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Magnetic ordering and spin fluctuations in nearly half-doped manganites
Materials Science and Engineering B63 (1999) 125 – 132 www.elsevier.com/locate/mseb
Magnetic ordering and spin fluctuations in nearly half-doped manganites H. Yoshizawa a,*, R. Kajimoto a, H. Kawano b,c, J.A. Fernandez-Baca c, Y. Tomioka d, H. Kuwahara d, Y. Tokura d,e a
Neutron Scattering Laboratory, I.S.S.P., Uni6ersity of Tokyo, Tokai, Ibaraki 319 -1106, Japan The Institute of Physical and Chemical Research (RIKEN), Wako, Saitama 351 -0918 Japan c Solid State Di6ision, Oak Ridge National Laboratory, Oak Ridge, TN 37831 -6393, USA d Joint Research Center for Atom Technology, Tsukuba, Ibaraki 305 -8562, Japan e Department of Applied Physics, Uni6ersity of Tokyo, Bunkyo-ku, Tokyo 113 -8656, Japan
b
Abstract We discuss unusual behavior discovered in spin dynamics in the nearly half-doped manganite systems. Nd0.45Sr0.55MnO3 is a metallic antiferromagnet, and exhibits very anisotropic spin wave dispersion relations. The ferromagnetic (FM) state of Pr1/2Sr1/2MnO3 and Nd1/2Sr1/2MnO3 also exhibit clear anisotropic dispersion relations. Such anisotropy reflects the underlying d(x2 −y2)-type orbital ordering. We also demonstrate that the high temperature paramagnetic state without charge ordering in doped manganites is characterized by the FM spin fluctuations with an anomalously small energy scale for a wide range of doping concentrations. © 1999 Elsevier Science S.A. All rights reserved. Keywords: Half-doped manganite; Orbital ordering
1. Introduction Recent experimental studies on the colossal magnetoresistance (CMR) phenomenon demonstrated that the orbital ordering is one of the important ingredients to understand the magnetic and transport properties in the doped perovskite manganites. For example, a Nd1 − x SrxMnO3 system shows a variety of magnetic ordering as a function of the hole concentration x around x: 1/ 2 [1]. With increasing x, this system exhibits various magnetic orderings in a sequence of FM CE-type AFMA-type AFM C-type AFM, where FM and AFM denote ferromagnetic and antiferromagnetic spin orderings, respectively. Recent experimental and theoretical studies revealed that each magnetic ordering is stabilized by the underlying orbital ordering which is specific to the respective spin ordering for a given hole concentration [1– 8]. The interplay among the spin, charge and orbital orderings near x :1/2 is especially interesting. For a commensurate value of the hole concentration x= 1/2, * Corresponding author.
a number of manganites exhibit the well-known insulating CE-type spin/charge ordering (CO), which is named after the pioneering work by Wollan and Koehler [9]. On the other hand, we have very recently demonstrated that some of manganites with x: 1/2 exhibit a layered A-type antiferromagnetic (AFM) ordering, in which the FM layers stack antiferromagnetically [2–4]. In contrast to the insulating behavior of the CE-type chargeordered system, the A-type manganites show the metallic resistivity. In this case, we found that the change of the magnetic structure as well as the transport property seems to be driven by a switching of the underlying orbital ordering. The orbital ordering also affects the spin fluctuations. Based on the detailed study of the lattice and spin structures of the A-type manganites, we pointed out the possibility of the two-dimensional character in both magnetic and transport properties [2–4]. By using a terminology of the two-dimensional character, we emphasize a layered-type large anisotropy of the physical properties in the A-type manganite. We found that the spin wave energy in the A-type AFM phase shows a strong directional dependence originated from the or-
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bital ordering. We also recently discovered that the orbital ordering gives rise to the strong anisotropy in the spin wave dispersion relation in the metallic FM state [10]. The second issue of the present report concerns the feature of the spin fluctuations in the paramagnetic state of doped manganites. For hole doped perovskite manganites, the metallic FM state has been qualitatively understood with the double exchange (DE) model [11–14]. The DE picture implies that, regardless of its FM or AFM ordering in the ground state, the spin fluctuations must be FM in the paramagnetic state. When the CO is formed, however, it will suppress the hopping of the holes, and will suppress the concomitant FM fluctuations which are mediated by the DE interactions. Furthermore, the orbital ordering is expected to turn on the AFM superexchange interactions between localized spins on the Mn sites. We observed that the spin fluctuations in the A-type AFM manganite Nd0.45Sr0.55MnO3 [2 – 4] and those in the charge-ordered insulator Pr1 − xCaxMnO3 [15,16] are FM in the paramagnetic state. Our studies established that the FM spin fluctuations prevail in the paramagnetic state of the doped manganites for a surprisingly wide range of the doping concentration even though the ground state of the system is AFM. When the orbital and spin orderings are formed, an AFM correlation takes over the FM spin fluctuations as a result of the superexchange interactions. In addition, the energy scale of the FM component is anomalously small when it is compared with the low temperature spin stiffness parameters.
