NMR Observation of Ferro-Quadrupole Order in PrTi₂Al₂₀

Abstract

We report the results of 27 Al-NMR measurements on a single crystal of PrTi 2 Al 20 . This compound shows a phase transition near 2 K associated with the quadrupole degree of freedom of Pr ions, for which the ground state of the crystalline electric field is a nonmagnetic doublet. When a magnetic field is applied along the 111 direction, the NMR lines split upon entering the low-temperature phase, indicating the breaking of the three fold rotation symmetry due to the field-induced magnetic dipole perpendicular to the field. This provides microscopic evidence for a ferro order of the O 20 quadrupole. Although a first-order transition is expected theoretically, the line splitting evolves continuously within the experimental resolution.KEYWORDS: PrTi 2 Al 20 , NMR, quadrupole order, symmetry breaking Multipoles of f electrons in rare-earth compounds show a wide variety of phenomena. [1][2][3][4] In particular, non-Kramers rare-earth ions with an even number of f electrons in a cubic environment have been attracting strong interest recently. [5][6][7][8][9][10][11] In these systems, it is possible that the ground states of the J multiplet split by the cubic crystalline electric field (CEF) are nonmagnetic, i.e., the matrix elements of the magnetic dipole J are identically zero, yet have a degeneracy that allows active higher-order multipoles such as electric quadrupoles or magnetic octupoles. Then various interesting phenomena such as multipole orders [12][13][14] or multichannel Kondo effects 15,16) are expected at low temperatures.These possibilities have indeed been realized in compounds containing Pr 3+ ions with the 4 f 2 electronic configuration. The nine states of the J = 4 ground multiplet are split by a cubic CEF into the Γ 1 nonmagnetic singlet, the Γ 3 nonmagnetic doublet, the Γ 4 magnetic triplet, and the Γ 5 magnetic triplet. If the CEF ground state is the Γ 3 doublet, we encounter an interesting situation that the ground state is nonmagnetic but has nonzero matrix elements for the two types of quadrupoles, O 20 = (3J 2 z −J 2 )/2 and O 22 = √ 3(J 2 x −J 2 y )/2, and one octupole T xyz = ( √ 15/6)J x J y J z , where the bar represents the sum over the possible permutations of the indices x, y, and z. 13) The series of compounds PrT 2 X 20 (T : transition metal, X: Zn or Al) provides particularly interesting examples of the Γ 3 CEF ground states. 4) As shown in Fig. 1 [18][19][20][21] all of which also show superconductivity. [21][22][23][24][25][26] Various measurements indicate that the Al-based materials are characterized by stronger hybridization between conduction and f electrons than the Zn-based materials, leading to anomalous transport properties and their pronounced pressure depen- * E-mail : taka.taniguchi@issp.u-tokyo.ac.jp dence. 4,[23][24][25][26][27][28][29][30] In this paper, we focus on PrTi 2 Al 20 . The magnetic susceptibility for H 111 is nearly independent of temperature below 20 K, indicating van Vleck paramagnetism with a nonmagnetic CEF ground state. 29) Specific heat measurements ...

Landau theory of multipolar orders in Pr(Y)2X20 Kondo materials ( Y=Ti , V, Rh, Ir; Lee1, Trebst2, Kim3 et al. 2018Phys. Rev. B470420View full textAdd to dashboardCite

“…The phase of φ u ≡ |φ u |e iθu is determined by the clock term v. For v > 0, we favor θ u = π/6 + 2nπ/3 (with integer n), while v < 0 pins θ u = π/6 + (2n + 1)π/3. In particular, either sign of v favors O 20 order over O 22 order, which is consistent with nuclear magnetic resonance (NMR) experiments 35 on PrTi 2 Al 20 . In the "hard-spin" limit, the theory for the PM-to-FQ transition is a Z 3 clock model which is known to exhibit a first-order transition in three dimensions (3D).…”

“…For a (111) field, there are a set of '3c' Al sites on the Frank-Kasper cage which are symmetry equivalent in the paramagnetic phase, and yield a single NMR line. 35 Based on symmetry, an AFQ-III state with S 4z symmetry is expected to split this into four NMR lines, with a 1:2 intensity ratio (i.e., two weak and two strong). However, the lower temperature AFQ-II state with broken S 4z should exhibit six NMR lines with equal intensity.…”

“…Further insights into the phase diagram come from experiments studying the impact of a magnetic field. 21,30,31,[34][35][36][37] For FQ order, it is well known that the magnetic field couples at O(B 2 ) directly to the order parameter, which converts the sharp paramagnetto-FQ thermal transition into a crossover; this has been observed in PrTi 2 Al 20 . 30 On the other hand, the multiple transitions in PrV 2 Al 20 at T Q and T * are found to survive at nonzero fields, and moreover evolve in a manner which depends strongly on the field direction.…”

Cubic hastatic order in the two-channel Kondo-Heisenberg model

“…At low temperatures, most of these materials order, and then become superconducting at even lower temperatures. PrTi 2 Al 20 and PrIr 2 Zn 20 order ferro-and antiferro-quadrupolarly at T Q = 2K 18,22,41,42 and 0.11K 21,43 , respectively, while the ordering in PrV 2 Al 20 18,41 and PrRh 2 Zn 20 23 is still undetermined. PrNb 2 Al 20 does not order to the lowest temperatures, instead exhibiting non-Fermi liquid behavior 44,45 .…”

Field-induced ferrohastatic phase in cubic non-Kramers doublet systems

“…The most straightforward way to positively identify FH order over the competing quadrupolar orders is to examine the fielddependence of the magnetic moments -in particular, their direction. FH moments will always be pinned to the field, and so all moments will align with the external field; by contrast, FQ order induces magnetic moments in field with a significant perpendicular component for some field directions 24,25,27 . Similarly, AFQ order generically induces FQ order and will have the same field dependence of the uniform moments.…”