- Email: [email protected]
Spin correlation in the quasi-1D spin glass FeMgBO4
Solid State Communications, Vol. 38, pp. 1 2 9 - 1 3 3 . Pergamon Press Ltd. 1981. Printed in Great Britain.
0038- i 098/81/020129-05502.00/0
SPIN CORRELATION IN THE QUASI-1D SPIN GLASS FeMgB04 A. Wiedenmann and P. Burlet Centre d'Etudes Nucldaires de Grenoble, Ddpartement de Recherche Fondamentale, Laboratoire de Diffraction Neutronique, 85 X, 38041 Grenoble Cedcx, France and H. Scheuer and P. Convert Institut Max Von Laue-Paul Langevin, 38042 Grenoble Cedex, France
(Received 8 October 1980 by E.F. Bertaut) In FeMgBO4 Fe 3÷ ions form isolated zig-zag chains cut off by Mg2+ impurities. The magnetic diffuse neutron scattering measured at different temperatures can be described by 1D spin correlations within the chain segments. Isotropic first and second neighbour interactions lead to a shortrange helical spin arrangement which is perturbed at each diamagnetic impurity. Spin pair correlations increase with decreasing temperature down to 15 K where they reach saturation values reflecting a spin glass state.
1. INTRODUCTION FeMgBO4 is a particular example o f an insulating quasi-one-dimensional magnetic system. Fe3+-ions form zig-zag chains with distances between nearest neighbours (n.n.) of 2.9 A and next nearest neighbours (nanan.) of 3.1 A, respectively. Individual magnetic chains are separated by diamagnetic Mg2+ and B3÷-ions by 6 A, Precise crystallographic studies (X-ray and neutron diffraction) [1] revealed a relatively large inversion o f about 15% of Fe 3÷ and blg2+-ions on their crystallographic sites which leads to an imperfect 1D-system with interesting features. Previous investigations may be summarized as follows [ 1 - 3 ] . (1) Strong antiferromagnetic intrachain interactions between both nan. and n.nan, are present. The corresponding exchange integrals were estimated from susceptibility measurement at J~/k s = -- 16 K and J2/k8 = -- 8 K. Such a competition should give rise to a helical ground state in the pure chain. (2) The magnetic behaviour is not compatible with theoretical predictions for simple 1 D-models, e.g. the temperature T[(xrnax ) = 7 K where the static susceptibility exhibits a maximum is very low compared to the temperature T(C~,,,) = 50 K where the magnetic specific heat presents a rounded Scbottky-type maximum which we ascribed to 1 D-spin correlations. The low temperature properties o f FeMgBO4 however are very similar to those of spin-glasses. So we observed below Tt(xm~ ) a thermoremanent magnetization and at a slightly higher temperature the onset o f magnetic hyperfine splitting in M6ssbauer spectra. The absence of a
critical anomaly in the specific heat and o f any magnetic Bragg reflections in the neutron diffraction pattern down to 0.7 K proves that there is no conventional transition to long range magnetic ordering in this system. In this paper we report on a detailed investigation of the diffuse magnetic neutron scattering from which we determined the temperature dependence o f the static spin correlation functions. 2. EXPERIMENTAL RESULTS Neutron diffraction measurements were performed on the high resolution multicounter spectrometer D lb of the ILL-Grenoble. The powder sample under investigation was enriched to 99.3% with the boron isotope B [11] in order to avoid the high neutron absorption cross-section of natural boron. Using an incident wavelength o f 2.52 A we measured tile scattering crosssection at different temperatures between 1.5 and 300 K over a range of momentum transfer 0.26 ~,- t < Q < 3.4 ~ - t and calibrated on the intensities o f nuclear Bragg reflections. As a first result we found again that there are no magnetic reflections down to 1.5 K. What showed up instead was a modulation of the scattering cross-section in the low angle part o f the spectra at temperatures below 200 K indicating a gradual onset of magnetic short range order. Above this temperature the intensity distribution is flat which reflects that the system is in a paramagnetic state as it was well established by susceptibility measurements [1, 3]. The total measured scattering is the sum of an 129
SPIN CORRELATION IN THE QUASI-1D SPIN GLASS FeMgBOa
130
experimental background due to a sample environment, a nuclear scattering and the magnetic scattering. The first two contributions were found to be independent of temperature (there is no change in the high angle part o f the pattern, in the intensities of nuclear reflections and in the empty can neutron pattern at different temperatures), so they are cancelled by subtracting the high temperature scattering from the low temperature one. The magnetic cross-section in the quasi static approximation is given by equation (1) [4]: dg/dg2 = (ro%) 2 ~.
