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Magnetism in oxide chains bridged with the hydride anion: LaSrCoO3H0.7 studied using muon-spin rotation
Physica B 326 (2003) 527–531
Magnetism in oxide chains bridged with the hydride anion: LaSrCoO3H0:7 studied using muon-spin rotation S.J. Blundella,*, I.M. Marshalla, F.L. Prattb, M.A. Haywardc, E.J. Cussenc, J.B. Claridgec, M. Bieringerc, C.J. Kielyc, M.J. Rosseinskyc a
Oxford University Department of Physics, Clarendon Laboratory, Parks Road, Oxford OX1 3PU, UK b ISIS, Rutherford Appleton Laboratory, Chilton, Oxfordshire OX11 0QX, UK c Department of Chemistry, University of Liverpool, Liverpool L69 7ZD, UK
Abstract The transition metal oxide hydride, LaSrCoO3 H0:7 ; adopts an unprecedented structure in which oxide chains are bridged by hydride anions to form a two-dimensional extended network in which magnetic ordering is found up to at least 350 K: Muon-spin rotation has been used to demonstrate that this material is uniformly magnetically ordered throughout its bulk. Our results are compared with those on Sr2 CuO3 and Ca2 CuO3 which adopt a similar oxide chain structure and we demonstrate the crucial role of the bridging hydride ions. r 2002 Elsevier Science B.V. All rights reserved. Keywords: Hydride; Magnetic chain; Superexchange
1. Introduction Superexchange [1], the exchange spin-coupling through intermediate non-magnetic atoms, is responsible for the antiferromagnetism observed in many transition metal oxides. It arises because electrons can gain energy by delocalising over nonorthogonal orbitals when the moments are aligned antiparallel, but not when they are parallel, so that there is a kinetic energy gain [2]. The mutual repulsion of electrons on the same ion prevents the permanent occupation of excited states in which electrons transfer via the intermediate O2 anion, *Corresponding author. Tel.: +44-1865-272310; fax: +441865-272400. E-mail address: [email protected] (S.J. Blundell).
but virtual occupation of excited states (connected to the ground state by the transfer integral) leads to a gain in energy. Superexchange through O2 anions is thus responsible for many of the magnetic properties of transition metal oxides [3] and oxyhalides [4]. We have recently shown that it is possible to prepare an extended transition metal oxide array with hydride ions ðH Þ inserted into the structure [5]. Using various experimental techniques, including muon-spin rotation ðmSRÞ; we find that in our new material LaSrCoO3 H0:7 the hydride ion transmits exchange interactions between the transition metal cations at least as effectively as O2 ; opening up a new mechanism for designing co-operative effects in solids. Here we report the mSR data in detail and discuss the magnetic properties of LaSrCoO3 H0:7 :
0921-4526/03/$ - see front matter r 2002 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 0 2 ) 0 1 6 8 2 - 4
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S.J. Blundell et al. / Physica B 326 (2003) 527–531
2. Experimental results The sample was prepared by reacting CaH2 with the Co(III) oxide LaSrCoO4 ; which itself adopts the layered K2 NiF4 structure with square planar CoO2 sheets alternating with (La/Sr) O rock–salt layers and octahedral co-ordination around Co(III) [5]. The resulting orthorhombic phase is structurally related to the starting material and its lattice parameters suggest a one-dimensional Sr2 CuO3 structure that consists of chains of corner sharing MO4 squares (see Fig. 1(a)). The transformation to such a structure suggests that the sample is the Co(I) phase LaSrCoO3 ; formed by the reductive topotactic extraction of O2 to afford CaO. The 290 K synchrotron X-ray diffraction pattern was readily indexed with the orthorhombic Sr2 CuO3 -type unit cell in the Immm space group, an assignment confirmed by selected area electron diffraction. Structural refinement showed that the cations occupy the metal positions expected for the Sr2 CuO3 structure [5]. Sr2 CuO3 is a spin-half antiferromagnetic chain with a Ne! el temperature ðTN Þ of 5 K and an intrachain exchange interaction JB1300 K [6–8]. Half-odd integer spin chains have spin-singlet
Fig. 1. (a) The structure of Sr2 CuO3 and Ca2 CuO3 showing the Cu–O chains along the x-axis. (b) The structure of LaSrCoO3 H0:7 illustrating that the CoO4 squares are linked by hydride ions which provide y-axis bridges between the x-axis Co–O chains.
