Experiments on magnetically-ordered superconductors

Journal of Magnetism and Magnetic Materials 31-34 (1983) 479-483

479

EXPERIMENTS ON MAGNETICALLY-ORDERED SUPERCONDUCTORS M.B. M A P L E

Department of Physics and Institute for Pure and Applied Physical Sciences, University of California, San Diego, La Jolla, CA 92093, USA

Certain ternary rare earth compounds exhibit long-range magnetic order in the superconducting state. Superconductivity coexists with antiferromagnetic order, but is destroyed by the onset of ferromagnetic order at a second transition temperature Tc2 ~ TM, where TM is the Curie temperature. In antiferromagnetic superconductors, the antiferromagnetic order modifies superconducting properties such as the curve of the upper critical magnetic field which exhibits a feature in the vicinity of the N6el temperature. In ferromagnetic superconductors, a long wavelength ( -- 102 A) sinusoidally modulated magnetic state develops in the superconducting state as a result of the superconducting-ferromagnetic interactions. Recent experiments on magnetically-ordered ternary and pseudoternary rare earth superconductors are briefly reviewed.

1. Introduction The subject of the interaction between superconductivity and magnetism is now about two and one-half decades old. The first theoretical inquiry into this problem was made by Ginzburg [1] in 1957, and experimental investigations by Matthias, Suhl and Corenzwit [2] soon followed in 1958. The early experiments were carried out on binary and pseudobinary systems in which a rare earth (RE) impurity ion with a partially-filled 4f electron shell and corresponding magnetic moment was dissolved into a superconducting element or binary compound, e.g., Lal_~RE ~ and (Yl_~REx)Os2. These early experiments were very provocative, but largely inconclusive with regard to questions concerning the coexistence of superconductivity and long-range magnetic order. This was primarily due to complications associated with chemical clustering a n d / o r short range or "glassy" types of magnetic order. However, the experiments stimulated some important theoretical work on the coexistence question which actually anticipated several of the more recent experimental developments on this subject, even though the theories were largely inapplicable to the binary and pseudobinary systems then being investigated. An important "spin-off" of the early work on the coexistence problem was the achievement of a rather complete understanding of the effect of paramagnetic impurities on superconductivity including crystalline electric fields, the Kondo effect, localized spin fluctuations, etc. [3]. The problem of magnetically-ordered superconductors experienced a revival in about 1976, when certain ternary and pseudoternary RE compounds were found to exhibit long-range magnetic order below their superconducting transition temperatures Tc. Superconductivity was observed to coexist with antiferromagnetic order [4-6], but to be destroyed by the onset of ferromagnetic order at a second transition temperature T~2 --- TM, where T M is the Curie temperature [7-9]. In this paper, we will briefly review the current experimental situation re-

garding the interaction between superconductivity and long-range magnetic order in ternary and pseudoternary RE systems.

2. Ternary rare earth systems The series of isostructural ternary RE compounds that have been investigated the most extensively in connection with the interaction between superconductivity and long-range magnetic order include the rhombohedral RE molybdenum chalcogenides REMo6S 8 and REMo6Ses, and the tetragonal RE rhodium borides RERh4B 4 [10,11]. The long-range magnetic order that many of these compounds exhibit can be traced in part to the ordered RE sublattice. The persistence of super* conductivity, even in the presence of relatively large concentrations of RE ions, can be attributed to the relatively weak exchange interaction between the conduction electron spins and the RE magnetic moments. This, in turn, appears to be associated with transition metal molecular units or "clusters" which, along with the RE ions, are the basic building blocks of these ternary RE phases. The superconductivity is believed to be primarily associated with the transition metal d-electrons that are relatively confined within the clusters and thereby interact only weakly with the RE ions. Recently, other ternary RE systems have been investigated such as RERh 1.i Sn 3.6, RE z Fe3 Si 5, RERuB2, etc. [ 10,11].

3. Superconducting-magnetic interactions In zero magnetic field, the superconducting electrons interact with the paramagnetic RE ions via the exchange interaction

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which, in the limit of low concentrations n of RE ions, is linear in n. According to Abrikosov and Gor'kov [12], the initial rate of the depression of T~ with n is given by

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where N(EF) is the conduction electron density of states at the Fermi level E F. Eq. (2) has been used to estimate the magnitude of for the RERh4B 4 compounds from the depression of T~ of LuRh4B 4 by RE impurities with partially-filled 4f electron shells [13]. The initial depression of T~ of LuRh4B 4 by G d impurities, ( d T J d n ) , _ o = - 19 K per atomic fraction of G d in Lu, yields the value I~] = 2.3 x 10 -2 eV-atom, assuming N ( E v ) = 0.35 states/eVatom-spin direction [13]. The exchange interaction also produces long-range magnetic ordering in ternary RE compounds via the R K K Y mechanism, although dipolar contributions may be important in certain cases. The polarized RE magnetic moments can then interact with the conduction electrons in two ways: by means of the Zeeman interaction of the exchange field and the conduction electron spins, and via the electromagnetic interaction of the magnetization and the persistent current.

