Our major finding is:

Common energy scale for magnetism and superconductivity in the cuprates

One of the most challenging tasks of solid-state physics today is to understand the mechanism for superconductivity in cuprates. These materials, which have a relatively high critical temperature T_c, are based on doped CuO₂ planes. Since at zero doping they are antiferromagnets, several theories ascribe their superconductivity to holes interacting via a magnetic medium. Yet the phenomenon of superconductivity begins at doping levels in which magnetism almost disappears, and therefore there is no clear evidence relating the two. Fortunately, there is a narrow doping range in which superconductivity and magnetism, in the form of randomly oriented static spins, co-exist below a critical temperature T_g<T_c. We thus focus on this doping range and examine T_g and T_c in numerous superconducting families. We find that in all cases a common energy scale controls both critical temperatures. This is demonstrated in the figure where we plot both T_c/T_c^max and T_g/T_c^max as a function of holes in the system. In this normalized plot all data points of T_c and T_g, for various materials, collapse into a single curve. This clearly indicates that superconductivity and magnetism in the cuprates share a common energy scale.

We have published the following papers on the subject:

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• A.Kanigel, A.Keren, L.Patlagan, K.B.Chashka and P.King, Muon Spin Relaxation Measurements of Na_x CoO₂* y H₂O  Phys. Rev. Lett. 92, (2004) 257007. 

Abstract:
Using the transverse field muon spin relaxation technique,we measure the temperature dependence of the magnetic field penetration depth ,i n the Na_x CoO₂ y H₂ O system.We find that ,which is determined by the superfluid density n s and the effective mass m ,is very small and on the edge of the TF-mSR sensitivity.Nevertheless,the results indicate that this system obeys the Uemura relation.By comparing with the normal state electron density,we conclude that m of the superconductivity carrier is 70 times larger than the mass of bare electrons.Finally,the order parameter in this system cannot be described by a complete gap over the entire Fermi surface.

 

The paper in PDF format(325Kb).

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• A. Keren and A. Kanigel, Common energy scale for magnetism and superconductivity in cuprates   Phys. Rev. B 68, (2003) 12507. 

Abstract:
Many compounds based on CuO₂ planes (cuprates) superconduct below a critical temperature T_c. Some of them show a second phase where a spontaneous static magnetic field appears below a critical temperature T_g, which is lower than T_c. By comparing T_c and T_g in numerous superconducting families,each with its own maximum T_c,we find that the same energy scale determines both critical temperatures. This clearly indicates that the origin of superconductivity in the cuprates is magnetic.
 
 

• Amit Keren, Amit Kanigel, James S. Lord, and Alex Amato, Universal superconducting and magnetic properties of the  (Ca_xLa_1-x)(Ba_1.75-xLa_0.25+x)Cu₃O_y system: a mSR investigation

Abstract:
The(Ca_xLa_1-x)(Ba_1.75-xLa_0.25+x)Cu₃O_ysystem is ideal for testing theories of high temperature superconductivity, since nearly the full range of doping is controlled by y, and T_c^max is continuously controlled by x, with minimal structural changes. We investigate this system with both transverse and longitudinal field mSR. This allows us to re-examine the Uemura relation, the nature of the spontaneous magnetic fields below Tc, and the relation between their appearance temperature T_g and T_c^max. Our major findings are: (1) the Uemura relation is respected by this system more adequately than by other cuprates, (2) T_g and T_c are controlled by the same energy scale, (3) the phase separation between hole poor and hole rich regions is a microscopic one, and (4) spontaneous magnetic fields appear gradually with no moment size evolution

• Amit Kanigel, Amit Keren, Yaakov Eckstein, Arkady Knizhnik, James S. Lord, and Alex Amato, Common energy scale for magnetism and superconductivity in underdoped cuprates: a m SR investigation of (Ca_xLa_1-x)(Ba_1.75-xLa_0.25+x)Cu₃O_y, Phys. Rev. Lett. 88, 137003 (2002). 

