Pressure evolution of the metamagnetic transition in UCoAl As measured using 59Co NMR

We have performed NMR measurements under pressure in UCoAl with a quantum critical endpoint of the metamagnetic transition from the paramagnetic phase to the ferromagnetic (FM) phase. 59Co-NMR sensitively detects the evolution of the internal field caused by applying the external field. The metamagnetic field Hm increases with increasing pressure consistently with other experimental methods, accompanied by the suppression of the magnetization in the field-induced FM phase and the magnetization jump at Hm. The loss of the NMR signal on approaching the QCEP indicates the development of the spin fluctuations.


I. INTRODUCTION
The terminal point of a first-order phase transition at 0 K, that is, a quantum critical endpoint (QCEP), is a fascinating target as a new type of quantum critical point. In itinerant ferromagnets with a tricritical point (TCP), the metamagnetic transition from the paramagnetic (PM) phase to the ferromagnetic (FM) phase possesses the wing structure of a first-order transition in the temperature(T )-pressure(P )-magnetic field(H) phase diagram [1][2][3][4][5]. The first-order metamagnetic (PM-FM transition) transition at low temperatures en- * E-mail: kotegawa@crystal.kobe-u.ac.jp counters a critical end point (CEP) above which the transition changes to a crossover. The temperature of CEP (T CEP ) reaches 0 K at the QCEP of P QCEP and H QCEP . Among several candidates, UCoAl is a good example with the moderately wide wing for which we can easily tune pressure from the vicinity of TCP, which presumably is present under a small negative pressure, to the PM region exceeding the QCEP [4].
UCoAl crystallizes in a ZrNiAl-type hexagonal structure stacked by U-Co(1) and Co(2)-Al layers [6]. It is a paramagnet, but a uniaxial pressure effect and chemical substitution have revealed that it is located in the vicinity of a FM critical point [7][8][9]. The FM state at zero field is thought to be already suppressed at a negative pressure of ∼ −0.2 GPa [9]. A first-order metamagnetic transition to the FM state with ∼ 0.3 µ B /U occurs at H m ∼ 0.7 T for H c axis at low temperatures [6]. The FM moment mainly originates from U-5f electrons [10]. The transition changes to a crossover at temperatures above T CEP ∼ 11 − 13 K [4,9,11]. Strong longitudinal magnetic fluctuations are observed in the vicinity of the CEP [11]. The T CEP is suggested to reach the QCEP at 0 K under P QCEP ∼ 1.5 GPa and H QCEP ∼ 7 T [4].