2. Orbital ordering and magnetic structure We shall begin with the overall features of the lattice and magnetic structure of the Nd1 − xSrxMnO3
Fig. 1. Phase diagram of Nd1 − x = SrxMnO3. [17]
system. Fig. 1 shows the x− T phase diagram of the Nd1 − xSrxMnO3 system for 0.35x 50.8 [17]. For xB 0.48, the ground state is a FM metal. In the region for 0.50 x 0.60, there appears a metallic AFM state with the layered-type AFM ordering, which is called as the A-type ordering [9]. With further increasing x, the C-type AFM ordering was observed for x 0.60. In this phase, the resistivity monotonically increases with lowering temperature, indicating that the sample remains insulating for all temperature [17]. Only within a small range of the Sr concentration around x: 0.50, the Nd1 − xSrxMnO3 system exhibits an insulating charge-ordered phase which is accompanied with the CE-type AFM spin ordering after the metallic FM state below TC [18]. As mentioned in the introduction, the crystal structure plays an important role to determine its transport and magnetic properties near x: 1/2 through the orbital ordering. To elucidate the characteristics of the crystal structures, we performed a standard Rietveld analysis [1,19] on their powder pattern data. We found that, in the case of Nd1 − xSrxMnO3, there appear two orthorhombic structures near x:1/2: the one is the well-known orthorhombic O% structure with the lattice constants b/ 2 BaB c in the Pnma setting [20], while the other is an O‡ structure with a:cBb/
2 [1,17]. Although both structures belong to the Pnma symmetry, their physical properties are distinctly different, and they transform through a first order phase transition as indicated by a thick line in Fig. 1. From the characteristics of the crystal structure with the results of Rietveld analysis, one can make a reasonable speculation on the possible orbital ordering for each structure. When the lattice constants of Nd1 − xSrxMnO3 with x: 1/2 satisfy the relation b/
2 B aB c for the O% structure [1–4,20], the Mn-O distance between the FM layers is the shortest, and one expects that the eg orbitals lie within the FM layers. Therefore, the orbitals of the d(3x2 −r2)- or d(x2 − y2)-type will be favored in the O% structure. These two orbital orderings are easily distinguished from their magnetic and transport properties. For the d(3x2 − r2)-type orbitals, the manganites with x1/2 exhibit the CE-type CO depicted in Fig. 2(a), and they are insulating. On the other hand, the d(x2 −y2)type orbital ordering favors the metallic A-type AFM spin structure depicted in Fig. 2(b). By contrast, in the O‡ structure, the MnO6 octahedron is elongated towards the apical direction as shown in Fig. 2(c). In this case. the apically stretched MnO6 octahedra favor the ordering of the d(3z2 − r2) orbitals, and stabilizes the C-type AFM ordering in which the magnetic moments are parallel to the b axis.
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in Fig. 3(a) and (b), one can easily see that the spin waves propagating within the FM planes have higher spin wave energy. (Note that 2qa is close to qb in units of A, − 1 as a result of a pseudo-cubic feature of the lattice constants.) The obtained dispersion relations are depicted in Fig. 3 (c), where one can see a clear anisotropy of the excitation energy between the [101] and [010] directions which is caused by the d (x2 −y2)type orbital ordering in the metallic A-type AFM state. The temperature dependence of the spin wave profiles was measured at selected q’s, and the typical results observed at Q= (0.95, 1, 0.95) are shown in Fig. 3 (d). With increasing temperature, the AFM spin wave energy gradually softens, and the AFM spin fluctuations vanish above TN except for the tail of the incoherent scattering. As is discussed in the next section, this indicates a switching of spin fluctuations to the FM character in the paramagnetic phase.
3.2. Anisotropic spin wa6e dispersion relations in the ferromagnetic metallic state with x= 0.5
Fig. 2. Schematic picture of the orderings of the eg orbitals in the AFM phase. The directions of the spins are represented by arrows. (a) CE-type, (b) A-type, (c) C-type.
3. Anomalous spin waves As we saw in the previous section, the orbital ordering has clear influence on the magnetic ordering, but it also affects strongly the spin fluctuations. In this section, we show the examples of such influence on the spin wave excitation spectra observed in the A-type AFM state and in the metallic FM state in the Nd1 − xSrxMnO3 system [2 – 4,10].
3.1. Anisotropic spin wa6es in the A-type AFM metal In the orbital-ordering induced A-type AFM state of Nd0.45Sr0.55MnO3, the spin dynamics show the clear quasi-two-dimensional character [2 – 4]. The AFM spin wave excitations in Nd0.45Sr0.55MnO3 were observed at :12 K along the directions parallel and perpendicular to the FM layers depicted in the left panel of Fig. 4. Typical profiles observed at selected reduced wave vectors are illustrated in Fig. 3(a) and (b), where qa and qb denote the reduced wave vectors along the [101] and [010] directions, respectively. By comparing the profiles
In this subsection, we show the anomalous dispersion relations observed in the FM state of two 50% doped manganite systems Pr1/2Sr1/2MnO3 and Nd1/2Sr1/2MnO3 [10] In order to understand the anisotropy of the dispersion relation in the FM phase, we first need to discuss the low temperature AFM structure in these systems. Both systems exhibit the A-type AFM state at low temperatures, although the CE-type spin ordering is dominant in Nd1/2Sr1/2MnO3 [10]. The propagation vector of the orthorhombic Nd1/2Sr1/2MnO3 and Nd0.45Sr0.55MnO3 is along the [010] direction as illustrated in Fig. 4. Because of the P21/n monoclinic structure, however, the propagation vector of Pr1/2Sr1/ 2MnO3 is along the [101] direction which is rotated by 90° from the [010] direction. Unexpectedly, we found that the spin wave excitations in the metallic FM state are strongly anisotropic. As shown in Fig. 5, the observed spin wave dispersion relations both in Pr1/2Sr1/2MnO3 and in Nd1/2Sr1/2MnO3 exhibit a clear directional anisotropy. By examining the direction of the FM sheet in the low temperature A-type AFM ordering depicted in Fig. 4, one finds that the spin wave energy perpendicular to the FM sheets is anomalously low. As discussed in the previous section, the A-type AFM structure is driven by the d(x2 −y2)type orbital ordering for both Pr1/2Sr1/2MnO3 and Nd1/ 2Sr1/2MnO3. The present results strongly indicate that such orbital ordering persists in the FM phase, and causes a strong anisotropy in spin fluctuations. For the case of Nd1/2Sr1/2MnO3, this is consistent with the orthorhombic O% crystal structure with b/ 2 BaBc at x: 1/2 shown in the phase diagram of Fig. 1.