Abstract:
We characterize the spontaneous magnetic field, and determine the associated temperature T_g, in the superconducting state of (Ca_xLa_1-x)(Ba_1.75-xLa_0.25+x)Cu₃O_y using zero and longitudinal field mSR measurements for various values of x and y. Our major findings are: (I) T_g and T_c are controlled by the same energy scale, (II) the phase separation between hole poor and hole rich regions is a microscopic one, and (III) spontaneous magnetic fields appear gradually with no moment size evolution.
 
 

• A. Keren, H. Alloul, P. Mendels, Y. Yoshinari, NMR study of ¹⁷O transverse relaxation in YBa₂Cu₃(¹⁶O_1-c¹⁷O_c)₇, Phys.Rev. Lett. 78, (1997) 3547-3550. 

Abstract:
NMR transverse relaxation (TR) measurements of ¹⁷O in the O(2,3) sites of YBa₂Cu₃(¹⁶O_1-c¹⁷O_c)₇ are presented. A Gaussian-like relaxation is found. The origin of this relaxation is investigated by varying the isotopic concentration of the oxygen, the temperature, the external field, and by comparing it with the O(4) site. Our results are consistent with a model in which this relaxation is caused by the dynamical fluctuation of copper nuclei, including both spin lattice and flip-flop processes. With this model we can explain consistently the TR of ⁸⁹Y and ^63,65Cu(1) as well. We use our results to re-analyze previous NMR ^63,65Cu(2) TR data.
 
 

• A. Keren, L. P. Le, G. L. Luke, B. J. Sternlieb, W. D. Wu, Y. J. Uemura, S. Tajima, and S. Uchida, Muon Spin Rotation Measurements in Infinite Layer and Infinite Chain Cuprate Antiferromagnets: Ca_0.86Sr_0.14CuO₂ and Sr₂CuO₃, Phys. Rev. B 48, (1993) 12926-12935. 

Abstract:
We have performed zero-field muon spin rotation (mSR) measurements of the ``infinite layer'' cuprate compound Ca<sub>0.86</sub>Sr<sub>0.14</sub>CuO<sub>2</sub>and the ``infinite chain'' system Sr₂CuO₃. A spontaneous magnetic field from the ordered Cu moments is observed below T_N=540(5)K in Ca_0.86Sr_0.14CuO₂: below T=360 K, we observe muon spin precession with a frequency n (T-> 0)=16 MHz (corresponding to a local field of 1.2 kG). The precession signal is replaced by a rapid depolarization above T=360~K due to the onset of muon diffusion. The hopping rate followed an Arrhenius law, with an activation energy of E_a=0.39(1) eV. The sub-lattice magnetization M_s, proportional to n(T), showed a slower decay with increasing temperature in Ca_0.86Sr_0.14CuO₂, compared with that observed in La₂CuO₄ and Sr₂CuO₂C_l2, indicating that a wider CuO₂ layer separation results in more 2-dimensional magnetic behavior. In the ``infinite chain'' system Sr₂CuO₃, the onset of magnetic order was found at T~5 K with a local field of ~30 G at the muon site at T->0. The exchange interaction, inferred from susceptibility measurements is on the order of 10³ K, implying a remarkable suppression of the ordering temperature with k_BT_N/J<=0.01 in Sr₂CuO_3. These results demonstrate clear signatures of low dimensional magnetic behavior in the CuO chains.
 
 

• A. Keren, K. Kojima, L. P. Le, G. L. Luke, W. D. Wu, Y. J. Uemura, S. Tajima and S. Uchida, Muon-Spin-Rotation Measurements in the ``Infinite-Chain'' Ca₂CuO₃  JMMM 140-144 (1995) 1641-1642. 

Abstract:
We performed zero-field muon-spin-rotation measurements of the ``infinite-chain'' compound Ca₂CuO₃. A spontaneous magnetic field is observed below 13 K. The exchange interaction inferred from susceptibility measurements and two-magnon Raman scattering is approximately 10³ K, which implies a remarkable suppression of the ordering temperature k_BT_N/J_1d~0.01. We discuss the relevance of these measurements to the problem of one dimensional spin-1/2 antiferromagnets.