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Nonmagnetic impurities in 1D and 3D triangular antiferromagnets
Physica B 284}288 (2000) 1629}1630
Nonmagnetic impurities in 1D and 3D triangular antiferromagnets L.A. Prozorova*, S.S. Sosin, I.A. Zalizniak P. Kapitza Institute for Physical Problems, RAS, Kosygin str. 2, 117334 Moscow, Russia
Abstract Various magnetic properties of diluted quasi-1D triangular antiferromagnets CsNi Mg Cl and RbNi Mg Cl \V V \V V were studied. The resonance spectrum, the phase diagram and the magnetic susceptibility of diluted crystals were found to di!er signi"cantly from those of pure systems. The in#uence of broken chains on the initial ground state and the spectra of excitations is suggested to explain the e!ects observed. 2000 Elsevier Science B.V. All rights reserved. Keywords: Quasi-1D antiferromagnets; Broken chains; AFMR spectrum; Magnetization
Unusual properties of 1D-AFMs with integer spins have many interesting consequences. One of them is the behavior of "nite or broken 1D spin chains in the Haldane state which was studied theoretically and in several experimental works on diluted NENP. On the other hand, additional degrees of freedom at the ends of chains broken by nonmagnetic impurities must also a!ect quasi-1D systems in an ordered antiferromagnetic phase, which was considered in Ref. [1] in terms of a classical spin-wave approach. The purpose of the present work was to study magnetic properties of diluted AFMs CsNiCl and RbNiCl with di!erent J/J ratios (+50 and +10, respectively) in order to reveal the contribution of defects to the magnetic ordering and spectrum of excitations in a system of weakly correlated linear spin chains. Several samples of (Cs}Rb)Ni Mg Cl with di!er\V V ent concentrations of magnesium were grown and investigated. First, we studied AFMR spectra of all crystals at various temperatures in a wide range of "elds and frequencies. Main AFMR results for CsNiCl and RbNiCl at H "" C are shown in Figs. 1 and 2. The basic e!ect in CsNiCl was a large (comparatively to x) decrease in the relativistic gap u (H"0) and in the "eld of a spin-#op transition H (by one half at x+0.075). The Neel * Corresponding author. E-mail address: [email protected] (L.A. Prozorova)
temperature ¹ at this x was also found to decrease from , 5 to 3 K. AFMR in diluted RbNiCl is changed in a quite di!erent way. The gap u (0) and the "eld H at x+0.015 become 10% larger than those in a pure crystal while ¹ remains just the same. In addition, a third AFMR, branch u appears in the frequency range 5}20 GHz. Being associated with the axial distortion of an ideal 1203-exchange structure, this branch was never observed in a pure system and is estimated to be +300 MHz. Next, we performed a series of magnetization measurements by a SQUID magnetometer for two samples of CsNiCl with x"0.033 and 0.07 and a sample of RbNiCl with x"0.015. We studied the temperature dependencies of the magnetization at H"4 kOe and its "eld dependencies at ¹"1.8 K. In both measurements (the former one for H "" C and H N C is represented in Fig. 3) a large additional contribution to the magnetization was observed. It appears at ¹+25 K and grows as &1/¹ till ¹ after which the growth slows down. At the , lowest temperature ¹"1.8 K the total susceptibility of the "rst sample is s +2.5s and that of the second sample is s +4s . The relative increase of magnetiz ation in diluted RbNiCl is about 3 times smaller. These phenomena can be explained by the following model. In the presence of an AFM order all additional degrees of freedom at the ends of broken chains are imposed by long-range molecular "elds. If the system is quasi-1D this "eld is much weaker than the basic exchange "eld and the additional susceptibility per one
0921-4526/00/$ - see front matter 2000 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 9 ) 0 2 8 0 8 - 2
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L.A. Prozorova et al. / Physica B 284}288 (2000) 1629}1630
Fig. 1. The AFMR spectra of diluted CsNiCl at several values of x. Solid lines "t the experimental data for a pure system.
Fig. 2. The AFMR spectrum of diluted RbNi Mg Cl . Dashed lines "t the experimental data for a pure system, and the solid line is the best "t with modi"ed anisotropy.
defect remains large. The classical spin-wave theory gives the following results in the "rst order of perturbation for the total susceptibility of a diluted quasi-1D AFM: s(x)"s(0)(1#ax(J/J ), where s(0) is a susceptibility of a pure system. One can see that the small parameter of the perturbation is x(J/J rather than x [1]. Using a hydrodynamical approach [2] one can obtain a lowfrequency part of an AFMR spectrum whose general
Fig. 3. The susceptibility M/H of diluted CsNiCl versus tem perature for H "" C (lower curve in each pair) and H N C (upper curve).
form is represented in Figs. 1 and 2 by lines. The parameters mentioned above are u (H"0)"D/s , , H"D/(s !s ), where D is an anisotropy constant, , s and s are two main values of the tensor of suscepti , bility. The observed 4 times increase in susceptibility should therefore lead to a double decrease in u (0) and H which is exactly the case in the diluted CsNiCl . The decrease in Neel temperature may be explained by the opening of the quasi-classical gap in the spectrum of excitations of broken linear spin chains D&xJ which reduces strongly ¹ &(JJ if J
References [1] I.Ya. Korenblit, E.F. Shender, Phys. Rev. B 48 (1993) 9478. [2] A.F. Andreev, V.I. Marchenko, Sov. Phys. Usp. 23 (1980) 21.
