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Spin correlations and magnetoresistance in the bilayer manganite La1.2Sr1.8Mn2O7
ARTICLE IN PRESS
Physica B 312–313 (2002) 763–765
Spin correlations and magnetoresistance in the bilayer manganite La1:2Sr1:8 Mn2 O7 S. Rosenkranza,b,*, R. Osborna, L. Vasiliu-Dolocc,d, J.W. Lynnc, S.K. Sinhad, J.F. Mitchella a
Materials Science Division, Argonne National Laboratory, Argonne, IL 60439, USA b Department of Physics, University of Illinois, Chicago, IL 60607, USA c NIST Center for Neutron Research, NIST,Gaithersburg, Maryland 20899, USA d Advanced Photon Source, Argonne National Laboratory, Argonne, IL 60439, USA
Abstract We have studied the magnetic correlations in the x = 40% hole doped bilayer manganite La1:2 Sr1:8 Mn2 O7 using neutron scattering. The in-plane correlations obey standard two-dimensional scaling above TC B113 K with a crossover towards three-dimensional critical behavior close to TC ; consistent with quasi two-dimensional critical fluctuations. This suggests that conventional magnetism drives the phase transition while simultaneously destroying the charge correlations observed in the paramagnetic region. r 2002 Elsevier Science B.V. All rights reserved. Keywords: Manganites; Spin correlations; Magnetoresistance
Colossal magnetoresistance in optimally doped manganese oxides is believed to involve a strong coupling among spin, charge, and lattice degrees of freedom [1]. However, the nature of the ferromagnetic and concomitant insulator–metal transition has yet to be clearly established. Studying the nature of the transition and the interplay among correlations is greatly facilitated in the layered manganites because the reduced dimensionality increases the importance of fluctuations and extends the temperature region of significant correlations. For the 40% bilayer compound La1:2 Sr1:8 Mn2 O7 ; inelastic neutron scattering measurements of the spin-wave excitations yield a ratio of the nearest neighbor exchange constants J between spins within the same plane and J 0 between spins in different bilayers of J=J 0 B150 [2,3], comparable to the anisotropy in the transport properties [4]. This quasi-two-dimensionality is also observed in the paramagnetic diffuse scattering above TC ; which appears in the form of rods perpendicular to the planes [5,6]. Here, we present our detailed investigation of the *Corresponding author. Department of Physics, University of Illinois, Chicago, IL 60607, USA. Tel.: (312) 413-1844; fax: (312) 996-9016. E-mail address: [email protected] (S. Rosenkranz).
temperature dependence of the in-plane correlation length x and static susceptibility wðq ¼ 0Þ; which are related to the width and the height of these rods, respectively, using neutron scattering. The experiments were performed at the NIST Center for Neutron Research on the BT2 triple-axis spectrometer operating in two-axis mode with a fixed incident energy 13.7 meV and horizontal collimations of 600 -200 -200 ; full-width at half- maximum (FWHM). Pyrolytic graphite was used both as monochromator and filter against higher order contamination. In this two-axis mode, the diffuse scattering is, in the quasistatic approximation, proportional to the wavevector-dependent susceptibility SðQÞ = T * wT ðqÞ; where q ¼ Q t; Q is the momentum transfer and t denotes a reciprocal lattice vector of the magnetic structure. Scans were taken around the magnetic Bragg reflection at Q = ½h02; where the nuclear Bragg contribution is extremely weak. The validity of the quasistatic approximation was verified by comparing the results of these scans with those obtained from scans at Q = ½1 þ h; 0; 1:83 for which an optimal energy integration is obtained because, given the experimental conditions, the scattered wavevector is parallel to the c-axis [7].
