Hidden Order and Nexus between Quantum Criticality and Phase Formation : The Case of URu 2 Si 2

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1 Hidden Order and Nexus between Quantum Criticality and Phase Formation : The Case of URu 2 Si 2 J. A. Mydosh Max Planck Institute for Chemical Physics of Solids, Dresden and Kamerlingh Onnes Laboratory, Leiden University

2 Main Collaborators M. Jaime N. Harrison NHMFL-LANL K. H. Kim* H. Amitsuka Hokkaido Univ. Haung Ying Kai Amsterdam/Leiden *Seoul National University

3 Outline Introduction to URu 2 Si 2 and Hidden Order (HO) Pressure Tuning : Neutron Diffraction and NMR Theories, Models and Conjectures over HO Destruction of HO with Field : Magnetization and Transport Properties Phase Diagram Effects of Rh-doping Simplified Phase Diagram only Phase II Nexus between Quantum Criticality and Phase Formation Characterization of Phase II via C(T,H) and MCE

4 Introduction ThCr 2 Si 2 bct - type ( I4/mmm ) URu 2 Si 2 U Ru Si a = (Å) c = (Å) ρ (µω cm ) T o ~ 17.5 K T c ~ 1.2 K Coexistence of HO with SC I // a I // c T.T.M. Palstra et al.(1985) W. Schlabitz et al.(1986) M.B. Maple et al.(1986)

5 Magnetic susceptibility URu 2 Si 2 χ (10-3 emu / mol) T o µ eff z ~ 2.2 µ B H // c 2 H // a T (K)

6 Specific heat vs. magnetic Bragg-peak intensity C 5f / T (mj/k 2 mol) T c URu 2 Si 2 S mag ~ 0.2 R ln T o µ ord ~ µ B Intensity (arb.unit) 1 0 Q = (1,0,0) Mason Fåk Honma T (K) Type-I AF ξ c ~ 100 Å

7 Pseudo-gap in URu 2 Si 2 measured through optical conductivity, D. A. Bonn et al. PRL (1988)

8 Zone-center gap in URu 2 Si 2 measured through neutron scattering, C. Broholm et al. PRL (1987) & PRB (1991) Similarity between optics and neutrons suggests magnetic excitations are strongly coupled to charge excitations

9 Magnetization as function of temperature, C. Pfleiderer et al. to be published (2005) M/B (µ B /U-atom tesla) T 6T 1T T(K) M/B (µ B /U-atom tesla) T 1.0 T 6.0 T 12 T T(K) ab-plane c-axis

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12 Neutron scattering under hydrostatic pressure H. Amitsuka, M. Sato, N. Metoki, M. Yokoyama, K. Kuwahara, T. Sakakibara, H. Morimoto, S. Kawarazaki, Y. Miyako, and JAM PRL 83 (1999) 5114

13 29 Si NMR in Aligned Powder Matsuda, et al., PRL 87 (2001) NMR, under pressure [P-induced IAF] Bernal et al., PRL 87 (2001) Ambient Pressure [Internal Field] 15 URu 2 Si 2 Γ Si 1 Si 2 λ (G) 10 5 H _ _ c H c s = 1/2 Mean Field Temperature (K) U (110) Γ 2 (Η,θ,Τ ) = α 2 Μ 2 (Η,θ,Τ ) + λ 2 (Τ ) OAF?

14 Orbital Antiferromagnet U Is the internal field also isotropic at Ru sites? U-U Bond Current Direction Resultant Magnetic Field

15 Hidden Order Unique Enough to Stimulate New Ideas: Dipolar order with small g values crystal fields Niewenhuys 86 quant. spin fluctuation Sikkema et al. 96 duality: loc./itin. Okuno, Miyake 98 spin-orbital cancellation Yamagami 99 fragile AF order Bernhoeft et al. 02 Non-dipolar order quadrupole Miyako et al. 91 triple spin Barzykin, Gor kov 93 quadrupole (Γ 4 ) Santini, Amoretti 94 quadrupole (Γ 5 ) H. A., Sakakibara 94 structural distortion Barzykin, Gor kov 95 U dimer Kasuya 97 d-wave SDW Ikeda, Ohhashi 98 quadrupole (Γ 5 ) Shimizu, Ohkawa 99 bond order - OAF Chandra et al. 01 unconventional SDW Virosztek, Maki, Dóra 02 S µ=gµ B S?

16 Hidden Order Unique Enough to Stimulate New Ideas: Non-translational-symmetry breaking Landau-Pomeranchuk Varma 03/ 05 Valency transition Gor kov 04 Octupolar Kiss & Fazekas 05 SDW Mineev & Zhitomir. 05 Falicov-Kimble Zlatic 05 Itinerant quadrupole Harrison et al. 05 Itinerancy & HO Tripathi & (PC) 2 05

17 Switching to the Metamagnetic Transition in URu 2 Si 2 Magnetization (a.u.) K 8.00 K 7.00 K 6.00 K 5.75 K 5.50 K 5.00 K 4.00 K 1.55 K 0.46 K B (T) N. Harrison, M. Jaime, and JAM, PRL 90(2003)

18 What happens as T is lowered? χ exhibits divergence for T > 6 K as for CeRu 2 Si 2, Sr 3 Ru 2 O 7 and UPt 3 THEN SUDDENLY crossover splits for T <6K (T-stability crucial for discovery) H decreasing Transitions consistent with specific heat measurements [Jaime et al. PRL 89, (2002)] CAN FIELD-INDUCED QCP INSTIGATE NEW PHASES?

