Rare earth magnetic ordering in exchange-coupled superconductors

Journal of Alloys and Compounds 250 (1997) 552–558

L

Rare earth magnetic ordering in exchange-coupled superconductors J.W. Lynn Reactor Radiation Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, and Center for Superconductivity Research, University of Maryland, College Park, MD 20742, USA

Abstract Magnetic neutron diffraction measurements are reviewed for two families of superconductors where exchange interactions dominate the energetics of the magnetic system. One system is cuprates that contain Pr, which exhibit magnetic rare earth ordering temperatures that are an order-of-magnitude higher than for the other rare earths, and where f-electron hybridization effects destroy any chance for superconductivity. The second family of materials is the quaternary RNi 2 B 2 C borocarbides. These materials have comparable magnetic and superconducting transition temperatures, and exhibit a rich variety of commensurate and incommensurate magnetic structures that coexist and compete with the superconducting state. Keywords: Rare earth; Magnetic order; Superconductivity; Exchange interactions; Neutron scattering

1. Introduction The magnetic ordering of the rare earth ions in superconducting systems has been a topic of active interest for many years [1]. In the conventional ‘‘magnetic superconductors’’ such as RMo 6 S 8 (R5rare earth ion) the rare earth moments are coupled very weakly both to the metallic electrons and to each other, resulting in very low (|1 K) magnetic ordering temperatures and a delicate energetic balance with superconductivity mediated by dipolar interactions. A similar situation occurs for most of the cuprate superconductors in that the development of long range rare earth magnetic order also occurs at very low temperatures [2]. In contrast to the earlier systems, though, the superconductivity in the cuprates typically occurs at much higher temperatures, and the antiferromagnetic order that develops on the rare earth sublattice coexists with the superconducting state. These materials are of further interest because many exhibit low-dimensional magnetic behavior [3,4], and the properties of these rare earth / superconductor systems have already been reviewed in some detail. However, from the very early days of cuprate superconductors it was known that a dramatic exception occurs for Pr, and this singular exception has been the subject of extensive research. The magnetic ordering temperatures are an order-of-magnitude higher for Pr than for the other rare earth materials, and consequently the magnetic coupling must be dominated by exchange rather than dipole interactions. Moreover, with the exception of Pr 2 CuO 4 where the crystal field ground state is an isolated 0925-8388 / 97 / $17.00  1997 Elsevier Science S.A. All rights reserved PII S0925-8388( 96 )02634-5

singlet, the Pr materials are not superconducting at all. The origins of this suppression and the nature of the Pr magnetism are still under active investigation and debate, and here we will review the neutron studies of the magnetic properties of the cuprate superconductors that contain Pr. A related class of exchange-coupled materials is the new quaternary intermetallic superconductors, namely the borocarbide series RNi 2 B 2 C. The magnetic ordering temperatures for these materials are high enough (|10 K) that exchange interactions must dominate the energetics of the magnetic systems, but in many cases they are also superconducting, and indeed exhibit an interesting competition between the magnetic and superconducting states. A wide variety of both commensurate and incommensurate magnetic structures are realized in these materials, and we will also review the neutron investigations carried out to date on these systems.

2. Pr cuprates We start our discussion with the RBa 2 Cu 3 O 61d (1-2-3) system, which was the first rare earth cuprate to be investigated in detail. The magnetism in these cuprate superconductors is quite rich and interesting because the Cu ions as well as the rare earth ions can carry magnetic moments, and this can of course complicate the nature of the magnetic order and phase transitions that occur. For this reason we will describe the magnetic ordering of the