ground states, so that the antiferromagnetic ground state of Sr2 CuO3 is due to the non-zero interchain coupling J 0 (the interchain separation is ( The strong quantum fluctuations never3:49 A). theless reduce the moment on the Cu cation down to B0:06mB [8]. In isostructural Ca2 CuO3 the ( is slightly smaller and chain separation ð3:25 AÞ 0 hence J is larger so that both TN and the ordered moment are somewhat larger (11 K and B0:1mB ; respectively [8]). For our apparently isostructural ( is larger than sample, the chain separation ð3:60 AÞ in Sr2 CuO3 so the ordered moment might be expected to be tiny ðo0:06mB Þ and TN very low ðo5 KÞ: Despite the X-ray and electron diffraction results, the ambient temperature neutron powder diffraction data [5] for our sample could not be indexed purely on the basis of the Sr2 CuO3 structure; a doubling of the basal ab plane area was required to account for additional diffraction reflections observed at large d-spacings. The absence of these reflections in the X-ray and electron diffraction data, which would be sensitive to superstructure formation due to chemical or crystallographic ordering, suggests they are of magnetic origin. An excellent refinement of the neutron data was possible by using (i) a simple antiferromagnetic (AF) ordering model, with antiparallel spin alignment of all neighbouring Co spins and (ii) the incorporation, with 70% occupancy, of H midway between the Co atoms along the y-axis at the vacant oxide anion position in the CoO2x sheets. The ordered magnetic moment carried by the cobalt cations increases from 1:77ð5ÞmB at 290 K to 1:95ð4ÞmB at 2 K: The þ1:7 oxidation state of Co is deduced from the refined composition: LaSrCoO3 H0:7 [5]. The structure of LaSrCoO3 H0:7 consists of chains of CoO4 squares sharing corners along the x-axis to form chains which are linked into a 2D array in the xy plane by H bridges along y (see Fig. 1(b)). The CoO2 sheets in the xy plane of the starting material have been replaced with CoOH0:7 sheets in the oxide hydride product, consistent with a reduction–insertion mechanism in which oxide vacancies are created in the xy plane followed by their filling by the H anions.
S.J. Blundell et al. / Physica B 326 (2003) 527–531
529
(a)
(b)
Fig. 2. mSR data for LaSrCoO3 H0:7 : The oscillations in the asymmetry demonstrate long-range magnetic order at all temperatures measured (up to 310 K).
mSR data (Fig. 2) show clear oscillations over the entire temperature range, signifying a quasistatic magnetic field at the muon site. This result demonstrates unambiguously that LaSrCoO3 H0:7 is uniformly magnetically ordered throughout its bulk at temperatures of up to at least 310 K: The amplitude of the oscillations corresponds to a signal from the whole sample so these results exclude the possibility that only a small region of the sample is ordered. The frequency of the oscillations approaches 71 MHz as T-0 (corresponding to an internal field of 0:53 T) and decreases as the sample is warmed to 310 K (Fig. 3(b)). At the highest temperatures the relaxation rate of the oscillations began to increase and probably reflects the approach of the phase transition (Fig. 3(a)). These results do not allow us to determine precisely the Ne! el temperature, but show that it is likely to be above 350 K:
Fig. 3. (a) The temperature dependence of the relaxation rate of the oscillations (dotted line is a guide to the eye) and (b) the mSR frequency and the corresponding magnetic field at the muon site. In (b) the line represents a fit to a phenomenological expression for the temperature dependence of the order parameter in a magnetic material. Good fits could be obtained by fixing the transition temperature at values in the range 350–450 K; demonstrating that the magnetic ordering temperature probably lies above 350 K:
