Specific heat and anisotropic superconducting and normal-state magnetization of HoNi2B2C

PHYSICA Physica C 230 (1994) 397-406

ELSEVIER

Specific heat and anisotropic superconducting and normal-state magnetization of HoNi2B2C P.C. Canfield *, B.K. Cho, D.C. Johnston, D.K. Finnemore Ames Laboratory and Department of Physics and Astronomy, Iowa State University, Ames, IA 50011, USA

M.F. Hundley Los Alamos National Laboratory, Los Alamos, N M 8 7545, USA

Received 18 May 1994; revised manuscript received 11 July 1994

Abstract

The magnetization of single-crystal HoNi2B2C has been measured as a function of applied field (H) and temperature in order to probe the interplay between superconductivity and magnetism in this complex layered system. The normal-state magnetic susceptibility of HoNi2BEC is highly anisotropic with a Curie-Weiss-like temperature dependence for H applied perpendicular to the c-axis and with a much weaker temperature dependence for H applied parallel to the c-axis, indicating that the Ho +3 magnetic moments lie predominately in the tetragonal a-b plane below 20 K. High-field magnetization (2000 Oe), low-field magnetization (20 Oe) and zero-field specific heat all give an antiferromagnetic ordering temperature of TN= 5.0 K. Remarkably, in 20 Oe applied field both superconductivity (Tc = 8.0 K) and antiferromagnetism (TN = 5.0 K) clearly make themselves manifest in the magnetization data. From these magnetization data a phase diagram in the H - T plane was constructed for both directions of applied field. This phase diagram shows a non-monotonic temperature dependence of He2 with a deep minimum at Tr~= 5 K. The high-field magnetization data for H applied perpendicular to the c-axis also reveal a cascade of three phase transitions for T< 5 K and H< 15 000 Oe, contributing to the rich H versus T phase diagram for HoNi2BECat low temperatures.

1. Introduction

Since the discovery of RMo6Ss, RMo6Ses, and RRh4B4 ( R = r a r e earth) cluster compounds in the 1970's [ 1 ] these three material groups have been the primary systems for study of the interaction of superconductivity and long-range magnetic order. With the discovery o f the RNi2B2C system [2,3 ], the possibility of a new model system for studying this interplay has presented itself. In addition, the availability of relatively large, high-quality, single crystals [4] allows for the study of anisotropies in single-phase ma* Corresponding author.

terials. The RNi2B2C system also offers a much clearer structural segregation of the local moments than is found in the cluster compounds. The rare earths are in well defined R - C planes that are separated by well defined Ni2B2 slabs [ 5 ]. This raises the possibility that these materials might act as an intermediate system between the three-dimensional cluster compounds such as RRh4B4 or RMo6Ss and the quasitwo-dimensional cuprate high-temperature superconductors such as the RBaECU307 materials, where there is little interaction between the rare-earth magnetic moments and the superconducting current cartiers [ 1 ]. The existence of low-temperature magnetic order

0921-4534/94/$07.00 © 1994 Elsevier Science B.V. All rights reserved SSDI 0921-4534 ( 94 )00463-3

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P.C. Canfield et al. /Physica C 230 (1994) 397-406

in the RNi2B2C system has been confirmed by specific-heat measurements on TmNi2B2C [6] which clearly show a large lambda-type anomaly at 1.5 K, indicating some form of magnetic ordering, most likely antiferromagnetic. Indeed, recent magneticsusceptibility measurements on polycrystalline samples [ 7 ] indicate magnetic order below Tc for R = Tin, Ho and Er members of the RNi2B2C series. The higher magnetic-ordering temperature of HoNi2B2C in combination with the lower Tc gives rise to the possibility of a strong interaction between superconductivity and magnetic order. The ratio T,,/TN for HoNi2B2C in zero applied field is 1.6 as compared with 6.6 for TmNi2B2C. Indeed, initial results of He2 versus temperature determined resistively [7] indicate that HoNi2B2C has a non-monotonic temperature dependence of Hc2 with a minimum near 5 K. These considerations, as well as the availability of large single crystals which allow for the study of magnetic anisotropies have lead to the following study of the specific heat and temperature and field-dependent anisotropic magnetization of HoNi2B2C.