19 Hall Effect Results for URu 2 Si 2 in Pulsed Magnet 360 ρ xx for URu 2 Si 2 ρ xy for URu 2 Si 2 URu 2 Si 2 Curvature change? I//ab, H//c ρ xx (µωcm) K FS change µ 0 H (T)

20 Multiple phases nearby a QCP: H decreasing 12 K URu 2 Si 2 ρ (µ Ωcm) T (K) ρ max T* URu 2 Si µ 0 H (T) 4 2 Hidden Order (I) II V III Fermi Liquid (IV) µ 0 H (T) Phase transitions observed as extremities in dρ/db and dρ/dt confirmed in M, C and sound velocity v s

21 Multiple phases nearby a QCP: H decreasing ρ (µω cm) URu 2 Si 32.5T T (K) T (K) Hidden Order (I) ρ max II V Metamagnetic transition III Fermi Liquid (IV) µ 0 Η (T) URu 2 Si 2 T* Multiple new phases result from (1) multiple competing interactions and/or (2) close proximity of B M to Hidden Order phase

22 Summary of Transport Results for URu 2 Si 2 T (K) n ρ max HO (I) II V III URu 2 Si 2 Metamagnetic transition FL (IV) T* ρ (µωcm) A -1/2 (K/µΩcm -1/2 ) All the smoking guns indicate H QCP ~37 T!! URu 2 Si 2 : Another example of order created at quantum critical point?? ρ=ρ 0 +AT n ~0.6K T 3 K µ H (T) 0 K.H.Kim, N.Harrison, M.Jaime, G.S.Boebinger and JAM. PRL 91, 03

23 Effects of Rh-doping in URu 2 Si 2 K.H.Kim, N.Harrison, H.Amitsuka, G.A.Jorge, M.Jaime and JAM, PRL 93(2004) Phase diagram simplified on doping with Rh, yielding single field-induced phase (II) [without phase I (Hidden Order)] and clearer evidence for quantum critical point Quantum criticality occurs in absence of hidden order: so hidden order not responsible for quantum criticality Nexus between quantum critical point, phase II and B M observed as a function of Rh, indicating causality link (magnetization in pulsed fields and transport in dc fields)

24 Quantum criticality and Phase II Evidence for quantum criticality occurs at at low and high magnetic fields, pointing to single quantum critical point concealed inside phase II, with scaling: T* A -1/2 ε F α ~ 1 α ~ 0.7 Fits of A to (B-B M ) α support divergence in m* at quantum critical point: formation of phase II leads to suppression of fluctuations Phase II likely holds key to understanding magnetism, because it has 1/3rd of full saturated moment (neutrons should be able to detect large moment that is absent in Hidden Order phase): Ising moments imply broken translational symmetry likely

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26 Metamagnetism and Quantum Criticality T or ε non Fermi liquid A Paramagnetic Fermi liquid B Fully polarized f - electrons + Fermi liquid Transition from Fermi surface A to Fermi surface B B M H Metamagnetism expected to be first order (no symmetry change?) Experimentally first order transition not seen in itinerant electron metamagnets CeRu 2 Si 2 or UPt 3 [Sakakibara et al. PRB 51,12030(1995)]. Existence of Fermi liquid at B M nevertheless quite unthinkable? Understanding Fermi surface topology holds the key to everything Issue of Fermi surface change at antiferromagnetic QCP in antiferromagnetic heavy fermion systems

27 Fermi Liquids and Quantum Criticality T or ε non Fermi liquid Paramagnetic Fermi liquid Phase II ferrimagnetic? Fully polarized f - electrons + Fermi liquid Quantum critical point between two Fermi liquids: one with polarized f-electrons H New phase forms so as to avoid quantum critical point Phase with 1/3 rd saturated moment possibly analogous to to Q = 2/3c* ferrimagnetic phase in UPd 2 Si 2? [Honma et al.,j.phys.soc.japan 67,1017(1998)]

28 A.V.Silhanek, N.Harrison, C.D.Batista, M.Jaime, A.Lacerda, H.Amitsuka and JAM, PRL 95(2005)

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32 C/T X = 0.04 X T 2 (K 2 )

33 Low T ~ 2 K High T ~ 6 K

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37 Summary of Progress 1) URu 2 Si 2 exhibits quantum critical behaviour associated with itinerant electron metamagnetism 2) Quantum criticality is involved in creation of new phase(s) at high magnetic fields 3) New phases may also help us to understand Hidden Order parameter 4) Rh doping greatly simplifies the phase diagram with a single phase II surrounded by two low temperature Fermi liquid phases 5) Phase II exhibits an enormous specific heat discontinuity indicative of a first order phase transition tricritical points