3. Discussion The muon site in LaSrCoO3 H0:7 is likely to be similar to that found in Sr2 CuO3 and Ca2 CuO3 ; in which the muon is believed to form an O–mþ bond ( [7,8]. However the with a bond length of B1 A measured muon precession frequency for these materials is much lower, corresponding to 2.32 and 3:5 mT for Sr2 CuO3 and Ca2 CuO3 ; respectively [8]. The precession frequency in the present case is > 200 times greater than in Sr2 CuO3 ; which is consistent with the moment refined from powder neutron diffraction. Our dipole-field calculations
S.J. Blundell et al. / Physica B 326 (2003) 527–531
530
identify several candidate muon sites close to the planes containing Co ions. The large value of TN and the ordered moment observed for LaSrCoO3 H0:7 point to a large interchain coupling. This is surprising because, as stated above, the chains have a larger separation than in Sr2 CuO3 and Ca2 CuO3 : It therefore implies that the hydride ion provides an effective superexchange pathway. The measured relationship between kB TN =J and J 0 =J for Sr2 CuO3 and Ca2 CuO3 [8] fitted well to the prediction of chainmean field theory [9], which is shown in Fig. 4(a) and which is expected to be valid for J 0 5J: We expect that the intrachain exchange in LaSrCoO3 H0:7 to be broadly similar to that in Sr2 CuO3 (since, for example, TN for both La2 CuO4 and La2 CoO4 are similar [10]). The large TN in LaSrCoO3 H0:7 therefore implies that J 0 EJ: We have performed spin wave calculations to crudely model the effect of coupling the CoO3 oxide chains by H anions. We find that increasing the effective exchange between chains in one direction to close to the intrachain exchange J is sufficient to raise the Ne! el temperature to the order of J=kB ; even if the coupling in the orthogonal interchain direction is quite weak; the size of the moment will then be near the full value (this scenario is appropriate for LaSrCoO3 H0:70 ; in which we observe a large moment and TN \350 K which is roughly of the order of J=kB ). If, however the interchain exchange is weak in both directions,
the Ne! el temperature is largely controlled by that weak interchain exchange and the size of the moment is greatly reduced because of quantum fluctuations (this scenario is then appropriate for Sr2 CuO3 ; in which the moment is reduced to 0:06mB and TN ¼ 5 K [8]). We illustrate this effect in Fig. 4(b) by plotting the spin wave reduction factor (shown for S ¼ 12 where the quantum effects are largest). When J ¼ J 0 this equals 0.844 as expected [11] but drops very rapidly as J 0 =J decreases for chains, but not for planes. The hydride anion H has a 1s2 electronic configuration and is known to engage in strong covalent bonding with transition metal centres in discrete molecular species [12]. It is therefore ideally suited to transmit exchange interactions or electron delocalization between transition metal cations in an oxide hydride. The H bridge couples metal centres as effectively as O2 ; although the different frontier orbital symmetry (s only in H ; s þ p in O2 ) promises interesting property differences to be revealed in future studies of this new class of extended solid. The ( is shorter than either of Co–H distance of 1:80 A the Co–O distances and this, coupled with the strong covalency expected for the interaction between Co2þ and H ; produces strong antiferromagnetic coupling between the Co(II) cations within the two-dimensional sheets. A qualitative comparison between H and O2 oxide bridges can be made by noting that LaSrCoO3:5 [13] has a Ne! el temperature of 110 K; with a similar concentration of bridging anions in the ab plane, demonstrating the efficiency of hydride superexchange. We thank EPSRC for financial support and the staff of the PSI muon facility for technical assistance.
(a)
(b)
Fig. 4. (a) Predictions of chain mean-field theory for a S ¼ 12 chain [9]. (b) The spin wave reduction factor at T ¼ 0 for a chain (solid line, Jx ¼ J and Jy ¼ Jz ¼ J 0 ) and a plane (broken line, Jx ¼ Jy ¼ J and Jz ¼ J 0 ) where J and J 0 are therefore the intrachain (or intraplane) and interchain (or interplane) exchange constants, respectively.