* JQSmJ@) exp (iQR,,m') (I) fmf,~(Sm
Vol. 38, No. 2
1
o , , , , ,T28o
b
•-=' .5~
1 ]
ee
i
,
ee
4
9 - 5 4i
Ili
•
T,
1 5~
:.
1",
160
i
rn, rtl'
where the summation is taken over all pair of magnetic atoms m, m' connected by the vector R,n, ,n'; Sm IQ is the component o f the magnetic moment perpendicular to the scattering vector Q , f m is the magnetic form factor and (ro%) = = 0.29 barn. This cross-section can be expressed as:
1.0 I
[sinQri cosQritl
sin Qr i 2 Ci ai i
--+Qri
bilT r7
(Ori;" / )
(3)
where ci is the number o f atoms connected to a given atom at a distance r i and the summation is taken over all interatomic distances. The coefficients a i and bi are related to the correlation function (4) by equation (5): (~OSi} u,
-
s
1 -
ai = (SoiSil);
( +
)
bi = 2(SIoISill)--(SolSil}
~
(4) (5)
where S~, S/II represent the component o f magnetic moment perpendicular and parallel to the radius vector ri. In the particular case o f isotropic interactions the spin pair correlations do not depend on the orientation o f the magnetic moment so that (So*&*) = 2
,7~1;
I
. . . .
I
20
_ '
r ]
~ '
'
- ~-~
Fig. 1. Observed difference cross-section at the low angle part for T = 1.5 K (points) and T = 160 K (stars). The solid curves are fits to equation (3) for isotropic interactions. sin Qr i
(2)
The first term in equation (2) represents the scattering by an assembly o f free atoms and corresponds to the magnetic scattering in the paramagnetic state at high temperatures. The second term corresponds to the scattering due to spin pair correlations in the short range order state at low temperatures. The difference between low temperature (T) and high temperature (To = 280 K) consists only in the contribution of pair correlations since as well the experimental, the nuclear and the paramagnetic scattering are cancelled. Such difference spectra are shown in Fig. 1. In a powder sample the scattering function S'(Q) can be expressed as [5, 6] S'(Q) :
. . . .
1.5
10
dS/dg2 = (ro%l=N./2m(O)[2/3S(S + 1) + S'(Q)] x exp [-- 2W(T)].
t
S'(Q)i~o
= Y. c , a i - - ;
i
Qri
3 ai -/i -
2
S:
(6)
Then, it is convenient to calculate the radial Fourier transform o f the experimental scattering (Qt and Q2 are the limits o f the experimental O range). 02
F(r) =
J" S ' ( Q ) Q sin Qr dO
O,
(7)
02 sin Or i = ~ cia i } sin Qr dQ i ()2 ri which have the particularity to present extrema at rvalues corresponding to the interatomic distances. This is no longer true when the interactions are anisotropic [bi :/: 0 in equation (3)]. When performing the Fourier transform o f our observed difference cross-sections multiplied by Q, we found maxima and minima at r-values corresponding to the first intra-chain radius vectors as known from crystallographic studies (Fig. 2). This is an important indication that the spin correlations in FeMgBO4 are principally isotropic and one-dimensional in character. Absolute values of the correlation functions -/i were obtained with the aid of a least-square routine by fitting directly the observed difference cross-section to equation (3) as well as its Fourier transform to equation (7). The only adjusted parameters were the correlation coefficients ai and bi since we use crystallographic data for the radius vectors r and c = 2 for the number of neighbours. As -/i decreases rapidly with increasing distance we have limited the fits at r = 9 A. Moreover % and "/2 cannot be determined individually but only the sum of both since the distances rl and r 2 are nearly the same. Good agreement between observed and
Vol. 38, No. 2
131
SPIN CORRELATION IN THE QUASI-1D SPIN GLASS FeMgBO~
Table 1. Spin pair correlation functions o f FeMgBO4 obtained by a least square fit o f data to a 1D model o f isotropic interactT'ons (value o f standard deviation in brackets) T [°K] 1.5 5 9 15 20 30 50 80 100 130 160