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Cu spins as well as the rare earth magnetism, since most of the other materials investigated are simply related to this classic system. For this 1-2-3 layered cuprate there are three types of magnetic sites, two associated with the Cu and one with the rare earth, as shown in Fig. 1. The crystal structure is essentially tetragonal (a¯b) with c¯3a, and there are three sets of Cu layers. Two of these are equivalent Cu layers that have an oxygen between each Cu ion, and are referred to as the Cu plane layers. The second type of Cu layer contains oxygen ions only along one (b) axis (and is then referred to as the Cu chain layer), and these oxygen ions can be removed by suitable heat treatment. With an oxygen-depleted chain layer (d 50) the system is an antiferromagnetic insulator with the Cu plane layers developing long range magnetic order for temperatures as high as |525 K. The spins lie within the a–b plane and are always coupled antiferromagnetically in this plane. With appropriate doping either directly on the chain site, or on the Ba site, the chain spins can also develop an ordered moment. Adding oxygen has the effect of doping the plane ´ temperature to layers with holes, and this causes the Neel drop to zero at d |0.4. Further addition of oxygen renders the system superconducting, with T c exceeding 90 K for d →1. The single rare earth ion in the chemical unit cell, on the other hand, sits in the body-centered position between the two Cu plane layers. The rare earth nearest neighbors are then a distance a away, and without direct bonding orbitals the magnetic interactions are very weak. Along the c-axis the nearest neighbor distance is three

Fig. 1. Crystal structure for RBa 2 Cu 3 O 61d . The CuO 2 plane layers order antiferromagnetically at small d, where d is the oxygen occupancy in the Cu chain layer. The spin direction is in the a–b plane, and structure is always antiferromagnetic in this plane. The rare earth ion is in the bodied centered position, between the two Cu plane layers.

553

times longer so that the magnetic interactions are much weaker still, and this crystallographic anisotropy renders many of these rare earth subsystems two-dimensional in behavior. For PrBa 2 Cu 3 O 61d we find quite a different behavior [5]. The material is a semiconductor for the full range of d, with the Cu ions retaining their high magnetic ordering temperature. This anomalous behavior originates from felectron hybridization, which is strong enough in Pr (compared to the other rare earths) to completely disrupt the Cooper pairing of the electrons on the Cu plane layers. This hybridization has been observed directly by inelastic neutron scattering experiments, which have found that there are substantial linewidths to the crystal field excitations of the Pr [6–9]. This has the effect of dramatically increasing the exchange interactions, thereby increasing the ordering temperature by an order of magnitude and rendering the rare earth ordering three dimensional. The first neutron diffraction experiments were carried out on fully oxygenated PrBa 2 Cu 3 O 7 [10]. A simple magnetic ordering developed below T N 517 K, with antiferromagnetic coupling between nearest neighbors Pr moments in all three directions in the crystal. The observed ordering temperature was in good agreement with specific heat and susceptibility results, which studies have elucidated the systematics of this ordering by following it as a function of oxygen concentration and as a function of Y (and other rare earths) substitution on the Pr site [5,11]. Bulk measurements show that as oxygen is removed T N (Pr) monotonically decreases to 12 K for PrBa 2 Cu 3 O 6 , and this has been confirmed by neutron diffraction measurements on the depleted system [12]. Replacing Pr with non-magnetic Y has the expected behavior that T N (Pr) decreases (towards zero), while superconductivity appears above 40% replacement and monotonically increases as the pure Y composition is approached. Studies have also been carried out to observe the effects on both the Cu and Pr order by chemical substitution on other sites in the Pr 1-2-3 system. Zn is found to substitute on the Cu planes, and this has no effect on either the Pr ordering temperature or size of the ordered moment [13], but it does change the coupling along the c-axis from antiferromagnetic to ferromagnetic. Ga, on the other hand, substitutes preferentially on the Cu chain sites. This also changes the magnetic structure along the c-axis from antiferromagnetic to ferromagnetic, but in addition T N is reduced [14] while the ordered moment remains unchanged. Neither of these substitutions has any significant effect on the Cu Bragg peaks in the temperature regime where the Pr orders. Another type of substitution can occur for the ‘‘pure’’ PrBa 2 Cu 3 O 61d , where the Pr can substitute on the Ba site forming Pr 11x Ba 22x Cu 3 O 61d . This has the effect of reducing the ordering temperature for the Pr [15]. Studies on single crystals of the ‘‘pure’’ PrBa 2 Cu 3 O 61d have also been carried out more recently, but the results have been complicated because of some contamination of

