Unconventional T H Phase Diagram in the Noncentrosymmetric Compound Yb2Fe12P7

Yb2Fe12P7 R. E. Baumbach, J. J. Hamlin, L. Shu, D.A. Zocco, J. R. O’Brien, P.-C. Ho, and M.B. Maple* Department of Physics, University of California, San Diego, La Jolla, California 92093, USA Quantum Design, 6325 Lusk Boulevard, San Diego, California 92121, USA Department of Physics, California State University, Fresno, Fresno, California 93740, USA (Received 2 January 2010; published 1 September 2010; corrected 2 September 2010)

The QCP model has been widely applied to situations where a second order phase transition, usually antiferromagnetic, is suppressed to T ¼ 0 K by a control parameter () such as chemical composition (x), pressure (P), or magnetic field (H), terminating in a QCP at T ¼ 0 K. Order parameter fluctuations are manifested as NFL behavior at T's above the QCP, and a line emanating from the QCP delineates a gradual crossover from NFL to FL behavior at lower temperature and higher values of the control parameter. Extensive investigations of several prototypical systems (e.g., CeCu 6Àx Au x [18] and YbRh 2 Si 2 [19]) have been analyzed within the context of the QCP model and support the predicted ''V-shaped'' T À phase diagram.
We report measurements on single crystals of the ternary compound Yb 2 Fe 12 P 7 , in which the Yb ions undergo magnetic ordering which is accompanied by an unconventional magnetic field tuned quantum ground state. This behavior is particularly interesting because it deviates strongly from the widely accepted QCP scenario described above, in that two NFL regions are observed, the first inside the magnetically ordered state and the second extending far beyond the extrapolated QCP as the tuning parameter H is increased. In particular, we find (1) a magnetically ordered ground state (T M $ 0:9 K) for which the signatures in electrical resistivity and specific heat measurements are suppressed to lower T with increasing H, (2) an NFL ground state for T < T M with a large H ¼ 0 T electronic specific heat coefficient ðTÞ ¼ CðTÞ=T that is suppressed with increasing H, and (3) a rapid crossover from the low H NFL state to another extended NFL region at the value of H where T M can no longer be identified in the CðH; TÞ and ðH; TÞ data, which is stabilized for large values of H. These kinds of behavior suggest a quantum phase transition (QPT) between two phases that exhibit NFL behavior with different power law exponents of the electrical resistivity.
During our efforts to synthesize LnFePO and LnFe 2 P 2 compounds, we found that Ln 2 Fe 12 P 7 -type single crystals will often form in a Sn flux instead of the desired phase [20]. These compounds are members of a broad class of pnictogenbased systems with noncentrosymmetric structures and the chemical formula Ln nðnÀ1Þ T ðnþ1Þðnþ2Þ M nðnþ1Þþ1 , where Ln is a lanthanide (or actinide), T is a transition metal, and M is a metalloid (phosphorus, arsenic) [21,22]. X-ray powder diffraction measurements reveal single phase samples with a hexagonal structure (space group P " 6) and lattice parameters a ¼ 9:111 # A and c ¼ 3:626 # A, in agreement with earlier growth experiments where single crystals were synthesized in a Sn flux using only elemental starting materials [21]. In order to verify the stoichiometry, x-ray photoelectron spectroscopy measurements were performed, which revealed that Yb, Fe, and P are present in these crystals in a ratio consistent with the 2:12:7 formula.
The magnetic susceptibility ðTÞ ¼ MðTÞ=H System. The ðTÞ data reveal Curie-Weiss (CW) behavior where the effective magnetic moments ( eff ¼ 4:1 B =Yb and 4:8 B =Yb for H k c and H?c, respectively) are close to the Yb 3þ free ion value ( eff ¼ 4:53 B =Yb) according to Hund's rules. The crystalline anisotropy is reflected in the CW temperatures ( CW ) taken from fits to the data, for which CW ¼ 1 K and À27 K for H k c and H?c, respectively. The MðHÞ data [Figs. 1(b) and 1(c)] reveal that the c direction is the easy axis and the a or b directions are the hard axes. For ? ðTÞ, a CW law is observed down to T $ 30 K, below which the data increase more weakly than expected from the high T CW behavior. The departure from CW behavior occurs near the onset of correlated electron phenomena inferred from the behavior of C p ðT; HÞ and ðT; HÞ. A similar trend is observed for k ðTÞ for T < 10 K.
