Single Crystal Growth of URu 2 Si 2 by the Modified Bridgman Technique

We describe a modified Bridgman growth technique to produce single crystals of the strongly correlated electron material URu2Si2 and its nonmagnetic analogue ThRu2Si2. Bulk thermodynamic and electrical transport measurements show that the properties of crystals produced in this way are comparable to those previously synthesized using the Czochralski or conventional molten metal flux growth techniques. For the specimens reported here, we find residual resistivity ratios RRR = ρ300K/ρ0 as large as 116 and 187 for URu2Si2 and ThRu2Si2, respectively.


Introduction
Research into URu 2 Si 2 has been fueled by interest in an unusual amalgam of phenomena that are believed to originate from a blend of local and itinerant electron behavior, including a peculiar non-magnetic low temperature broken symmetry state ("hidden order"), for which the order parameter has yet to be identified [1][2][3][4].The fact that it also hosts unconventional superconductivity makes this material even more attractive.Recent success in producing high quality specimens [5][6][7] has resulted in a surge of experimental work, including electronic Raman spectroscopy [8], elastoresistance [9], resonant ultrasound [10], Kerr rotation [11], X-ray scattering [12], and quantum oscillation measurements [13][14][15], which have provided unprecedented insight into the electronic, ordered state, and superconducting behavior.However, progress is limited by restricted access to high quality specimens, particularly due to challenges that are inherent to the mainstream growth techniques.For instance, the highest quality specimens are produced using the Czochralski method followed by solid state electrotransport refining (CZO/SSE), which is accomplished by passing a large electrical current through the as-grown crystalline rod under ultra-high vacuum conditions.This is a challenging two-step process [6,7] that is not available in most laboratories.It was recently demonstrated that molten indium is a suitable flux to produce single crystal specimens [5].While this approach is straightforward, so far its usefulness is limited by the small samples that are produced, low batch yields, and the long growth times.As a result, it remains attractive to develop other techniques to produce high quality single crystal specimens of URu 2 Si 2 .
Here we report the synthesis of single-crystal URu 2 Si 2 and ThRu 2 Si 2 specimens using a modified Bridgman method, which is based on the previous work using a molten indium flux [5].This is an important advance in crystal growth for these materials, because it provides an alternative way to produce single crystals that are needed for a variety of experiments: e.g., not only is it possible to cleave them, but their quality is also high enough to observe quantum oscillations, as seen in other specimens of similar quality [16,17].Furthermore, previous studies of URu 2 Si 2 have benefitted from investigation of chemical substitution series [16,[18][19][20][21][22][23].Most such work has focused on the substitution of elements with low vapor pressures that are easily dissolved in a stoichiometric melt.This characteristic is a prerequisite for crystals grown using standard methods such as the Czochralski technique, where electrical arcs are typically used to heat the sample.The approach presented here opens the door to introduce a wider variety of substituents, including those with high vapor pressure.This is essential for the exploration of chemical substitution on the Si site, where unexplored possibilities include high vapor pressure elements such as Si → Sn, P, As, S, Se, and Te.Such work is attractive, as evidenced by recent studies of Si → P in URu 2 Si 2 that have uncovered a fascinating phase diagram featuring an unusual disconnect between hidden order and magnetism [16].We also expect that our technique will be useful for the production of single crystals of the related materials UT 2 X 2 (T = transition metal and X = Si and Ge) [24].