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4. Anomaly in the paramagnetic spin fluctuations Now we examine the spin fluctuations observed in the paramagnetic phase. As we mentioned in the introduction, one can expects that the DE interactions favor the FM spin fluctuations in the paramagnetic state in doped manganites, and we, indeed, observed intense FM spin fluctuations in the paramagnetic phase of many doped manganites for a wide concentration range of x, regardless of its ground state spin ordering. In the following, we show two typical examples which have an AFM ground state.
4.1. Switching of spin fluctuations in Nd0.45Sr0.55MnO3 We found the anomalous FM spin fluctuations in the paramagnetic phase of the A-type antiferromagnet Nd0.45Sr0.55MnO3 [2 – 4]. With increasing temperature, the AFM spin fluctuations disappear above TN as
shown in Fig. 3 (d), and the intense FM spin fluctuations appear at around the nuclear Bragg reflections. The temperature dependence of the FM component was observed near TN at Q= (1− q, 0, 1−q) with q= 0.1 around the FM Bragg point, and it is summarized in Fig. 6. At the top panel, one can see the diffusive FM spin fluctuations in the paramagnetic phase. The evolution of the peak structure below TN is attributed to the AFM spin waves. The middle panel shows that the diffusive FM component exhibits a sudden decrease below TN, indicating that the major spectral weight of the spin fluctuations is transferred from the FM component in the paramagnetic phase to the AFM component below TN. The similar switching in the spin fluctuations is also observed in the Pr1 − xCaxMnO3 system in the present study, [15,16] and has been recently reported in another charge-ordered insulating manganite (Bi, Ca) MnO3 [21] and even in a vanadium oxide, V2O3 [22]. For all
Fig. 3. (a) and (b): Spin wave profiles at 12 K in Nd0.45Sr0.55MnO3 measured at Q= (1− qa, 1, 1 −qa) and (0,1 + qb, 0) which correspond to the spin waves propagating within and perpendicular to the FM sheets in the A-type AFM, respectively. (c): Spin wave dispersion in the A-type AFM Nd0.45Sr0.55MnO3. Dashed curves indicate the dispersion relation of LaMnO3. Labels ‘q ZB b ’ indicate the zone boundary for the [010] direction, while that for the [101] direction is located at q: 0.82A, − 1. (d): Spin wave profiles observed at Q = (0.95, 1, 0.95) at 210 K and 150 K B TN, and 250 K\ TN.
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because the formation of the orbital ordering leads to the simultaneous magnetic and structural transitions at TN : 325 K, but the CO is not formed, and the resistivity remains metallic.
4.2. Spin fluctuations in Pr1 − xCaxMnO3
Fig. 4. A-type layered AFM structure and its propagation vector t for the orthorhombic Nd0.45Sr0.55MnO3 and the monoclinic Pr1/2Sr1/ 2MnO3.
these transition metal oxides, the orbital ordering is the crucial mechanism which triggers the switching of spin fluctuations. These observations indicate that the switching of the spin fluctuations as a result of an orbital ordering is rather common phenomena in the transition-metal oxides with a freedom of the orbitals. The case of the present system is, however, very unique
We found that the insulating AFM Pr1 − xCaxMnO3 system also shows strong FM spin fluctuations in the paramagnetic state [15,16]. At first, we shall briefly describe the temperature dependences of the order parameters and the FM spin fluctuations in Pr1 − xCaxMnO3, because this compound shows a rather complicated ordering process. Fig. 7(a) is the temperature dependence of the order parameters of the charge and AFM orderings in the x= 0.35 sample. The holes order below TCO = 230 K, and with further decreasing temperature, the spins order antiferromagnetically below TN = 160 K. The CO component shows a slight increase below TN because of the superposition of the AF component. Fig. 7 (b) shows the temperature dependence of the elastic component of the FM spin fluctuations observed near the FM Bragg points for the three samples with x= 0.35, 0.40, and 0.50. For the x= 0.35 sample, the FM fluctuation is suppressed clearly in two steps. First, it suddenly decreases to half at the onset of the CO. On the other hand, it remains finite for TCO \ T\TN with little temperature dependence, and then it completely vanishes at the onset of the AFM spin ordering. The intensity for TCO \ T\ TN becomes weaker as the hole concentration x approaches the commensurate value 1/2, but a finite amount of the intensity persists even for the x= 0.5 sample.
Fig. 5. (a): Dispersion curve within and between plane directions for Pr1/2Sr1/2MnO3 observed at 175 K. (b): Dispersion curve within and between plane directions for Nd1/2Sr1/2MnO3 observed at 175 K (circles) and at 220 K (squares). The inset shows a constant-Q scan profile observed at (1, 0.7, 1), and arrows indicate the position of spin wave peaks. Solid curves are drawn as guides to the eye.
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tions actuate the AFM spin fluctuations. Therefore, the remanence of the FM spin fluctuation below TCO indicates the existence of the orbital fluctuations. In the CE-type ordering, both orbitals and spins form a complicated pattern of a mixture of FM and AFM arrangements [23–27]. As a result, it may be unstable against thermal agitations, and there may exist a sufficient amount of orbital fluctuations for TCO ] T]TN. The present data prove that the CE-type ordering is not a true long range order, and that it allows the orbital and FM spin fluctuations for TCO ] T] TN Consequently, the orbital pattern in the CE-type ordering is not fully stabilized even for x=0.5 until the spin ordering is established at TN. Fig. 8 (a) shows the temperature dependence of the energy spectra of the FM fluctuations in the x=0.35 sample. Solid lines are the fits to the Lorentzian form convoluted with the instrumental resolution. The intense quasielastic scattering is evident in the paramagnetic phase, and it changes over to the AFM spin wave excitations below TN. The spin wave peaks at 160 K are not resolved from the central component. With decreasing temperature, however, they show a hardening, and reach to E 0.9 meV at 100 K. In order to quantitatively characterize the FM spin fluctuations, we have studied the q dependence just above TCO. The quasielastic peaks were fitted to a Lorentzian, and the width G is plotted against q2 in Fig. 8 (b). For all three samples, G shows an excellent linearity on q 2 (G=Lq 2), which indicates that the Fig. 6. (a): Ferromagnetic (FM) scattering observed above and below TN in the A-type antiferromagnet Nd0.45Sr0.55MnO3. (b): Temperature dependence of the FM component observed at Q= (1 −qa, 0, 1 − qa) with qa =0.1 and with E= 0 meV. (c): Wave vector dependence of the energy width G of the ferromagnetic component observed at T =300 K.
