Journal of Experimental and Theoretical Physics, Vol. 94, No. 1, 2002, pp. 119–122.Translated from Zhurnal Éksperimental’no

œ

i Teoretichesko

œ

Fiziki, Vol. 121, No. 1, 2002, pp. 142–145.Original Russian Text Copyright © 2002 by Prozorova, Pupkov, Sosin, Petrov.

SOLIDSStructure

Magnetic Resonance in Dilute Quasi-One-Dimensional Antiferromagnet CsNi1 – xMgxBr3

L. A. Prozorova*, G. V. Pupkov, S. S. Sosin, and S. V. PetrovKapitza Institute of Physical Problems, Russian Academy of Sciences, Moscow, 117334 Russia

*e-mail: prozorov@kapitza.ras.ruReceived September 5, 2001

Abstract—The effect of alloying with nonmagnetic Mg2+ ions on the low-frequency branch of resonance of anoncollinear quasi-one-dimensional CsNiBr3 antiferromagnet is investigated experimentally. It is found that a weak dilution(x = 2 to 4%) leads to a considerable (up to 15%) reduction of the resonant gap and of the spin-flop field. Theresults agree with the theory of Korenblit and Schender, according to which the small parameter of perturbation of the initial

system is x rather than the impurity concentration x; i.e., a quasi-one-dimensional amplification coefficient exists, whichis equal in this case to approximately six. © 2002 MAIK “Nauka/Interperiodica”.

J /J'

1. INTRODUCTION

The introduction of nonmagnetic impurities into amagnetic material brings about considerable changes in itsproperties. These changes are especially pronounced inmagnetic structures of reduced dimensions, in particular,in quasi-one-dimensional antiferromagnets. The problemon the properties of dilute antiferromagnetic chains wastreated theoretically by Bulaevskiœ [1]. He has demon-strated that the rupture of antiferromagnetic chains due tononmagnetic inclusions is accompanied by the emergenceof magnetic defects (additional degrees of freedom) asso-ciated with the fact that half of the chain segments willexhibit uncompensated spin. The emerging defects behaveas a paramagnetic impurity.

Real quasi-one-dimensional antiferromagnets at T <

TN ~ (J is the constant of exchange interaction alongthe chain and J' is the interchain interaction constant) arecharacterized by three-dimensional magnetic order. Atlow temperatures, the magnetic defects due to alloyingcease to be independent and come to be associated withother spins. This fact must influence the process of order-ing and all of the magnetic properties of the system. Theeffect of impurity on the properties of a quasi-one-dimen-sional antiferromagnet was treated theoretically within theclassical approximation of the spin-wave theory at T = 0by Korenblit and Schender [2]. The corrections to the val-ues of the susceptibility χ⊥ and of the gap in the spin wavespectrum ω(q = 0), calculated in the first order of perturba-tion theory, are defined by the following expressions,depending on the impurity concentration x:

(1)

J J'

χ χ x 0=( ) 1 αxJJ'----+

,=

ω ω x 0=( ) 1αx2

------ JJ'----–

,=

1063-7761/02/9401- $22.00 © 20119

where α is a numerical coefficient of the order of unity,dependent on the configuration of spins and on thenumber of nearest neighbors. Therefore, the small

parameter of perturbation is x rather than theimpurity concentration x; i.e., a “quasi-one-dimen-sional amplification” of the impurity effect exists.

Considerable variations of the ordering temperatureTN and magnetic susceptibility in the case of alloyingwere observed in a number of experimental studies(see, for example, [3–5]). It was further found [6] thatthe introduction of Mg2+ ions into a quasi-one-dimen-sional antiferromagnet with a noncollinear (“triangu-lar”) structure, CsNiCl3, caused a reduction of theenergy gap in the spectrum ν1(H = 0) (at x = 0.07, thefrequency of antiferromagnetic resonance in zero fielddecreased almost by half) in accordance with theoreti-cal predictions [2]. However, the introduction of a2−3% Mg impurity into single crystals of RbNiCl3 iso-morphic to CsNiCl3 brought about qualitatively differ-ent results [7]: an insignificant increase in the gapν1(H = 0) was accompanied by the emergence of addi-tional resonance absorption in the range from 3 to20 GHz. The field dependence of the frequency of thisadditional line resembles the acoustic branch of reso-nance ν3(H) characteristic of triangular structures ofstrong easy-axis anisotropy. Note that no resonanceabsorption is present in this frequency range for pureRbNiCl3, and the frequency ν3(H = 0) is estimated atonly 0.5 GHz. In order to interpret this strange phenom-enon, it was assumed that the Mg2+ ions introduced intoRbNiCl3 did not get to the lattice sites, this resulting instrong distortions and in the emergence of additionalanisotropy causing an increase in the oscillation fre-quencies ν1 and ν3. This assumption is supported by thefact that it is impossible to grow single crystals of