2. Experimental Crystals of HoNi2B2C were grown via high-temperature flux growth [4]. Stoichiometric HoNi2B2C was arc-melted under an argon atmosphere and quenched on a water-cooled copper hearth. Ni2B flux was prepared in a similar manner. The HoNi2B2C was then annealed at 1050 ° C for 24 h to insure it was single phase. 2 g of NizB and 1 g of HoNi2BzC were then placed in an alumina crucible and heated to 1500°C under a flowing atmosphere of argon. The growth was then cooled to 1200°C at a rate of 10°C/h at which point the furnace was shut offand allowed to cool to room temperature. Plates of HoNizB2C with dimensions as large as 6 × 6 × 0.1 mm 3 were removed from the flux. These plates grow perpendicular to the c-axis and have surfaces relatively clean of flux. The magnetization measurements reported here were performed on two such crystals with masses 10.1 and 2.5 mg and the specific-heat measurements were performed on a single crystal of mass 4.9 mg. Magnetization measurements were carried out on the HoNi2B2C crystals using a Quantum Design SQUID magnetometer. Since these data were found

to depend on the temperature/field history of the sample, a brief description of the temperature/field profiles used to examine these samples is given here. Zero-field-cooled to 2 K data [ ZFC (2 K) ] were taken as follows: The sample was cooled in a field of less than 1 0 e to 2 K, at which point the measuring field was applied and data were collected upon warming to 4 K. The sample was then warmed to 20 K, the field was reduced to below I Oe again and the sample was cooled to 4.5 K at which point the measurement field was again applied and the rest of the data set was collected on warming. This process avoids possible field cooling for data above 4 K due to a nuance of temperature control in the Quantum Design SQUID. Zero-field-cooling to other temperatures [such as ZFC (6 K)] simply denotes the temperature to which the sample was cooled in zero field before the application of the measurement field. Data are then taken either on subsequent warming or cooling. This is necessary to probe the superconducting regions that, for certain applied fields, have normal states both at higher and lower temperatures than the temperature cooled to. For field-cooled (FC) runs, the measurement field was applied when the sample was in the normal state and subsequently cooled in the measuring field. None of the magnetization data are corrected for demagnetization factors. The specific-heat measurements were performed from 1.5 to 20 K in a small sample mass calorimeter that employs a thermal relaxation measurement technique [ 8 ].

3. Data Fig. l(a) shows the temperature dependent, anisotropic magnetic susceptibility of HoNizB2C for an applied field of 20 Oe perpendicular and parallel to the c-axis of the crystal as well as for a field of 2000 Oe applied perpendicular to the c-axis. Both the anisotropy of the magnetization and the coexistence of superconductivity and antiferromagnetism are illustrated in this figure. The data can be broken into three temperature regimes: T> 8 K, 5 K < T< 8 K, and T< 5 K. For T> 8 K there is a striking anisotropy in the induced moment between the two directions of applied field. With the field perpendicular to the c-axis ( H L c) the data show a Curie-Weiss-like tempera-

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/teff= 10.60/~a as well as with previously reported values for polycrystalline samples [ 7 ]. Fig. 2 shows the anisotropic magnetic susceptibility of HoNi2B2C for 2 K < T < 300 K. The anisotropy seen in Fig. 1 for low temperature persists up to 300 K, but becomes less pronounced as the temperature increases. The anisotropy in general, as well as the broad maximum seen at T ~ 70 K for Hllc can be associated with CEF effects. Preliminary data on (YI_xHOx)NiEBEC dilutions indicate that both anisotropy and the feature at T ~ 70 K are single-ion effects. A fit to the Curie-Weiss form for temperatures greater than 150 K gives pelf= 9.90#B and 0= + 17 K for H ± c and/t~ff= 10.46/za and 0= - 5 7 K for Hllc, where the differences in 0 are likely to be a manifestation of crystalline electric field (CEF) effects. Further evidence of this can be seen in the reduced entropy associated with the magnetic ordering of TmNiEB2C [ 6 ], as well as the reduced entropy associated with the antiferromagnetic ordering of HoNi2B2C which will be discussed below. These CEF effects evidently cause the Ho magnetic moment to lie predominately within the a-b plane at low temperatures, resulting in a nearly X Y magnetic symmetry. In the second temperature regime, 5 K < T < 8 K,