0921-4526/02/$ - see front matter r 2002 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 0 1 ) 0 1 2 2 4 - 8
ARTICLE IN PRESS S. Rosenkranz et al. / Physica B 312–313 (2002) 763–765
764
Fig. 1 shows the in-plane correlation length x and neutron scattering intensity Sðq ¼ 0Þ obtained from these scans assuming the Ornstein–Zernike form of the scattering. Above TC both, x and Sðq ¼ 0Þ; grow with decreasing temperature in agreement with purely twodimensional behavior, as expected because of the strong anisotropy. On approaching TC however, we observe a crossover to three-dimensional scaling at a correlation length x2D E3a (in units of the nearest neighbor Mn– Mn distance a). Below TC we also observe threedimensional critical scaling close to TC until the correlation length again reaches x2D ; from where on it remains constant on further cooling. The above observations are in good quantitative agreement with the effective finite size model for singlelayer quasi-2D XY magnets, such as Rb2 CrCl4 ; in which there is a strong exchange anisotropy J=J 0 ; where J and J 0 are the in-plane and interlayer exchange constants, respectively [8–11]. In such systems, both above and below TC ; spin fluctuations on length scales that are small compared to the characteristic length Leff E OðJ=J 0 Þ are not affected by the interlayer coupling and are therefore purely 2D. When approaching TC from above, one expects the correlation length and the static susceptibility wT ðq ¼ 0Þ to increase according to the Kosterlitz–Thouless expressions x=a ¼ x0 exp½bðT=TKT 1Þ1=2 ; wT ðq ¼ 0Þ ¼ Cexp½BðT=TKT 1Þ1=2 ;
ð1Þ
where TKT is the topological ordering temperature of the 2D XY model [12]. Once the interlayer interaction becomes important, i.e., when the correlation length reaches the order of Leff ; a crossover to 3D scaling is expected. Renormalization group theory estimates a 3D
ξ (Å)
20
10 5
Counts (a.u.)
correlation length
15
400
effective finite size 2D
3D
2D
S(q=0)
300 200 100 50
100 150 Temperature (K)
ordering temperature TC ; that is related to TKT by TC ¼ TKT ½1 þ ðb=ln Leff Þ2 [9]. Below TC ; the correlation length decreases rapidly to Leff ; where spin fluctuations are again unaffected by the interlayer coupling and the correlation length remains constant. From this point on, although the magnetization is 3D, the fluctuations are 2D and the system can be modeled by a 2D system of effective size Leff [10]. From a least-squares fit of Eq. (1) to the observed correlation length above 120 K, we obtain x0 ¼ 0:3ð1Þ; TKT ¼ 64ð5Þ K; and b ¼ 2:1ð2Þ; in excellent agreement with the theoretical value of bE1:9 [10,11]. For the static susceptibility we obtain B ¼ 3:9ð4Þ; very close to the theoretical value B ¼ b * ð2 ZÞ; where the critical exponent Zo1=4: Using the fitted values for b and TKT and J=J 0 ¼ 150; we obtain TC E109 K; consistent with the value TC ¼ 113:2 K derived from the order parameter. Also, the deviation from the purely 2D behavior above TC and the effective finite size observed below TC are both in rough agreement with the value of Leff E10 predicted from the measured in-plane and interbilayer exchange constants. Furthermore, the linear temperature dependence of the neutron scattering intensity Sðq ¼ 0Þ below TC is a clear indication of 2D fluctuations in this temperature region [5]. Interestingly, the development of the spin correlations in the paramagnetic regime above TC occurs in the same temperature region in which a growth of static diffuse Xray and neutron scattering, arising from the strain field produced by localized charge defects (polarons), has been observed [13]. However, from the good quantitative agreement with the quasi-2D XY model, we conclude that the spin correlations develop independently of the formation of quasistatic polarons and that, in fact, the ferromagnetic phase transition is driven by conventional magnetism, whereas the polarons and their short-range correlations with each other explain the low hole mobility in the paramagnetic state, which cannot be due to double exchange alone [1]. However, once the magnetic correlations extend over a large enough region, the double exchange interaction can overcome the mechanism responsible for localizing the charges and the polarons start to collapse, resulting in the metal– insulator transition. This work was supported by US DOE BES-DMS under Contract no. W-31-109-ENG-38, the NSF DMR 97-01339 and the Swiss NSF.