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the sample from the crucible, and / or Pr substitution on the Ba site. Rosov et al. [16] studied a single crystal of PrBa 2 Cu 3 O 61d as a function of oxygen concentration, and found that at small d both the Cu chains and planes order at 370 K, while for the fully oxygenated sample the planes ordered at 370 K while the ordering of the chain spins occurred at 160 K as shown in Fig. 2. Note that when the chain spins order the symmetry of the magnetic structure changes, and the Bragg peaks (hkl) with l an integer all decrease in intensity while the peaks with l half-integer increase. Because this chain ordering has the same symmetry as the Pr ordering observed in powders, these two order parameters are expected to be strongly coupled. Changes in the Bragg intensities were observed at low temperatures consistent with Pr ordering, but it turned out to be difficult to unambiguously identify the Pr contribution at low T without an extensive magnetic Bragg peak survey. In this situation the best way to make this distinction is to use the dependence of the Bragg peak intensities on the magnetic form factor f(Q); f(Q) for Cu decreases much more rapidly with wave vector Q than f(Q) for Pr. Such a single crystal study has been carried out recently by Longmore et al. [17] on both depleted and fully oxygenated single crystals, which contained Al (from the crucible) on the Cu chain site. The Pr ordering temperatures were reduced compared to the nominally pure materials (which may also indicate Pr on the Ba site [15]), and the magnetic long range order was disrupted due to the chemical disorder in the system. However, they were able to unambiguously identify an ordered Pr moment (0.5 mB ) from the very different magnetic form factors for Pr and Cu. All of this work contrasts strongly with the recent NMR work of Nehrke and Pieper [18], who concluded that there

is (essentially) no magnetic moment on the Pr, in analogy with the situation found in Pr 2 CuO 4 where the Pr ions are in a singlet ground state that is well separated in energy (|18 meV) from the first excited state. There are significant exchange interactions in Pr 2 CuO 4 as measured by the dispersion of the excited state crystal field levels [19], but the exchange is too small to mix much of a moment from the high-lying crystal field levels into the ground state. Thus there is only a small moment on the Pr, which is induced via an exchange interaction with the ordered Cu spins [20,19]. The situation for Pr 1-2-3, however, is quite different in that the exchange interactions are much larger than for Pr 2 CuO 4 . More importantly, there are a number of low-lying crystal field levels within a few meV of the ground state, and these exchange interactions will strongly mix these levels with the ground state [6–9]. Hence a magnetic ground state is expected for Pr. The complicated nature of the magnetic orderings due to the Cu plane and chain magnetism, and the strong influence of impurities on the Cu magnetism [21], make a completely unambiguous resolution of this discrepancy between the NMR and other experimental probes difficult at the present time, and it will likely have to await the growth of high quality and defect free PrBa 2 Cu 3 O 61d single crystals. There is, however, considerable additional evidence for magnetic moments and magnetic ordering of the Pr in the cuprate class of materials. Table 1 lists the properties for Pr systems investigated with neutrons in this class of materials. For PrBa 2 Cu 2 NbO 8 [22] the Cu chain layer is replaced with a (fully oxygenated) NbO 2 layer, which of course carries no moment. This eliminates the complication of the chain magnetism, and we still find a high ordering temperature for the Pr and no influence on

Fig. 2. Magnetic ordering of the Cu plane layers in PrBa 2 Cu 3 O 7 at 370 K, which give rise to the magnetic Bragg peaks with l whole-integral. At 160 K the Cu chain layers become ordered, which results in new Bragg peaks for l half-integral, while the intensities of the whole integral peaks decreases towards zero (after Rosov et al. [16]).