The important finding in Fig. 7 is two successive sharp suppressions of the FM spin fluctuation at TCO and at TN. In principle, the FM correlation is expected to be suppressed at TCO, because the charge localization inhibits the FM DE interactions mediated by electron hopping. Since the FM diffuse scattering for TCO ] T] TN decreases as x approaches x =1/2 as seen in Fig. 7 (b), one may consider that excess eg electrons over the commensurate concentration mediate the FM fluctuations. However, we have observed that the intense FM fluctuation persists below TCO and vanishes at TN even in the x =0.5 sample. This result clearly excludes the above interpretation. The origin of the FM diffuse component in the intermediate temperature region for TCO ] T ] TN can be interpreted as follows. We first note that the spin fluctuation in the paramagnetic state of the DE system is FM when it lacks the orbital ordering. After the system forms the orbital ordering of the eg orbitals, the superexchange interac-
Fig. 7. (a): Temperature dependences of order parameters for the charge and AFM ordering for x =0.35. (b): Temperature dependences of FM diffuse scattering observed near (101) at E =0 meV. The temperature axis is scaled at TCO of the x =0.35 sample as described in the text.
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wave stiffness constant DSW and the spin diffusion constant L should be of the same order in magnitude when the same exchange interactions control the spin wave propagation as well as the spin diffusion process. The values of DSW in doped manganites found in literature are of the order of 100 meV [28,30–32] and, in fact, the values L of the FM metallic samples, La0.8Sr0.2MnO3 and La0.7Sr0.3MnO3, are reported to be of the same order with DSW [31,32]. We think that the discrepancy of the energy scale between DSW and L in Nd0.45Sr0.55MnO3 and Pr1 − xCaxMnO3 should be attributed to its narrower one-electron bandwidth W. In a system with a small W, the small hopping integral suppresses the mobility of holes, and increases the possibility of the coupling of hole motion with the lattice distortion. When the spin diffusion process is controlled by the DE mechanism, the characteristic energy scale of the spin diffusion L may be renomalized from a bare superexchange interactions through the coupling to the lattice distortions. It should be note that the existence of the two energy scales in doped manganites is recently pointed out by studies of thermopower and resistivity measurements, and it is argued as evidence of small polaron hopping conductivity in the paramagnetic state [33–35].
5. Conclusion Fig. 8. (a) Energy spectra at Q =(1, 0, 0.95) for the x= 0.35 sample. (b) Energy widths G of quasielastic scattering versus q2 above TCO; open circle: x= 0.35 at (1, 0, 0.95) and 245 K, triangle: x =0.40 at (0.95, 0, 0.95) and 250 K, closed circle: x =0.50 at (0.95, 0, 0.95) and 260 K.
scattering originates from a spin diffusion-like process. The spin diffusion constant L deduced from the fits is practically x-independent for all three samples, yielding 16 (4) meV A, 2 for x =0.35, 13 (2) meV A, 2 for x= 0.40, and 16 (4) meV A, 2 for x = 0.50. As shown in the bottom panel of Fig. 6, we found that the FM component in the paramagnetic state of Nd0.45Sr0.55MnO3 is also well described by the same spin diffusion formula with L:14.19 1 meV A, 2. It should be note that a similar anomalous FM component is recently reported in the metallic FM manganites, La0.67Ca0.33MnO3 [28] and Nd0.7Sr0.3MnO3 [29]. Therefore, the present results corroborate the fact that a sharp FM central component exists in the paramagnetic state of the hole-doped manganites with a narrow one-electron band width over a wide range of the hole concentration, 0.35 nh 5 0 55. We would like to point out that the energy scale L of such FM fluctuations is an order of magnitude smaller than the value of the spin stiffness constant DSW evaluated from the exchange parameters. In general, the spin
In conclusion, we have studied the distorted perovskite manganite systems, Pr1 − xCaxMnO3, Nd1 − xSrxMnO3 and Pr1 − xSrxMnO3 with x: 1/2. While Pr − xCaxMnO3 and Nd1/2Sr1/2MnO3 exhibits the CEtype AFM ordering, Pr1/2Sr1/2MnO3 and Nd1 − xSrxMnO3 with x: 1/2 show the layered A-type AFM ordering. The CE-type AFM state exhibits a clear charge-ordered state, while the A-type AFM state has no clear sign of superlattice peaks of CO, reflecting its metallic behavior of the resistivity. From the viewpoint of the crystal structure, one can expect eg electrons be in d(x2 − y2) orbitals. From these results, we predicted two-dimensional behavior for magnetic and transport properties in the A-type AFM state, and indeed we have observed a clear two-dimensional anisotropy of spin wave dispersion relations in the A-type AFM Nd0.45Sr0.55MnO3, and even the metallic FM phase of Pr1/2Sr1/2MnO3 and Nd1/2Sr1/2MnO3. All these results are consistent with the d(x2 − y2)-type orbital ordering near x :1/2.
Acknowledgements This work was supported by a Grant-In-Aid for Scientific Research from the Ministry of Education, Science and Culture, Japan, by Special Researcher’s
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Basic Science Program (RIKEN) and by the New Energy and Industrial Technology Development Organization (NEDO) of Japan. The work at ORNL was supported by US DOE under contract No. DE-AC05840R21400 with Lockheed Martin Energy Systems, Inc., and was carried out under the US-Japan Cooperative Program on Neutron Scattering.
