APS/123-QED

Low temperature thermodynamic investigation of the phase diagram of Sr3Ru2O7

D. Sun1, A. W. Rost2,3,4, R. S. Perry5, A. P. Mackenzie1,4 and M. Brando11Max Planck Institute for Chemical Physics of Solids, D-01187 Dresden, Germany

2 Max Planck Institute for Solid State Research, D-70569 Stuttgart, Germany3 Institute for Functional Matter and Quantum Technologies,

University of Stuttgart, Pfaffenwaldring 57, D-70569 Stuttgart, Germany4 Scottish Universities Physics Alliance, School of Physics and Astronomy,

University of St. Andrews, St. Andrews, Fife KY16 9SS, UK5 London Centre for Nanotechnology and Department of Physics and Astronomy,

University College London, London WC1E 6BT, UK(Dated: March 20, 2018)

We studied the phase diagram of Sr3Ru2O7 by means of heat capacity and magnetocaloric effectmeasurements at temperatures as low as 0.06 K and fields up to 12 T. We confirm the presence ofa new quantum critical point at 7.5 T which is characterized by a strong non-Fermi-liquid behaviorof the electronic specific heat coefficient C/T log T over more than a decade in temperature,placing strong constraints on theories of its criticality. In particular logarithmic corrections are foundwhen the dimension d is equal to the dynamic critical exponent z, in contrast to the conclusionof a two-dimensional metamagnetic quantum critical endpoint, recently proposed. Moreover, weachieved a clear determination of the new second thermodynamic phase adjoining the first one atlower temperatures. Its thermodynamic features differ significantly from those of the dominant phaseand characteristics expected of classical equilibrium phase transitions are not observed, indicatingfundamental differences in the phase formation.

Keywords: Sr3Ru2O7, quantum criticality, Gruneisen parameter

INTRODUCTION

The formation of new phases and the emergence ofquantum critical points (QCPs) play a key role in thephase diagrams of a wide range of strongly correlatedelectron systems. Since first being synthesized in sin-gle crystal form [1, 2], the layered perovskite metalSr3Ru2O7 has been the subject of intense study due toits peculiar correlated electron properties [3]. In par-ticular an unusual phase stabilized in the vicinity of anunderlying metamagnetic quantum critical end point hasattracted significant interest [3]. The fine balance of theenergetics involved in the formation of this phase dueto competing interactions at the quantum critical pointin Sr3Ru2O7 is evidenced by the dependence of the ob-served properties on sample purity. Single crystals canbe grown in image furnaces, and, with care, residual re-sistivities 0 below 1 cm can be achieved [4]. For 0in the range 3-5cm, a single metamagnetic transitionis observed. For fields applied in the ab plane the transi-tion occurs near 5 T with a magnitude of 0.25B/Ruand is first-order below a critical end-point at approxi-mately 1.2 K. As the field is rotated to the c axis, themetamagnetic field rises to nearly 8 T and the end-pointtemperature falls to below 100 mK [5]. If 0 is reduced tobelow 1 cm, however, qualitatively different behavioris seen, with the phase diagram as currently known be-ing summarized in Fig. 1. Most prominently, a new phase(labelled A) bounded in field by first-order phase tran-sitions at 7.8 and 8.1 T and in temperature by a second-order transition at 1.1 K was reported [68], with signa-tures of another metamagnetic feature at 7.5 T.

More recent work on the latest generation of samplesrevealed evidence for a putative second phase (B) ex-tending from 8.1 to 8.5 T, with a lower onset T c of lessthan 0.6 K [9, 10]. This was shown particularly clearlyin breakthrough neutron scattering measurements thatestablished incommensurate order with Q = (0.233, 0, 0)within the A phase and Q = (0.218, 0, 0) within the Bphase. In both cases the correlation length of the orderedsignal was greater than 350 A and the characteristic fre-quency of any fluctuations less than 1 GHz [11].

This phase diagram is unusual in several ways. Firstly,the application of a uniform magnetic field stimulatesthe formation of phases that feature finite q order. Sec-ondly, the resistivity rises substantially over the back-ground value in both enclosed phases. Thirdly, in-planetransport in these phases has a giant susceptibility toanisotropy [10, 12] that can be stimulated both by in-plane magnetic fields and by in-plane uniaxial strain[13]. Finally, the curvature of the first-order transitionlines just above H1 and H2 implies that the entropywithin the A phase is higher than that at lower or higherfields. Although not unprecedented (for example suchphenomenology is at the root of the Pomeranchuk effectin 3He) this is unexpected.