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temperature (K) Fig. 1. (a) Anisotropic M/Hvs. temperature of HoNi2B2C:H = 20 Oe applied perpendicular to the c-axis (open circles), H = 20 Oe applied parallel to the c-axis (open squares), and H=2000 Oe applied perpendicular to the c-axis (filled circles). Inset: M/H vs. temperature full scale to show full H parallel to c-axis signal at low temperature. (b) Anisotropic M/H vs. temperature of HoNi2B2C: H=20 Oe applied parallel to the c-axis (open squares), H = 20 Oe applied perpendicular to the c-axis after subtraction of H = 2000 Oe M/H data (open circles ).

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ture dependence and with the field parallel to the caxis (HI[c) the data show a much smaller, paramagnetic response. The susceptibility of a polycrystalline sample can be estimated by the average of the anisotropic magnetic susceptibilities [ (2/3)Znj_c+ (1/3)Xm~], a fit to which of the Curie-Weiss form C / ( T - O ) from 10 K to 20 K gives an effective moment, #elf= 10.41/tB, and a paramagnetic Curie temperature, 0= - 0 . 8 K. This value of#elf compares well with the effective moment of the free H o +3 ion,

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P. C. Canfield et al. / Physica C 230 (1994) 397-406

both directions of applied field show a drop in the magnetization toward diamagnetism with decreasing temperature (Fig. 1 ( a ) ) . The onset of diamagnetism measured for HIIc (To= 8.0 K ) is consistent with the values of Tc determined resistively [ 3,7 ]. For H ± c the magnetization remains paramagnetic, but there is a distinct drop in signal at Tc. Indeed, if the normal-state susceptibility is subtracted from the H Z c magnetization, the data for H[[c and H ± c are remarkably similar. Such a subtraction is shown in Fig. l(b). At T = 5 K there is an antiferromagnetic transition, the magnetic signature of which can be seen in the H ± c data for an applied field of 2000 Oe shown by filled circles in Fig. 1. As will be shown, this field suppresses Tc to well below TN = 5 K. The magnetic ordering of the Ho sublattice manifests itself as a sharp feature in the superconducting-state magnetization data for both applied field directions. For T< 5 K the HIIc diamagnetic signal increases suddenly by a factor of almost 40 and saturates (inset of Fig. 1 ( a ) ) , while for H ± c the signal becomes diamagnetic and also saturates. This dramatic feature in the magnetic susceptibility seems to be associated with the onset of antiferromagnetic order of the local Ho moments. The two-step nature of the diamagnetic signal associated with the superconducting state, specifically for H[Ic is striking. The well defined nature of the three plateaus that are separated by well defined, sharp drops at Tc = 8 K and TN = 5 K warrants theoretical attention. Fig. 3 presents zero applied field specific heat (Cp) data for HoNi2B2C. While the peak associated with the magnetic order is clearly seen at 5.0 K, the hightemperature tail of the magnetic transition makes it difficult to resolve the change in specific heat that would be associated with the superconducting transition temperature To= 8.0 K. This is not surprising because the high-temperature tail of the specific-heat anomaly associated with the magnetic order at 5 K is still much larger than the jump in specific heat associated with the superconducting transition in either TmNi2B2C or YNizBzC [6 ]. Also plotted in Fig. 3 is d ( z T ) / d T f o r the H = 2 0 0 0 Oe, H L c data shown in Fig. 1. As anticipated [9] the temperature dependence of d ( z T ) / d T is qualitatively the same as that of the specific heat close to TN. The other distinct features in the Cp data are the

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temperature (K) Fig. 3. ( a ) Specific heat (('r,) ° f H°Ni2B2 C vs. "temperature shown by open squares and d ( z T ) / d T for 2000 Oe applied perpendicular to the c-axis of HoNi2B2C shown by open circles. (b) Exp a n d e d scale to show features at 5.5 and 6.0 K.

