High purity specimens of URu2Si2 produced by a molten metal flux technique

We report a molten metal flux technique to produce high purity specimens of URuSi. Magnetic susceptibility (), heat capacity () and electrical resistivity () measurements show that the bulk properties of these crystals are similar to those that are produced by the Czochralski technique followed by solid-state electro-transport. In particular, we find residual resistivity ratios RRR / as large as 220.


Introduction
For nearly three decades, URu 2 Si 2 has been a central topic in the field of strongly correlated electrons, due to the fact that it exhibits two robust mean field second-order phase transitions: one at the "hidden order" temperature T 0 ≈ 17.5 K and another at the superconducting phase transition T c ≈ 0.8-1.4 K [1][2][3]. The hidden order transition is given its name because, although roughly 0.2Rln2 of entropy is released at T 0 (clearly showing a phase transition to a new state for T ≤ T 0 ), intense experimental and theoretical efforts to uncover the order parameter have been unsuccessful: e.g. neutron scattering and µSR techniques yield ordered moments that are much too small to account for the entropy that is released at T 0 [4,5]. Considerable interest has also been paid to the superconducting state, which is clearly unconventional as evidenced by: (1) its occurrence deep inside the hidden order state [1][2][3], (2) the low carrier density from which it emerges [6,7], (3) the large upper critical field [8] and (4) measurements which suggest the presence of nodes in the superconducting energy gap [7,[9][10][11]. Furthermore, a variety of studies have shown that magnetism is found on the border of the hidden order state. For instance, measurements under applied pressure show that at P c ≈ 0.5 GPa, there is a first-order phase transition from hidden order to conventional antiferromagnetism, which is accompanied by destruction of the superconductivity [12][13][14]. Similar behaviour is observed with chemical pressure in the substitution series URu 2−x Fe x Si 2 [15]. For these and other reasons, the effort to understand URu 2 Si 2 remains an active field of research.
Many of the recent advances in understanding URu 2 Si 2 stem from the relationship between advanced measurement techniques and improved sample quality. Regarding sample quality, it was recently recognized that ultra high purity specimens with residual resistivity ratios RRR = ρ 300K /ρ 0 ≈ 100-1000 can be produced by synthesizing a single crystal using the Czochralski technique, followed by solid-state electro-transport (also referred to as "electrorefining") [16,17]. This is in contrast to "as-grown" samples that are produced by the Czochralski technique, where RRR ≈ 10 (e.g. see [14,18]).
An early benefit to studying high purity specimens was the resolution of a long-standing question relating to the coexistence of the hidden order phase and small moment antiferromagnetism at P = 0. Systematic studies of crystals with different RRR have shown that the small moment antiferromagnetism is likely due to internal strain, which produces rare regions of antiferromagnetism which are analogous to what is seen for P ≥ P c (e.g. see [19]). Measurements of high purity specimens have also driven investigations of the Fermi surface which, surprisingly, shows little change as the ground state is driven from hidden order to antiferromagnetism as a function of pressure [6,[20][21][22]. High quality specimens have also been essential for sensitive measurements such as STM [23,24] and ARPES [25]. In fact, the influence of sample purity is even reflected in bulk measurements such as electrical resistivity, where T c , T 0 and the power law dependence of ρ(T ) at low temperatures are all related to RRR [17]. Therefore, it is clear that investigation of high purity specimens is essential to develop an understanding of this compound. However, present synthesis techniques severely limit access to quality specimens.
Herein, we report a new molten metal flux technique to produce high purity specimens of URu 2 Si 2 . Our initial investigation reveals that it is possible to routinely produce singlecrystal platelets where RRR is as large as 220. We report magnetic susceptibility, heat capacity and electrical resistivity measurements which demonstrate that the bulk properties of these crystals are comparable to those that are produced by the Czochralski technique followed by solid-state electro-transport. We expect that this growth technique will expand access to high quality URu 2 Si 2 , and may thereby accelerate progress towards an understanding of this material.

Experimental details
Single crystals of URu 2 Si 2 were grown from elements with purities >99.9% in a molten In flux. The reaction ampoules were prepared by loading the elements into a 5 cm 3 tantalum crucible in the ratio 1(U):2(Ru):2(Si):22(In). The crucible was then loaded into an alumina tube spanning the bore of a high temperature vertical furnace. Ultra high purity argon gas was passed through the tube and a zirconium getter was placed in a pot above the tantalum crucible in order to purify the argon at high temperatures. The crucible was then heated to 1400 o C at 70 o C/hr, held at this temperature for 10 h and quickly cooled to room temperature at an average rate of 100 C/hr. The indium flux was subsequently removed using hydrochloric acid, to which the URu 2 Si 2 crystals are impervious. This technique produced single crystal ab-plane platelets similar to the one shown in Figure 1.
Magnetization M(T, H ) measurements were carried out for a mosaic of single crystals for temperatures T = 1.8-350 K under an applied magnetic field of H = 1 kOe applied parallel to the c-axis using a Quantum Design Magnetic Property Measurement System. The specific heat C(T, H ) was measured for a mosaic of single crystals for T = 0.3-30 K using a Quantum Design Physical Property Measurement System. The electrical resistivity

