Magnetic order of non-magnetic ions

K. Kubo1) and T. Hotta2)
1): R. G. for Materials Physics for Heavy Element Systems, ASRC, JAEA
2): Tokyo Metropolitan Univ.

Magnetism of a material originates from electrons in it sinceelectrons behave as tiny magnets and align in the same direction
in an ordinary macroscopic magnet. Such a property of anelectron as a magnet is called spin. Thus, the basic researches
for understanding and manipulating spins in materials are very
important.
If there are two electrons in an ion, however, magnetism canbe canceled out by aligning their spins in opposite directions.
Such an ion is called a non-magnetic ion. We call an ion with an
odd number of electrons a Kramers ion and an ion with an evennumber of electrons a non-Kramers ion. To become a nonmagnetic ion, its spins need to be canceled out and it should be a
non-Kramers ion. Conversely, a Kramers ion, for example,
neodymium ion, is always a magnetic ion and a good candidate
for an ingredient of a strong magnet.
On the other hand, non-magnetic ions cannot possessmagnetism in an ordinary manner. However, surprisingly,according to quantum mechanics, which describes themicroscopic world such as ion and electron, a magnetic object ispossible to emerge from non-magnetic objects.
When we have two different non-magnetic states, byfollowing a principle of quantum mechanics, it is allowed toconstruct a “superposed state” by adding these states with acoefficient of the imaginary unit i (Fig. 1). This state has
circulating currents of the electrons and magnetism revives,
since a circulating current generates a magnetic field like aelectromagnet. In this state, the magnetic field produced by thecurrents cannot be described as a single magnet, since thedirection of the axis of the circulation changes depending on
position. Such a state is described by a complex of magnets andis called a higher-order magnetic state.
Such higher-order magnetic states have been investigated andactually discovered in some materials [1-3], but only inmaterials with magnetic ions to date.
To investigate whether it is possible to realize such amagnetic state from non-magnetic states, we have studied atheoretical model for non-Kramers ions with two electrons ineach ion [4]. In this model, we can compose two non-magneticstates for each ion with different shape of electron distribution
as shown in Fig. 1. In both states, the spins of the two electronsalign opposite directions and magnetism is canceled out. Then,
we search for stable states for several kinds of lattice structure.
We find that the alignment of the non-magnetic states [nonmagnetic order, Fig. 2(a)] occurs when ions align along a
direction of a lattice axis. On the other hand, the alignment of
the magnetic states [magnetic order, Fig. 2(b)] occurs when ionsalign along a diagonal direction. Thus, it is interesting to search
lattices in which ions locate diagonal directions for such an
exotic magnetic state.
This work was supported by JSPS KAKENHI Grants No.
JP15K05191, No. JP16H04017, and No. JP16H01079 (JPhysics).

+ i=Fig. 1 Magnetic state composed of non-magnetic states with different
shape of electron distribution. In the red and blue areas, the axes of
the circulating currents are in opposite directions and produce
opposite magnetic fields.

(a)(b)

Fig. 2 (a) Non-magnetic state for ions aligned along a direction of alattice axis. (b) Magnetic state for ions aligned along a diagonal
direction.

Reference[1] J. A. Paixão et al., Phys. Rev. Lett. 89, 187202 (2002).
[2] K. Kubo et al., J. Phys. Soc. Jpn. 72, 1859 (2003).
[3] K. Kubo et al., J. Phys. Soc. Jpn. 73, 216 (2004).
[4] K. Kubo et al., Phys. Rev. B 95, 054425 (2017).