Tz + 3'2
T3
T4
(ri = 2.9 •, r: = 3.1 A)
(r3 = 5.2 A)
(r4 = 6.2/1~)
-- 1.034 (0.09) -- 1.030 (0.09) -- 1.0375 (0.10) --0.957 (0.091 ) -- 0.832 (0.11 ) -- 0.779 (0.09) -- 0.6993 (0.09) -- 0.583 (0.06) -- 0.387 (0.03) -- 0.295 (0.03) -- 0.215
1.299 (0.03) 1.302 (0.03) 1.308 (0.04) 1.125 (0.031 ) 0.971 (0.04) 0.865 (0.35) 0.673 (0.03) 0.718 (0.04) 0.471 (0.027) 0.408 (0.025) 0.300
-- 1.00 (0.03) 1.05 (0.04) -- 1.05 (0.04) --0.867 (0.035) -- 0.845 (0.044) -- 0.752 (0.040) -- 0.629 (0.034) -- 0.695 (0.041) -- 0.492 (0.031) -- 0.437 (0.027) -- 0.31
(o.o3)
F(r)
We
'
11
r12
'
'ir
4
3
'
(o.o3)
(o.o3)
Numerical values of (3't + 3':), 3'3 and 3'4 are given in Table 1. The normalization error is of the order of 10%. One comment on the absolute values of 3'3 and 3'4 may be given. The rather large low temperature values may be due to the fact that the contribution of pair correlations to the observed magnetic intensity decreases with the distance so that the precision on the 3'i values decreases with increasing radius vector r i. The individual resolution of 3'3 and 3'4, which are of opposite sign, is further reduced by the small difference in the radius vectors r3 (5.27 A) and r4 (6.19 A), essentially at higher temperatures (note that for T > 80 K 3'3 + 3'4 ~
i' fi
"1--
-1-
0). . I
I
t
I
. [
] I
I
L
I
Fig. 2. The Fourier transform of observed difference cross-section at T = 9 K (points) in arbitrary units, The peaks are centered on r-values corresponding to the I D radius vectors ri marked by arrows, The solid line represents a fit to the isotropic model [equation (4)]. calculated data was obtained for fits based on an isotropic model as it is shown in Figs. 1 and 2 (full lines). All attempts to use anisotropic models lead to non significant values of a i and b i with enormous standard deviations.
3. DISCUSSION The diffuse magnetic scattering in FeMgBO4 is well described by isotropic spin-pair correlations of the iron inside of the zig-zag chains. We consider now the saturation values of 3'i below 15 K. The sum of 3"1 + 3'2 is close to unity with a negative sign, 3'3 is nearly one with a positive sign and 3'4 is again negative. Such a sequence of sign and the absolute values of the correlation functions are not compatible with a simple antiferromagnetic ground state, for which 3'x + 3': should be equal zero and 3'3 = -- 1. In an assumed helical ground state of the pure spin chain however the static
132
SPIN CORRELATION IN THE QUASI-1 D SPIN GLASS FeMgBO~
1.0 t
i +'¢2 I i
I
i
[
I
i
is not compatible with this infinite spin chain model. We explain this particular behaviour by the presence of Mg'+ impurities within the magnetic chains which can transform the quasi-I D system into a spin glass in the following way. Each single non-magnetic impurity creates a perturbation of the helical spin arrangement because it breaks up the n.n. interaction J1 but not the n.n.n• coupling Jz so that either the phase of the helix or its rotation sense may be changed. This means that with decreasing temperature the coherence length can only increase up to a certain limit representing the average impurity separation. Therefore the magnetic diffuse neutron scattering intensity of a powder sample will reach saturation at a finite temperature. As long as two consecutive impurities are neglected the individual correlation functions are then given by equation (10):
I
i
O Experiment • 0.7
k~
DE RAEDT
5I ,x ~
!
Jt/kB=-16K d2/kB=_8 K
0.6 0.5 0.4 0.3
I
0
I
20
I
I
40
I
I
60
I
I
80
I
T [K]
Fig. 3. Temperature dependence of the sum (71 + 72)Experimental values are scaled by a factor 0.86. The full line results from a Monte-Carlo simulation (De Raedt [7]) of an I D helical system. spin correlation functions are related to the step angle 'P between neighbour spins by equation (8): (Si .Si+,,)T=o = COS (nq O.