two shoulders in the specific heat seen at 5.5 K and 6.0 K shown in Fig. 3(b). These features also make themselves weakly manifest in the d ( z T ) / d T data. Based only on the specific heat and high-field magnetization data, it might be tempting to dismiss these small features as second-phase effects, but, as will be discussed later, anomalies associated with these two temperatures also make themselves manifest in the low-field, temperature-dependent magnetization measurements of the superconducting state, indicating that these features can be associated with the bulk sample. In addition, recent temperature-dependent, elastic, neutron-scattering experiments on single crystals of HoNi2B'gC show that magnetic satellites associated with an incommensurate, modulated magnetic structure begin to develop between 6 K and 5 K. This incommensurate, modulated structure is

P.C CanfieMet al. / Physica C 230 (1994) 397-406 suddenly replaced by a simple antiferromagnetic structure below 5 K [ 10 ]. The temperature dependences of the magnetic scattering from the incommensurate and simple antiferromagnetic structures are consistent with the three features seen in Fig. 3. Finally, temperature-dependent, elastic, neutronscattering experiments on HoNi2B~C powders rule out the possibility that the two smaller features in Fig. 3 are due to magnetic ordering of an unidentified second phase [ 10]. By determining the entropy associated with the magnetic-ordering transition centered at 5 K we can determine the nature of the CEF ground state in HoNi2B2C. The three contributions to Cp are Cp = 7T+ fiT s + CM (T), where the 7 and fl terms are the electronic and phonon contributions, respectively, and CM is the magnetic contribution. To determine CM from the measured data we must first determine 7 and fl, but due to the magnetic contribution from the 5 K transition that is clearly present in the Cp data at all measured temperatures ( 1.5 to 20 K) it is impossible to determine these parameters from our data. Crude but useful estimates of 7 and fl can be made from the specific-heat measurements on other members of the RNiEB2C system. Based on Cp measurements of TmNi2B2C 6, 7 ~ 2 0 m J / m o l e K 2 and fl~0.35 m J / m o l e K 4 ( 0 0 = 3 2 0 K) are consistent values for HONiEB2C. These values lead to a nonmagnetic background that varies monotonically from 0.020 J/mole K at T = 1 K to 0.260 J/mole K at T = 7 K. (See Fig. 3 (b) for comparison. ) The magnetic entropy for HONiEB2C as estimated with these parameters nearly saturates to 9.1 J / m o l e K at 20 K. This value is consistent with a triplet ground state ( S = R In 3=9.13 J/mole K). In tetragonal symmetry, the Ho 3+ J = 8 ground state is expected to split into nine singlest and four doublets due to CEF interactions [ 11 ]. Hence, the total entropy associated with the 5 K feature suggests that a closely spaced doublet and singlet are involved in this magnetic transition. Further, the other eleven CEF levels must be spaced well above the two nearly degenerate ground-state levels. This is consistent with the large CEF induced anisotropy that is evident in the magnetic susceptibility measurements. Figs. 1 and 3 clearly indicate that superconductivity and antiferromagnetism coexist below 5 K in small applied fields. In order to further examine the inter-

401

actions between magnetism and superconductivity in HoNi2B2C, a series of M versus T runs at constant applied field were performed for both nllc and H / c . Figs. 4 (a) and (b) show representative data for H I c for fields of 200 Oe, where the superconductivity is apparent, and 2000 Oe, where the superconductivity has been suppressed to below 2 K. In this direction of applied field there is the large, intrinsic temperature-dependent magnetization associated with the H • local moments, but there is still a significant diamagnetic component to the M ( T ) / H versus Tdata shown for 200 Oe. By comparing the M ( T ) / H data at H = 200 Oe and 2000 Oe in Figs. 4(a) and (b) three superconducting transition temperatures can be determined for Ho-

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temperature (K) Fig. 4. M/H vs. temperature for H applied perpendicular to the c-axisofHoNi2B2C. (a) H=2000 Oe (filled circles), ZFC(2 K) H=200 Oe (open squares), FC H=200 Oe (open circles). (b) Expanded scale to show detail. ZFC(6 K) H=200 Oe (filled triangles).