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Magnetic ordering and spin fluctuations in nearly half-doped manganites H. Yoshizawa a,*, R. Kajimoto a, H. Kawano b,c, J.A. Fernandez-Baca c, Y. Tomioka d, H. Kuwahara d, Y. Tokura d,e a
Neutron Scattering Laboratory, I.S.S.P., Uni6ersity of Tokyo, Tokai, Ibaraki 319 -1106, Japan The Institute of Physical and Chemical Research (RIKEN), Wako, Saitama 351 -0918 Japan c Solid State Di6ision, Oak Ridge National Laboratory, Oak Ridge, TN 37831 -6393, USA d Joint Research Center for Atom Technology, Tsukuba, Ibaraki 305 -8562, Japan e Department of Applied Physics, Uni6ersity of Tokyo, Bunkyo-ku, Tokyo 113 -8656, Japan
b
Abstract We discuss unusual behavior discovered in spin dynamics in the nearly half-doped manganite systems. Nd0.45Sr0.55MnO3 is a metallic antiferromagnet, and exhibits very anisotropic spin wave dispersion relations. The ferromagnetic (FM) state of Pr1/2Sr1/2MnO3 and Nd1/2Sr1/2MnO3 also exhibit clear anisotropic dispersion relations. Such anisotropy reflects the underlying d(x2 −y2)-type orbital ordering. We also demonstrate that the high temperature paramagnetic state without charge ordering in doped manganites is characterized by the FM spin fluctuations with an anomalously small energy scale for a wide range of doping concentrations. © 1999 Elsevier Science S.A. All rights reserved. Keywords: Half-doped manganite; Orbital ordering
1. Introduction Recent experimental studies on the colossal magnetoresistance (CMR) phenomenon demonstrated that the orbital ordering is one of the important ingredients to understand the magnetic and transport properties in the doped perovskite manganites. For example, a Nd1 − x SrxMnO3 system shows a variety of magnetic ordering as a function of the hole concentration x around x: 1/ 2 [1]. With increasing x, this system exhibits various magnetic orderings in a sequence of FM CE-type AFMA-type AFM C-type AFM, where FM and AFM denote ferromagnetic and antiferromagnetic spin orderings, respectively. Recent experimental and theoretical studies revealed that each magnetic ordering is stabilized by the underlying orbital ordering which is specific to the respective spin ordering for a given hole concentration [1– 8]. The interplay among the spin, charge and orbital orderings near x :1/2 is especially interesting. For a commensurate value of the hole concentration x= 1/2, * Corresponding author.
a number of manganites exhibit the well-known insulating CE-type spin/charge ordering (CO), which is named after the pioneering work by Wollan and Koehler [9]. On the other hand, we have very recently demonstrated that some of manganites with x: 1/2 exhibit a layered A-type antiferromagnetic (AFM) ordering, in which the FM layers stack antiferromagnetically [2–4]. In contrast to the insulating behavior of the CE-type chargeordered system, the A-type manganites show the metallic resistivity. In this case, we found that the change of the magnetic structure as well as the transport property seems to be driven by a switching of the underlying orbital ordering. The orbital ordering also affects the spin fluctuations. Based on the detailed study of the lattice and spin structures of the A-type manganites, we pointed out the possibility of the two-dimensional character in both magnetic and transport properties [2–4]. By using a terminology of the two-dimensional character, we emphasize a layered-type large anisotropy of the physical properties in the A-type manganite. We found that the spin wave energy in the A-type AFM phase shows a strong directional dependence originated from the or-
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bital ordering. We also recently discovered that the orbital ordering gives rise to the strong anisotropy in the spin wave dispersion relation in the metallic FM state [10]. The second issue of the present report concerns the feature of the spin fluctuations in the paramagnetic state of doped manganites. For hole doped perovskite manganites, the metallic FM state has been qualitatively understood with the double exchange (DE) model [11–14]. The DE picture implies that, regardless of its FM or AFM ordering in the ground state, the spin fluctuations must be FM in the paramagnetic state. When the CO is formed, however, it will suppress the hopping of the holes, and will suppress the concomitant FM fluctuations which are mediated by the DE interactions. Furthermore, the orbital ordering is expected to turn on the AFM superexchange interactions between localized spins on the Mn sites. We observed that the spin fluctuations in the A-type AFM manganite Nd0.45Sr0.55MnO3 [2 – 4] and those in the charge-ordered insulator Pr1 − xCaxMnO3 [15,16] are FM in the paramagnetic state. Our studies established that the FM spin fluctuations prevail in the paramagnetic state of the doped manganites for a surprisingly wide range of the doping concentration even though the ground state of the system is AFM. When the orbital and spin orderings are formed, an AFM correlation takes over the FM spin fluctuations as a result of the superexchange interactions. In addition, the energy scale of the FM component is anomalously small when it is compared with the low temperature spin stiffness parameters.