(8)
Then the observed saturation values of 9'1 + 3'2 "" -- 1 and 3'3 ~ + 1 as well as the negative sign of 3'4 are consistent with an angle q.' of the order of 120 °. First, second and fourth neighbour are correlated antiferromagnetically whereas the third neighbour has a ferromagnetic correlation relative to a spin at the origin. Furthermore the step angle qz of the ground state is connected to the exchange integrals J1 and./2 representing n.n and n.n.n interactions respectively, by equation (8): COS ~ = JJ4[J2[.
Vol. 38, No• 2
(9)
Using the above value ofqJ = 120 ° we find for the
ratioJl/J2 = 2, which is the same as we have already derived from susceptibility measurements. Recently De Raedt [7] used a Monte Carlo method to calculate the temperature dependence of the static spin pair correlation function of a classical 1D-Heisenberg chain with n.n. and n.n.n, interactions for various ratios of J1/J2 including our experimental values [8]. The calculated values of the sum 71 + 3'2 (full line in Fig. 3) present the same principal feature as the experimental values for temperatures above 15 K. A difference in absolute values between observed and calculated data may be explained by systematic normalization errors so that scaling of experimental values by a factor 0.85, which give good agreement with the Monte Carlo simulation (Fig. 3) is justified. The observed saturation effect below 15 K however
(SiSi+n)r=o = (1 - - x ) 2 cos [(i-- 2v)q~ + vn]
(10)
where v is the number of Mg-ions between the spins at sites i and i + n. In the ground state these functions are never zero even for infinite distances, but the average over all pairs i, n: (g(r))r= o = 1/N ~ (SiSi+,~)6(ri, i+n -- r)
i,r*.
(I 1)
vanishes rapidly when r -+ oo as a consequence of the random impurity distribution. The impure quasi-1D system FeMgB04 therefore satisfy the two conditions of Villain's definition of a spin g/ass ground state, i.e. the absence of any long range magnetic order [equation (11)] in spite of finite values of the individual correlation function [equation (10)] [9]• This is quite different from conventional I D models with only first neighbour interaction. Each nonmagnetic impurity cut the magnetic correlation so that such a system can not have a spin glass ground state. Furthermore a weak interchain coupling always leads to 3D magnetic order at low temperatures; only the transition temperature TN is lowered in the presence of non-magnetic impurities [ 10]. In the impure chain with n.n. and n.n.n, interaction however such a crossover is only possible if the effective interchain interaction J'/x is large enough to oppose the change in the I D correlations which is created by each impurity, i.e. only if the impurity concentration x is small and ot the order of [11]: x ~ x/(JtlJ21).
(12)
Otherwise the interchain coupling leads to a highly frustrated 3D spin glass state. From equation (12) we can estimate that even a relatively strong interchain integral YTJ: = 10-: would not lead to long range ordering in FeMgBO,, with x = O. 15. In conclusion it is the first time that the neutron
Vol. 38, No. 2
SPIN CORRELATION IN THE QUASI-1 D SPIN GLASS FeMgBO~
diffraction measurements over a large Q-range allows an extensive study of spin pair correlation in an insulating spin-glass. The interest of this subject is increased by the one dimensional character of the magnetic interactions. Two distinct regimes are defined. Below T r the spin correlations show saturation reflecting the spin glass state. Above T r there is a gradual decrease of the correlations with increasing temperature typical for I D-short range order. Another important result is the first experimental evidence of an helical ground state in one dimensional system.
Acknowledgements - We are very much indebted to Prof. Dr E.F. Bertaut and Dr J. Villain for their continuous interest in this work and for their helpful suggestions. We are grateful to Dr H. De Raedt for Monte Carlo computer simulations. This work was supported in part by the Commission of European Communities and the Bundesministerium fiir Forschung Projekt No. 03-41E-2 IP.
133
i T REFERENCES
1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11.
A. Wiedenmann & P. Burlet, J. de Yhy~ 39, 8-6C, 720 (1978). A. Wiedenmann, P. Butler & R. Chevalier, J. Magn. MagrL Mat. 1 5 - 1 8 , 2 1 6 (1980). A. Wiedenmann, Thesis, Hamburg (1980). See for example: W. Marshall & S.W. Lovesey, Theory of Thermal Neu tron Scattering. Oxford (1977). 1. Blech & B.L. Averbach,Physics 1, 31 (1964). P. Burlet & E.F. Bertaut, SolMState Commura 5, 279 (1967). H. De Raedt & B. De Raedt,Phyz Rev. B19, 5, 2595 (1979). H. De Raedt (private communication). J. Villain, Z. Phy~ B33,31 (1979). D. Hone, D.A. Montano, T. Tonegawa & J. Imry, Phys. Rev. B12, 11,5141 (1975). J. Villain (private communication).