Results
Shown in the left panel of Figure 1 is a typical single crystal platelet of URu 2 Si 2 , for which the dimensions are ∼1.2 mm length and ∼0.05 mm thickness. The image was taken using a Nomarski polarized light filter, where the lack of texture on the flat surfaces suggests minimal surface strain. In the right panel of Figure 1, we show a Laue backscatter image which reveals that the crystals form with the c-axis perpendicular to the plate surface.
In Figure 2(a), we show the magnetic susceptibility χ(T ) = M(T )/H with a magnetic field H = 1 kOe applied to the c-axis. As expected, χ(T ) increases with decreasing T for T < 350 K and evolves through a maximum near 50 K. For 100 K ≤ T ≤ 350 K, χ(T ) exhibits Curie-Weiss behaviour given by the expression, where χ 0 = 0.0013 cm 3 /mol, = −59 K and µ e f f = 3.1 µ B . The values for θ and µ e f f are comparable to those found in previous reports [1]. As shown in Figure 2 is abruptly reduced at the hidden order temperature T HO ≈ 17.5 K. For T ≤ 12 K, χ(T ) shows a weak upturn with decreasing T . In Figure 2(c), we show the evolution of M(H ) at T = 2 K, which is consistent with previous results. The heat capacity divided by temperature C/T vs. T data, taken for a mosaic of single crystals, are shown in Figure 3(a). Again, we see behaviour that is characteristic of high quality specimens of URu 2 Si 2 . The hidden order temperature is found near T HO ≈ 17.5 K, with a width T HO = 0.6 K (Figure 3(b)). The entropy under the HO transition is comparable to results for crystals prepared using other techniques. The superconducting transition occurs near T c ≈ 1.3 K, with a width T c = 0.4 K (Figure 3(c)). We also find that C/T gradually increases with decreasing T for T c ≤ T ≤ 7 K.
Electrical resistivity ρ vs. T data for a representative single-crystal specimen are presented in Figure 4(a), where the current is applied in the ab plane. ρ(T ) initially  increases with decreasing temperature and evolves through a maximum near the coherence temperature at 82 K. The resistivity then drops quickly until the hidden order transition opens a gap which results in an anomaly near T HO ≈ 17.8 K with a width of T HO ≈ 0.44 K, as shown in Figure 4(b). Following the hidden order transition, the resistivity falls towards 2 µ cm near 1.5 K. We perform a fit to the data for 1.5 K ≤ T ≤ 15 K using the expression, where ρ 0 = 1.37 µ cm is the residual resistivity at zero temperature, A = 0.51µ cm/K n is the coefficient of the power law behaviour, n = 1.35 is the power law exponent, B = 7823 µ cm is the coefficient of the exponential behaviour and = 77 K is the gap size. These fit parameters are in good agreement with earlier results on UHP samples [17]. From the value of ρ 0 , we estimate that RRR = 220 for this specimen. Throughout the batch, we find that RRR ranges from 50 to 220. Finally, we observe a superconducting transition at T c = 1.4 K with a transition width T c = 0.17 K (Figure 4(c)).
In Figure 5, we show ρ(T ) near T c under applied magnetic fields for H parallel and perpendicular to the c-axis.As expected, T c is suppressed with increasing H . We plot the field dependence of T c for each direction in Figure 6. Here, T c is defined as the temperature where ρ(T ) falls to 50% of the normal state value just above the transition. The transition width, illustrated as bars, is defined as the temperature where ρ(T ) falls 10 and 90% of the normal state value. We also show the temperature where ρ(T ) falls to zero. Another important feature of the data shown in Figure 5 is that ρ(T ) increases strongly with increasing H . This behaviour has been observed previously and is related to the fact that URu 2 Si 2 is a compensated electron-hole semimetal, for which ρ(H )/ρ 0 is proportional to H 2 [7].
We next consider the initial slopes of H c2 (T ) near T c , where we find (∂ H c2 (T )/ ∂ T ) Tc = −45 kOe/K and −130 kOe/K for H and ⊥ c, respectively. These values are similar to those previously observed for URu 2 Si 2 [8]. From these values, we calculate the Ginzburg-Landau coherence lengths parallel and perpendicular to the ab-plane, ξ abs and ξ c , respectively, using the expressions [26], and d H ⊥,c c2 /dT where is the Planck constant, k B is the Boltzmann constant, and v F,ab = 7.4 × 10 5 cm/s and v F,c = 2.6 × 10 5 cm/s are the Fermi velocities calculated from ξ ab and ξ c , respectively. The values that we find for ξ and v F are consistent with earlier results [2,18]. In Figure 7, we plot the hidden order and superconducting transition temperatures, T HO and T c , vs. RRR for several representative samples that were grown using the molten indium flux growth technique described above. For comparison, we also plot these quantities for single-crystal specimens that were prepared using the Czochralski technique, where those with large RRR were post-processed by electrorefining. Here, we see that T HO and T c follow the same trends for other high purity specimens, further supporting the point of view that these samples are comparable to those that are produced by Czochralski followed by electrorefining, and should be described as being ultra high purity.

Summary
We have demonstrated a molten indium flux technique to produce high quality specimens of URu 2 Si 2 . Crystals grown by this technique show RRR = 50-220, which is a significant improvement over what is typically found for single crystals grown using the Czochralski technique without post-processing by zone refinement. In fact, RRR for the flux grown crystals approaches that of zone refined Czochralski grown samples. We have shown that the bulk properties of the flux grown samples (i.e. magnetic susceptibility, heat capacity and electrical resistivity) are consistent with earlier results for such high purity samples. Figure 7. (colour online) Comparison between ultra high purity URu 2 Si 2 crystals grown by the Czochralski technique followed by electrorefining (blue circles) and those that were produced in a molten indium flux (red triangles) (a) Dependence of the hidden order transition temperature T HO on the residual resistivity ratio RRR = ρ 300K /ρ 0 , where RRR is defined as described in the text. The bars represent the transition width (see Figure 4(b)). (b) Dependence of the superconducting transition temperature T c on RRR. The bars represent the transition width, as defined in the text. Therefore, since the technique reported here relies only on equipment that is readily available in many synthesis laboratories, we expect that it will expand access to high quality URu 2 Si 2 , and may thereby accelerate progress towards an understanding of this material.