Experimental Methods
Single crystals of URu 2 Si 2 and ThRu 2 Si 2 were produced using a modified Bridgman growth method using the apparatus shown in Figure 1.Elemental U, Th, Ru, Si, and In were sealed in the ratio 1:2:2:22 inside a tantalum crucible using a standard arc-furnace under argon gas.This is similar to what was reported previously for molten metal flux growth of URu 2 Si 2 in a resistive furnace [5,16].The ampoule had an outer diameter of 1.01 cm, an inner diameter of 0.76 cm, and a length of 5 cm.The Ru, Si, and In were sourced from Alfa Aesar (metal basis) and had purities 99.95%, 99.999%, and 99.999%, respectively.The uranium was taken from a vacuum induction melted ingot that was supplied from Los Alamos National Laboratory.The thorium was taken from an unpurified rod with purity >99%.In particular, we note that the uranium was not refined using solid state electrotransport prior to use, and it is expected that it included trace impurities of iron and copper, as previously observed in similar material [25].
The ampoule was suspended from a 0.04 cm diameter tantalum wire that was attached to an alumina pull rod inside of a quartz tube in an environment of purified Ar gas.The argon pressure was maintained near one atmosphere during the growth.The coil of a 6 kW rf-furnace was wrapped around the quartz tube to provide heat during the growth.The sample was first heated to 80% of the growth temperature and held there for two hours to dissolve the starting elements into the melt, after which the power was turned off over a period of 20 min.The ampoule was subsequently lifted until 0.5 cm of its length remained in the coil and the coil power was raised such that the ampoule temperature, once fully in the coil, would be similar to that used in previous flux growth experiments (T growth = 1400-1450 • C).Without changing the coil power or dwelling in this position, the ampoule was subsequently drawn through the coil at a rate of 0.5 cm/h until 3.5 cm of the ampoule extended out from the bottom of the coil.This process was repeated several times, depending on the batch (see Table 1).At the end of the final pull, the power was turned off over a period of twenty minutes.Cooling occurred under flowing argon.Finally, the ampoules were opened and the indium was removed by etching the resulting ingot in hydrochloric acid with a concentration near 38%.Pictures of URu 2 Si 2 crystals produced in this way are shown in Figure 1c-e.
The crystal structure and stoichiometry were verified using single-crystal X-ray diffraction and energy dispersive spectroscopy.Magnetization M(T, H) measurements were carried out for a mosaic of single crystals mounted in GE varnish at temperatures T = 1.8-300K under an applied magnetic field of H = 5 kOe for H applied both parallel ( ) and perpendicular (⊥) to the c axis using a Quantum Design VSM Magnetic Property Measurement System.Electrical resistivity ρ measurements at temperatures T = 1-300 K were performed in a four-wire configuration with the electrical current applied in the ab-plane using a Quantum Design Physical Property Measurement System with a He3 insert.
Table 1.Growth parameters and characteristics of two representative samples from each batch.Includes the number of times the sample was passed through the hot zone, the residual resistivity ratio RRR = ρ 300K /ρ 0 (where ρ 300K is the room temperature resistivity and ρ 0 is the extrapolated zero temperature resistivity), the hidden order temperature T 0 , and the superconducting transition temperature T sc .For the URu 2 Si 2 "two-pass" batch, we have measured ρ(T) for ten different samples (not shown).We find that RRR varies between 95-110, revealing consistent sample quality thoughout the batch.