J /J'

002 MAIK “Nauka/Interperiodica”

120

PROZOROVA

et al

.

RbNi1 – xMgxCl3 with an Mg concentration of more than3%. Therefore, there is no doubt interest in investigat-ing the effect of substitutional impurity on resonancefrequencies in other triangular quasi-one-dimensionalantiferromagnets, in which the oscillation branch ν3 isknown to be in the microwave-frequency range, and tofind out how it varies when an impurity is introduced.

We investigated CsNiBr3 whose magnetic proper-ties were experimentally studied by a number ofresearchers (see, for example, [8–10]). According to theresults of those studies, three-dimensional magneticordering occurs at T < TN ~ 12 K, and, as in the case ofCsNiCl3 and RbNiCl3, a plane “triangular” magneticstructure arises, with the spin plane being perpendicularto the basal plane of the crystal. The acoustic branchesof oscillation at H || C6, H < Hc are described by the fol-lowing formulas (see [11, 12]):

(2)

where

Hc is the spin-flop field, = D/(χ|| – χ⊥ ), and D is theeasy-axis anisotropy constant.

At H ⊥ C6, the first two branches are the roots of thebiquadratic equation

(3)

and the third branch is independent of the field.

ν12 γ2 ηHc

2 H2+( ), ν22 0,= =

ν32 η∆3

2 Hc2 H2–

ηHc2 H2+

----------------------- 1HHc

------ 2

–3

,=

η χ || χ⊥–( )/χ⊥ , ∆3 ν1 H 0=( )DJ'----,∼=

Hc2

ν4 ν2 H2 ηHc2 η2H2+ +( )–

+ γ2η2H2 Hc2

H2+( ) 0,=

0.95

0.80

0.65

0.50

0.35

0.20

W, rel. units

0 10 20 30 40H, kOe

1

2

18.09 GHz

20.83

1

2

Fig. 1. Lines of absorption of a microwave signal in (1) pureand (2) dilute CsNiBr3 at different frequencies. The impu-rity concentration in dilute substance x = 0.04, T = 1.3 K.

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2. EXPERIMENTAL PROCEDUREAND SAMPLES

Microwave spectrometers with direct amplificationwere used to investigate the antiferromagnetic reso-nance. The measurements were performed at heliumtemperatures in the frequency range from 9 to 36 GHzand in fields of up to 65 kOe.

Single crystals of CsNiBr3 were grown similarly to sin-gle crystals of CsMnBr3 [13]. The method used to preparesingle crystals of solid solutions of CsNi1 – xMgxBr3 was asfollows. Single crystals of CsNiBr3 and metallic mag-nesium in the form of shavings (1–2% by weight) wereplaced in a quartz ampoule. The ampoule was evacu-ated and sealed. It was then cautiously heated by aburner to initiate the CsNiBr3 + Mg = CsMgBr3 + Nireaction. After that, the ampoule contents were meltedand stirred. The ampoule was placed into a furnace forgrowing a single crystal. According to our observa-tions, CsMgBr3 melts at a lower temperature thanCsNiBr3; therefore, the top portion of the obtained sin-gle crystal is richer in magnesium than its bottom por-tion. The impurity of metallic nickel formed does notinterfere with the crystal growth. The Mg content in thesamples selected for measurements was determined byγ-activation analysis [6].