4. Antiferromagnetic superconductors Coexistence of superconductivity and long-range antiferromagnetic order was initially observed in the RE molybdenum chalcogenides REMotS a ( R E = Gd, Tb,

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M.B. Maple / Magnetically-orderedsuperconductors magnons; (4) the reduction of the available phase space for virtual pair scattering by the change in lattice periodicity associated with antiferromagnetic order and (5) the pairing of electrons with finite momentum. Finite momentum pairing of electrons into states (k T, - k + Q ~.), where Q corresponds to translation by a reciprocals lattice vector, was originally proposed by Baltensperger and Str~issler [17] in 1963, and has since been incorporated into several recent theories [16]. It should be emphasized that there are some antiferromagnetic superconductors where He2 actually increases below T N, or in other words, superconductivity seems to be enhanced below TN. A notable example is the compound SmRh4B 4 whose resistively determined He2 vs. T curve, shown in fig. l, exhibits a sharp break in slope at T N = 0.87 K [18]. In contrast, the He2 vs. T curves of the other two antiferromagnetic superconductors in the RERh4B 4 series (fig. 1) display different behaviors with decreasing temperature: for NdRh4B4, which undergoes two antiferromagnetic transitions at TN1 ----1.31 K and TN2 = 0.89 K, He2 abruptly decreases at TN1, and then increases sharply at TN2, whereas for TmRh4B4, H¢2 hardly changes at TN = 0.4 K [18]. The data in fig. 1 indicate that there is no universal behavior of He2 vs. T for antiferromagnetic superconductors. Both enhancements and depressions of H¢2 are found below TN, which appear to be determined by a combination of the mechanisms outlined above.

5. Ferromagnetic superconductors Two ternary RE compounds, HoMorS s [9] and ErRh4B 4 [7], have been found to exhibit re-entrant superconductivity due to the onset of long-range ferromagnetic ordering of their RE magnetic moments. These two materials, which become superconducting at an upper critical temperature Tel, lose their superconductivity at a lower critical temperature T¢2--TM, where T M is the Curie temperature. Thermal hysteresis in various physical properties and a spike-shaped feature in the heat capacity near T¢2 indicate that a first-order transition from the superconducting to the ferromagnetic normal state occurs at Tc2 [11]. The resistively determined He2 vs. T curve for ErRh4B 4 is shown in fig. 1 [18]. Neutron diffraction measurements established that the ground states of HoM06S 8 [19] and ErRh4B 4 [8] are ferromagnetic. In addition, small angle scattering studies of HoMorS a [20] and ErRh4B 4 [21,22] have revealed the existence of a sinusoidally modulated magnetic state with a wavelength of the order of 10 2 A that coexists with superconductivity in a narrow temperature interval above T~2. Moreover, in ErRh4B 4 the regions within which superconductivity and the sinusoidally modulated magnetic state coexist appear to be interspersed with normal ferromagnetic domains to form a spatially inhomogeneous state.

481

The sinusoidally modulated magnetic state that coexists with superconductivity in HoM%S 8 and ErRh4B 4 is reminiscent of the cryptoferromagnetic state proposed by Anderson and Suhl [23] in 1959 and has been the subject of much recent theoretical interest. Whereas the original theory of Anderson and Suhl is based on the exchange interaction, recent theories such as those of Blount and Varma [24], Ferrell et al. [25], and Matsumoto et al. [26] are based on the electromagnetic interaction. Although, as discussed earlier, the exchange interaction is operative in these materials, the electromagnetic interaction appears to be primarily responsible for the sinusoidally modulated magnetic state that coexists with superconductivity. This conclusion follows from estimates of the wavelength )~ of the sinusoidalloY modulated magnetic state in ErRh 4 B4 which are _< l0 A for the exchange interaction, and -- l 0 2 ,~ for the electromagnetic interaction. Other possibilities for the periodic magnetic structure above Tc2 that have been considered are (l) a spontaneous vortex lattice, (2) a laminar structure, stabilized by the RE magnetization in a self-consistent manner, and (3) combined spiral magnetic and spontaneous vortex states [16,27]. Many other techniques have been applied to investigate the physical properties of HoMorS 8 and ErRh4B 4, and the reader is referred to several reviews on this subject [l l]. Very recent investigations include electron tunneling studies on sputtered films of ErRh4B 4 [28], as well as neutron diffraction [22] and critical field measurements on single crystal specimens of ErRh4B 4 [29].

