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such as re-entrant superconductivity, can occur in other quantum materials.
One of the most remarkable properties of the QOBD theory is that it explains order in which moments appear along magnetic hard axes [2]. In zero field, this is manifest by the spiral states SDW1 and SDW2 with modulated moments along both the a-axis (easy-axis) and b-axis (hard-axis) directions. Resonant X-ray scattering for field along the easy axis showed SDW1 and SDW2 are strongly suppressed by an extremely modest field of 0.02 T, in qualitative agreement with QOBD theory. Additionally, SDW1 is found to be strongly polarisable with field, revealing the importance of the anisotropy of different competing phases for understanding why two successive SDW states form on cooling in zero field rather than just one.
Applying a carefully aligned magnetic field along the hard axis had more striking consequences. SDW1 and SDW2 were found to survive up to 2 T, before undergoing a transition to a newly discovered modulated state, SDW3. The SDW3 state persists at high field to the lowest temperatures available, forming a ridge around ferromagnetism. The structure of SDW3, consistent with both experiment and
Fig. 93: The schematic temperature-field phase diagram for PrPtAl with fields applied along the easy a-axis (vertical) and hard b-axis (horizontal) based on resonant X-ray measurements. SDW1 (blue), SDW2 (green), and SDW3 (red) modulated states form a ridge around ferromagnetism (yellow), across which the magnetic moment reverses. The phase boundaries between the different modulated states and on the low-field, low-temperature side of the ridge are first order. Schematics of the moment directions viewed along the c-axis for one modulation period for each SDW state are shown below the phase diagram.
theory, is a modulated fan around the hard b-axis. The results, with schematics of each magnetic structure, are summarised in the temperature-field phase diagram shown in Figure 93. Increasing the field further eventually leads to the suppression of SDW3 and a continuous transition to a polar paramagnetic state. Therefore, SDW3 lies between uniform ferromagnetic and polarised paramagnetic states, with different moment orientations. This provides an ideal setting for the QOBD mechanism, since the difference in energy between the two orientations in this region is low.
Magneto-transport and inelastic neutron scattering measurements also provide compelling evidence that SDW3 is driven by QOBD. Upon entering the SDW3 state, the temperature coefficient of magnetoresistance shows an increase in density of states, while an increase in neutron scattering from magnetic excitations was observed throughout the entire field range that SDW3 spans.
In conclusion, PrPtAl is shown to provide an archetypal example for the experimental realisation of QOBD-induced modulated magnetism. For the first time, magnetic field has been used to tune a ferromagnet into a QOBD-modulated state in the limit of very low temperature. This work could help understand other field-tuneable phenomena.
PRINCIPAL PUBLICATION AND AUTHORS Field-Induced Modulated State in the Ferromagnet PrPtAl , C.D. O Neill (a), G. Abdul-Jabbar (a) D. Wermeille (b), P. Bourges (c), F. Krüger (d,e), A.D. Huxley (a), Phys. Rev. Lett. 126, 197203 (2021); https:/doi.org/10.1103/PhysRevLett.126.197203 (a) School of Physics and CSEC, University of Edinburgh (UK) (b) XMaS/BM28 CRG, ESRF (c) Laboratoire Léon Brillouin (UMR12 CEA-CNRS) (France) (d) London Centre for Nanotechnology, University College London (UK) (e) ISIS, STFC, Rutherford Appleton Laboratory, Chilton (UK)
REFERENCES
[1] G. Abdul-Jabbar et al., Nat. Phys. 11, 321 (2015). [2] M. Brando et al., Rev. Mod. Phys. 88, 025006 (2016).