J.W. Lynn / Journal of Alloys and Compounds 250 (1997) 552 – 558 Table 1 The magnetic ordering temperature and ordered moment for Pr in a series of cuprate compounds Material

T N (Pr)

m (Pr)

T N (Cu)

PrBa 2 Cu 3 O 7 PrBa 2 Cu 3 O 6 PrBa 2 Cu 2.7 Zn 0.3 O 7 PrBa 2 Cu 2.88 Ga 0.12 O 7 PrBa 2 Cu 2.76 Ga 0.24 O 7 PrBa 2 Cu 2 NbO 8 Pr 1.5 Ce 0.5 Sr 2 Cu 2 (Nb, Ta)O 102d Pb 2 Sr 2 PrCu 3 O 8 TlBa 2 PrCu 2 O 7 TlBaSrPrCu 2 O 7 Pr 2 CuO 4 BaPrO 3

17 12 17 14 10 12.6 10 7 8 5 Induced 11.7

0.74 1.9 0.70 0.76 0.76 1.2

370 370

0.43 1.05 0.08 0.35

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Cu ordering of any kind, exhibits a similar Pr ordering temperature and reduced moment [27] as for the cuprates. Thus the preponderance of the evidence suggests that the Pr carries a moment and is ordered magnetically in the layered cuprate materials.

3. RNi 2 B 2 C systems 340 200 370 350 280 –

The ordering temperature for the Cu spins is also given. References are given in the text.

the Cu plane ordering when the Pr subsystem orders. A similar situation occurs for the TlBa 22y Sr y PrCu 2 O 7 [23,24] where the CuO chains are replaced by TlO. Fig. 3 shows the results for the Cu and Pr order in TlBa 2 PrCu 2 O 7 , where we see that there is no effect on the intensity of the Cu Bragg peaks when the Pr orders. This is expected since these ordered magnetic structures are orthogonal. If these new low temperature peaks were in fact associated with the Cu order as suggested by Nehrke and Pieper [18], then we would expect strong variations in the Cu Bragg peaks similar to that shown in Fig. 2. The fact that we do not see such changes argues strongly that it is indeed the Pr that is ordering at low temperature. Similar behavior is observed for the more complicated Pr 1.5 Ce 0.5 Sr 2 Cu 2 (Nb, Ta)O 102d [25] system. Again there can be no Cu chain magnetism, and there is a high observed T N for the Pr. The Pb 2 Sr 2 PrCu 3 O 8 material [26] is somewhat different in that it has no oxygen in the Cu chain layer, while the properties of the Pr are quite similar to the other systems. Finally, we note that the related BaPrO 3 material, which obviously has no complications of

The magnetic and superconducting properties of the new class of quaternary intermetallic RNi 2 B 2 C superconductors [28,29] have attracted a great deal of attention recently. The crystal structure is body-centered tetragonal (I4 / mmm), and consists of R–C planes separated by Ni 2 B 2 layers stacked along the c-axis. These systems have relatively high superconducting transition temperatures (up to 23 K for YPd 2 B 2 C) [28] while exhibiting magnetic ordering temperatures as high as 19 K for GdNi 2 B 2 C [30]. The much higher magnetic transition temperatures for these new materials ensures that the energetics for the magnetic systems are dominated by exchange rather than dipolar (electromagnetic) interactions, and the interplay between superconductivity and magnetism should therefore be much stronger than in the ternary Chevrel-phase and related systems [1]. Shortly after the discovery of these new materials, Eisaki et al. [31] investigated the systematics of rare earth substitution in the system. They found that almost all the rare earths ordered magnetically, and that many were superconducting as well. The most interesting system appeared to be HoNi 2 B 2 C, which became superconducting at |8 K, but then reentered the normal state at |5 K, only to quickly become superconducting again with further reduction of temperature. The first neutron investigations were therefore carried out on this system [32], and they revealed the development of long range magnetic order at |8 K along with the superconductivity. Two types of magnetic order were observed, a commensurate antiferromagnetic structure consisting of sheets of ferromagnetic

Fig. 3. Magnetic ordering of the Cu plane layers (left) and the Pr moments (right) in TlBa 2 PrCu 2 O 7 (after Li et al. [23]). Note that there is no effect on the Bragg peaks associated with the Cu ordering when the Pr moments order.