References [1] H. Kramers, Physica 1 1934 (182). [2] P.W. Anderson, Phys. Rev. 79 (1950) 350; P.W. Anderson, Phys. Rev. 115 (1959) 2. [3] J.B. Goodenough, J.S. Zhou, Chem. Mater. 10 (1998) 14. [4] S.M. Loureiro, C. Felser, Q. Huang, R.J. Cava, Chem. Mater. 12 (2000) 3181.
S.J. Blundell et al. / Physica B 326 (2003) 527–531 [5] M.A. Hayward, E.J. Cussen, J.B. Claridge, M. Bieringer, M.J. Rosseinsky, C.J. Kiely, S.J. Blundell, I.M. Marshall, F.L. Pratt, Science 295 (2002) 1882. [6] T. Ami, M.K. Crawford, R.L. Harlow, Z.R. Wang, D.C. Johnston, Q. Huang, R.W. Erwin, Phys. Rev. B 51 (1995) 5994. [7] A. Keren, L.P. Le, G.M. Luke, B.J. Sternlieb, W.D. Wu, Y.J. Uemura, S. Tajima, S. Uchida, Phys. Rev. B 48 (1993) 12926. [8] K.M. Kojima, Y. Fudamoto, M. Larkin, G.M. Luke, J. Merrin, B. Nachumi, Y.J. Uemura, N. Motoyama,
[9] [10]
[11] [12] [13]
531
H. Eisaki, S. Uchida, K. Yamada, Y. Endoh, S. Hosoya, B.J. Sternlieb, G. Shirane, Phys. Rev. Lett. 78 (1997) 1787. H.J. Schulz, Phys. Rev. Lett. 77 (1996) 2790. K. Yamada, M. Matsuda, Y. Endoh, B. Keimer, R.J. Birgeneau, S. Onodera, J. Mizusaki, T. Matsuura, G. Shirane, Phys. Rev. B 39 (1989) 2336. P. Fazekas, Lecture Notes on Electron Correlation and Magnetism, World Scientific, Singapore, 1999. Z.Y. Lin, M.B. Hall, Coord. Chem. Rev. 135 (1994) 845. M.A. Hayward, M.J. Rosseinsky, Chem. Mater. 12 (2000) 2182.
Magnetism in oxide chains bridged with the hydride anion: LaSrCoO3H0:7 studied using muon-spin rotation S.J. Blundella,*, I.M. Marshalla, F.L. Prattb, M.A. Haywardc, E.J. Cussenc, J.B. Claridgec, M. Bieringerc, C.J. Kielyc, M.J. Rosseinskyc a
Oxford University Department of Physics, Clarendon Laboratory, Parks Road, Oxford OX1 3PU, UK b ISIS, Rutherford Appleton Laboratory, Chilton, Oxfordshire OX11 0QX, UK c Department of Chemistry, University of Liverpool, Liverpool L69 7ZD, UK
Abstract The transition metal oxide hydride, LaSrCoO3 H0:7 ; adopts an unprecedented structure in which oxide chains are bridged by hydride anions to form a two-dimensional extended network in which magnetic ordering is found up to at least 350 K: Muon-spin rotation has been used to demonstrate that this material is uniformly magnetically ordered throughout its bulk. Our results are compared with those on Sr2 CuO3 and Ca2 CuO3 which adopt a similar oxide chain structure and we demonstrate the crucial role of the bridging hydride ions. r 2002 Elsevier Science B.V. All rights reserved. Keywords: Hydride; Magnetic chain; Superexchange
1. Introduction Superexchange [1], the exchange spin-coupling through intermediate non-magnetic atoms, is responsible for the antiferromagnetism observed in many transition metal oxides. It arises because electrons can gain energy by delocalising over nonorthogonal orbitals when the moments are aligned antiparallel, but not when they are parallel, so that there is a kinetic energy gain [2]. The mutual repulsion of electrons on the same ion prevents the permanent occupation of excited states in which electrons transfer via the intermediate O2 anion, *Corresponding author. Tel.: +44-1865-272310; fax: +441865-272400. E-mail address: [email protected] (S.J. Blundell).