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P.C. Canfield et al. /Physica C 230 (1994) 397-406

Ni2B2C at 200 Oe H ± c. The 2000 Oe curve, shown by filled circles, represents the normal-state susceptibility since at 2000 Oe applied field Tel is suppressed to below 2 K. The ZFC(2 K) H = 2 0 0 Oe data, shown by open squares, start to fall below the H = 2000 Oe data for T< 4.6 K. In addition there is a significant difference between the FC data, shown by open circles, and the ZFC (2 K) H = 200 Oe data for temperatures below this temperature. This then gives the lower limit of Tc3=4.6 K for H = 2 0 0 Oe H ± c . This is a lower limit due to questions of reversibility when comparing the ZFC(2 K) and FC curves. Upon further warming the 200 Oe data again deviate from the 2000 Oe data for temperatures between 5.3 K and 7.2 K. This is consistent with a re-entering of the superconducting region at Tc2=5.4 K and leaving it again at Tel = 7.2 K. The fact that there is no apparent difference between the FC and ZFC(2 K) data (open circles and open squares, respectively) for temperatures above 4.6 K, and specifically for temperatures between 5.4 and 7.2 K, is significant. It is evidence that the sample has been in the normal state for temperatures between the lower ( T < 4.6 K) and upper (5.3 K < T< 7.2 K) superconducting regions. To further examine the nature of the magnetization in the upper superconducting region, ZFC (6 K) data, shown by filled triangles, are also shown in Fig. 4 (b). The significant difference between the ZFC (2 K) or FC data and the ZFC(6 K) data is further evidence that the upper region is indeed superconducting. The temperature difference between where the FC data and the ZFC(6 K) data diverge and where the FC and 2000 Oe data diverge is probably due to a region of reversibility. Critical temperatures for which the applied field is Hc2 a r e determined by taking the extremal temperature at which the low-field data sets diverge from the normal-state data set. In this case, the temperatures used to construct the He2 versus T plot are those taken from the divergence of the ZFC(2 K) or FC data from the 2000 Oe data. In a similar manner, Fig. 5 shows representative data for Hllc with H = 5 0 0 and 10000 Oe. The applied field of H = 10000 Oe is in excess of Hc2(2 K) and the M ( T ) / H versus T data are representative of the paramagnetic background of the sample (filled circles). This background varies slightly from sample to sample and is likely due to four components: an intrinsic paramagnetic signal, a signal due to small

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amounts of flux on the surface of the crystal, a signal from fine-grain HoNi2BzC adhering to the surface of the crystal, and a signal due to a slight misalignment of the crystallographic c-axis with the applied field. At 500 Oe applied field the ZFC(2 K) M ( T ) / H versus T plot (open squares) differs dramatically from the H = l0 000 Oe one. The data can be thought of qualitatively as a superposition of the small paramagnetic background shown for the 10 000 Oe run and a highly non-monotonic, diamagnetic signal. The temperature dependence of this diamagnetic component can be thought of as being due to cutting across the ttc2 v e r s u s Tphase diagram at fields large enough to cause the sample to become normal near TN = 5 K. therefore giving rise to three superconducting transition temperatures Tc~=7.3 K, T , , 2 = 5 . 4 K, and 7c3 = 4.3 K. It should be noted that there are also two features in the H = 500 Oe magnetization for temperatures close to T=5.5 K and 6.0 K. These are the temperatures at which anomalies are seen in the specific-heat data shown in Fig. 3. The fact that these features are seen in the superconducting state but not in the normal state indicates that these features are associated with the electrons that condense into the superconducting ground state. This, then, also supports the conjecture that these features are associated with an intrinsic, bulk effect. Fig. 6 shows the He2 versus T data extracted from

P.C. Canfieldet al. IPhysica C 230 (1994)397-406

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Fig. 6. Upper critical field, He2,of HoNi2B2Cvs. temperature. H applied parallel to the c-axis (open squares) and H applied perpendicular to the c-axis (filled diamonds). Lines are added to guide the eye. M ( T ) runs similar to those shown in Figs. 4 and 5. The existence o f a deep, well defined m i n i m u m in He2 at 5 K for both directions of applied field is the most dramatic feature o f this figure. Both the Hllc (open squares) and H ± c (filled diamonds) data show evidence of superconductivity at 5 K for H = 20 Oe. However, for an applied field o f 200 Oe the H ± c magnetization data deafly show evidence of an intermediate temperature normal state near T = 5 K (Fig. 4), while the Hlic data show indications o f just barely having an intermediate normal state. For applied fields higher than 500 Oe it is difficult to determine whether there is an upper superconducting region between 5 K and 8 K for H ± c, while for HIJc it is clear that the superconductivity persists in the upper region to applied fields greater than 1000 Oe for T-~ 6 K. In order to better understand the nature of the normal-state magnetism, several M versus H isotherms and M ( T ) / H versus T runs were performed for an applied field comparable to and larger than He2 (0 K). Fig. 7 (a) shows M versus H data at T = 2 K for H ± c. There is a hysteretic phase transition at roughly 3800 Oe, a second transition at 8600 Oe and a third one at 13 200 Oe. M versus H data at 3 K, 4 K and 4.5 K