6. Superconductivity and competing magnetic interactions Experiments on pseudoternary RE compounds provide an alternate method for studying the interaction between superconductivity and long-range magnetic order, as well as for exploring the effects of competing types of magnetic moment anisotropy a n d / o r magnetic order. Two types of RERh4B 4 pseudoternaries have been formed, one in which a second RE element is substituted at the RE sites, and another in which a different transition element is substituted at the Rh sites. An example of the first type of pseudoternary RERh4B 4 system is (Er~_xHOx)Rh4B 4 whose low temperature phase diagram, delineating the paramagnetic, superconducting, and magnetically ordered phases, is shown in fig. 2. The phase boundaries have been determined from ac magnetic susceptibility [18,30] and neutron diffraction measurements [31]. The phase diagram displays regions in which the Er 3+ and Ho 3+ magnetic moments independently order ferromagnetically within the basal plane and along the tetragonal c-axis, respectively, separated by a region of mixed magnetic phases. The temperature interval above To2

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within which the sinusoidally modulated magnetic phase in ErRh4B 4 coexists with normal ferromagnetic domains is also indicated in fig. 2. This inhomogeneous phase presumably presists within a certain region in the T - x plane (shaded area in the figure). There is a tricritical point at the concentration x c = 0.89 at which T¢~, T~2 and T M become coincident. The T~2vs. x phase boundary for x < x¢ is depressed relative to a linear extrapolation of T M vs. x for x > x¢ (dashed curve in fig. 2). Analysis of neutron diffraction data on a (Er0. 4 Ho0.6)Rh 4 B4 sample [32] indicates that the actual T M of 3.67 K is M about 0.2 K less than would have occurred in the absence of superconductivity, in accord with the dashed-line extrapolation as well as theoretical predictions. A striking example of the second type of pseudoternary RERh4B 4 system is Ho(Rh I _xlrx)4B 4. This system was first investigated by Ku et al. [33] and provided evidence for the coexistence of superconductivity and antiferromagnetic order with T N > Tc for x ~ 0.6. Subseq u e n t l y , several d e t a i l e d i n v e s t i g a t i o n s of a Ho(Rh0.3Ir0.7)4B 4 compound were carried out; heat capacity measurements [34] confirmed the bulk character of the antiferromagnetic order in this material, while neutron diffraction experiments [35] revealed the magnetic structure. Recently, low temperature specific heat, ac magnetic susceptibility, and electrical resistance measurements were used to investigate the nature of magnetic ordering and the dependence of the magnetic ordering temperature on x in the Ho(Rhl_xlrx)4B 4 system [36]. The low temperature phase diagram that emerged from this study is shown in fig. 3. The first study of this system yielded a similar phase diagram, but with no evidence for magnetic ordering at temperatures T > 1.2 K for 0.2 < x < 0.6.

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Several other pseudotenary RERh4B 4 systems have been investigated, and the reader is referred to more comprehensive reviews for discussion and references [ 11]. A n interesting low temperature phase diagram has recently been reported for the (Ho~.;,Eu;)Mo6S s system [37]. The author would like to thank S.E. Lambert for useful discussions. The support of the US Department of Energy under Contract No. DE-AT03-76ER70227 and the National Science Foundation under G r a n t No. DMRg0-17723 is gratefully acknowledged. References

[1] V.L. Ginzburg, Soy. Phys. JETP 4 (1957) 153. [2] B.T. Matthias, H. Suhl and E. Corenzwit, Phys. Rev. Lett. 1 (1959) 92. [3] For a review, see M.B. Maple, Appl. Phys. 9 (1976) 179. [4] M. Ishikawa and O. Fischer, Solid State Commun. 24 (1977) 747. [5] R.W. McCallum, D.C. Johnston, R.N. Shelton and M.B. Maple, Solid State Commun. 24 (1977) 391. [6] H.C. Hamaker, L.D. Woolf, H.B. MacKay, Z. Fisk and M.B. Maple, Solid State Commun. 31 (1979) 139. [7] W.A. Fertig, D.C. Johnston, L.E. DeLong, R.W. McCallure, M.B. Maple and B.T. Matthias, Phys. Rev. Lett. 38 (1977) 387. [8] D.E. Moncton, D.B. McWhan, J. Eckert, G. Shirane and W, Thomlinson, Phys. Rev. Lett. 39 (1977) 1164. [9] M. lshikawa and O. Fischer, Solid State Commun. 23 (1977) 37. [i 0] See Superconductivity in Ternary Compounds I, Topics in Current Physics, Vol. 32, eds. O. Fischer and M.B. Maple (Springer, Berlin, Heidelberg, New York, 1982), and references cited therein. [11] See Superconductivity in Ternary Compounds II, Topics in Current Physics, Vol. 34, eds. M.B. Maple and O. Fischer (Springer, Berlin, Heidelberg, New York, 1982), and references cited therein.