The low T upturn in ? ðTÞ below 10 K can be described by various functions, depending on whether the behavior is assumed to be extrinsic or intrinsic. In order to explore the first possibility, the data were fitted below 10 K with a modified Curie-Weiss law ? ðTÞ ¼ 0 þ C=ðT À Þ, where 0 represents the contribution from nonmagnetic Yb 2 Fe 12 P 7 and the Curie-Weiss term is attributed to magnetic impurities. This fit yields the parameters 0 ¼ 0:1 cm 3 =mol, C ¼ 0:3 cm 3 K=mol, and ¼ À0:6 K. If the magnetic impurity is assumed to be Gd 3þ , for which eff ¼ 7:94 B B, then this value for C would be equivalent to the occupation of 2% of the Yb sites by Gd 3þ . However, this concentration is far too large for this to be a viable possibility. We also note that crystal misalignment with respect to H could be responsible for this behavior. On the other hand, assuming that the behavior is intrinsic and consistent with NFL behavior, we find that ? ðTÞ can be described using either power law or logarithmic functions of the forms ? ðTÞ ¼ aT Àn , where a ¼ 0:27 cm 3 K n =mol and n ¼ 0:32, or ? ðTÞ ¼ b À c lnT, where b ¼ 0:25 cm 3 =mol and c ¼ 0:05 cm 3 =mol. From this analysis, we conclude this T dependence represents a departure from FL behavior.
The H ¼ 0 T specific heat divided by temperature C p ðT; H ¼ 0Þ=T data, measured for T ¼ 50 mK-300 K using a QD Physical Properties Measurement System (PPMS) and a QD 3 He- 4 He dilution refrigerator (DR) [ Fig. 2(d)], exhibit a broad peak near 120 K, which can be attributed to phonons. Below the peak, C p ðT; H ¼ 0Þ=T decreases down to T $ 10 K, passes through a minimum, then increases rapidly, suggesting the formation of a strongly correlated electron ground state. A sharp peak is then observed [ Fig. 2(b)], indicating that Yb 2 Fe 12 P 7 undergoes a phase transition near T M $ 0:9 K. With an applied magnetic field (H?c), this feature is completely suppressed by H ¼ 1 T, although the large background upon which it is superimposed is barely affected. Since the phase transition is suppressed with H, we conclude that it likely includes an antiferromagnetic component. Below T M , C p ðT; H ¼ 0Þ=T goes through a broad maximum where C max ðT; H ¼ 0Þ=T $ 3:4 J=mol Yb K 2 for T $ 0:27 K, followed by a shallow minimum near 0.15 K, after which C p ðT; H ¼ 0Þ=T increases again for T < 0:15 K. For H > 1 T, C p ðT; HÞ=T is suppressed and the location of the broad maximum shifts towards higher T. This behavior is consistent with an increase of the Zeeman energy with H and the recovery of a FL state.
We also note that the strong increase in C p ðTÞ=T for T < 10 K could be due to a Schottky anomaly from  crystalline electric field (CEF) splitting of the J ¼ 7=2 Yb 3þ multiplet. Assuming the ground and first excited states are doublets, the specific heat data should be described by the expression C p ðTÞ ¼ C 0 þ C Sch ðTÞ, where C Sch ðTÞ ¼ RðÁ=TÞ 2 expfðÁ=TÞ=½1 þ expðÁ=TÞ 2 g, for which R is the ideal gas constant and Á is the splitting between the doublets. If such a fit is performed for the H ¼ 1 T data, we then find that C 0 % 1345 mJ=mol K and Á % 2:2 K. However, as shown in Fig. 2(c), the entropy SðT; H ¼ 0Þ only reaches a value of R ln2 near 5 K, which is too small to account for the entropy associated with both the magnetic ordering and the two level CEF energy scheme. Therefore, we exclude this scenario.
We last consider the low T upturn in C p =T, which is consistent with a nuclear Schottky anomaly and can be described by the expression CðTÞ ¼ C el þ C 2 T À2 , where C el and C 2 T À2 are the electronic and nuclear contributions, respectively. If we plot CðTÞT 2 vs T 3 , it is possible to extract C 2 ðHÞ from the T ¼ 0 K intercepts. As expected for a nuclear Schottky anomaly, C 2 ðHÞ ¼ þ H 2 ( % 1:14 mJ K=mol and % 0:09 mJ=mol K 2 ). In principle, Yb, Fe, or P nuclei could contribute to this term. Shown in Fig. 3 are ðT; HÞ data for H?c which were measured in a four-wire configuration (for several samples) using a PPMS, an Oxford Kelvinox DR, and a QD DR for T ¼ 50 mK-300 K. The H ¼ 0 T electrical resistivity data decrease from room T, indicating metallic behavior down to T $ 50 K. Below T $ 30 K, ðT; H ¼ 0Þ evolves through a pronounced shoulder, which could be consistent with the two level Schottky anomaly scenario described above for C p ðTÞ, after which it decreases dramatically around T M $ 0:9 K. For T < 2 K, the H ¼ 0 T measurements [ Fig. 2(a)] reveal that @ðT; HÞ=@T exhibits a maximum at T M $ 0:9 K. Most remarkably, ðT; H ¼ 0Þ is nearly linear for more than a decade in T below T M [ Fig. 3(a)]. By applying H?c, the maximum in @ðT; HÞ=@T is suppressed and is no longer observable by H $ 0:7 T. As expected for electron transport phenomena near a critical point where magnetic fluctuations are dominant, the shapes of @ðTÞ=@T and C p ðTÞ=T are similar and the resulting estimates for T M from these two measurements are in good agreement [23]. To characterize ðT; HÞ at low T, the data were fitted using the expression ðTÞ ¼ 0 þ AT n . The best fit was determined from a plot of lnð À 0 Þ vs lnðTÞ in which the value of 0 was selected to maximize the linear region of the fit extending from low T. Examples of these fits are shown in Fig. 3(b). The quantities 0 , A, and n are plotted in Figs. 4(a)-4(c), where 0 increases and A decreases with increasing H. The behavior of n is discussed below.