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10.1 mg with H applied perpendicular to the c-axisfor increasing field (open circles) and decreasing field (open triangles). (b) M/H vs. temperature for H applied perpendicular to the c-axis of HoNi2B2C crystal of mass 2.5 mg for H=2000 Oe (open circles), H=6000 Oe (filled squares) and H=10000 Oe (open diamonds). indicate that there are weak temperature dependences associated with these transitions. M ( T ) / H versus T plots at representative applied fields are shown in Fig. 7 (b). The M ( T ) / H versus T data for H = 2000 Oe (open circles) are consistent with antiferromagnetic order. Preliminary data indicate a similar magnetization versus temperature behavior for a variety of directions of H within the a-b plane at low fields. This suggests that even the low-field magnetic structure is complex in nature and may well be non-collinear. For applied fields o f 6000 Oe and l0 000 Oe (filled squares and open diamonds, respectively) the M / H versus T plots are more consis-

P.C. Canfield et al. / Physica C 230 (I 994) 397-406

404

tent with complex magnetic order where the net moment per magnetic unit cell does not average to zero. The saturation moment associated with the H > 15 000 Oe data is 9.0#B which is 90% of that of the free H o +3 ion, so the magnetism associated with fields H > 15000 Oe is likely to be saturated paramagnetism. A composite H - T p h a s e diagram for the superconducting and normal states of HoNi2B2C is presented in schematic form in Fig. 8. The structure of the superconducting phase boundary (Hc2 versus T) is novel, specifically the depth of the local minimum in H~2 at T = 5 K. The normal-state, H versus T phase diagram is exceptionally complex too, with three regions of magnetic order existing below T = 5 K and H = 15 000 Oe. Details of this phase diagram such as the nature of the magnetic order and the fine structure of phase boundaries will have to be determined by field-dependent elastic and inelastic neutron scattering as well as detailed field-dependent specific-heat and anisotropic-magnetization measurements,

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4. Discussion

In other systems that have coexisting superconductivity and antiferromagnetism, the existence of the antiferromagnetic transition has been deduced from kinks in the Hc2(T) data, specific-heat measurements or neutron-scattering measurements [ 1 ]. In the case of HoNi2B2C the antiferromagnetic phase transition makes itself manifest directly in the temperature-dependent magnetization measurements at fixed magnetic field. The two-stepped structure associated with the low-field, temperature-dependent magnetization for both Hllc and ttd_c as shown in Fig. 1, is striking. While the exact cause of the two diamagnetic plateaus in not yet clear, there must be a dramatic reduction in pair breaking associated with the onset of long-range antiferromagnetic order below TN=5 K. The He2 (T) data presented in Fig. 6 are quantitatively remarkable but not qualitatively unprecedented. This is because in earlier antiferromagnetic materials such as ErM06S8 [ 1,12,13 ] peaks in Hc2 (T) for temperatures higher than TN followed by local minima in H¢2(T) at 7~ have been observed, but never with such high magnetic-ordering temperatures or such deep local minima at TN. Indeed, based upon the comparison or HIIc and H L c data in Fig. 1 (b), there is a strong tendency toward re-entering the normal state at exceptionally low applied fields for H ± c. It seems clear from this figure that for fields not much larger than 20 Oe there will be an intermediate normal state between the two superconducting states for H I c. Qualitatively, the form of the temperature dependence of H~2 can be associated with the magnetization of the rare-earth sublattice suppressing the bare He2. For the case of ErM06S8, He2(T) has been quantitatively fit [ 1,12,13 ] by Hc2 ( T ) v c H c * 2 ( T ) - M ( t t c 2 .

