Phase diagram of cuprate superconductors at ultrahigh magnetic fields

Phase diagram of cuprate superconductors at ultrahigh magnetic fields

L. Krusin-Elbaum^{I, *}; T. Shibauchi^{II, †}; C. H. Mielke^III

^IIBM T. J. Watson Research Center, Yorktown Heights, New York 10598, USA

IIDepartment of Electronic Science and Engineering, Kyoto University, Kyoto 606-8501, Japan

IIINational High Magnetic Field Laboratory, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA

ABSTRACT

We have investigated the field-temperature (H - T) diagram of the superconducting and pseudogapped states of Bi₂Sr₂CaCu₂O_8+y over a wide range of hole doping (0:10 < p < 0:225). Using interlayer tunneling transport in magnetic fields up to 60 T to probe the density-of states (DOS) depletion at low excitation energies we mapped the pseudogap closing field H_pg. We found that H_pg and the pseudogap onset temperature T* are related via a Zeeman relation gm_BH_pg » k_BT*, irrespective of whether the magnetic field is applied along the c-axis or parallel to CuO₂ planes. In contrast to large anisotropy of the superconducting state, the field anisotropy of H_pg is due solely to the g-factor. Our findings indicate that the pseudogap is of singlet-spin origin, consistent with models based on doped Mott insulator.

1 Introduction

In the phase diagram of cuprate superconductors, the most salient and fiercely debated feature is the normal state pseudogap [1], whose link to the superconductivity with high transition temperature (T_c) is still unresolved. The central issue is whether the pseudogap originates from spin or charge degrees of freedom and, in particular, whether it derives from some precursor of Cooper pairing that acquires the superconducting coherence at T_c. Experimentally, the situation appears deeply conflicted. On the one hand, photoemission [2] and surface tunneling spectroscopy [3,4] show the pseudogap continuously evolving into a superconducting gap below T_c. The reports of anomalous and large Nernst effect in the normal state [5] led to claims of vortex-like excitations surviving up to temperatures close to T^*. On the other hand, intrinsic tunneling measurements revealed a double gap structure [6], indicating the pseudogap distinct even below T_c. With very different magnetic field sensitivities [7], the two gap features have been viewed by some as being unrelated [8].

Recently we have shown that in magnetic fields along the c-axis, the field H_pg that closes the pseudogap D_pg relates to T^* via a simple Zeeman relation [9] (Fig. 1), suggesting that D_pg is controlled by the spin- rather than orbital degrees of freedom. However, several 'precursor superconductivity' scenarios, for example, those based on BCS-Bose Einstein crossover [10] or on intermediate coupling [11] models, argue that Zeeman scaling is compatible with the superconducting origin of the pseudogap. Conventionally, the upper critical field H_c2@ F₀/2px² is determined not directly by the gap, but by the coherence length x (the size of the Copper pair). The orbital motion of the Cooper pairs with increasing field eventually leads to diamagnetic pair breaking, restoring the normal state. Ginzburg-Landau description of anisotropic 3D superconductor gives = F₀/2px_ab x_c (for the field in the ab-plane) and = F₀/2p (for the field along the c-axis), where F₀ denotes the flux quantum [12]. In cuprates, the field anisotropy g = / = x_ab/x_c is large [13], since the coherence length x_c along the c-axis (~ 2 Å) is much shorter than the in-plane x_ab (~ 30 Å). In the 'precursor' view, one would similarly expect an orbital frustration of preformed pairs (related to their center of mass motion) at the pseudogap closing field.

Here we will discuss our experiments probing the field anisotropy of H_pg. We find that while in the superconducting state anisotropy is large, H_pg(T) displays only a small anisotropy of the g-factor, independently known from the magnetic susceptibility measurements [14]. This rules out the diamagnetic pair-breaking at H_pg. Furthermore, given the scales for H_pg (here, ~ 70 -100 T) and T^* (here, ~ 100 K), the Zeeman splitting for the spin degrees of freedom is not in correspondence with pair-breaking via a conventional paramagnetic (Pauli) effect [15]. The observed absence of orbital frustration naturally points to a singlet spin-correlation gap closed with a triplet spin excitation at H_pg.