The unusual nature of the phase diagram motivateddetailed studies of the electronic properties of this mate-rial by, e.g., band structure calculations [14, 15], angle-resolved photoemission spectroscopy (ARPES) [16, 17],de Haas-van Alphen (dHvA) [18, 19] and magneticGruneisen parameter measurements [20]. Although theband structure calculations correctly predict the basic to-pography of the Fermi surface, the ARPES experiments

arX

iv:1

605.

0039

6v4

[co

nd-m

at.s

tr-e

l] 1

6 M

ar 2

018

2

7 7.5 8 8.5 9

Field (T)

0

0.5

1

1.5

2

2.5

3T

em

pe

ratu

re (

K)

0.04

0.06

0.08

0.1

0.12

0.14

C/T

(J/R

u-m

olK

2)

H0

H1 H2 H3

Phase A

Phase B

Ref. 6

T*1

T*2

T*

TATBH3

FIG. 1. Phase diagram of Sr3Ru2O7 with H c show-ing the locations in the (T,H) plane of the key thermody-namic features deduced from the specific heat and magne-tocaloric measurements described here and those publishedin Ref. [6]. In the background we show a color plot of in-terpolated C/T = (C(T,H) C(T, 0))/T data to show thetemperature and field development of the energy scales in-dicated by the points. T 1 is a crossover identified from amaximum in C/T (Fig. 3a for 7.3 7.6 T). T 2 is a similarlydefined crossover deduced from C/T data for 8.3 9 T. T is a second crossover scale as indicated in Fig. 3a. TA and TBare identified from features in C/T as labeled in Fig. 4a,band d. H3 is identified from magnetocaloric data as shown inFig. 4c. See also Fig. 7 of the Appendix.

have shown that Sr3Ru2O7 is strongly renormalized, withbandwidths a factor of 7 20 narrower than the cal-culated values [16, 17]. This is reflected in the specificheat, which is 0.11 J/Ru-molK 2 in zero applied magneticfield [2]. The strong correlations implied by these obser-vations are also evident in the magnetic properties. Theq = 0 magnetic susceptibility is large, corresponding toa Wilson ratio of 10 and suggesting that Sr3Ru2O7 is onthe border of ferromagnetism. Indeed, modest uniaxialpressure can drive it ferromagnetic [21], and applied fieldsin the range 5 8 T lead to metamagnetism [22]. In con-trast to uniaxial pressure, hydrostatic pressure weakensthe magnetism, as would be qualitatively expected in aStoner picture in which sharp features in the density ofstates near the Fermi level are at the root of the strongcorrelations and magnetism [2325]. However, the situa-tion seems to be more complex: In a work carried out inparallel to this work, Tokiwa et al. have established theexistence of a second metamagnetic quantum critical end-point (QCEP) at about 7.5 T (H0 in Fig. 1) in additionto the previously known one near 7.85 T and proposedquantum critical regimes of both instabilities. Accordingto this analysis and the field dependence of the Sommer-feld coefficient, the authors suggested that the nature ofthe QCP near 7.85 T is that of a two-dimensional (2D)QCEP [20, 26].

Overall these findings establish Sr3Ru2O7 to be aquasi-2D strongly correlated metal in which magnetic in-teractions play a crucial role. The role and interplay ofthe two QCEPs in controlling the low temperature / highfield phase diagram and in particular the question of thenature of the phases stabilized in the quantum criticalregime clearly merit further detailed studies. Althougha first generation of thermodynamic experiments estab-lished the phase boundaries of the A phase, it revealedno strong signatures of the B phase [7]. In addition,the experiments were cut off for technical reasons below0.2 K, an uncomfortably high temperature when studyinga phase diagram with a characteristic temperature scaleof 0.5 1 K. The purpose of the current work is to studythe specific heat and magnetocaloric effect in Sr3Ru2O7in more detail, at higher resolution and at lower temper-atures than in the previous work. We show that thermo-dynamic signatures of the B phase can be resolved, butthat they are much weaker than those of the A phaseindicating significant differences in the order parameter.Crucially a detailed quantitative analysis shows that theycannot unambiguously be associated with classical equi-librium phase transitions raising the question of the roleof (quantum-) fluctuations. Our low temperature mea-surements also reveal that a thermodynamic feature at7.5 T (previously assumed to be a crossover because ofits width in field of 0.2 K) in fact has the characteristicsof a zero temperature QCEP related to a lower energyscale than those previously identified as being crucial tothe physics of Sr3Ru2O7. Intriguingly the temperatureevolution of this new quantum critical regime is cut offat a scale associated with the dominant critical pointat 8 T, implying a clear hierarchy of the energy scalesand thereby making Sr3Ru2O7 a rare example of a sys-tem with multiple quantum phase transitions. The na-ture of the new QCEP is discussed in light of the recentobservation of quantum critical s