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8

Fig. 8. Magnetic field vs. temperature phase diagram for HoNi2B2C. Crosses are data collected from the M vs. H isotherms similar to that shown in Fig. 7(a); the solid line represents a composite of the two H¢2 phase boundaries shown in Fig. 6, and the dotted line represents an as yet undetermined phase boundary between the paramagnetic and magnetically ordered states.

where H~*2(T) is the bare He2, i.e. the He2(T) that the system would have in the absence of the local Ho moments, M ( H , T) is the temperature- and field-dependent magnetization of the local moment lattice, and A, for the purposes of this discussion, can be treated as a fitting parameter. In light ofEq. ( 1 ), the fact that the H~2(T) for HJlc

P.C. Canfieldet al. /PhysicaC 230 (1994)397-406 has higher values for all temperatures than for HA_c is easily understood by virtue of the anisotropy of the magnetization: since there is a much smaller magnetization for HII c, nc2 (T) is closer to the bare He*2(T) value. There is, though, great difficulty in explaining how, based upon Eq. ( I ) , Hc2(T) for HIIc acquires its form: i.e. why is the Hc2(T) for HIIc not simply the bare H¢'2 (T)? Because the magnetization for HIIc is essentially zero and temperature independent for the applied fields in question, any deviations from the bare H~*2(T) must be due to terms other than those simply proportional to M(H, T). The existence of the well defined suppression of the superconducting region in the vicinity of 5 K for Hllc cannot be accounted for by terms solely proportional to powers of the magnetization. One possible source of such extra term is magnetic fluctuations in the R-C plane. This would be consistent with the analysis of the specific-heat data for TmNizBzC6. In addition, a rich excitation and fluctuation spectrum is consistent with the complex normal-state H versus T phase diagram shown in Fig. 8, specifically the cascade of magnetic transitions for T < 5 K and H < 15 000 Oe. Given the well defined minimum in Hc2 at 5 K and the well defined upper superconducting region created by it, one fundamental question that the HoNi2B2C system raises is: Will there be a difference in M(T, H) depending upon whether the upper superconducting region is entered from high or low temperatures? In other words, for the case of HoNi2B2C in an applied field of 500 Oe Hllc, will the magnetization M(500 Oe, 6 K) be the same when the sample is field cooled from 10 K to 6 K and when the sample is field warmed from 5 K to 6 K? In both cases the sample enters the superconducting state from the normal state in an applied field, but the magnitude of M(H, T) and the degree of fluctuations present at the superconducting transition temperatures will differ because, expressed in the effective temperature T~ TN), there is a significant difference between Tc2 elf= 1.08 and Tcl eff= 1.46. Initial results [ 14] indicate that there is indeed a significant difference between the magnitude of M(H, T) reached in these two manners. Further work on understanding the details of this difference is clearly needed.

405

5. Conclusions Temperature-dependent magnetization measurements on single crystals of HoNi2B2C show a striking anisotropy in the normal-state magnetic susceptibility. Below 20 K, the susceptibility is much larger for HA_c than for HIIc, indicating that the HO+3 ion magnetic moments lie predominately in the a-b plane. This anisotropy evidently results from large splittings (much greater than 20 K) between the crystalline electric field levels, which lead to XYbehavior of the Ho +3 magnetic moment. This reduction of the J multiplet degeneracy is consistent with the reduced magnetic entropy associated with the magnetic transition at TN= 5.0 K found in our specific-heat measurements: AS~ R In 3, as opposed to the R In 17 that would be associated with the full J = 8 multiplet for the free Ho ÷ 3 ion. Remarkably, this anisotropy is also observed at low fields ( H < 1000 Oe) in the superconducting state. In addition, while in the superconducting state, a dramatic signature of antiferromagnetic ordering at TN = 5 K is seen in the temperature dependent, low-field, magnetization at fixed field plots. He2(T) has been determined by analysis of Mversus T at constant H data and it is in qualitative agreement with that found by resistivity measurements [ 7 ]. While some effect of the normal-state magnetization anisotropy can be seen in He2 versus T for the respective field directions, it is the lack of a much larger anisotropy in the H~2(T), which might have been anticipated from the very large anisotropy of the Ho sublattice magnetization, that will require careful theoretical attention. In order to explain the observed He2 (T) data, terms in addition to powers of M(T, H) will have to be considered. One possible such term could incorporate the effects of magnetic fluctuations near TN based on detailed understanding of the normal-state magnetic interactions. The full H versus T phase diagram of HoNi2B2C is found to be rich in detail, with the complex interplay between superconductivity and local moments occurring at low applied fields followed by a cascade of magnetic transitions at higher fields: a first-order transition at 3800 Oe followed by two second-order phase transitions at 8600 Oe and 13 200 Oe, respectively. It is this wealth of detail seen at both low and high applied fields, the phenomenal anisotropy, and