but virtual occupation of excited states (connected to the ground state by the transfer integral) leads to a gain in energy. Superexchange through O2 anions is thus responsible for many of the magnetic properties of transition metal oxides [3] and oxyhalides [4]. We have recently shown that it is possible to prepare an extended transition metal oxide array with hydride ions ðH Þ inserted into the structure [5]. Using various experimental techniques, including muon-spin rotation ðmSRÞ; we find that in our new material LaSrCoO3 H0:7 the hydride ion transmits exchange interactions between the transition metal cations at least as effectively as O2 ; opening up a new mechanism for designing co-operative effects in solids. Here we report the mSR data in detail and discuss the magnetic properties of LaSrCoO3 H0:7 :
0921-4526/03/$ - see front matter r 2002 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 0 2 ) 0 1 6 8 2 - 4
528
S.J. Blundell et al. / Physica B 326 (2003) 527–531
2. Experimental results The sample was prepared by reacting CaH2 with the Co(III) oxide LaSrCoO4 ; which itself adopts the layered K2 NiF4 structure with square planar CoO2 sheets alternating with (La/Sr) O rock–salt layers and octahedral co-ordination around Co(III) [5]. The resulting orthorhombic phase is structurally related to the starting material and its lattice parameters suggest a one-dimensional Sr2 CuO3 structure that consists of chains of corner sharing MO4 squares (see Fig. 1(a)). The transformation to such a structure suggests that the sample is the Co(I) phase LaSrCoO3 ; formed by the reductive topotactic extraction of O2 to afford CaO. The 290 K synchrotron X-ray diffraction pattern was readily indexed with the orthorhombic Sr2 CuO3 -type unit cell in the Immm space group, an assignment confirmed by selected area electron diffraction. Structural refinement showed that the cations occupy the metal positions expected for the Sr2 CuO3 structure [5]. Sr2 CuO3 is a spin-half antiferromagnetic chain with a Ne! el temperature ðTN Þ of 5 K and an intrachain exchange interaction JB1300 K [6–8]. Half-odd integer spin chains have spin-singlet
Fig. 1. (a) The structure of Sr2 CuO3 and Ca2 CuO3 showing the Cu–O chains along the x-axis. (b) The structure of LaSrCoO3 H0:7 illustrating that the CoO4 squares are linked by hydride ions which provide y-axis bridges between the x-axis Co–O chains.
ground states, so that the antiferromagnetic ground state of Sr2 CuO3 is due to the non-zero interchain coupling J 0 (the interchain separation is ( The strong quantum fluctuations never3:49 A). theless reduce the moment on the Cu cation down to B0:06mB [8]. In isostructural Ca2 CuO3 the ( is slightly smaller and chain separation ð3:25 AÞ 0 hence J is larger so that both TN and the ordered moment are somewhat larger (11 K and B0:1mB ; respectively [8]). For our apparently isostructural ( is larger than sample, the chain separation ð3:60 AÞ in Sr2 CuO3 so the ordered moment might be expected to be tiny ðo0:06mB Þ and TN very low ðo5 KÞ: Despite the X-ray and electron diffraction results, the ambient temperature neutron powder diffraction data [5] for our sample could not be indexed purely on the basis of the Sr2 CuO3 structure; a doubling of the basal ab plane area was required to account for additional diffraction reflections observed at large d-spacings. The absence of these reflections in the X-ray and electron diffraction data, which would be sensitive to superstructure formation due to chemical or crystallographic ordering, suggests they are of magnetic origin. An excellent refinement of the neutron data was possible by using (i) a simple antiferromagnetic (AF) ordering model, with antiparallel spin alignment of all neighbouring Co spins and (ii) the incorporation, with 70% occupancy, of H midway between the Co atoms along the y-axis at the vacant oxide anion position in the CoO2x sheets. The ordered magnetic moment carried by the cobalt cations increases from 1:77ð5ÞmB at 290 K to 1:95ð4ÞmB at 2 K: The þ1:7 oxidation state of Co is deduced from the refined composition: LaSrCoO3 H0:7 [5]. The structure of LaSrCoO3 H0:7 consists of chains of CoO4 squares sharing corners along the x-axis to form chains which are linked into a 2D array in the xy plane by H bridges along y (see Fig. 1(b)). The CoO2 sheets in the xy plane of the starting material have been replaced with CoOH0:7 sheets in the oxide hydride product, consistent with a reduction–insertion mechanism in which oxide vacancies are created in the xy plane followed by their filling by the H anions.