Nonmagnetic impurities in 1D and 3D triangular antiferromagnets L.A. Prozorova*, S.S. Sosin, I.A. Zalizniak P. Kapitza Institute for Physical Problems, RAS, Kosygin str. 2, 117334 Moscow, Russia
Abstract Various magnetic properties of diluted quasi-1D triangular antiferromagnets CsNi Mg Cl and RbNi Mg Cl \V V \V V were studied. The resonance spectrum, the phase diagram and the magnetic susceptibility of diluted crystals were found to di!er signi"cantly from those of pure systems. The in#uence of broken chains on the initial ground state and the spectra of excitations is suggested to explain the e!ects observed. 2000 Elsevier Science B.V. All rights reserved. Keywords: Quasi-1D antiferromagnets; Broken chains; AFMR spectrum; Magnetization
Unusual properties of 1D-AFMs with integer spins have many interesting consequences. One of them is the behavior of "nite or broken 1D spin chains in the Haldane state which was studied theoretically and in several experimental works on diluted NENP. On the other hand, additional degrees of freedom at the ends of chains broken by nonmagnetic impurities must also a!ect quasi-1D systems in an ordered antiferromagnetic phase, which was considered in Ref. [1] in terms of a classical spin-wave approach. The purpose of the present work was to study magnetic properties of diluted AFMs CsNiCl and RbNiCl with di!erent J/J ratios (+50 and +10, respectively) in order to reveal the contribution of defects to the magnetic ordering and spectrum of excitations in a system of weakly correlated linear spin chains. Several samples of (Cs}Rb)Ni Mg Cl with di!er\V V ent concentrations of magnesium were grown and investigated. First, we studied AFMR spectra of all crystals at various temperatures in a wide range of "elds and frequencies. Main AFMR results for CsNiCl and RbNiCl at H "" C are shown in Figs. 1 and 2. The basic e!ect in CsNiCl was a large (comparatively to x) decrease in the relativistic gap u (H"0) and in the "eld of a spin-#op transition H (by one half at x+0.075). The Neel * Corresponding author. E-mail address: [email protected] (L.A. Prozorova)
temperature ¹ at this x was also found to decrease from , 5 to 3 K. AFMR in diluted RbNiCl is changed in a quite di!erent way. The gap u (0) and the "eld H at x+0.015 become 10% larger than those in a pure crystal while ¹ remains just the same. In addition, a third AFMR, branch u appears in the frequency range 5}20 GHz. Being associated with the axial distortion of an ideal 1203-exchange structure, this branch was never observed in a pure system and is estimated to be +300 MHz. Next, we performed a series of magnetization measurements by a SQUID magnetometer for two samples of CsNiCl with x"0.033 and 0.07 and a sample of RbNiCl with x"0.015. We studied the temperature dependencies of the magnetization at H"4 kOe and its "eld dependencies at ¹"1.8 K. In both measurements (the former one for H "" C and H N C is represented in Fig. 3) a large additional contribution to the magnetization was observed. It appears at ¹+25 K and grows as &1/¹ till ¹ after which the growth slows down. At the , lowest temperature ¹"1.8 K the total susceptibility of the "rst sample is s +2.5s and that of the second sample is s +4s . The relative increase of magnetiz ation in diluted RbNiCl is about 3 times smaller. These phenomena can be explained by the following model. In the presence of an AFM order all additional degrees of freedom at the ends of broken chains are imposed by long-range molecular "elds. If the system is quasi-1D this "eld is much weaker than the basic exchange "eld and the additional susceptibility per one
0921-4526/00/$ - see front matter 2000 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 9 ) 0 2 8 0 8 - 2
1630
L.A. Prozorova et al. / Physica B 284}288 (2000) 1629}1630
Fig. 1. The AFMR spectra of diluted CsNiCl at several values of x. Solid lines "t the experimental data for a pure system.
Fig. 2. The AFMR spectrum of diluted RbNi Mg Cl . Dashed lines "t the experimental data for a pure system, and the solid line is the best "t with modi"ed anisotropy.
defect remains large. The classical spin-wave theory gives the following results in the "rst order of perturbation for the total susceptibility of a diluted quasi-1D AFM: s(x)"s(0)(1#ax(J/J ), where s(0) is a susceptibility of a pure system. One can see that the small parameter of the perturbation is x(J/J rather than x [1]. Using a hydrodynamical approach [2] one can obtain a lowfrequency part of an AFMR spectrum whose general
Fig. 3. The susceptibility M/H of diluted CsNiCl versus tem perature for H "" C (lower curve in each pair) and H N C (upper curve).
form is represented in Figs. 1 and 2 by lines. The parameters mentioned above are u (H"0)"D/s , , H"D/(s !s ), where D is an anisotropy constant, , s and s are two main values of the tensor of suscepti , bility. The observed 4 times increase in susceptibility should therefore lead to a double decrease in u (0) and H which is exactly the case in the diluted CsNiCl . The decrease in Neel temperature may be explained by the opening of the quasi-classical gap in the spectrum of excitations of broken linear spin chains D&xJ which reduces strongly ¹ &(JJ if J
References [1] I.Ya. Korenblit, E.F. Shender, Phys. Rev. B 48 (1993) 9478. [2] A.F. Andreev, V.I. Marchenko, Sov. Phys. Usp. 23 (1980) 21.