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moments in the a–b plane, with adjacent sheets coupled antiferromagnetically along the c-axis, and an incommensurate spiral state in which these ferromagnetic sheets are canted at an angle of |168 from the antiparallel position. The intensities from both types of Bragg peaks initially grew with decreasing temperature at the same rate. At |5 K the superconductivity is reentrant as evidenced by a deep minimum in H c2 near 5 K [31], below which the incommensurate spiral order is suppressed in favor of a simple commensurate antiferromagnetic structure. This magnetic transition then permits the return of superconductivity and a coexistence to low T. Goldman et al. [33] found an additional incommensurate magnetic component that developed along the a-axis. The temperature dependence of all three components of the magnetic order is shown in Fig. 4. We see that the initial magnetic ordering that develops is associated with the antiferromagnetic and spiral states. The intensity for both types of peaks increases with decreasing temperature, but in the vicinity of the reentrant superconducting transition at |5 K the intensity of the spiral state suddenly begins to rapidly decrease while the intensity for the commensurate antiferromagnetic peak rapidly increases, until it saturates at low temperatures. The a-axis component exists over a narrower T range than the spiral, but both components drop rapidly around 5 K and disappear at low temperatures in favor of the simple commensurate antiferromagnetic state. We have found that the relative intensities for these three components are different for different samples [34], suggesting

Fig. 4. Intensity of the antiferromagnetic, c-axis spiral, and a-axis magnetic peaks as a function of temperature for HoNi 2 B 2 C [38]. The intensities for the incommensurate magnetic peaks are suppressed below the temperature where the superconducting state reemerges.

that they are coming from separate regions of the samples. We note that the superconducting as well as the magnetic properties are very sensitive functions of the composition [35], and the underlying property that is controlling this very subtle dependence on composition is still an active area of research. At low temperature, on the other hand, the magnetic ground state is a simple antiferromagnetic structure, with its fully ordered magnetic moment, that readily coexists with superconductivity. The behavior of HoNi 2 B 2 C contrasts sharply with that of DyNi 2 B 2 C [36–38], which orders at |11 K with the same commensurate magnetic structure that is observed for Ho at low T. Thus there are no incommensurate magnetic phases observed in this system. Initially superconductivity was thought to be absent in Dy, but then a superconducting transition of 6 K [39] was discovered (again emphasizing the strong dependence on composition [35]). The presence of the superconducting state does not appear to have much influence on the magnetic order in the system. Finally, we note that the Pr material [38] also orders with the identical magnetic structure as for Dy and Ho, i.e. ferromagnetic sheets of spins in the a–b plane that are coupled antiferromagnetically along the c-axis. The ordered moment is only 0.8 mB . In this case no superconducting transition has been seen yet, but its absence may have a different origin as discussed in the previous section, and this is an area that requires further investigation. For ErNi 2 B 2 C we have quite a different type of magnetic structure and behavior. The superconducting transition occurs at T c |11 K, and superconductivity persists to low temperatures with no reentrant transitions or evidence of strong coupling to the magnetic state. Antiferromagnetic ordering develops at T N 56.8 K, with the Er ions forming a transversely-polarized, incommensurate spin density wave state (SDW) [40,41]. The modulation wave vector for this state is approximately temperature independent, with the direction along the a-axis (or equivalently along the b-axis in this tetragonal system) with the spins directed along b (or a). The staggered magnetization increases smoothly as the temperature is decreased below T N , and is non-hysteretic. Higher-order harmonics develop at lower temperatures, indicating a squaring-up of the magnetic structure. This squaring-up of the spin density wave is expected; a purely sinusoidal spin density wave cannot be the ground state of a local-moment system because this leaves many of the moments in a partially disordered state. We note that the magnetic structure observed in ErNi 2 B 2 C is reminiscent of the small a-axis peaks found in the HoNi 2 B 2 C material as discussed above. Since this large-moment magnetic structure readily coexists with superconductivity in the Er system, it seems unlikely that the weak a-axis peaks in the Ho material could be the cause of the reentrant behavior in HoNi 2 B 2 C. However, the Tb system also orders with a similar magnitude incommensurate wave vector as for the Er material, and this wave vector is also only weakly temperature dependent [42,38]. In this case,