200
Fig. 1. Temperature dependence of the correlation length x; obtained from a Lorentzian profile analysis of the scans along Q = ½h02 (circles) and ½1 þ h; 0; 1:83 (squares), and neutron scattering intensity Sðq ¼ 0Þ measured at Q = ½1 þ h; 0; 1:83: The solid line denotes a fit to the quasi two-dimensional XY model.
References [1] [2] [3] [4] [5]
A.J. Millis, et al., Phys. Rev. Lett. 77 (1996) 175. H. Fujioka, et al., J. Phys. Chem. Solids 60 (1999) 1165. S. Rosenkranz, et al., J. Appl. Phys. 87 (2000) 5816. Q. Li, et al., Phys. Rev. B 59 (1999) 9357. S. Rosenkranz, et al., J. Appl. Phys. 83 (1998) 7348.
ARTICLE IN PRESS S. Rosenkranz et al. / Physica B 312–313 (2002) 763–765 [6] R. Osborn, et al., Phys. Rev. Lett. 81 (1998) 3964. [7] J. Als-Nielsen, Phase Transitions and Critical Phenomena, Vol. 5A, Academic Press, New York 1976. [8] V.L. Berezinskii, A. Ya Blank, Sov. Phys.-JETP 37 (1973) 369. [9] S. Hikami, T. Tsuneto, Prog. Theor. Phys. 63 (1980) 387.
765
[10] S.T. Bramwell, P.C.W. Holdsworth, J. Phys.: Condens. Matter 5 (1993) L53. [11] J. Als-Nielsen, et al., J. Phys.: Condens. Matter 5 (1993) 7871. [12] J.M. Kosterlitz, D.J. Thouless, J. Phys. C 6 (1973) 1181. [13] L. Vasiliu-Doloc, et al., Phys. Rev. Lett. 83 (1999) 4393.
Physica B 312–313 (2002) 763–765
Spin correlations and magnetoresistance in the bilayer manganite La1:2Sr1:8 Mn2 O7 S. Rosenkranza,b,*, R. Osborna, L. Vasiliu-Dolocc,d, J.W. Lynnc, S.K. Sinhad, J.F. Mitchella a
Materials Science Division, Argonne National Laboratory, Argonne, IL 60439, USA b Department of Physics, University of Illinois, Chicago, IL 60607, USA c NIST Center for Neutron Research, NIST,Gaithersburg, Maryland 20899, USA d Advanced Photon Source, Argonne National Laboratory, Argonne, IL 60439, USA
Abstract We have studied the magnetic correlations in the x = 40% hole doped bilayer manganite La1:2 Sr1:8 Mn2 O7 using neutron scattering. The in-plane correlations obey standard two-dimensional scaling above TC B113 K with a crossover towards three-dimensional critical behavior close to TC ; consistent with quasi two-dimensional critical fluctuations. This suggests that conventional magnetism drives the phase transition while simultaneously destroying the charge correlations observed in the paramagnetic region. r 2002 Elsevier Science B.V. All rights reserved. Keywords: Manganites; Spin correlations; Magnetoresistance
Colossal magnetoresistance in optimally doped manganese oxides is believed to involve a strong coupling among spin, charge, and lattice degrees of freedom [1]. However, the nature of the ferromagnetic and concomitant insulator–metal transition has yet to be clearly established. Studying the nature of the transition and the interplay among correlations is greatly facilitated in the layered manganites because the reduced dimensionality increases the importance of fluctuations and extends the temperature region of significant correlations. For the 40% bilayer compound La1:2 Sr1:8 Mn2 O7 ; inelastic neutron scattering measurements of the spin-wave excitations yield a ratio of the nearest neighbor exchange constants J between spins within the same plane and J 0 between spins in different bilayers of J=J 0 B150 [2,3], comparable to the anisotropy in the transport properties [4]. This quasi-two-dimensionality is also observed in the paramagnetic diffuse scattering above TC ; which appears in the form of rods perpendicular to the planes [5,6]. Here, we present our detailed investigation of the *Corresponding author. Department of Physics, University of Illinois, Chicago, IL 60607, USA. Tel.: (312) 413-1844; fax: (312) 996-9016. E-mail address: [email protected] (S. Rosenkranz).