M.B. Maple / Magnetically-orderedsuperconductors [12] A.A. Abrikosov and L.P. Gor'kov, Soy. Phys. JETP 12 (1961) 1243. [13] H.B. MacKay, L.D. Woolf, M.B. Maple and D.C. Johnston, J. Low Temp. Phys. 41 (1980) 639. [14] D.E. Moncton, G. Shirane, W. Thomlinson, M. Ishikawa and O. Fischer, Phys. Rev. Lett. 41 (1978) 1133. [15] M.B. Maple, L.D. Woolf, C.F. Majkrzak, G. Shirane, W. Thomlinson and D.E. Moncton, Phys. Lett. 77A (1980) 487. [16] For a review, see P. Fulde and J. Keller, Chap. 9 of ref. [ll]. [ 17] W. Baltensperger and S. Str/issler, Phys. Cond. Materiel (1963) 20. [18] M.B. Maple, H.C. Hamaker and L.D. Woolf, Chap. 4 of ref. [11]. [19] J.W. Lynn, D.E. Moncton, W. Thomlinson, G. Shirane and R.N. Shelton, Solid State Commun. 26 (1978) 493. [20] J.W. Lynn, G. Shirane, W. Thomlinson, R.N. Shelton and D.E. Moncton, Phys. Rev. B24 (1981) 3817. [21] D.E. Moncton, D.B. McWhan, P.H. Schmidt, G. Shirane, W. Thomlinson, M.B. Maple, H.B. MacKay, L.D. Woolf, Z. Fisk and D.C. Johnston, Phys. Rev. Lett. 45 (1980) 2060. [22] S.K. Sinha, G.W. Crabtree, D.G. Hinks and H.A. Mook, Phys. Rev. Lett. 48 (1982) 950. [23] P.W. Anderson and H. Suhl, Phys. Rev. 116 (1959) 898. [24] E.I. Blount and C.M. Varma, Phys. Rev. Lett. 42 (1979) 1079. [25] R.A. Ferrell, J.K. Bhattacharjee and A. Bagchi, Phys. Rev. Left. 43 (1979) 154.

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[26] H. Matsumoto, H. Umezawa and M. Tachiki, Solid State Commun. 31 (1979) 157. [27] M. Tachiki, J. Magn. Magn. Mat. 31-34 (1983) 484. [28] C.P. Umbach and A.M. Goldman, Phys. Rev. Lett. 48 (1982) 1433. [29] G.W. Crabtree, F. Behroozi, S.A. Campbell and D.G. Hinks, Phys. Rev. Left. 49 (1982) 1347. [30] D.C. Johnston, W.A. Fertig, M.B. Maple and B.T. Matthias, Solid State Commun. 26 (1978) 141. [31] H.A. Mook, O.A. Pringle, S. Kawarazaki, S.K. Sinha, G.W. Crabtree, D.G. Hinks, M.B. Maple, Z. Fisk, D.C. Johnston, L.D. Woolf and H.C. Hamaker, Proc. IV Conf. Superconductivity in d- and f-Band Metals, Karlsruhe (28-30 June 1982) p. 201. [32] L.D. Woolf, D.C. Johnston, H.A. Mook, W.C. Koehler, M.B. Maple and Z. Fisk, Physica 109&110B (1982) 2045. [33] H.C. Ku, F. Acker and B.T. Matthias, Phys. Lett. 76A (1980) 399. [34] L.D. Woolf, S.E. Lambert, M.B. Maple, F. Acker, H.C. Ku, W. Odoni and H.R. Ott, to be published. [35] H.C. Hamaker, H.C. Ku, M.B. Maple and H.A. Mook, Solid State Commun. 43 (1982) 455. [36] K.N. Yang, S.E. Lambert, H.C. Hamaker, M.B. Maple, H.A. Mook and H.C. Ku, Proc. IV Conf. Superconductivity in d- and f-Band Metals, Karlsruhe (28-30 June 1982) p. 217. [37] M. Ishikawa, M. Sergent and O. Fischer, Phys. Left. 82A (1981) 30.