Results
In Figure 1c-e we show URu 2 Si 2 crystals from three different batches.The largest specimens have dimensions 2 mm × 2 mm × 0.04 mm, with masses near 1.25 mg.Typical masses are near 0.1-0.5 mg.We observed that the overall size and stacking along the c-axis increases with increasing number of pulls.The ThRu 2 Si 2 crystals are smaller, with dimensions 0.25 mm × 0.25 mm × 0.05 mm.For most batches, 80% of the U:Ru:Si starting material was converted to single crystal specimens of URu 2 Si 2 .The batch yield for ThRu 2 Si 2 is smaller, and an abundant secondary phase of RuIn 3 also forms as separate needle-shaped crystals.Single-crystal X-ray diffraction measurements revealed the expected ThCr 2 Si 2 type structure with lattice constants a U = 4.133 (3) Å and c U = 9.58 (1) Å and a Th = 4.189 (2) Å and c Th = 9.745 (6) Å for URu 2 Si 2 and ThCr 2 Si 2 , respectively.These values are similar to those reported earlier [1][2][3][4]16,26].For both materials, the direction perpendicular to the crystal surface is the c-axis, in agreement with earlier results from molten indium flux growth of URu 2 Si 2 (Figure 1f) [16].Energy dispersive spectroscopy (EDS) measurements further confirm the expected URu 2 Si 2 and ThRu 2 Si 2 stoichiometry.We note that for the URu 2 Si 2 specimens, there is frequently a small amount of residual material that is embedded on the facet surface (Figure 1g).EDS measurements suggest that this is a mixture of Ru and Si in the ratio 1:4.
In Figure 2, we summarize magnetic susceptibility χ = M/H vs. temperature T for magnetic fields H = 5000 Oe applied parallel and perpendicular ⊥ to the c-axis for URu 2 Si 2 .χ(T) shows pronounced anisotropy where the c-axis is the easy axis, which is characteristic of the paramagnetism in URu 2 Si 2 [3,4].The inverse magnetic susceptibility χ −1 reveals a Curie-Weiss temperature dependence χ(T) = C/(T−θ), and a fit to the data yields µ eff = 3.72 µ B and θ = −90.5 K. Near T coh,Ø ≈ 55 K, χ(T) evolves through a broad hump that may be associated with the onset of Kondo coherence [1][2][3][4].At the "hidden-order" temperature T 0 , χ(T) is abruptly reduced.All of these features are consistent with earlier results for poly-and single-crystal specimens [1][2][3][4].Room temperature normalized electrical resistivity ρ 300K /ρ 0 vs. T measurements are shown in Figure 3 for three different batches of URu 2 Si 2 and a single batch of ThRu 2 Si 2 , where the only difference between these batches is the number of passes through the induction furnace hot zone (Table 1).The room temperature resistivities were ρ 300K ≈ 450 µΩ•cm and 100 µΩ•cm for URu 2 Si 2 and ThRu 2 Si 2 , respectively.For all batches, ρ(T)/ρ 300K shows features that are consistent with earlier results for both materials.For URu 2 Si 2 , ρ(T)/ρ 300K initially increases with decreasing T and goes through a broad maximum near T coh,ae = 75-85 K. Following T coh,ae , ρ(T)/ρ 300K decreases rapidly and evolves through a sharp peak at T 0 .At low temperatures, ρ(T)/ρ 300K becomes linear in temperature until the onset of superconductivity at T sc .We note that there are numerous proposals regarding the anomalous low temperature behavior of URu 2 Si 2 [4,27], and the study of high quality single-crystal specimens is necessary to understand this behavior.ThRu 2 Si 2 exhibits simple metallic behavior, as previously reported [26].
B r i d g m a n     From Figure 3, it is evident that there is a difference in the residual resistivity ratio RRR = ρ 300K /ρ 0 between these batches.Within a given metallic material, RRR provides an estimate of the amount of disorder, since the zero temperature resistivity ρ 0 is determined by scattering from defects such as impurities and crystal imperfections, and increases with higher occurrence of such features.Hence, a larger RRR indicates higher sample quality when comparing specimens of a given material.The differences between batches 1-3 for URu 2 Si 2 indicate that multiple passes through the hot zone tends to improve sample quality, although RRR saturates after two pulls (Table 1).We speculate that the saturation of RRR relates to the native impurities in the starting materials which are not removed by this process.An important result that has been noted earlier is that both T 0 and T sc slightly increase with increasing RRR up to RRR ≈ 100, where they become constant [5][6][7].The results for the samples produced using our method are consistent with this trend (Figure 4).Finally, we add that for the URu 2 Si 2 "two-pass" batch, we have measured ρ(T) for ten different samples (not shown).We find that RRR varies between 95-110, revealing consistent sample quality throughout the batch.