temperature dependence of the in-plane correlation length x and static susceptibility wðq ¼ 0Þ; which are related to the width and the height of these rods, respectively, using neutron scattering. The experiments were performed at the NIST Center for Neutron Research on the BT2 triple-axis spectrometer operating in two-axis mode with a fixed incident energy 13.7 meV and horizontal collimations of 600 -200 -200 ; full-width at half- maximum (FWHM). Pyrolytic graphite was used both as monochromator and filter against higher order contamination. In this two-axis mode, the diffuse scattering is, in the quasistatic approximation, proportional to the wavevector-dependent susceptibility SðQÞ = T * wT ðqÞ; where q ¼ Q t; Q is the momentum transfer and t denotes a reciprocal lattice vector of the magnetic structure. Scans were taken around the magnetic Bragg reflection at Q = ½h02; where the nuclear Bragg contribution is extremely weak. The validity of the quasistatic approximation was verified by comparing the results of these scans with those obtained from scans at Q = ½1 þ h; 0; 1:83 for which an optimal energy integration is obtained because, given the experimental conditions, the scattered wavevector is parallel to the c-axis [7].
0921-4526/02/$ - see front matter r 2002 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 0 1 ) 0 1 2 2 4 - 8
ARTICLE IN PRESS S. Rosenkranz et al. / Physica B 312–313 (2002) 763–765
764
Fig. 1 shows the in-plane correlation length x and neutron scattering intensity Sðq ¼ 0Þ obtained from these scans assuming the Ornstein–Zernike form of the scattering. Above TC both, x and Sðq ¼ 0Þ; grow with decreasing temperature in agreement with purely twodimensional behavior, as expected because of the strong anisotropy. On approaching TC however, we observe a crossover to three-dimensional scaling at a correlation length x2D E3a (in units of the nearest neighbor Mn– Mn distance a). Below TC we also observe threedimensional critical scaling close to TC until the correlation length again reaches x2D ; from where on it remains constant on further cooling. The above observations are in good quantitative agreement with the effective finite size model for singlelayer quasi-2D XY magnets, such as Rb2 CrCl4 ; in which there is a strong exchange anisotropy J=J 0 ; where J and J 0 are the in-plane and interlayer exchange constants, respectively [8–11]. In such systems, both above and below TC ; spin fluctuations on length scales that are small compared to the characteristic length Leff E OðJ=J 0 Þ are not affected by the interlayer coupling and are therefore purely 2D. When approaching TC from above, one expects the correlation length and the static susceptibility wT ðq ¼ 0Þ to increase according to the Kosterlitz–Thouless expressions x=a ¼ x0 exp½bðT=TKT 1Þ1=2 ; wT ðq ¼ 0Þ ¼ Cexp½BðT=TKT 1Þ1=2 ;
ð1Þ
where TKT is the topological ordering temperature of the 2D XY model [12]. Once the interlayer interaction becomes important, i.e., when the correlation length reaches the order of Leff ; a crossover to 3D scaling is expected. Renormalization group theory estimates a 3D
ξ (Å)
20
10 5
Counts (a.u.)