J.W. Lynn / Journal of Alloys and Compounds 250 (1997) 552 – 558

though, the SDW is longitudinally polarized, and squares up at low temperature. The Gd system has been investigated with magnetic x-ray scattering techniques, and is also observed to order with an a-axis incommensurate magnetic state, with a spin direction that is a complicated function of temperature [43]. No superconductivity has been observed in either the Tb or Gd systems. Another rare earth that exhibits an incommensurate magnetic state is TmNi 2 B 2 C [38]. This system becomes superconducting at 11 K, while it orders magnetically at only 1.5 K. However, the modulated magnetic structure is completely different from any of the other systems. The modulation wave vector is in the a–b plane, but is along the [110] direction with a temperature independent mag˚ 21 . The direction of the magnetic moment, nitude of 0.24 A on the other hand, is along the c-axis. Thus the magnetic structure is a transversely polarized SDW state as for ErNi 2 B 2 C, but with the spins pointing along the c-axis rather than in the a–b plane. Again the SDW squares up at low temperature, with the magnetic structure remaining incommensurate. Fig. 5 shows the development of the long range order in this material, where we see that we have strong intensity and a nicely defined phase transition at 1.5 K. This long range magnetically ordered state coexists with superconductivity. Finally, we find that the light rare earths Pr and Nd both order in commensurate antiferromagnetic structures [38]; the Pr ordering has already been described. The magnetic structure for Nd is antiferromagnetic along the a-axis with the moment direction along a (with an equivalent domain along the b-axis in this tetragonal system), ferromagnetic coupling along b, while along the c-axis one adjacent neighbor is ferromagnetic while the other is antiferromagnetically aligned, doubling the c-axis periodicity. The modulation wave vector is then (1 / 2, 0, 1 / 2), and the ordered moment is |2 mB . We note that the magnetic moments are much smaller than for the heavy rare earth

557

Table 2 ´ temperature, superconducting transition temperature, magnetic strucNeel ture, and modulation wave vector for the RNi 2 B 2 C systems. R

TN

Tc

Structure

d

Pr Nd Gd Tb Dy Ho

4.0 4.8 19 15 10.6 8.5 6.3 5 6.8 1.5 –

– –

Comm. AF Comm. AF a-axis a-axis Comm. AF c-axis Spiral a-axis Comm AF a-axis SDW SDW –

0, 0, 1 1 / 2, 0, 1 / 2 0.55, 0, 0 0.55, 0, 0 0, 0, 1 0, 0, 0.09 0.55, 0, 0 0, 0, 1 0.5526, 0, 0 0.093, 0.093, 0 –

Er Tm Yb, Ce

– 6 8 5 11 11 –

References are given in the text.

systems, and thus these must also be exchange-coupled systems even though the magnetic ordering temperatures are typically lower than for the heavy rare earths. Lastly, we note that no magnetic order or superconductivity have been observed in either the Ce or Yb systems. However, the Yb system exhibits some moderate heavy fermion effects [44]. A summary of the type of magnetic ordering and the transition temperatures is given in Table 2. We see that there is quite a variety of magnetic structures exhibited by this class of materials, a number of which are incommensurate. This behavior is reminiscent of the elemental rare earths, and suggests that the exchange is mediated by RKKY interactions. In this case the magnetic structures are controlled by the conduction electron susceptibility, and calculations of the enhanced susceptibility indicate a peak along the a-axis direction [45] which could explain this type of modulated structure. Further calculations will be necessary before it is clear whether this mechanism can provide an explanation for the full range of magnetic structures observed in this class of materials.

Acknowledgments It is a pleasure to acknowledge my collaborators on various aspects of the work reviewed here. I would like to thank A. T. Boothroyd, J. E. Crow, Q. Huang, W-H. Li, C.K. Loong, W. G. Moulton, N. Rosov, H. B. Radousky, and S. Skanthakumar for helpful conversations and assistance in preparing this review. Research at the University of Maryland is supported by NSF, DMR 93-02380.

References

Fig. 5. Magnetic Bragg peak intensity associated with the incommensurate ordering in TmNi 2 B 2 C [38]. The modulation wave vector for this material is [0.093, 0.093, 0], which is unique for this class of materials.

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