2. Orbital ordering and magnetic structure We shall begin with the overall features of the lattice and magnetic structure of the Nd1 − xSrxMnO3
Fig. 1. Phase diagram of Nd1 − x = SrxMnO3. [17]
system. Fig. 1 shows the x− T phase diagram of the Nd1 − xSrxMnO3 system for 0.35x 50.8 [17]. For xB 0.48, the ground state is a FM metal. In the region for 0.50 x 0.60, there appears a metallic AFM state with the layered-type AFM ordering, which is called as the A-type ordering [9]. With further increasing x, the C-type AFM ordering was observed for x 0.60. In this phase, the resistivity monotonically increases with lowering temperature, indicating that the sample remains insulating for all temperature [17]. Only within a small range of the Sr concentration around x: 0.50, the Nd1 − xSrxMnO3 system exhibits an insulating charge-ordered phase which is accompanied with the CE-type AFM spin ordering after the metallic FM state below TC [18]. As mentioned in the introduction, the crystal structure plays an important role to determine its transport and magnetic properties near x: 1/2 through the orbital ordering. To elucidate the characteristics of the crystal structures, we performed a standard Rietveld analysis [1,19] on their powder pattern data. We found that, in the case of Nd1 − xSrxMnO3, there appear two orthorhombic structures near x:1/2: the one is the well-known orthorhombic O% structure with the lattice constants b/ 2 BaB c in the Pnma setting [20], while the other is an O‡ structure with a:cBb/
2 [1,17]. Although both structures belong to the Pnma symmetry, their physical properties are distinctly different, and they transform through a first order phase transition as indicated by a thick line in Fig. 1. From the characteristics of the crystal structure with the results of Rietveld analysis, one can make a reasonable speculation on the possible orbital ordering for each structure. When the lattice constants of Nd1 − xSrxMnO3 with x: 1/2 satisfy the relation b/
2 B aB c for the O% structure [1–4,20], the Mn-O distance between the FM layers is the shortest, and one expects that the eg orbitals lie within the FM layers. Therefore, the orbitals of the d(3x2 −r2)- or d(x2 − y2)-type will be favored in the O% structure. These two orbital orderings are easily distinguished from their magnetic and transport properties. For the d(3x2 − r2)-type orbitals, the manganites with x1/2 exhibit the CE-type CO depicted in Fig. 2(a), and they are insulating. On the other hand, the d(x2 −y2)type orbital ordering favors the metallic A-type AFM spin structure depicted in Fig. 2(b). By contrast, in the O‡ structure, the MnO6 octahedron is elongated towards the apical direction as shown in Fig. 2(c). In this case. the apically stretched MnO6 octahedra favor the ordering of the d(3z2 − r2) orbitals, and stabilizes the C-type AFM ordering in which the magnetic moments are parallel to the b axis.
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in Fig. 3(a) and (b), one can easily see that the spin waves propagating within the FM planes have higher spin wave energy. (Note that 2qa is close to qb in units of A, − 1 as a result of a pseudo-cubic feature of the lattice constants.) The obtained dispersion relations are depicted in Fig. 3 (c), where one can see a clear anisotropy of the excitation energy between the [101] and [010] directions which is caused by the d (x2 −y2)type orbital ordering in the metallic A-type AFM state. The temperature dependence of the spin wave profiles was measured at selected q’s, and the typical results observed at Q= (0.95, 1, 0.95) are shown in Fig. 3 (d). With increasing temperature, the AFM spin wave energy gradually softens, and the AFM spin fluctuations vanish above TN except for the tail of the incoherent scattering. As is discussed in the next section, this indicates a switching of spin fluctuations to the FM character in the paramagnetic phase.
3.2. Anisotropic spin wa6e dispersion relations in the ferromagnetic metallic state with x= 0.5
Fig. 2. Schematic picture of the orderings of the eg orbitals in the AFM phase. The directions of the spins are represented by arrows. (a) CE-type, (b) A-type, (c) C-type.
3. Anomalous spin waves As we saw in the previous section, the orbital ordering has clear influence on the magnetic ordering, but it also affects strongly the spin fluctuations. In this section, we show the examples of such influence on the spin wave excitation spectra observed in the A-type AFM state and in the metallic FM state in the Nd1 − xSrxMnO3 system [2 – 4,10].
3.1. Anisotropic spin wa6es in the A-type AFM metal In the orbital-ordering induced A-type AFM state of Nd0.45Sr0.55MnO3, the spin dynamics show the clear quasi-two-dimensional character [2 – 4]. The AFM spin wave excitations in Nd0.45Sr0.55MnO3 were observed at :12 K along the directions parallel and perpendicular to the FM layers depicted in the left panel of Fig. 4. Typical profiles observed at selected reduced wave vectors are illustrated in Fig. 3(a) and (b), where qa and qb denote the reduced wave vectors along the [101] and [010] directions, respectively. By comparing the profiles
In this subsection, we show the anomalous dispersion relations observed in the FM state of two 50% doped manganite systems Pr1/2Sr1/2MnO3 and Nd1/2Sr1/2MnO3 [10] In order to understand the anisotropy of the dispersion relation in the FM phase, we first need to discuss the low temperature AFM structure in these systems. Both systems exhibit the A-type AFM state at low temperatures, although the CE-type spin ordering is dominant in Nd1/2Sr1/2MnO3 [10]. The propagation vector of the orthorhombic Nd1/2Sr1/2MnO3 and Nd0.45Sr0.55MnO3 is along the [010] direction as illustrated in Fig. 4. Because of the P21/n monoclinic structure, however, the propagation vector of Pr1/2Sr1/ 2MnO3 is along the [101] direction which is rotated by 90° from the [010] direction. Unexpectedly, we found that the spin wave excitations in the metallic FM state are strongly anisotropic. As shown in Fig. 5, the observed spin wave dispersion relations both in Pr1/2Sr1/2MnO3 and in Nd1/2Sr1/2MnO3 exhibit a clear directional anisotropy. By examining the direction of the FM sheet in the low temperature A-type AFM ordering depicted in Fig. 4, one finds that the spin wave energy perpendicular to the FM sheets is anomalously low. As discussed in the previous section, the A-type AFM structure is driven by the d(x2 −y2)type orbital ordering for both Pr1/2Sr1/2MnO3 and Nd1/ 2Sr1/2MnO3. The present results strongly indicate that such orbital ordering persists in the FM phase, and causes a strong anisotropy in spin fluctuations. For the case of Nd1/2Sr1/2MnO3, this is consistent with the orthorhombic O% crystal structure with b/ 2 BaBc at x: 1/2 shown in the phase diagram of Fig. 1.