S.J. Blundell et al. / Physica B 326 (2003) 527–531
529
(a)
(b)
Fig. 2. mSR data for LaSrCoO3 H0:7 : The oscillations in the asymmetry demonstrate long-range magnetic order at all temperatures measured (up to 310 K).
mSR data (Fig. 2) show clear oscillations over the entire temperature range, signifying a quasistatic magnetic field at the muon site. This result demonstrates unambiguously that LaSrCoO3 H0:7 is uniformly magnetically ordered throughout its bulk at temperatures of up to at least 310 K: The amplitude of the oscillations corresponds to a signal from the whole sample so these results exclude the possibility that only a small region of the sample is ordered. The frequency of the oscillations approaches 71 MHz as T-0 (corresponding to an internal field of 0:53 T) and decreases as the sample is warmed to 310 K (Fig. 3(b)). At the highest temperatures the relaxation rate of the oscillations began to increase and probably reflects the approach of the phase transition (Fig. 3(a)). These results do not allow us to determine precisely the Ne! el temperature, but show that it is likely to be above 350 K:
Fig. 3. (a) The temperature dependence of the relaxation rate of the oscillations (dotted line is a guide to the eye) and (b) the mSR frequency and the corresponding magnetic field at the muon site. In (b) the line represents a fit to a phenomenological expression for the temperature dependence of the order parameter in a magnetic material. Good fits could be obtained by fixing the transition temperature at values in the range 350–450 K; demonstrating that the magnetic ordering temperature probably lies above 350 K:
3. Discussion The muon site in LaSrCoO3 H0:7 is likely to be similar to that found in Sr2 CuO3 and Ca2 CuO3 ; in which the muon is believed to form an O–mþ bond ( [7,8]. However the with a bond length of B1 A measured muon precession frequency for these materials is much lower, corresponding to 2.32 and 3:5 mT for Sr2 CuO3 and Ca2 CuO3 ; respectively [8]. The precession frequency in the present case is > 200 times greater than in Sr2 CuO3 ; which is consistent with the moment refined from powder neutron diffraction. Our dipole-field calculations
S.J. Blundell et al. / Physica B 326 (2003) 527–531
530
identify several candidate muon sites close to the planes containing Co ions. The large value of TN and the ordered moment observed for LaSrCoO3 H0:7 point to a large interchain coupling. This is surprising because, as stated above, the chains have a larger separation than in Sr2 CuO3 and Ca2 CuO3 : It therefore implies that the hydride ion provides an effective superexchange pathway. The measured relationship between kB TN =J and J 0 =J for Sr2 CuO3 and Ca2 CuO3 [8] fitted well to the prediction of chainmean field theory [9], which is shown in Fig. 4(a) and which is expected to be valid for J 0 5J: We expect that the intrachain exchange in LaSrCoO3 H0:7 to be broadly similar to that in Sr2 CuO3 (since, for example, TN for both La2 CuO4 and La2 CoO4 are similar [10]). The large TN in LaSrCoO3 H0:7 therefore implies that J 0 EJ: We have performed spin wave calculations to crudely model the effect of coupling the CoO3 oxide chains by H anions. We find that increasing the effective exchange between chains in one direction to close to the intrachain exchange J is sufficient to raise the Ne! el temperature to the order of J=kB ; even if the coupling in the orthogonal interchain direction is quite weak; the size of the moment will then be near the full value (this scenario is appropriate for LaSrCoO3 H0:70 ; in which we observe a large moment and TN \350 K which is roughly of the order of J=kB ). If, however the interchain exchange is weak in both directions,