0038- i 098/81/020129-05502.00/0
SPIN CORRELATION IN THE QUASI-1D SPIN GLASS FeMgB04 A. Wiedenmann and P. Burlet Centre d'Etudes Nucldaires de Grenoble, Ddpartement de Recherche Fondamentale, Laboratoire de Diffraction Neutronique, 85 X, 38041 Grenoble Cedcx, France and H. Scheuer and P. Convert Institut Max Von Laue-Paul Langevin, 38042 Grenoble Cedex, France
(Received 8 October 1980 by E.F. Bertaut) In FeMgBO4 Fe 3÷ ions form isolated zig-zag chains cut off by Mg2+ impurities. The magnetic diffuse neutron scattering measured at different temperatures can be described by 1D spin correlations within the chain segments. Isotropic first and second neighbour interactions lead to a shortrange helical spin arrangement which is perturbed at each diamagnetic impurity. Spin pair correlations increase with decreasing temperature down to 15 K where they reach saturation values reflecting a spin glass state.
1. INTRODUCTION FeMgBO4 is a particular example o f an insulating quasi-one-dimensional magnetic system. Fe3+-ions form zig-zag chains with distances between nearest neighbours (n.n.) of 2.9 A and next nearest neighbours (nanan.) of 3.1 A, respectively. Individual magnetic chains are separated by diamagnetic Mg2+ and B3÷-ions by 6 A, Precise crystallographic studies (X-ray and neutron diffraction) [1] revealed a relatively large inversion o f about 15% of Fe 3÷ and blg2+-ions on their crystallographic sites which leads to an imperfect 1D-system with interesting features. Previous investigations may be summarized as follows [ 1 - 3 ] . (1) Strong antiferromagnetic intrachain interactions between both nan. and n.nan, are present. The corresponding exchange integrals were estimated from susceptibility measurement at J~/k s = -- 16 K and J2/k8 = -- 8 K. Such a competition should give rise to a helical ground state in the pure chain. (2) The magnetic behaviour is not compatible with theoretical predictions for simple 1 D-models, e.g. the temperature T[(xrnax ) = 7 K where the static susceptibility exhibits a maximum is very low compared to the temperature T(C~,,,) = 50 K where the magnetic specific heat presents a rounded Scbottky-type maximum which we ascribed to 1 D-spin correlations. The low temperature properties o f FeMgBO4 however are very similar to those of spin-glasses. So we observed below Tt(xm~ ) a thermoremanent magnetization and at a slightly higher temperature the onset o f magnetic hyperfine splitting in M6ssbauer spectra. The absence of a
critical anomaly in the specific heat and o f any magnetic Bragg reflections in the neutron diffraction pattern down to 0.7 K proves that there is no conventional transition to long range magnetic ordering in this system. In this paper we report on a detailed investigation of the diffuse magnetic neutron scattering from which we determined the temperature dependence o f the static spin correlation functions. 2. EXPERIMENTAL RESULTS Neutron diffraction measurements were performed on the high resolution multicounter spectrometer D lb of the ILL-Grenoble. The powder sample under investigation was enriched to 99.3% with the boron isotope B [11] in order to avoid the high neutron absorption cross-section of natural boron. Using an incident wavelength o f 2.52 A we measured tile scattering crosssection at different temperatures between 1.5 and 300 K over a range of momentum transfer 0.26 ~,- t < Q < 3.4 ~ - t and calibrated on the intensities o f nuclear Bragg reflections. As a first result we found again that there are no magnetic reflections down to 1.5 K. What showed up instead was a modulation of the scattering cross-section in the low angle part o f the spectra at temperatures below 200 K indicating a gradual onset of magnetic short range order. Above this temperature the intensity distribution is flat which reflects that the system is in a paramagnetic state as it was well established by susceptibility measurements [1, 3]. The total measured scattering is the sum of an 129
SPIN CORRELATION IN THE QUASI-1D SPIN GLASS FeMgBOa
130
experimental background due to a sample environment, a nuclear scattering and the magnetic scattering. The first two contributions were found to be independent of temperature (there is no change in the high angle part o f the pattern, in the intensities of nuclear reflections and in the empty can neutron pattern at different temperatures), so they are cancelled by subtracting the high temperature scattering from the low temperature one. The magnetic cross-section in the quasi static approximation is given by equation (1) [4]: dg/dg2 = (ro%) 2 ~.