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4. Anomaly in the paramagnetic spin fluctuations Now we examine the spin fluctuations observed in the paramagnetic phase. As we mentioned in the introduction, one can expects that the DE interactions favor the FM spin fluctuations in the paramagnetic state in doped manganites, and we, indeed, observed intense FM spin fluctuations in the paramagnetic phase of many doped manganites for a wide concentration range of x, regardless of its ground state spin ordering. In the following, we show two typical examples which have an AFM ground state.
4.1. Switching of spin fluctuations in Nd0.45Sr0.55MnO3 We found the anomalous FM spin fluctuations in the paramagnetic phase of the A-type antiferromagnet Nd0.45Sr0.55MnO3 [2 – 4]. With increasing temperature, the AFM spin fluctuations disappear above TN as
shown in Fig. 3 (d), and the intense FM spin fluctuations appear at around the nuclear Bragg reflections. The temperature dependence of the FM component was observed near TN at Q= (1− q, 0, 1−q) with q= 0.1 around the FM Bragg point, and it is summarized in Fig. 6. At the top panel, one can see the diffusive FM spin fluctuations in the paramagnetic phase. The evolution of the peak structure below TN is attributed to the AFM spin waves. The middle panel shows that the diffusive FM component exhibits a sudden decrease below TN, indicating that the major spectral weight of the spin fluctuations is transferred from the FM component in the paramagnetic phase to the AFM component below TN. The similar switching in the spin fluctuations is also observed in the Pr1 − xCaxMnO3 system in the present study, [15,16] and has been recently reported in another charge-ordered insulating manganite (Bi, Ca) MnO3 [21] and even in a vanadium oxide, V2O3 [22]. For all
Fig. 3. (a) and (b): Spin wave profiles at 12 K in Nd0.45Sr0.55MnO3 measured at Q= (1− qa, 1, 1 −qa) and (0,1 + qb, 0) which correspond to the spin waves propagating within and perpendicular to the FM sheets in the A-type AFM, respectively. (c): Spin wave dispersion in the A-type AFM Nd0.45Sr0.55MnO3. Dashed curves indicate the dispersion relation of LaMnO3. Labels ‘q ZB b ’ indicate the zone boundary for the [010] direction, while that for the [101] direction is located at q: 0.82A, − 1. (d): Spin wave profiles observed at Q = (0.95, 1, 0.95) at 210 K and 150 K B TN, and 250 K\ TN.
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because the formation of the orbital ordering leads to the simultaneous magnetic and structural transitions at TN : 325 K, but the CO is not formed, and the resistivity remains metallic.
4.2. Spin fluctuations in Pr1 − xCaxMnO3
Fig. 4. A-type layered AFM structure and its propagation vector t for the orthorhombic Nd0.45Sr0.55MnO3 and the monoclinic Pr1/2Sr1/ 2MnO3.
these transition metal oxides, the orbital ordering is the crucial mechanism which triggers the switching of spin fluctuations. These observations indicate that the switching of the spin fluctuations as a result of an orbital ordering is rather common phenomena in the transition-metal oxides with a freedom of the orbitals. The case of the present system is, however, very unique
We found that the insulating AFM Pr1 − xCaxMnO3 system also shows strong FM spin fluctuations in the paramagnetic state [15,16]. At first, we shall briefly describe the temperature dependences of the order parameters and the FM spin fluctuations in Pr1 − xCaxMnO3, because this compound shows a rather complicated ordering process. Fig. 7(a) is the temperature dependence of the order parameters of the charge and AFM orderings in the x= 0.35 sample. The holes order below TCO = 230 K, and with further decreasing temperature, the spins order antiferromagnetically below TN = 160 K. The CO component shows a slight increase below TN because of the superposition of the AF component. Fig. 7 (b) shows the temperature dependence of the elastic component of the FM spin fluctuations observed near the FM Bragg points for the three samples with x= 0.35, 0.40, and 0.50. For the x= 0.35 sample, the FM fluctuation is suppressed clearly in two steps. First, it suddenly decreases to half at the onset of the CO. On the other hand, it remains finite for TCO \ T\TN with little temperature dependence, and then it completely vanishes at the onset of the AFM spin ordering. The intensity for TCO \ T\ TN becomes weaker as the hole concentration x approaches the commensurate value 1/2, but a finite amount of the intensity persists even for the x= 0.5 sample.
Fig. 5. (a): Dispersion curve within and between plane directions for Pr1/2Sr1/2MnO3 observed at 175 K. (b): Dispersion curve within and between plane directions for Nd1/2Sr1/2MnO3 observed at 175 K (circles) and at 220 K (squares). The inset shows a constant-Q scan profile observed at (1, 0.7, 1), and arrows indicate the position of spin wave peaks. Solid curves are drawn as guides to the eye.
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tions actuate the AFM spin fluctuations. Therefore, the remanence of the FM spin fluctuation below TCO indicates the existence of the orbital fluctuations. In the CE-type ordering, both orbitals and spins form a complicated pattern of a mixture of FM and AFM arrangements [23–27]. As a result, it may be unstable against thermal agitations, and there may exist a sufficient amount of orbital fluctuations for TCO ] T]TN. The present data prove that the CE-type ordering is not a true long range order, and that it allows the orbital and FM spin fluctuations for TCO ] T] TN Consequently, the orbital pattern in the CE-type ordering is not fully stabilized even for x=0.5 until the spin ordering is established at TN. Fig. 8 (a) shows the temperature dependence of the energy spectra of the FM fluctuations in the x=0.35 sample. Solid lines are the fits to the Lorentzian form convoluted with the instrumental resolution. The intense quasielastic scattering is evident in the paramagnetic phase, and it changes over to the AFM spin wave excitations below TN. The spin wave peaks at 160 K are not resolved from the central component. With decreasing temperature, however, they show a hardening, and reach to E 0.9 meV at 100 K. In order to quantitatively characterize the FM spin fluctuations, we have studied the q dependence just above TCO. The quasielastic peaks were fitted to a Lorentzian, and the width G is plotted against q2 in Fig. 8 (b). For all three samples, G shows an excellent linearity on q 2 (G=Lq 2), which indicates that the Fig. 6. (a): Ferromagnetic (FM) scattering observed above and below TN in the A-type antiferromagnet Nd0.45Sr0.55MnO3. (b): Temperature dependence of the FM component observed at Q= (1 −qa, 0, 1 − qa) with qa =0.1 and with E= 0 meV. (c): Wave vector dependence of the energy width G of the ferromagnetic component observed at T =300 K.