2 Experimental

The magnetic field range required to close the pseudogap is immense in the underdoped regime, but decreases rather fast with doping [9]. Thus, to explore the field anisotropy, we have chosen to work with overdoped Bi-2212 crystal annealed in 200 atm O₂ for three days at 375^°C to obtain a sharp transition at T_c(H = 0) » 60 K, corresponding to the hole doping p = 0.225. Measurements were performed at 100 kHz in a 60 ms pulse 60 T magnet at National High Magnetic Field Laboratory (NHMFL) in Los Alamos using a lock-in technique. Negligible eddy-current heating was verified by the consistency of the data taken with successive pulses to different target fields. In overdoped samples, T^* can be very close to T_c, or may be below T_c (Ref. [6]). In our crystal, a semiconducting-like (dr_c(T)/dT < 0) upturn in the c-axis resistivity r_c(T) - a consistent signature of the pseudogap [9,14] - is very obvious when T_c is suppressed by only a ~ 10 T field (Fig. 2). Here, the upturn - a result of the depletion in the quasiparticle density of states (DOS) near the Fermi energy - onsets at T^* ~ 100 K. Fig. 2 illustrates how at high fields (~ 55 T) the upturn is suppressed, extending the metallic (dr_c(T)/dT > 0) region to lower temperatures where the high-field r_c(T) systematically approaches the normal ungapped resistivity (T) (Ref. [6]).

3 Results and Discussion

In the superconducting state, r_c(H) becomes finite above the irreversibility field H_irr (º zero resistivity field H_0r, see Fig. 3). A characteristic peak is observed at a higher field H_sc. This peak arises from a competition between two parallel tunneling conduction channels [16]: of Cooper pairs (Josephson tunneling that decreases with increasing field) and quasiparticles (dominating at high fields). At H_sc, the quasiparticle and the Josephson tunneling currents are comparable. Above the peak, the magnetoresistance is negative until the pseudogap is quenched at H_pg when r_c(H) reaches (Fig. 3a).

H_sc is a good measure - a reliable lower bound on H_c2 (Ref. [16]). The temperature dependence of H_sc in Fig. 4a shows that not only the initial slope for the two field alignments is very different, namely, d/ = - 3 T/K is much larger than d/ = - 0.27 T/K, but also the overall curvature changes from concave to convex when the field is rotated from the out- to in-plane. This is reflected in the strong temperature dependence of the anisotropy ratio g_sc = /, which is ~ 12 close to 55 K but decreases by a factor of 3 near 0.5 T_c (Fig. 4b). The irreversibility anisotropy (also T-dependent) is even larger; » 20-30 near 30 K, as shown in Figs. 4c and 4d.

To quantify the anisotropy of the pseudogapped state we use an identical procedure for H || c and H || ab to evaluate the excess quasiparticle resistivity Dr_c due to the density-of-states (DOS) depletion associated with the pseudogap (the difference between r_c and ) (Ref. [9]). Dr_c(H) follows a power-law at high fields above H_sc [9,16], and when taken at each temperature to the limit Dr_c® 0 it gives the value of the pseudogap closing field H_pg(T). Fig. 5 (top) illustrates that for the in-plane applied field r_c(H) has to be extrapolated somewhat further to reach the ungapped normal state value than for H||c. The values of H_pg(T) can be independently tracked from the high-field scaling behavior of Dr_c for H ® H_pg shown in Fig. 5 (bottom). However, in contrast to H_sc and H_irr, H_pg(T) is temperature-independent below ~ 0.8T^*, as shown in the H-T diagram in Fig. 6. The anisotropy ratio g_pg = / » 1.35 holds throughout the entire temperature range below T^*.

Hence, we conclude that a Zeeman scaling relation also holds for H||ab. This can be written as g^||cm_B (T = 0) = g^||abm_B (T = 0) » k_BT^*(H = 0), with the g-factor anisotropy g^||c/g^||abº g_pg. The value of g_pg is in excellent agreement with the (spectroscopic splitting) g-factor anisotropy of ~ 1.3 obtained independently from the measurements of uniform spin susceptibilities [14] in fields ||ab and ||c. Note that, given the scales of H_pg and T^*, the observed absence of orbital anisotropy at the pseudogap closing field appears inconsistent with the simple paramagnetic Pauli pair-breaking effect, H_p|_{T = 0} = 1.84 T_c|_{H = 0} [15], and the one deduced for anisotropic singlet pairing, H_p = 1.58 T_c [18]. It is fully consistent with a singlet-spin (pseudo)gap closed by a triplet excitation at H_pg arising in the spin-charge separation scenarios for high-T_c based on a doped Mott insulator [19,20,21].

Acknowledgments

We thank F. F. Balakirev and J. Betts for technical assistance, T. Tamegai for the use of the crystal growth facilities, and G. Blatter, V. G. Kogan, and M. P. A. Fisher for valuable comments. Measurements were performed at NHMFL supported by the NSF Cooperative Agreement No. DMR-9527035. T. S. is supported by a Grant-in-Aid for Scientific Research from MEXT.

[19] Patrick A. Lee, cond-mat/0210113 (2002).

Received on 24 July, 2003

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Publication Dates

• Publication in this collection
  25 Nov 2005
• Date of issue
  Dec 2003