The discovery of superconductivity in bilayer and trilayer Ruddlesden–Popper nickelates
under pressure has stimulated intense interest in the relationship between superconductivity,
magnetism, and density-wave order in these materials. An important question is how the magnetic
ground state evolves under pressure on approaching the superconducting regime and to
what extent the lattice participates in the formation of the ordered states.
In this talk, I will present a series of muon-spin rotation/relaxation (μSR) studies of the
bilayer nickelates La3Ni2O7−δ and La2PrNi2O7, and the trilayer compounds La4Ni3O10 and
Pr4Ni3O10, performed at ambient and hydrostatic pressures [1, 2, 3, 4, 5, 6, 7, 8, 9]. The
μSR measurements provide a microscopic view of the spin-density-wave (SDW) order and allow
its evolution under pressure to be followed through the magnetic volume fraction, transition
temperature, and internal magnetic fields.
A distinct pressure response is found for the bilayer and trilayer systems. In the bilayer nickelates,
pressure enhances the SDW ordering temperature, while the ordered magnetic moment
remains nearly unchanged [1, 2]. In contrast, pressure suppresses the SDW transition in the
trilayer compounds and progressively weakens the ordered magnetic state [3, 5]. The trilayer
systems additionally display multiple magnetic transitions associated with changes in the SDW
structure.
Complementary oxygen-isotope-substitution experiments provide insight into the coupling
between the magnetic, charge, and lattice degrees of freedom. While substitution of 16O by
18O affects the charge-density-wave transition in both bilayer and trilayer systems [3, 4, 6], its
influence on the magnetic transition is strongly material dependent. A measurable isotope effect
on TSDW is observed when the SDW and CDW orders are intertwined, whereas it is absent when
the two transitions are separated [3, 4]. In Pr4Ni3O10, the SDW isotope shift remains essentially
unchanged under hydrostatic pressure, providing an additional constraint on the microscopic
origin of the density-wave state [6].
Together, the pressure and isotope studies reveal systematic differences in the evolution of
magnetism across the layered nickelate family and provide microscopic insight into the interplay
of spin, charge, lattice, and superconducting degrees of freedom.

References
[1] R. Khasanov et al., “Pressure-enhanced splitting of density wave transitions in La3Ni2O7−δ,” Nature Physics 21,
430–436 (2025); arXiv:2402.10485.
[2] R. Khasanov et al., “Pressure Effect on the Spin Density Wave Transition in La2PrNi2O6.96,” Physical Review
Research 7, L022046 (2025); arXiv:2503.06560.
[3] R. Khasanov et al., “Effect of Pressure and Oxygen-Isotope Substitution on Density-Wave Transitions in
La4Ni3O10,” Physical Review Research 8, 013249 (2026); arXiv:2503.04400.
[4] R. Khasanov et al., “Oxygen-isotope effect on density wave transitions in La3Ni2O7,” Physical Review Research
8, L012055 (2026); arXiv:2504.08290.
[5] R. Khasanov et al., “Multiple Magnetic Transitions in the Trilayer Nickelate Pr4Ni3O10 Revealed by Muon-Spin
Rotation,” Superconductor Science and Technology 39, 085020 (2026); arXiv:2603.11823.
[6] R. Khasanov et al., “Pressure-Invariant Isotope Effect as Evidence for Electronically Driven Intertwined Order
in Pr4Ni3O10,” accepted for publication as a Letter in Physical Review B (2026); arXiv:2603.20871.
[7] R. Khasanov et al., “Magnetism of the alternating monolayer-trilayer phase of La3Ni2O7,” arXiv:2512.22371
(2025).
[8] I. Plokhikh et al., “Unraveling Spin Density Wave Order in Layered Nickelates La3Ni2O7 and La2PrNi2O7 via
Neutron Diffraction,” Physical Review Research 8, 033151 (2026); arXiv:2503.05287.
[9] L. B. Braz et al., “Density waves in low-pressure bilayer nickelates,” arXiv:2606.29527 (2026).