The important finding in Fig. 7 is two successive sharp suppressions of the FM spin fluctuation at TCO and at TN. In principle, the FM correlation is expected to be suppressed at TCO, because the charge localization inhibits the FM DE interactions mediated by electron hopping. Since the FM diffuse scattering for TCO ] T] TN decreases as x approaches x =1/2 as seen in Fig. 7 (b), one may consider that excess eg electrons over the commensurate concentration mediate the FM fluctuations. However, we have observed that the intense FM fluctuation persists below TCO and vanishes at TN even in the x =0.5 sample. This result clearly excludes the above interpretation. The origin of the FM diffuse component in the intermediate temperature region for TCO ] T ] TN can be interpreted as follows. We first note that the spin fluctuation in the paramagnetic state of the DE system is FM when it lacks the orbital ordering. After the system forms the orbital ordering of the eg orbitals, the superexchange interac-
Fig. 7. (a): Temperature dependences of order parameters for the charge and AFM ordering for x =0.35. (b): Temperature dependences of FM diffuse scattering observed near (101) at E =0 meV. The temperature axis is scaled at TCO of the x =0.35 sample as described in the text.
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wave stiffness constant DSW and the spin diffusion constant L should be of the same order in magnitude when the same exchange interactions control the spin wave propagation as well as the spin diffusion process. The values of DSW in doped manganites found in literature are of the order of 100 meV [28,30–32] and, in fact, the values L of the FM metallic samples, La0.8Sr0.2MnO3 and La0.7Sr0.3MnO3, are reported to be of the same order with DSW [31,32]. We think that the discrepancy of the energy scale between DSW and L in Nd0.45Sr0.55MnO3 and Pr1 − xCaxMnO3 should be attributed to its narrower one-electron bandwidth W. In a system with a small W, the small hopping integral suppresses the mobility of holes, and increases the possibility of the coupling of hole motion with the lattice distortion. When the spin diffusion process is controlled by the DE mechanism, the characteristic energy scale of the spin diffusion L may be renomalized from a bare superexchange interactions through the coupling to the lattice distortions. It should be note that the existence of the two energy scales in doped manganites is recently pointed out by studies of thermopower and resistivity measurements, and it is argued as evidence of small polaron hopping conductivity in the paramagnetic state [33–35].
5. Conclusion Fig. 8. (a) Energy spectra at Q =(1, 0, 0.95) for the x= 0.35 sample. (b) Energy widths G of quasielastic scattering versus q2 above TCO; open circle: x= 0.35 at (1, 0, 0.95) and 245 K, triangle: x =0.40 at (0.95, 0, 0.95) and 250 K, closed circle: x =0.50 at (0.95, 0, 0.95) and 260 K.
scattering originates from a spin diffusion-like process. The spin diffusion constant L deduced from the fits is practically x-independent for all three samples, yielding 16 (4) meV A, 2 for x =0.35, 13 (2) meV A, 2 for x= 0.40, and 16 (4) meV A, 2 for x = 0.50. As shown in the bottom panel of Fig. 6, we found that the FM component in the paramagnetic state of Nd0.45Sr0.55MnO3 is also well described by the same spin diffusion formula with L:14.19 1 meV A, 2. It should be note that a similar anomalous FM component is recently reported in the metallic FM manganites, La0.67Ca0.33MnO3 [28] and Nd0.7Sr0.3MnO3 [29]. Therefore, the present results corroborate the fact that a sharp FM central component exists in the paramagnetic state of the hole-doped manganites with a narrow one-electron band width over a wide range of the hole concentration, 0.35 nh 5 0 55. We would like to point out that the energy scale L of such FM fluctuations is an order of magnitude smaller than the value of the spin stiffness constant DSW evaluated from the exchange parameters. In general, the spin
In conclusion, we have studied the distorted perovskite manganite systems, Pr1 − xCaxMnO3, Nd1 − xSrxMnO3 and Pr1 − xSrxMnO3 with x: 1/2. While Pr − xCaxMnO3 and Nd1/2Sr1/2MnO3 exhibits the CEtype AFM ordering, Pr1/2Sr1/2MnO3 and Nd1 − xSrxMnO3 with x: 1/2 show the layered A-type AFM ordering. The CE-type AFM state exhibits a clear charge-ordered state, while the A-type AFM state has no clear sign of superlattice peaks of CO, reflecting its metallic behavior of the resistivity. From the viewpoint of the crystal structure, one can expect eg electrons be in d(x2 − y2) orbitals. From these results, we predicted two-dimensional behavior for magnetic and transport properties in the A-type AFM state, and indeed we have observed a clear two-dimensional anisotropy of spin wave dispersion relations in the A-type AFM Nd0.45Sr0.55MnO3, and even the metallic FM phase of Pr1/2Sr1/2MnO3 and Nd1/2Sr1/2MnO3. All these results are consistent with the d(x2 − y2)-type orbital ordering near x :1/2.
Acknowledgements This work was supported by a Grant-In-Aid for Scientific Research from the Ministry of Education, Science and Culture, Japan, by Special Researcher’s
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Basic Science Program (RIKEN) and by the New Energy and Industrial Technology Development Organization (NEDO) of Japan. The work at ORNL was supported by US DOE under contract No. DE-AC05840R21400 with Lockheed Martin Energy Systems, Inc., and was carried out under the US-Japan Cooperative Program on Neutron Scattering.
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