correlation length
15
400
effective finite size 2D
3D
2D
S(q=0)
300 200 100 50
100 150 Temperature (K)
ordering temperature TC ; that is related to TKT by TC ¼ TKT ½1 þ ðb=ln Leff Þ2 [9]. Below TC ; the correlation length decreases rapidly to Leff ; where spin fluctuations are again unaffected by the interlayer coupling and the correlation length remains constant. From this point on, although the magnetization is 3D, the fluctuations are 2D and the system can be modeled by a 2D system of effective size Leff [10]. From a least-squares fit of Eq. (1) to the observed correlation length above 120 K, we obtain x0 ¼ 0:3ð1Þ; TKT ¼ 64ð5Þ K; and b ¼ 2:1ð2Þ; in excellent agreement with the theoretical value of bE1:9 [10,11]. For the static susceptibility we obtain B ¼ 3:9ð4Þ; very close to the theoretical value B ¼ b * ð2 ZÞ; where the critical exponent Zo1=4: Using the fitted values for b and TKT and J=J 0 ¼ 150; we obtain TC E109 K; consistent with the value TC ¼ 113:2 K derived from the order parameter. Also, the deviation from the purely 2D behavior above TC and the effective finite size observed below TC are both in rough agreement with the value of Leff E10 predicted from the measured in-plane and interbilayer exchange constants. Furthermore, the linear temperature dependence of the neutron scattering intensity Sðq ¼ 0Þ below TC is a clear indication of 2D fluctuations in this temperature region [5]. Interestingly, the development of the spin correlations in the paramagnetic regime above TC occurs in the same temperature region in which a growth of static diffuse Xray and neutron scattering, arising from the strain field produced by localized charge defects (polarons), has been observed [13]. However, from the good quantitative agreement with the quasi-2D XY model, we conclude that the spin correlations develop independently of the formation of quasistatic polarons and that, in fact, the ferromagnetic phase transition is driven by conventional magnetism, whereas the polarons and their short-range correlations with each other explain the low hole mobility in the paramagnetic state, which cannot be due to double exchange alone [1]. However, once the magnetic correlations extend over a large enough region, the double exchange interaction can overcome the mechanism responsible for localizing the charges and the polarons start to collapse, resulting in the metal– insulator transition. This work was supported by US DOE BES-DMS under Contract no. W-31-109-ENG-38, the NSF DMR 97-01339 and the Swiss NSF.
200
Fig. 1. Temperature dependence of the correlation length x; obtained from a Lorentzian profile analysis of the scans along Q = ½h02 (circles) and ½1 þ h; 0; 1:83 (squares), and neutron scattering intensity Sðq ¼ 0Þ measured at Q = ½1 þ h; 0; 1:83: The solid line denotes a fit to the quasi two-dimensional XY model.
References [1] [2] [3] [4] [5]
A.J. Millis, et al., Phys. Rev. Lett. 77 (1996) 175. H. Fujioka, et al., J. Phys. Chem. Solids 60 (1999) 1165. S. Rosenkranz, et al., J. Appl. Phys. 87 (2000) 5816. Q. Li, et al., Phys. Rev. B 59 (1999) 9357. S. Rosenkranz, et al., J. Appl. Phys. 83 (1998) 7348.
ARTICLE IN PRESS S. Rosenkranz et al. / Physica B 312–313 (2002) 763–765 [6] R. Osborn, et al., Phys. Rev. Lett. 81 (1998) 3964. [7] J. Als-Nielsen, Phase Transitions and Critical Phenomena, Vol. 5A, Academic Press, New York 1976. [8] V.L. Berezinskii, A. Ya Blank, Sov. Phys.-JETP 37 (1973) 369. [9] S. Hikami, T. Tsuneto, Prog. Theor. Phys. 63 (1980) 387.
765
[10] S.T. Bramwell, P.C.W. Holdsworth, J. Phys.: Condens. Matter 5 (1993) L53. [11] J. Als-Nielsen, et al., J. Phys.: Condens. Matter 5 (1993) 7871. [12] J.M. Kosterlitz, D.J. Thouless, J. Phys. C 6 (1973) 1181. [13] L. Vasiliu-Doloc, et al., Phys. Rev. Lett. 83 (1999) 4393.