* JQSmJ@) exp (iQR,,m') (I) fmf,~(Sm
Vol. 38, No. 2
1
o , , , , ,T28o
b
•-=' .5~
1 ]
ee
i
,
ee
4
9 - 5 4i
Ili
•
T,
1 5~
:.
1",
160
i
rn, rtl'
where the summation is taken over all pair of magnetic atoms m, m' connected by the vector R,n, ,n'; Sm IQ is the component o f the magnetic moment perpendicular to the scattering vector Q , f m is the magnetic form factor and (ro%) = = 0.29 barn. This cross-section can be expressed as:
1.0 I
[sinQri cosQritl
sin Qr i 2 Ci ai i
--+Qri
bilT r7
(Ori;" / )
(3)
where ci is the number o f atoms connected to a given atom at a distance r i and the summation is taken over all interatomic distances. The coefficients a i and bi are related to the correlation function (4) by equation (5): (~OSi} u,
-
s
1 -
ai = (SoiSil);
(
bi = 2(SIoISill)--(SolSil}
~
(4) (5)
where S~, S/II represent the component o f magnetic moment perpendicular and parallel to the radius vector ri. In the particular case o f isotropic interactions the spin pair correlations do not depend on the orientation o f the magnetic moment so that (So*&*) = 2
,7~1;
I
. . . .
I
20
_ '
r ]
~ '
'
- ~-~
Fig. 1. Observed difference cross-section at the low angle part for T = 1.5 K (points) and T = 160 K (stars). The solid curves are fits to equation (3) for isotropic interactions. sin Qr i
(2)
The first term in equation (2) represents the scattering by an assembly o f free atoms and corresponds to the magnetic scattering in the paramagnetic state at high temperatures. The second term corresponds to the scattering due to spin pair correlations in the short range order state at low temperatures. The difference between low temperature (T) and high temperature (To = 280 K) consists only in the contribution of pair correlations since as well the experimental, the nuclear and the paramagnetic scattering are cancelled. Such difference spectra are shown in Fig. 1. In a powder sample the scattering function S'(Q) can be expressed as [5, 6] S'(Q) :
. . . .
1.5
10
dS/dg2 = (ro%l=N./2m(O)[2/3S(S + 1) + S'(Q)] x exp [-- 2W(T)].
t
S'(Q)i~o
= Y. c , a i - - ;
i
Qri
3 ai -/i -
2
S:
(6)
Then, it is convenient to calculate the radial Fourier transform o f the experimental scattering (Qt and Q2 are the limits o f the experimental O range). 02
F(r) =
J" S ' ( Q ) Q sin Qr dO
O,
(7)
02 sin Or i = ~ cia i } sin Qr dQ i ()2 ri which have the particularity to present extrema at rvalues corresponding to the interatomic distances. This is no longer true when the interactions are anisotropic [bi :/: 0 in equation (3)]. When performing the Fourier transform o f our observed difference cross-sections multiplied by Q, we found maxima and minima at r-values corresponding to the first intra-chain radius vectors as known from crystallographic studies (Fig. 2). This is an important indication that the spin correlations in FeMgBO4 are principally isotropic and one-dimensional in character. Absolute values of the correlation functions -/i were obtained with the aid of a least-square routine by fitting directly the observed difference cross-section to equation (3) as well as its Fourier transform to equation (7). The only adjusted parameters were the correlation coefficients ai and bi since we use crystallographic data for the radius vectors r and c = 2 for the number of neighbours. As -/i decreases rapidly with increasing distance we have limited the fits at r = 9 A. Moreover % and "/2 cannot be determined individually but only the sum of both since the distances rl and r 2 are nearly the same. Good agreement between observed and
Vol. 38, No. 2
131
SPIN CORRELATION IN THE QUASI-1D SPIN GLASS FeMgBO~
Table 1. Spin pair correlation functions o f FeMgBO4 obtained by a least square fit o f data to a 1D model o f isotropic interactT'ons (value o f standard deviation in brackets) T [°K] 1.5 5 9 15 20 30 50 80 100 130 160
Tz + 3'2
T3
T4
(ri = 2.9 •, r: = 3.1 A)
(r3 = 5.2 A)
(r4 = 6.2/1~)
-- 1.034 (0.09) -- 1.030 (0.09) -- 1.0375 (0.10) --0.957 (0.091 ) -- 0.832 (0.11 ) -- 0.779 (0.09) -- 0.6993 (0.09) -- 0.583 (0.06) -- 0.387 (0.03) -- 0.295 (0.03) -- 0.215
