μ+SR studies of the magnetic and superconducting states of URu2Si2

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Physica B 186-188 (1993) 300-302 North-Holland

x+SR studies of the magnetic and superconducting states of URu2Si2 E.A. Knetsch a, A.A. Menovsky a, G.J. Nieuwenhuys a, J.A. Mydosh a, A. Amato b, R. Feyerherm b, F.N. Gygax b, A. Schenck b, R.H. Heffner c and D.E. MacLaughlin ° "Kamerlingh Onnes Laboratory, Leiden University, The Netherlands blnstitut fi~r Mittelenergiephysik der ETH Zi~rich, Villigen, Switzerland CLos Alamos National Laboratory, Los Alamos, NM, USA aPhysics Department, University of California, Riverside, CA. USA We have performed tx+SR studies on single-crystal URuzSi2 in the temperature range 0.05-300K. Zero-field (ZF) measurements show an increase in relaxation rate below TN= 17.5 K. Transverse-field (TF) measurements in H = 2900 G along the a and c directions display a strongly anisotropic Knight shift which does not scale with the bulk susceptibility for T < 50 K. Low-T measurements reveal a penetration depth of -7000-10 000 A with a temperature-dependent linewidth in which two steps are observed near 0.3 and 0.9 K.

The discovery of URu2Si 2 established the first example of coexisting long-range antiferromagnetic order with superconductivity in a heavy-fermion material [1]. The AF ordering (with an ordered moment of -0.037/x B as determined from neutron scattering [2]) is now generally believed to be of the SDW type, where a strongly anisotropic energy gap is opening up over a large portion of the Fermi surface below T N = 17.5K. This compound crystallizes in the bodycentered tetragonal ThCrzSi 2 structure with U - U distances of 4.13 ,~ in the basal plane and 4.79 A along the c direction. Si and Ru are stacked symmetrically between the U layers in both halves of the unit cell which consists of two formula units. The AF structure consists of ferromagnetically coupled U-moments in the (a, b)-plane, stacked antiferromagnetically along the c direction. Contrary to our earlier reports [3] where the sample was measured a short time after preparation, and apparently due to aging effects [4] we have now observed a small ferromagnetic signal below T c = 35 K in low-field (50 G) magnetization measurements. This signal may originate from ferromagnetic coupling between adjacent layers along the c direction. Such a 'stacking fault' could be the result of some imperfection or disorder in the S i - R u layers, separating the U layers. This could result in a subtle modi-

Correspondence to: E.A. Knetsch, Kamerlingh Onnes Laboratory, Leiden University, 2300 RA Leiden, The Netherlands.

fication of the coupling between such layers from antiferromagnetic to ferromagnetic. Th'e amplitude of the ferromagnetic signal corresponds to a saturation magnetisation of only 1.2 x 10 4p,B/U-atom. If we contribute the magnetism to the uranium, the density of stacking faults required to induce a ferromagnetic signal of this amplitude, is therefore small. The average distance between two such defects would be of the order of 200-300 lattice spacings (900-1300 A), which is somewhat larger than, but comparable to the magnetic correlation length found in this direction [5]. The present zero-field (ZF) and transverse-field (TF) p,+SR studies were made on single-crystal samples of URu2Si 2, grown using a Czochralski tri-arc method. Two samples of 1 cm 2 area were studied with their surfaces perpendicular to the a and c directions, respectively. The ~ SR data have been recorded with the PSI low temperature p,+SR facility and general purpose spectrometer on the ~+SR dedicated beam line on the PSI-600 MeV proton accelerator. High-temperature measurements were made between 2.5-300 K using a flow cryostat. The ZF measurements at high temperatures were fitted to an exponential form. The results in fig. l show a sharp increase in exponential relaxation rate below the N6el temperature for P Ix L c. At lower temperatures, however, the relaxation rate does not saturate, but keeps increasing down to 2.5 K. A similar behavior was encountered in neutron-scattering and X-ray magnetic scattering experiments, where a linearly increasing

0921-4526/93/$06.00 © 1993- Elsevier Science Publishers BN. All rights reserved

301

E.A. Knetsch et al. / Iz+SR studies o f URu2Si 2

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Fig. 2. Knight shift for URu2Si2 in an applied field of 2.9 kO for HI] c and P, Z c. Note the deviation from the bulk susceptibility at about 50 K.