the Ne! el temperature is largely controlled by that weak interchain exchange and the size of the moment is greatly reduced because of quantum fluctuations (this scenario is then appropriate for Sr2 CuO3 ; in which the moment is reduced to 0:06mB and TN ¼ 5 K [8]). We illustrate this effect in Fig. 4(b) by plotting the spin wave reduction factor (shown for S ¼ 12 where the quantum effects are largest). When J ¼ J 0 this equals 0.844 as expected [11] but drops very rapidly as J 0 =J decreases for chains, but not for planes. The hydride anion H has a 1s2 electronic configuration and is known to engage in strong covalent bonding with transition metal centres in discrete molecular species [12]. It is therefore ideally suited to transmit exchange interactions or electron delocalization between transition metal cations in an oxide hydride. The H bridge couples metal centres as effectively as O2 ; although the different frontier orbital symmetry (s only in H ; s þ p in O2 ) promises interesting property differences to be revealed in future studies of this new class of extended solid. The ( is shorter than either of Co–H distance of 1:80 A the Co–O distances and this, coupled with the strong covalency expected for the interaction between Co2þ and H ; produces strong antiferromagnetic coupling between the Co(II) cations within the two-dimensional sheets. A qualitative comparison between H and O2 oxide bridges can be made by noting that LaSrCoO3:5 [13] has a Ne! el temperature of 110 K; with a similar concentration of bridging anions in the ab plane, demonstrating the efficiency of hydride superexchange. We thank EPSRC for financial support and the staff of the PSI muon facility for technical assistance.
(a)
(b)
Fig. 4. (a) Predictions of chain mean-field theory for a S ¼ 12 chain [9]. (b) The spin wave reduction factor at T ¼ 0 for a chain (solid line, Jx ¼ J and Jy ¼ Jz ¼ J 0 ) and a plane (broken line, Jx ¼ Jy ¼ J and Jz ¼ J 0 ) where J and J 0 are therefore the intrachain (or intraplane) and interchain (or interplane) exchange constants, respectively.
References [1] H. Kramers, Physica 1 1934 (182). [2] P.W. Anderson, Phys. Rev. 79 (1950) 350; P.W. Anderson, Phys. Rev. 115 (1959) 2. [3] J.B. Goodenough, J.S. Zhou, Chem. Mater. 10 (1998) 14. [4] S.M. Loureiro, C. Felser, Q. Huang, R.J. Cava, Chem. Mater. 12 (2000) 3181.
S.J. Blundell et al. / Physica B 326 (2003) 527–531 [5] M.A. Hayward, E.J. Cussen, J.B. Claridge, M. Bieringer, M.J. Rosseinsky, C.J. Kiely, S.J. Blundell, I.M. Marshall, F.L. Pratt, Science 295 (2002) 1882. [6] T. Ami, M.K. Crawford, R.L. Harlow, Z.R. Wang, D.C. Johnston, Q. Huang, R.W. Erwin, Phys. Rev. B 51 (1995) 5994. [7] A. Keren, L.P. Le, G.M. Luke, B.J. Sternlieb, W.D. Wu, Y.J. Uemura, S. Tajima, S. Uchida, Phys. Rev. B 48 (1993) 12926. [8] K.M. Kojima, Y. Fudamoto, M. Larkin, G.M. Luke, J. Merrin, B. Nachumi, Y.J. Uemura, N. Motoyama,
[9] [10]
[11] [12] [13]
531
H. Eisaki, S. Uchida, K. Yamada, Y. Endoh, S. Hosoya, B.J. Sternlieb, G. Shirane, Phys. Rev. Lett. 78 (1997) 1787. H.J. Schulz, Phys. Rev. Lett. 77 (1996) 2790. K. Yamada, M. Matsuda, Y. Endoh, B. Keimer, R.J. Birgeneau, S. Onodera, J. Mizusaki, T. Matsuura, G. Shirane, Phys. Rev. B 39 (1989) 2336. P. Fazekas, Lecture Notes on Electron Correlation and Magnetism, World Scientific, Singapore, 1999. Z.Y. Lin, M.B. Hall, Coord. Chem. Rev. 135 (1994) 845. M.A. Hayward, M.J. Rosseinsky, Chem. Mater. 12 (2000) 2182.