406

P.c. Canfield et al. /Physica C 230 (1994) 397-400

the availability o f well f o r m e d single crystals that m a k e s H o N i 2 B 2 C a p r o m i s i n g system for further, detailed studies o f the i n t e r a c t i o n b e t w e e n s u p e r c o n d u c t i v i t y a n d local m o m e n t m a g n e t i s m .

Acknowledgements We wish to t h a n k R.W. M c C a l l u m and K. D e n n i s for the use o f t h e i r a r c - f u r n a c e a n d L.L. Miller for technical assistance. M F H a c k n o w l e d g e s fruitful discussions with R. M o v s h o v i c h and J.D. T h o m p s o n . A m e s L a b o r a t o r y is o p e r a t e d for the U.S. D e p a r t m e n t o f Energy by I o w a State U n i v e r s i t y u n d e r contract N o W-740-Eng-82. T h i s w o r k was s u p p o r t e d by the D i r e c t o r for Energy R e s e a r c h , O f f i c e o f Basic Energy Sciences. W o r k at Los A l a m o s N a t i o n a l Laboratory was p e r f o r m e d u n d e r the auspices o f the U n i t e d States D e p a r t m e n t o f Energy.

References [1 ] ~. Fischer, Ferromagnetic Materials, vol. 5, ed. K.H.J. Buschow and E.P. Wohlfarth (North Holland, Amsterdam, 1990) p. 465.

[2] R. Nagaragan, C. Mazumdar, Z. Hossein, S.K. Dhar, K.V. Golpakrishnan, LC. Gupta, C. Godart, B.D. Padalia and R. Vijayaragharan, Phys. Rev. Lett. 72 (t994) 274. [3] R.J. Cava, H. Takagi, H.W. Zandbergen, J.J. Krajewski, W.F. Peck, T. Siegrist, B. Batlogg, R.B. van Dover, R.J. Felder, K. Mizuhashi, J.O. Lee, H. Eisaki and S. Uchida, Nature (London) 376 (1994) 252. [4] M. Xu, P.C. Canfield, J.E. Ostenson, D.K. Finnemore, B.K. Cho, Z.R. Wang and D.C. Johnston, Physica C 227 ( 1994 ) 321. [5] T. Siegrist, H.W. Zandbergen, R.J. Cava, J.J. Krajewski and W.F. Peck, Nature (London) 376 (1994) 254. [6]R. Movshovich, M.F. Hundley, J.D. Thompson, P.C. Canfield, B.K. Cho and A.V. Chubukov, Physica C 227 (1994) 381. [7 ] R.J. Cava, B. Batlogg, T. Siegrist, J.J. Krajewski, W.F. Peck, S. Carter, R.J. Felder, H. Takagi and R.B. van Dover, preprint. [8] R. Bachmann, F.J. Disalvo, T.H. GebaUe, R.L. Greene. R.E. Howard, C.N. King, H.C. Kitsch, K.N. Lee, R.E. Schwall, H.V. Thomas and R.B. Zubeck, Rev. Sci. Instr. 43 (1972) 205. [9] M.E. Fisher, Philos. Mag. 7 (1962) 1731. [10]A.I. Goldman, C. Stassis, P.C. Canfield, J. Zarestky, P. Dervengas, B.K. Cho, D.C. Johnston and B. Sternlieb, Phys. Rev. B, Rapid Communication, submitted. [ 11 ] U. Walter, PhD. Thesis, unpublished. [12] M. Ishikawa and O. Fischer, Solid State Commun. 24 (1977) 747. [ 13 ] O. Fischer, M. Ishikawa, M. Pelizzone and A. Yreyvaud, J. Phys. (Paris), C5-40 (1979) 89. [14]B.K. Cho, P.C. Canfield, D.C. Johnston and D.K. Finnemore, unpublished.