1.299 (0.03) 1.302 (0.03) 1.308 (0.04) 1.125 (0.031 ) 0.971 (0.04) 0.865 (0.35) 0.673 (0.03) 0.718 (0.04) 0.471 (0.027) 0.408 (0.025) 0.300
-- 1.00 (0.03) 1.05 (0.04) -- 1.05 (0.04) --0.867 (0.035) -- 0.845 (0.044) -- 0.752 (0.040) -- 0.629 (0.034) -- 0.695 (0.041) -- 0.492 (0.031) -- 0.437 (0.027) -- 0.31
(o.o3)
F(r)
We
'
11
r12
'
'ir
4
3
'
(o.o3)
(o.o3)
Numerical values of (3't + 3':), 3'3 and 3'4 are given in Table 1. The normalization error is of the order of 10%. One comment on the absolute values of 3'3 and 3'4 may be given. The rather large low temperature values may be due to the fact that the contribution of pair correlations to the observed magnetic intensity decreases with the distance so that the precision on the 3'i values decreases with increasing radius vector r i. The individual resolution of 3'3 and 3'4, which are of opposite sign, is further reduced by the small difference in the radius vectors r3 (5.27 A) and r4 (6.19 A), essentially at higher temperatures (note that for T > 80 K 3'3 + 3'4 ~
i' fi
"1--
-1-
0). . I
I
t
I
. [
] I
I
L
I
Fig. 2. The Fourier transform of observed difference cross-section at T = 9 K (points) in arbitrary units, The peaks are centered on r-values corresponding to the I D radius vectors ri marked by arrows, The solid line represents a fit to the isotropic model [equation (4)]. calculated data was obtained for fits based on an isotropic model as it is shown in Figs. 1 and 2 (full lines). All attempts to use anisotropic models lead to non significant values of a i and b i with enormous standard deviations.
3. DISCUSSION The diffuse magnetic scattering in FeMgBO4 is well described by isotropic spin-pair correlations of the iron inside of the zig-zag chains. We consider now the saturation values of 3'i below 15 K. The sum of 3"1 + 3'2 is close to unity with a negative sign, 3'3 is nearly one with a positive sign and 3'4 is again negative. Such a sequence of sign and the absolute values of the correlation functions are not compatible with a simple antiferromagnetic ground state, for which 3'x + 3': should be equal zero and 3'3 = -- 1. In an assumed helical ground state of the pure spin chain however the static
132
SPIN CORRELATION IN THE QUASI-1 D SPIN GLASS FeMgBO~
1.0 t
i +'¢2 I i
I
i
[
I
i
is not compatible with this infinite spin chain model. We explain this particular behaviour by the presence of Mg'+ impurities within the magnetic chains which can transform the quasi-I D system into a spin glass in the following way. Each single non-magnetic impurity creates a perturbation of the helical spin arrangement because it breaks up the n.n. interaction J1 but not the n.n.n• coupling Jz so that either the phase of the helix or its rotation sense may be changed. This means that with decreasing temperature the coherence length can only increase up to a certain limit representing the average impurity separation. Therefore the magnetic diffuse neutron scattering intensity of a powder sample will reach saturation at a finite temperature. As long as two consecutive impurities are neglected the individual correlation functions are then given by equation (10):
I
i
O Experiment • 0.7
k~
DE RAEDT
5I ,x ~
!
Jt/kB=-16K d2/kB=_8 K
0.6 0.5 0.4 0.3
I
0
I
20
I
I
40
I
I
60
I
I
80
I
T [K]
Fig. 3. Temperature dependence of the sum (71 + 72)Experimental values are scaled by a factor 0.86. The full line results from a Monte-Carlo simulation (De Raedt [7]) of an I D helical system. spin correlation functions are related to the step angle 'P between neighbour spins by equation (8): (Si .Si+,,)T=o = COS (nq O.
(8)
Then the observed saturation values of 9'1 + 3'2 "" -- 1 and 3'3 ~ + 1 as well as the negative sign of 3'4 are consistent with an angle q.' of the order of 120 °. First, second and fourth neighbour are correlated antiferromagnetically whereas the third neighbour has a ferromagnetic correlation relative to a spin at the origin. Furthermore the step angle qz of the ground state is connected to the exchange integrals J1 and./2 representing n.n and n.n.n interactions respectively, by equation (8): COS ~ = JJ4[J2[.