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Fig. 1. (a) Zero field (ZF) relaxation rate for URu2Si2 with the initial muon polarization, P~, ± c (O) and Hc (D). (b) Transverse field (TF) (H=2.9kGII c) relaxation rate for p~ ± c. Note the onset of AF order at 17.5 K, clearly indicated by a jump in relaxation rate for the ZF data. order parameter was found below TN for 3 - 1 7 K , saturating only below 3 K [5]. A similar increase in the ~+-relaxation rate was observed by Luke et al. [6], but these measurements, which do confirm the overall behavior, do not extend to low enough temperatures to unambiguously establish the continuing increase at low temperatures. Below 35 K a small increase in relaxation rate was observed originating from the small ferromagnetic signal. This contribution already saturates above 25 K and is not likely to influence the low-T behavior. At low temperatures we observe an exponential relaxation rate of - 0 . 1 ixs-1 for P , both parallel and perpendicular to the c direction. This implies that this linewidth is due to relaxation and not to the beginning of slow precession around a small uniform field. Transverse field (TF) measurements were performed in a field of 2.9 kG for both directions. A small temperature-independent exponential linewidth of - 0 . 0 3 7 ixs -a was found for the a direction. A small temperature-independent Knight shift of +250ppm was measured. For the c direction we observe the same exponential relaxation rate as in the ZF measurements. Only in the temperature range 17-35 K we observe a somewhat larger relaxation rate due to the saturation of the ferromagnetic signal in the external field of 2.9 kG, as can be clearly seen from fig. 1. In

fig. 2 it is shown that for H I1c the Knight shift is large and negative. For T > 50 K it tracks the bulk susceptibility, but for lower temperatures starts to deviate, becoming almost temperature-independent. Previous measurements [7] on a polycrystalline sample showed a small Knight shift, which tracked the susceptibility at low temperatures. For our measurements of the superconducting state, the sample was mounted on a cold finger, attached to the mixing chamber of a top-loading dilution refrigerator. TF measurements were made in H = 350 G, where HI] c and P ,L c. As H d < H < Hc2, a good flux-line lattice should be present in the sample, which allows investigation of the magnetic field penetration depth and its temperature dependence. From thermodynamic properties a penetration depth of ~8500 can be estimated. Recent AC-susceptibility measurements (317 Hz, 1 MHz and 13 MHz) yield a penetration depth of 8000-10 000 ~ [8]. From previous ~+SR measurements a lower bound on the penetration depth with H II c of - 6 0 0 0 , ~ was estimated by Luke et al. [6]. In measurements by Heffner et al. [9] no increase in relaxation rate below Tc was observed for a single crystal with H 11c for H = 500 G. This puts a lower limit on their estimate of the penetration depth of ~10000,~. Our results, obtained from the overall increase of the relaxation rate at the lowest temperature, indicate a penetration depth of 7000-10 000 ,~, in good agreement with the various reported values. If we now focus on fig. 3(a), which shows the TF relaxation rate at low temperatures, we observe two steps, occurring at --0.3 and --0.9K, respectively. These steps are not due to different metallurgical phases in our sample, as magnetization and specificheat measurements [3,8] do not show any sign of the 0.9 K anomaly for samples from the same single crystal. We suggest that these anomalies are reflecting

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E.A. Knetsch et al. / Ix+SR studies of URu2Si 2

dered state is also clearly visible. We do not observe the presence of any well-defined frequencies below T y as was recently reported [10]. In the superconducting state two anomalies were discovered at 0.3 and 0.9 K, which might be indications of transitions in the fluxline lattice.

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This work is part of the research program of the A m s t e r d a m - L e i d e n Materials Research Cooperation ( A L M O S ) and partially supported by the Dutch Foundations N W O and F O M , U.S. NSF Grant no. D M R 9114911, and the Univ. of California C o m m i t t e e on Research.

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References

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Fig. 3. Relaxation rate (a) and muon frequency (b) in the superconducting state of URu2Si 2 in an applied field of 350G, where P, ± H ]1c. A gaussian relaxation rate was considered in the fit procedure. Note the anomalies near 0.3 and 0.9 K in the relaxation rate and the frequency shift. transitions of the flux-line lattice (note that the onset of s u p e r c o n d u c t i v i t y in our sample occurs at 1.3 K found from thermodynamic measurements). Furtherm o r e the ix+-Larmor frequency shows an interesting t e m p e r a t u r e d e p e n d e n c e (see fig. 3(b)) in that the Knight shift above 0.9 K of about - 5 0 0 ppm (see fig. 2) decreases below 0.9 K to almost zero ppm at 0.3 K, with no further significant temperature dependence below. The positive shift is suggestive of spin-singlet pairing as it indicates a strong reduction of the spin susceptibility. We do not have so far any explanation for the near coincidence of the anomalies at 0.3 and 0.9 K in the relaxation rate and the frequency shift. In conclusion we can say that the behavior in the normal state of URu2Si 2 can be reasonably well understood. The presence of an increase in relaxation rate below 3 5 K can be well accounted for by the presence of a very weak ferromagnetic phase and the transition at 17.5 K to the antiferromagnetically or-

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