NMR, muSR and Moessbauer

Our main experimental tool, neutron scattering, is a momentum-resolved technique. In magnetic systems it probes temporal correlations between spatial Fourier components of the magnetization. Complementary information can be obtained by measuring local correlations, the behavior of the magnetization at a particular point in space. For this one obviously needs a microscopic local probe with sensitivity on the atomic scale. None of these techniques are practiced in our own lab, but we use them in two rather different ways. NMR and ESR we access through tight collaborations with research groups who specialize in these methods: we typically contribute the samples and the physics questions, and our students often travel along to take part in the measurements. muSR is a different story. Like neutron scattering, it is user-facility science: we write the proposals and run the experiments ourselves, exactly as we do at the neutron sources.

One approach is to use the nuclei of certain atoms that are part of the material's structure. In Nuclear Magnetic Resonance (NMR) experiments one measures how the precession of nuclear spins is influenced by local fields generated by the magnetic electrons in the system.

The simplest use of NMR is to measure the local static fields produced by long-range magnetic order in the sample. NMR lines are shifted and split, which carries information on the magnitude of the magnetic order parameter and the spin structure. Here are some measurements of such ³¹P NMR line splitting in Pb₂VO(PO₄)₂ carried out at the LNCMI-CNRS in Grenoble, France. These experiments revealed a new exotic pre-saturation phase in this frustrated quantum ferro-antiferromagnet. For more information see F. Landolt, S. Bettler, Z. Yan, S. Gvasaliya, A. Zheludev, S. Mishra, I. Sheikin, S. Krämer, M. Horvatić, A. Gazizulina, O. Prokhnenko, Pre-saturation phase in the frustrated ferro-antiferromagnet Pb₂VO(PO₄)₂ , Phys. Rev. B 102, 094414 (2020); arXiv:2006.04592.

NMR can also probe aspects of spin dynamics. The so-called relaxation rate measurements directly probe the local spin correlation function of the electronic spins at some small but finite frequency. It is an invaluable tool for studying critical dynamics. In the example below, our collaborators applied ¹⁴N NMR to measure quantum critical fluctuations in the Tomonaga-Luttinger spin liquid phase of the quantum spin ladder material DIMPY. For more details see M. Jeong (정민기), D. Schmidiger, H. Mayaffre, M. Klanjšek, C. Berthier, W. Knafo, G. Ballon, B. Vignolle, S. Krämer, A. Zheludev, M. Horvatić, Dichotomy between Attractive and Repulsive Tomonaga-Luttinger Liquids in Spin Ladders , Phys. Rev. Lett. 117, 106402 (2016); arXiv:1604.05252.

Another beautiful technique that uses nuclei as local probes for magnetism is Mössbauer spectroscopy. The idea is to measure the frequency shift of gamma quanta emitted by a radioactive nucleus present in the sample. That shift carries information about the local environment and magnetic field at the nucleus site. Unfortunately, this method can only be applied in very few special cases. We were involved in only one such experiment. The measurement revealed a microscopic coexistence of spin glass and long-range antiferromagnetic order in the compound PbFe_1/2Nb_1/2O₃. Some ⁵⁷Fe Mössbauer spectra are shown below, but for more details see Sh. Chillal, M. Thede, F. J. Litterst, S. N. Gvasaliya, T. A. Shaplygina, S. G. Lushnikov, A. Zheludev, Microscopic coexistence of antiferromagnetic and spin-glass states , Phys. Rev. B 87, 220403(R) (2013); arXiv:1211.4203.

What if there are no convenient nuclei in the material, or if they are all in the wrong positions? The solution is to artificially implant a local probe in the sample. For this purpose one uses positively charged muons. Their spin precesses in the local magnetic field and is deduced from the direction in which a positron is emitted when the muon decays a few microseconds later. The technique is called muSR. There are only four installations in the world that produce muons for such experiments. We are very fortunate to have one right next door, at the Paul Scherrer Institut, where we are quite regular users. muSR is particularly good at detecting very small magnetic moments. In the example below we measure muon precession to understand the chemical composition dependence of magnetic order in the random-bond quantum spin chain material BaCu₂(Si_1−xGe_x)₂O₇, looking for the so-called random-singlet phase. For more details see M. Thede, T. Haku, T. Masuda, C. Baines, E. Pomjakushina, G. Dhalenne, A. Revcolevschi, E. Morenzoni, A. Zheludev, Inhomogeneous ordering in weakly coupled Heisenberg S=1/2 chains with random bonds , Phys. Rev. B 90, 144407 (2014); arXiv:1407.0813.