3. EXPERIMENTAL RESULTS

Figure 1 gives examples of recordings of resonancelines for pure and doped CsNiBr3 at T = 1.3 K in a fielddirected parallel to the C6 axis. One can clearly see that,in the case of alloying, the resonance line correspond-ing to the ν3 mode broadens severalfold and shiftstowards lower fields. No absorption in fields higherthan Hc was observed in the region of the ν2 branch atany one of the measuring frequencies. No respectiverecordings at H ⊥ C6 are given, because the ν3 branchcannot be observed in this orientation due to theabsence of dispersion over the field, and the impurityhad almost no effect on the ν2 branch. Figure 2 gives theresults of our measurements of the ν2(H) and ν3(H)curves for pure single crystals and single crystals withan impurity of Mg2+ ions with the concentrations x =0.02 and 0.04 and field directions H || C6 and H ⊥ C6.The solid curves indicate the results of calculations byformulas (2) and (3) with the parameters η = 0.75, Hc =75.3, 64.0, and 53.4 kOe, and ∆3 = 25.3, 23.9, and22.1 GHz for x = 0, 0.02, and 0.04, respectively. Theinset gives the dependences of the relative variation of∆3 and Hc on the impurity concentration, as well as theirlinear fits with the coefficients three and seven, the first

ND THEORETICAL PHYSICS Vol. 94 No. 1 2002

MAGNETIC RESONANCE 121

of which defines, according to formula (1), the value ofquasi-one-dimensional amplification of the impurityeffect. In our case, this parameter is equal to approxi-mately six,

(4)

Note that the values of Hc, determined from our fitsfor all samples, prove to be less than the real field ofspin plane flop Hsf. For example, the spin-flop fielddetermined by the results of magnetostatic measure-ments for CsNiBr3 [8] is approximately 90 kOe. This isapparently due to the existence in the samples of twosuccessive spin-reorientation transitions, as wasobserved in another quasi-one-dimensional easy-axistriangular CsMnJ3 antiferromagnet [14]. In this case,the field dependence ν3(H) at H < Hc differs rather littlefrom that derived from formula (2); however, the ν3branch relaxes at both points. The field of first transitionis determined by fitting. Also indicative of this is theabsence of resonance absorption in fields H > Hc in asample with x = 0.04, in spite of the fact that the calcu-lated values of the resonance fields corresponding tothe ν1 andν2 branches lie within the accessible experi-mental range. Our results indicate that the effect ofimpurity on the field Hc proves to be twice as strong asits effect on the gap ∆3; this is possibly the result ofbroadening of the intermediate range Hc < H < Hsf dueto alloying. The dependences ν3(H) in the case of devi-ation of the magnetic field from rational directions arealso well described by the theoretical formulas of [12].Therefore, one can conclude that, in the case of lightalloying, a type of magnetic ordering persists, and theobserved reduction of the resonance gap and criticalfield with increasing impurity concentration is in qual-itative agreement with theory [2].

In order to perform a qualitative comparison, onemust determine the ratio J/J ' from other experiments.The value of J may be calculated from the results ofmagnetostatic measurements (according to [8], J = 17 K)or from the excitation spectrum obtained using theinelastic neutron scattering (it follows from [9] thatJ = 22 K). The difference in the values of J obtainedfrom different experiments is 20% (we assumed in cal-culations that J = 20 K). The constant J ' may be calcu-lated using the experimentally obtained value of ν3(H).It follows from our data, in view of the results of Kambeet al. [10], that J ' = 1.3 K.

Therefore, the experimentally observed quasi-one-dimensional amplification coefficient for CsNiBr3 isclose to the estimate that may be derived from the datagiven above for J and J '. The observed discrepancy maybe attributed both to the difference of the coefficient αfrom unity and to the errors in determining the param-eters J and J ', which are inevitable in the case ofdescribing quasi-one-dimensional magnetic systems

Q2x---

∆3 0( )∆3 x( )------------ 1–

α JJ'---- 6.≈= =

JOURNAL OF EXPERIMENTAL AND THEORETICAL PHY

within the classical approximation of the spin wave the-ory. Note that the inclusion of the contribution by zerooscillation to the magnetization and to the spin wavespectrum would bring about excess accuracy as com-pared with the theoretical results [2].

