Title: 令和 6 年 4 月１日 Zheyuan’s essay
Text: Review on What Neutrons Can Do
When introducing the neutron scattering technique, we always wrote that 'theneutron diffraction probes the lattice and magnetic structure' and 'the inelastic
neutron scattering (INS) probes the phonon and magnon'. Indeed, these properties
already made neutron scattering irreplaceable in condensed-matter research. However,there are far more things that neutron scattering can do if we review the neutroncondensed-matter system in detail.
Viewing from the properties of neutron, things can be divided into two; A.
Neutron interacts with the nucleus itself, as described by the Fermi pseudopotential. B.
Neutron has a spin-1/2, and interacts with the electromagnetic potential.
Viewing from what's in the condensed-matter system, of course we have nucleus
and electrons. They can be further classified as follows; A1. Nucleus itself, B1.
Electron spin & electron orbit*1, B2. Nucleus spin, B3. Nucleus charge & electron
charge, and interplays among them.

According to these frameworks but still limited to my knowledge in this field, I
list what can be detected by neutron scattering.
A1. Nuclear Bragg peak.
Phonon, Charge density wave*2.
Roton: an elementary excitation in Bose–Einstein condensates, e.g. INS on
rotons in liquid helium [1].
B1. Magnetic Bragg peak.
Magnon.
Spinon: fractionalized spin excitation in 1-D Luttinger liquid and quantum spin
liquid, e.g. INS on spinons in a spin-1/2 antiferromagnetic chain CuSO4·5D2O [2].
Magon is an excitation carrying integer magnetization Sz= +1/2 - (-1/2) = 1 inmagnetic long-range order system (paramagnon if short-range order). However,spinon can be excited in either an ordered spin-1/2 antiferromagnetic chain or adisordered spin liquid, carrying a fractional magnetization Sz = 1/2.
Triplon: bound states of spinon pair, e.g. INS on spinons and triplons infrustrated triangular antiferromagnet Cs2CuCl4 [3].
Orbiton: an elementary excitation carries the orbital degree of freedom ofelectrons, e.g. orbitons in the quasi-one-dimensional antiferromagnetic chain Sr2CuO3[4], though detected by resonant inelastic X-ray scattering.
Crystal electric field (CEF) excitation: excitation of the energy level of the spinorbit states*3 due to a static electric field produced by the surrounding anion neighbors.
In most magnetic materials, the ground state of magnetic ions in CEF has a nonzero
spin. This kind of CEF excitations is expected to be dispersiveless in reciprocal space
and well defined in both the magnetically ordered and paramagnetic states.
Magnetic exciton: When the ground state of magnetic ions in CEF is anonmagnetic singlet and the magnetic exchange interaction is relatively large, themagnetic order appears as result of a polarization instability of the singlet state rather
than the alignment of permanent moments. In this case, the magnetic excitations
originate from the CEF levels are called magnetic excitons, e.g. INS on magnetic
excitons in singlet-ground-state ferromagnets fcc Pr and Pr3T1 [5]. They aredispersive and relate to the magnetically ordered state.
Spin-roton: an analogy of the roton in superconductors, e.g. spin-roton in cuprate
superconductors [6].
B2. Disordered nucleus spins result in a part of incoherent (elastic or inelastic)
neutron scattering. This is usually annoying to us but it's actually very useful, e.g.
Hydrogen vibration excitations of ZrH1.8 and TiH1.84 [7].
Ordered nucleus spins appear in nano-Kelvin range in simple metals such as Cu,
Ag, and Rh [8]. This leads to magnetic Bragg peak and theoretically observablemagnon.
B3. Though the net charge of neutron is zero, neutron still weakly interacts with theelectric potential of the electrons and nucleus.
When neutron moves through an electric field (of electrons and nucleus) with afinite velocity, in the frame of neutron, a magnetic field appears. The effect of thismagnetic field to neutron is known as the spin-orbit interaction. Note that here the'spin' means a neutron spin and the 'orbit' means a neutron momentum.
If abandon the point charge approximation, the charge distribution of neutron
will give an electrostatic interaction with electrons and nucleus. This is known as theFoldy effect.
*1 Here we adopt the Born–Oppenheimer approximation, therefore no nucleus orbit.
*2 Realized as a zero-energy phonon mode.
*3 Can be considered as a J-multiplet state, where J is the total angular momentum ofthe ion.
[1] O. W. Dietrich et al., Phys. Rev. A 5, 1377 (1972).
[2] M. Mourigal et al., Nat. Phys. 9, 435 (2013).
[3] M. Kohno et al., Nat. Phys. 3, 790 (2007).
[4] J. Schlappa et al., Nature 485, 82 (2012).
[5] R. J. Birgeneau et al., Phys. Rev. Lett. 27, 1530 (1971).
[6] Y. J. Uemura, Physica B: Condensed Matter 374–375, 1 (2006).

[7] T. Hattori et al., Phys. Rev. B 106, 134309 (2022).
[8] A. S. Oja and O. V. Lounasmaa, Rev. Mod. Phys. 69, 1 (1997).