M(H) dependence (Figs. 6 and 7) with non-zero ferromagnetic moment seen on extrapolation of M(H) to H = 0. The transition observed near H 2.5 T is not of the spin-flop type but rather similar to that reported for Co33xMg3xV2O8 for Hkc (Fig. 4). This means that the magnetic field Hkc induces a rotation of antiferromagnetic vector from the a-axis towards the c-axis which near H 2.5 T has first-order like character.
H [T] Fig. 6. Magnetization curves at 2 K for Ni3V2O8 and Ni3V2O8:3%Co crystals for magnetic field Hkc.
3. Conclusions It was shown for the first time that the chemical disorder introduced by low level doping has a strong influence on magnetocrystalline effects in Kagome systems. This is because Co2+ ions are strongly connected with lattice. These ions also change the Dzyaloshinskii–Moriya exchange interactions responsible for the noncollinearity of magnetic moments in these Kagome crystals.
2
Ni3V2O8 + Co
H || b
M [μ Β/f.u.]
Acknowledgement
T=2K
1
The work was supported in part by the Ministry of Science under the Project N202 057 32/1201.
Ni3V2O8
References
0 0
1
2
3
4
5
H[T] Fig. 7. Magnetization curves at 2 K for Ni3V2O8 and Ni3V2O8:3%Co crystals for magnetic field Hkb.
of magnetic moments from the c-axis towards b-axis. This effect is seen also on Fig. 1 for x = 0.1. The Dzyaloshinskii–Moriya vector in this case is directed along the c-axis. In Fig. 4 the M(H) dependences are shown measured at 2 K for magnetic field Hkc. The magnetic field induces a rotation of magnetization from the a-axis towards the c-axis. At low magnetic fields this rotation has continuous character. For x = 0, a jump of the magnetization is observed with magnetic field increase. This first-order phase transition becomes smoothed for x 6¼ 0 due to disorder resulting from the doping. 2.2. Ni3(1x)Co3xV2O8 Neutron diffraction experiments [7,8] indicate an commensurate antiferromagnetic structure of Ni3V2O8 crystals at low temperatures, with the staggered magnetization primarily along the aaxis and a weak ferromagnetic moment along the c-axis. Results presented here confirm the antiferromagnetic ground state of Ni3V2O8 crystals. The M(H) dependence measured for Hkc in undoped Ni3V2O8 (Fig. 5) has typical antiferromagnetic character, confirmed by the presence of the spin-flop first-order phase transi-
[1] A.P. Ramirez, in: K.J.H. Buschow (Ed.), Handbook on Magnetic Materials, vol. 15, Elsevier, Amsterdam, 2001, p. 423. [2] S.T. Bramwell, M.J.P. Gingras, Science 294 (2001) 1495. [3] S.-H. Lee, C. Broholm, W. Ratcliff, G. Gasparovic, Q. Huang, T. Kim, S.W. Cheong, Nature 418 (2002) 856. [4] N. Rogado, G. Laves, D.A. Huse, A.P. Ramirez, R.J. Cava, Solid State Commun. 124 (2002) 229. [5] N. Rogado, M.K. Haas, G. Laves, D.A. Huse, A.P. Ramirez, R.J. Cava, J. Phys.: Condens. Matter 15 (2003) 907. [6] G. Balakrishnan, O.A. Petrenko, M.R. Lees, D.M.K. Paul, J. Phys.: Condens. Matter 16 (2004) L347. [7] G. Laves, A.B. Harris, T. Kimura, N. Rogado, R.J. Cava, A. Aharony, O. EntinWohlman, T. Yildirim, M. Kenzelmann, C. Broholm, A.P. Ramirez, Phys. Rev. Lett. 95 (2005) 097205. [8] G. Lawes, M. Kenzelmann, N. Rogado, K.H. Kim, G.A. Jorge, R.J. Cava, A. Aharony, O. Entin-Wohlman, A.B. Harris, T. Yildirim, Q.Z. Huang, S. Park, C. Broholm, A.P. Ramirez, Phys. Rev. Lett. 93 (2004) 247201. [9] R. Szymczak, M. Baran, R. Diduszko, J. Fink-Finowicki, M. Gutowska, A. Szewczyk, H. Szymczak, Phys. Rev. B 73 (2006) 094425. [10] M. Kenzelmann, A.B. Harris, A. Aharony, O. Entin-Wohlman, T. Yildirim, Q. Huang, S. Park, G. Lawes, C. Broholm, N. Rogado, R.J. Cava, K.H. Kim, G. Jorge, A.P. Ramirez, Phys. Rev. B 74 (2006) 014429. [11] Y. Chen, J.W. Lynn, Q. Huang, F.M. Woodward, T. Yildirim, G. Lawes, A.P. Ramirez, N. Rogado, R.J. Cava, A. Aharony, O. Entin-Wohlman, A.B. Harris, Phys. Rev. B 74 (2006) 014430. [12] N. Qureshi, H. Fuess, H. Ehrenberg, T.C. Hansen, C. Ritter, K. Prokes, A. Podlesnyak, G. Schwabe, Phys. Rev. B 74 (2006) 212407. [13] N. Qureshi, H. Fuess, H. Ehrenberg, T.C. Hansen, C. Ritter, G. Schwabe, Solid State Commun., 142 (2007) 169. [14] Y. Yasui, Y. Kobayashi, M. Soda, T. Moyoshi, M. Sato, N. Igawa, J. Phys. Soc. Jpn. 76 (2007) 034706. [15] A.B. Harris, T. Yildirim, A. Aharony, O. Entin-Wohlman, Phys. Rev. B 73 (2006) 184433. [16] N.R. Wilson, O.A. Petrenko, L.C. Chapon, Phys. Rev. B 75 (2007) 094432. [17] N.R. Wilson, O.A. Petrenko, L.C. Chapon, J. Phys.: Condens. Matter 19 (2007) 145257. [18] H. Szymczak, M. Baran, R. Szymczak, S.N. Barilo, G.L. Bychkov, S.V. Shiryaev, Acta Phys. Polon. A 111 (2007) 71. [19] N. Bellido, Ch. Martin, Ch. Simon, A. Maignan, J. Phys.: Condens. Matter 19 (2007) 056001.