Based on these measurements, it is possible to construct a T À H phase diagram, as shown in Fig. 4(d). First, T M decreases with H until it becomes impossible to track for H > 0:7 T. As a result, it is unclear whether there is a first order transition near 0.7 T or a second order transition in the vicinity of $1:5 T, where we have extrapolated Fig. 4(d)]. The power law fits described above reveal that n $ 1:1 for H ¼ 0 T. As H is increased, n rapidly crosses over to a value $1:5 near H ¼ 0:5 T, close to the H where T M is no longer observable. Starting near H $ 2:5 T, the n $ 1:5 dependence extends over an increasingly broad T region.
These results are striking, in light of the CðTÞ=T data which are consistent with the recovery of a FL state with increasing H. In order to elucidate this point, we consider the Kadowaki-Woods ratio R KW ¼ A= 2 , which gives the relationship between the coefficient of the electronic specific heat and the coefficient A of the T 2 contribution to the electrical resistivity, assuming that the system exhibits heavy FL behavior; i.e., C p ðTÞ=T $ and ðTÞ $ T 2 at low T. In the original treatment, R KW % 10 À5 cmðmol K 2 =mJÞ 2 [24]. More recently, it has been found that many (but not all) Yb based heavy fermion compounds follow the relationship R Yb % 0:36 Â 10 À6 cmðmol K 2 =mJÞ 2 [25]. From these quantities and the extrapolated T ¼ 0 K values for (e.g., % 2 J=mol K 2 for H ¼ 5 T), the coefficients A KW % 40 cm and A Yb % 1:44 cm (for H ¼ 5 T) are found. For A KW , the expected FL contribution to ðTÞ is much larger than the data. We thus rule out the possibility that Yb 2 Fe 12 P 7 is described by a simple heavy FL picture in the high H region. From A Yb , we find that the expected FL contribution to ðTÞ is smaller than the data, suggesting that if this is the correct description, then it is necessary to invoke another hypothetical scattering process to account for the difference between the calculated and measured ðTÞ. Since T M is suppressed near H ¼ 1 T, there are no obvious candidates for the enhanced scattering. Therefore, we conclude that, although CðTÞ=T suggests a return to FL behavior, ðTÞ reveals persistent NFL behavior up to the highest H measured. By comparison to classical QCP systems for which the NFL behavior is confined to a ''V-shaped'' region around the QCP, Yb 2 Fe 12 P 7 is anomalous. We emphasize that although there is a possible QCP, the ground state is disconnected from it and instead is more closely related to the H where T M is no longer observable. This result suggests an unconventional ground state which includes a QPT between two phases that exhibit NFL behavior with different power law exponents of ðT; HÞ. Therefore, we conclude that Yb 2 Fe 12 P 7 belongs to a growing class of compounds in which the NFL behavior does not conform to the standard QCP scenario, strengthening the point of view that the interrelationship between NFL behavior and QCP or QPT phenomena is far from being understood. A particularly important question is whether the ubiquitous appearance of NFL behavior can be described universally or if it arises from a multitude of situations. This question applies to many correlated electron materials and its solution likely will be accompanied by a greater understanding of other related phenomena, such as high temperature and unconventional superconductivity.
Crystal growth and characterization were funded by the U.S. DOE under Grants No. DE FG02-04ER46105 and No. DE FG02-04ER46178. Low-temperature measurements were funded by the NSF under Grant No. 0802478. The dashed line is an extrapolation of T M to 0 K. The color gradient represents @ lnð À 0 Þ=@ lnT, where 0 maximizes the T range for the low T power law behavior for each ðT; HÞ. The values of @ lnð À 0 Þ=@ lnT above the low T fit range do not represent the local exponent n since they are based on 0 values from the low T fits. Note that the low T power law fit range appears to be reduced from what would be inferred from Fig. 3(b). This is because the data are smoothed before taking @ lnð À 0 Þ=@ lnT, resulting in a reduction of the apparent fit range because adjacent averaging samples the lower slope data above the upper T limit of the fit range.