Multiple Metamagnetic Quantum Criticality inSr3Ru2O7

Abstract

Bilayer strontium ruthenate Sr 3 Ru 2 O 7 displays pronounced non-Fermi liquid behavior at magnetic fields around 8 T, applied perpendicular to the ruthenate planes, which previously has been associated with an itinerant metamagnetic quantum critical end point (QCEP). We focus on the magnetic Grüneisen parameter Γ H , which is the most direct probe to characterize field-induced quantum criticality. We confirm quantum critical scaling due to a putative two-dimensional QCEP near 7.845(5) T, which is masked by two ordered phases A and B, identified previously by neutron scattering. In addition we find evidence for a QCEP at 7.53(2) T and determine the quantum critical regimes of both instabilities and the effect of their superposition.Quantum criticality denotes critical behavior that is associated with continuous transformations of matter at zero temperature. Due to the absence of thermal fluctuations at T = 0 it is qualitatively different from classical criticality [1]. In metals the unconventional excitation spectrum near a quantum critical point (QCP) causes the breakdown of Fermi liquid (FL) behavior and its intimate relation to exotic states, such as unconventional superconductivity, adds even more importance to this topic. To date, the influence of quantum critical magnetic excitations on electrons in a metal is far from being understood. For instance the applicability of the itinerant Hertz-Millis-Moriya theory on f -electron based Kondo lattice systems has been disproved by several experiments [2] and alternative descriptions are not fully established yet. Quantum criticality related to itinerant metamagnetism is exceptional in the sense, that electronic degrees of freedom are irrelevant, and a quantitative application to experimental results should be possible [3].The generic metamagnetic quantum critical end point (QCEP) arises from the suppression to T = 0 of the end point of a line of first-order metamagnetic transitions in temperature-field phase space by tuning e.g. composition, pressure or the magnetic field orientation [3]. Metamagnetic QCEPs have been realized in the f -electron based compounds CeRu 2 Si 2 [4,5] We focus on bilayer strontium ruthenate Sr 3 Ru 2 O 7 . Magnetization of this compound along the tetragonal c-axis at low temperature exhibits three successive super-linear, i.e. metamagnetic, rises at µ 0 H M1 =7.5 T, µ 0 H M2 =7.85 T and µ 0 H M3 =8.1 T [9]. The first one is a metamagnetic cross-over (M1). The second and third ones are first order metamagnetic transitions (M2 and M3), ending at critical temperatures of about 1 and 0.5 K, respectively [10]. A line of second-order thermal phase transitions, connecting the critical end points of M2 and M3, has been discovered in electrical resistivity and thermodynamic experiments [10,11], which recently by neutron scattering has been identified as phase boundary of a spindensity-wave (SDW) "phase A" [12, 13] (see Fig. 1.). The lower and upper critical fields of SDW-A correspond respectively to H M2 and H M3 . Additionally, another SDW "ph...

Classification of materials with divergent magnetic Grüneisen parameter

“…This has been proposed for the bilayer strontium ruthenate Sr 3 Ru 2 O 7 [28]. Very recently a careful study of the magnetic Grüneisen parameter has revealed that this material actually realizes a more complicated scenario, with two subsequent field-induced QCPs (for the critical fields see Table 1) [12]. The Γ H data also allowed to determine scaling regimes associated with both QCPs and the phase space where scaling fails due to the interference of both instabilities.…”

“…The Grüneisen parameter diverges upon approaching the QCP at r = 0 following T −1/(νz) or respectively at T = 0 according to r −1 with universal prefactor G r = ν(d − z) [1,2]. Such divergences have been found in magnetic Grüneisen parameter measurements on various strongly correlated electron systems in recent years, which are listed in Table 1 [8,9,[11][12][13][14][15][16][19][20][21][22][23]. The table does not include low dimensional spin systems for which the magnetic Grüneisen parameter has been investigated experimentally and theoretically near field-induced quantum phase transitions [24][25][26].…”

Theory of the strange metal Sr 3 Ru 2 O 7

“…This scaling is distinct from the Kadowaki-Woods relation A ∼ γ 2 (24), which instead follows from the resistivity ρ ∝ m 2 h T 2 . Microscopically, the mass enhancement has been assumed to be tied up with metamagnetic quantum criticality of the hot electrons (2,(25)(26)(27). The results above are not sensitive to the details of these physics beyond requiring a divergent m h in a small region of the Brillouin zone.…”

Multicritical Fermi Surface Topological Transitions

“…Careful analysis 12 reveals a power law divergence of C/T as a function of reduced field h = (H − H C )/H C with an unexpected exponent of -1. It has been suggested that the singularities in C/T as a function of field or temperature are consistent with a 2D metamagnetic QCEP within the canonical description of quantum criticality 13 . The expected exponent within this theoretical framework is -1/3 and in general has to be fixed in any fit of this model 14 exponent of -1 in an assumption-free power law fit to C/T therefore raises the important question of whether the current theoretical understanding is incomplete.…”