Interplanar magnetic correlations in a high-temperature superconductor

A series of experiments carried out at the FRM II reactor as well as other neutron sources have revealed details of the magnetic order in the high-temperature superconductor La_1.88 Sr_0.12CuO₄. In this system, stripe-like magnetic order within the CuO2 planes coexists with superconductivity and displays a pronounced enhancement upon application of an external magnetic field perpendicular to the CuO₂ planes. Careful studies of the magnetic correlations between these planes have led to the revelation of the origin of the enhancement effect. The dominant source is an increase in the magnetic moments. A secondary source is due to the development of weak interplanar correlations. Surprisingly, fast cooling of the system also causes enhanced correlations between the CuO₂ planes. The results were published in Physical Review B 91, 174507 (2015) [6].

The high-temperature superconductor La_2-xSr_xCuO₄ is a member of the cuprate family of Copper-based superconductors. It derives from the parent compound La₂CuO₄ which is a Mott insulator with three-dimensional antiferromagnetic order. The antiferromagnetic order of the Mott insulating phase disappears rapidly as a function of doping, but magnetic order survives in the form of an incommensurate spin-density-wave order even above the doping value where superconductivity sets in. A full understanding of this transition from a Mott insulator to a superconductor is one of the greatest challenges of condensed matter physics.

Part of the puzzle stems from the fact that magnetic order coexists with superconductivity. It turns out that magnetic and superconducting regions are not always spatially separated, but in some compounds coexist microscopically. In La_2-xSr_xCuO₄, magnetic order is quasi-two dimensional and is manifested as a quartet of peaks around the position of the antiferromagnetic ordering vector. This structure has been interpreted as a signature of a magnetic stripe-like pattern, where antiferromagnetic regions are intercepted by rivers of charge [1]. Muon spin resonance measurements on La_1.88Sr[~0.12CuO₄ have revealed that magnetic order expands throughout the entire volume of the crystal [2]. Even so, application of a magnetic field leads to an enhancement of the magnetic order when measured by neutron scattering.

In fact, a number of neutron scattering experiments on La_2-xSr_xCuO₄ at different Strontium dopings have revealed that a boost in the magnetic order occurs upon application of an external magnetic field perpendicular to the Copper oxide planes. For dopings smaller than 13.5 %, an enhancement of preexisting magnetic order is observed [3], whereas in systems of larger doping which do not display zero-field magnetic order, the applied field can induce magnetic order [2,4].

The increase in magnetic ordering is connected to the presence of vortices surrounding the magnetic flux lines that penetrate the Copper oxide layers. Since the superconducting order is depressed in the vicinity of the vortex core, this region provides more favorable conditions for the development of magnetic order.

What has remained uncertain, however, is whether the increase in the magnetic signal measured by neutron scattering experiments is due to an actual increase in the magnetic volume fraction, or to an increase in the ordered magnetic moments. In fact, similar observations could stem from an enhancement of the spin-spin correlations out of the CuO₂ planes, without any additional magnetic order induced in the system. Indications that magnetic ordering becomes more three-dimensional upon application of an external magnetic field was presented in Ref. [5]. Other than this report, very little has been done to investigate three-dimensionality of the magnetic order in the cuprates and the observation in Ref. [5] motivated us to pursue the question of whether the field-induced signal, observed in experiments using the more common ₂ plane crystal orientation, may be due to the induced interplanar correlations, and not to an increase in the magnetic volume fraction or ordered magnetic moments in the superconductor.

To address this question, we performed scattering experiments where we specifically probed the magnetic intensity out of the CuO₂ plane. We used three different cold-neutron triple-axis spectrometers: PANDA at the FRM II research neutron source in Garching, RITA-II at the SINQ neutron source at PSI, Switzerland and FLEXX at the BER2 research reactor at HZB Berlin.

We found that spin-spin correlations between the CuO₂ planes do build up upon application of a field perpendicular to the planes, as shown on the left in Fig. 1. At the same time, the experiments revealed an increase in the magnetic moments, which in fact turned out to be the prevailing field effect.

To our surprise, we found from the experiments at PANDA that fast cooling of the sample can provoke a build- up of interplanar magnetic correlations and thereby cause an effect similar to the application of a magnetic field. The origin of cooling-induced interplanar correlations we ascribe to the presence of excess oxygen in the crystal. Excess oxygen is not easily avoided during crystal growth and fast cooling will freeze the oxygens at random positions. This could create pinning centers for magnetic correlations between neighbouring Copper oxide planes.