Summary
We have described a modified Bridgman growth technique for the production of single crystals of the strongly correlated electron material URu 2 Si 2 and its nonmagnetic analogue ThRu 2 Si 2 .Bulk thermodynamic and electrical transport measurements show that the properties of crystals produced in this way are comparable to those previously reported that are synthesized using the Czochralski or conventional molten metal flux growth techniques [5][6][7]16].For our specimens, we find residual resistivity ratios RRR = ρ 300K /ρ 0 ≈ 30-120 for URu 2 Si 2 and 190 for ThRu 2 Si 2 .By comparison to as-cast URu 2 Si 2 specimens grown by the Czochralski technique-where RRR typically is near 10 [28,29]-the specimens produced by our technique are of good quality.Nonetheless, it is clear that so far this technique does not produce specimens with RRR as large as that available from conventional indium flux or CZO/SSE techniques, where RRRs approaching 220 and 1000, respectively, have been reported [5][6][7].We speculate that larger RRR might be accomplished (1) by reducing the pull rate or optimizing the temperature gradient in the hot zone; and (2) by using higher quality starting elements.In particular, it is well known that uranium contains impurities of Fe and Cu, which are significantly reduced through solid state electrotransport refining [25].We further note that recent efforts to produce high quality ThRu 2 Si 2 using the CZO/SSE technique yielded specimens with RRR = 120 [17].Our specimens exhibit RRR approaching 190, which (to our knowledge) exceeds the best values for CZO/SSE specimens.
Given the difficulties associated with synthesizing high quality URu 2 Si 2 and ThRu 2 Si 2 using mainstream methods, we expect that the technique discussed here will accelerate progress in studies of this material by providing greater access to the good quality specimens that are required to develop our understanding of this fascinating material.Furthermore, the molten metal flux technique has the advantage that it enables chemical substitution using high vapor pressure elements.Finally, we hope that this technique will become the standard platform for the production of single-crystal specimens of other UT 2 X 2 materials, which are still receiving strong interest.Although not reported in detail here, we have already succeeded in synthesizing UFe 2 Si 2 , UFe 2 Ge 2 , UIr 2 Si 2 , and UPt 2 Si 2 using a molten indium flux technique, demonstrating the broad utility of this approach.

Figure 1 .
Figure 1.(a) Bridgman crystal growth apparatus showing the inert gas growth chamber, rf-heating coil, tantalum ampoule, pull rod, and crystal puller; (b) Schematic of the Bridgman crystal growth apparatus; (c-e) Images of representative crystals of URu 2 Si 2 that were produced using different numbers of passes through the hot zone; (f) Rocking curve for a single crystal of URu 2 Si 2 , showing that the direction perpendicular to the crystalline plate is the c-axis; (g) SEM image of a typical URu 2 Si 2 specimen.The surface impurity phase is indicated.

Figure 2 .
Figure 2. (left axis) Magnetic susceptibility χ = M/H vs. temperature T for magnetic field H = 5 kOe applied parallel and perpendicular ⊥ to the c-axis.(right axis) Inverse magnetic susceptibility χ −1 vs. T in the paramagnetic region for URu 2 Si 2 showing Curie-Weiss behavior.(inset) χ(T) in the region near the hidden order transition.

Figure 3 .
Figure 3. (a) Electrical resistivity ρ normalized to the value at room temperature ρ 300K vs. temperature T for several specimens from two different batches.The typical room temperature resistivities are ρ 300K ≈ 450 µΩ•cm and 100 µΩ•cm for URu 2 Si 2 and ThRu 2 Si 2 , respectively.Differences in growth parameters for the batches are shown in Table1; (b) ρ 300K /ρ 0 vs. T near the hidden order transition T 0 .The width of the transition is defined from the minimum (onset of kink) to the peak, with the midpoint indicated by the arrow; (c) ρ/ρ 300K vs. T near the superconducting transition.The width of the transition is defined as onset and termination of the step, with the midpoint indicated by the arrow.

R e s i 7 T
s t i v e F u r n a c e ( I n ) B r i d g m a n ( I n ) R e f .5 R e f .

Figure 4 .
Figure 4.Comparison between URu 2 Si 2 crystals grown by the two-step Czochralski/zone-refining (as performed by two different groups)[5][6][7], molten indium flux[5,16], and those that were produced using the modified Bridgman growth discussed here.(a) Dependence of the hidden order transition temperature T 0 on the residual resistivity ratio RRR = ρ 300K /ρ 0 , where RRR is defined in the main text.The bars represent the transition width as defined in Figure3.Note that RRR is presented on a logarithmic scale.(b) The superconducting transition temperature T c vs. RRR.The bars represent the transition width.