II. EXPERIMENTS AND DISCUSSION
The single crystal was grown using the Czochralski method in a tetra-arc furnace [12]. Powdered single crystals were used for NMR measurements at ambient pressure with an orientation H c. We used a single crystal for NMR measurements under pressure with the field applied along H c. Pressure was applied by using a piston-cylinder cell used Daphne7474 as a pressuretransmitting medium. [13] The pressure at low temperatures was estimated by using a Pb manometer. NMR was performed using a standard spin-echo method. Magnetization (M ) measurements was performed using a Magnetic Property Measurement System (MPMS:Quantum Design). Several NMR data at ambient pressure have already been reported in another paper [11]. Figure 1 shows NMR spectra for (a) 60 K and 0 GPa, (b) 4.2 K and 0 GPa, and (c) 1.6 K and 0.45 GPa. As shown in Fig. 1(a), 19 lines are totally observed in the PM phase at high temperatures for two Co sites (the nuclear spin I = 7/2) and the Al site (I = 5/2). Seven lines originating in the Co(2) site appear with almost an equal interval between each line due to the nuclear quadrupole interaction. At low temperatures, such clear lines disappear, and the spectrum changes discretely at H m due to the drastic change in the internal field H int caused by the metamagnetic (PM-FM) transition because of the resonance condition f 0 = γ(H + H int ) for the central transition, where f 0 is the NMR frequency, γ is the gyromagnetic ratio, and H is the external magnetic field. H m is ∼ 0.7 T at ambient pressure while it increases to ∼ 2.2 T at 0.45 GPa. As shown in the figure, the signals from the Co(1) site and the Al site are overlapped and cannot be separated at low temperatures, so we evaluated the internal field from the satellite lines (±5/2 ↔ ±3/2 transitions) of the Co(2) site. The field dependence can be detected continuously by changing the NMR frequency f 0 . Figure 2(a) shows the field dependence of the internal field, H int at the Co(2) site at different pressures. The H int was estimated from the shift in the resonance line for the frequency-swept spectrum at a fixed field. The magnetization at ambient pressure is also plotted [12]. A distinct metamagnetic transition can be observed at the metamagnetic field H m by using NMR measurements through the hyperfine field from the U site. Figure 2  an implicit parameter. The slope corresponding to the hyperfine coupling constant has already been given by the temperature dependence of the NMR shift and the susceptibility [11]. The estimated value A c spin = 2.58 T/µ B also reproduces the field dependence well, suggesting that the field dependence of A c spin is small. The H int in the high-field FM phase is suppressed gradually under pressure while the slopes in the PM phase are almost overlapped for the different pressures. The jump at H m (∆H int ) also decreases with increasing pressure. This behavior is almost consistent with previous magnetization data [9]. At 1.14 GPa, we could not observe the NMR signal at fields around H m due to the fast relaxation, suggesting that T CEP at 1.14 GPa is close to 1.6 K because of a suppression of T CEP from ∼ 12 K at ambient pressure. This is almost consistent with the estimate of T CEP ∼ 4 K based on resistivity measurements at the corresponding pressures [4]. Figure 3 shows the pressure evolutions of H m and ∆H int . The pressure evolution of H m is displayed along with the estimates obtained using the resistivity and the magnetostriction [4]. In the resistivity measurements, another anomaly is detected after exceeding the QCEP as denoted by H * [4]. The pressure dependences of H m from all the measurements agree with one another. The The internal field at the Co(2) site scales well to the magnetization. At 1.14 GPa, the NMR signal could not be observed due to the fast relaxation time, implying that it is located in the vicinity of the QCEP. (b) Magnetization vs. the internal field. The slope corresponds to the hyperfine coupling constant, which is almost unchanged between the PM phase and the FM phase.
loss of the NMR signal at 1.14 GPa and ∼ 1.6 K indicates that it is close to the QCEP, consistent with the estimate of P QCEP ∼ 1.5 GPa [4]. The ∆H int decreases monotonically under increasing pressure at least up to 1.14 GPa. If we use the hyperfine coupling constant A c spin = 2.58 T/µ B with the assumption that it is independent of pressure, a jump in the magnetization ∆M under pressure can be obtained. It should be noted that A c spin is unchanged between the PM phase and the FM phase, as shown in Ref. 11 and Fig. 2(b). The simple extrapolation gives ∆M ∼ 0.2µ B /U at the QCEP, which lower than the ∆M ∼ 0.34µ B /U at ambient pressure, but is still robust. In the vicinity of the CEP at ambient pressure (T CEP ∼ 12 K), the strong longitudinal magnetic fluctuations are observed [11]. The strong fluctuations are expected in the vicinity of the QCEP; however their detailed character is under investigation. In addition, the origin of another anomaly at H * at high-pressure and high-field, which might be related to an instability in the Fermi surface, will be investigated by using NMR The Hm increases monotonously with increasing pressure up to the QCEP, which is estimated to be located at PQCEP ∼ 1.5 GPa and HQCEP ∼ 7 T. [4] ∆Hint also decreases monotonically at least up to 1.14 GPa. ∆M is estimated using the hyperfine coupling constant A c spin = 2.58 T/µB [11]. measurements.

III. CONCLUSIONS
We have observed the metamagnetic transition under pressure in UCoAl by using NMR measurements. NMR can sensitively detect the evolution of the hyperfine filed from the U site due to the metamagnetic transition. The metamagnetic field H m increases with increasing pressure and is accompanied by the suppression of the magnetization in the FM phase and a jump in the magnetization at H m . Measurements under higher pressures are desired to investigate the magnetic properties in the vicinity of the QCEP and the origin of the branch off of the metamagnetic line.