Vol. 38, No• 2
(9)
Using the above value ofqJ = 120 ° we find for the
ratioJl/J2 = 2, which is the same as we have already derived from susceptibility measurements. Recently De Raedt [7] used a Monte Carlo method to calculate the temperature dependence of the static spin pair correlation function of a classical 1D-Heisenberg chain with n.n. and n.n.n, interactions for various ratios of J1/J2 including our experimental values [8]. The calculated values of the sum 71 + 3'2 (full line in Fig. 3) present the same principal feature as the experimental values for temperatures above 15 K. A difference in absolute values between observed and calculated data may be explained by systematic normalization errors so that scaling of experimental values by a factor 0.85, which give good agreement with the Monte Carlo simulation (Fig. 3) is justified. The observed saturation effect below 15 K however
(SiSi+n)r=o = (1 - - x ) 2 cos [(i-- 2v)q~ + vn]
(10)
where v is the number of Mg-ions between the spins at sites i and i + n. In the ground state these functions are never zero even for infinite distances, but the average over all pairs i, n: (g(r))r= o = 1/N ~ (SiSi+,~)6(ri, i+n -- r)
i,r*.
(I 1)
vanishes rapidly when r -+ oo as a consequence of the random impurity distribution. The impure quasi-1D system FeMgB04 therefore satisfy the two conditions of Villain's definition of a spin g/ass ground state, i.e. the absence of any long range magnetic order [equation (11)] in spite of finite values of the individual correlation function [equation (10)] [9]• This is quite different from conventional I D models with only first neighbour interaction. Each nonmagnetic impurity cut the magnetic correlation so that such a system can not have a spin glass ground state. Furthermore a weak interchain coupling always leads to 3D magnetic order at low temperatures; only the transition temperature TN is lowered in the presence of non-magnetic impurities [ 10]. In the impure chain with n.n. and n.n.n, interaction however such a crossover is only possible if the effective interchain interaction J'/x is large enough to oppose the change in the I D correlations which is created by each impurity, i.e. only if the impurity concentration x is small and ot the order of [11]: x ~ x/(JtlJ21).
(12)
Otherwise the interchain coupling leads to a highly frustrated 3D spin glass state. From equation (12) we can estimate that even a relatively strong interchain integral YTJ: = 10-: would not lead to long range ordering in FeMgBO,, with x = O. 15. In conclusion it is the first time that the neutron
Vol. 38, No. 2
SPIN CORRELATION IN THE QUASI-1 D SPIN GLASS FeMgBO~
diffraction measurements over a large Q-range allows an extensive study of spin pair correlation in an insulating spin-glass. The interest of this subject is increased by the one dimensional character of the magnetic interactions. Two distinct regimes are defined. Below T r the spin correlations show saturation reflecting the spin glass state. Above T r there is a gradual decrease of the correlations with increasing temperature typical for I D-short range order. Another important result is the first experimental evidence of an helical ground state in one dimensional system.
Acknowledgements - We are very much indebted to Prof. Dr E.F. Bertaut and Dr J. Villain for their continuous interest in this work and for their helpful suggestions. We are grateful to Dr H. De Raedt for Monte Carlo computer simulations. This work was supported in part by the Commission of European Communities and the Bundesministerium fiir Forschung Projekt No. 03-41E-2 IP.
133
i T REFERENCES
1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11.
A. Wiedenmann & P. Burlet, J. de Yhy~ 39, 8-6C, 720 (1978). A. Wiedenmann, P. Butler & R. Chevalier, J. Magn. MagrL Mat. 1 5 - 1 8 , 2 1 6 (1980). A. Wiedenmann, Thesis, Hamburg (1980). See for example: W. Marshall & S.W. Lovesey, Theory of Thermal Neu tron Scattering. Oxford (1977). 1. Blech & B.L. Averbach,Physics 1, 31 (1964). P. Burlet & E.F. Bertaut, SolMState Commura 5, 279 (1967). H. De Raedt & B. De Raedt,Phyz Rev. B19, 5, 2595 (1979). H. De Raedt (private communication). J. Villain, Z. Phy~ B33,31 (1979). D. Hone, D.A. Montano, T. Tonegawa & J. Imry, Phys. Rev. B12, 11,5141 (1975). J. Villain (private communication).