In the case of strong dilution, the form of the spec-trum changes. Figure 3 gives the experimental data forCsNi0.74Mg0.26Br3. This spectrum is close to that char-

10

00

ν, GHz

H, kOe

0.1

0 0.01

0.2

0.3

0.02 0.03

20

30

–20 25 50 75 100

H||C6

H⊥ C6

∆3(0)/∆3(x) – 1Hc(0)/Hc(x) – 1

Fig. 2. The resonance frequencies ν2, 3 as functions ofmagnetic field for CsNi1 – xMgxBr3 at T = 1.3 K: n, x = 0;d, x = 0.02; h, x = 0.04; solid curves, calculation by formu-las (2) and (3) (dashed curves, not observed experimen-tally). The inset gives the relative variation of the parame-ters ∆3 and Hc with the impurity concentration in view oflinear fits.

400 5

ν, GHz

H, kOe

50

60

70

80

90

10 15 20

Fig. 3. The resonance absorption frequency as a function ofmagnetic field at T = 1.3 K for CsNi0.74Mg0.26Br3. Thecurves indicate the theoretically obtained dependence forspin glass, calculated by formula (5).

SICS Vol. 94 No. 1 2002

122 PROZOROVA et al.

acteristic of transversely polarized resonant modes ofspin glass [15],

(5)

The theoretically obtained dependence ν1, 2(H) forspin glass with ∆ = 65 GHz and γ = 3 GHz/kOe isshown in the same graph by solid curves. However,additional investigations are required before making aconclusive statement to the effect that spin glass isformed in this case.

ACKNOWLEDGMENTS

We are grateful to Yu.M. Tsipenyuk for performingthe γ-activation analysis of samples. This study wassupported in part by the Russian Foundation for BasicResearch (project no. 00-02-170317), as well as byINTAS (grant no. 99-0155) and CRDF (grant no. RP1-2097).

REFERENCES

1. L. N. Bulaevskiœ, Fiz. Tverd. Tela (Leningrad) 11, 1132(1969) [Sov. Phys. Solid State 11, 921 (1969)].

2. I. Ya. Korenblit and E. F. Schender, Phys. Rev. B 48,9478 (1993).

3. C. Dupas and J. P. Renard, Phys. Rev. B 18, 401 (1978).

ν1 2, ∆2 γH2

-------

2

+γH2

-------.±=

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4. D. Visser, A. Harrison, and D. J. McIntyre, J. Phys.(Paris) 49, C8-1255 (1988).

5. J. Chadwick, D. H. Jones, J. A. Johnson, et al., J. Phys.:Condens. Matter 1, 6731 (1989).

6. S. S. Sosin, I. A. Zaliznyak, L. A. Prozorova, et al., Zh.Éksp. Teor. Fiz. 112, 209 (1997) [JETP 85, 114 (1997)].

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9. K. Kakurai, Physica B (Amsterdam) 180–181, 153(1992).

10. T. Kambe, H. Tanaka, Sh. Kimura, et al., J. Phys. Soc.Jpn. 65, 1799 (1996).

11. I. A. Zaliznyak, V. I. Marchenko, S. V. Petrov, et al.,Pis’ma Zh. Éksp. Teor. Fiz. 47, 172 (1988) [JETP Lett.47, 211 (1988)].

12. S. I. Abarzhi, M. E. Zhitomirskiœ, O. A. Petrenko, et al.,Zh. Éksp. Teor. Fiz. 104, 3232 (1993) [JETP 77, 521(1993)].

13. I. A. Zaliznyak, L. A. Prozorova, and S. V. Petrov, Zh.Éksp. Teor. Fiz. 97, 359 (1990) [Sov. Phys. JETP 70, 203(1990)].

14. V. I. Marchenko and A. M. Tikhonov, Pis’ma Zh. Éksp.Teor. Fiz. 68, 844 (1998) [JETP Lett. 68, 887 (1998)].

15. A. F. Andreev and V. I. Marchenko, Usp. Fiz. Nauk 130,39 (1980) [Sov. Phys. Usp. 23, 21 (1980)].

Translated by H. Bronstein

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