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CONDENSED MATTER

22 NIST CENTER FOR NEUTRON RESEARCH

Spin stripe order in a square planar 

trilayer nickelate

J. Zhang,1,2 D.M. Pajerowski,3 A.S. Botana,1,4 H. Zheng,1 L. Harriger,5 J. Rodriguez-Rivera,5,6 J.P.C. Ruff,7

N.J. Schreiber,8 B. Wang,1 Y.-S. Chen,9 M.R. Norman,1 S. Rosenkranz,1 J.F. Mitchell,1 and D. Phelan1

1 Argonne National Laboratory, Lemont, IL 60439

2 Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831

3 Neutron Scattering Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831

4 Arizona State University, Tempe, AZ 85287

5 NIST Center for Neutron Research, National Institute of Standards and Technology, Gaithersburg, MD 20899

6 University of Maryland, College Park, MD 20742

7 CHESS, Cornell University, Ithaca, NY 14853

8 Cornell University, Ithaca, NY 14853

9 The University of Chicago, Lemont, IL 60439

L

ike medieval knights chasing the Holy Grail, condensed 

matter physicists have long been allured by the glitter of 

high temperature superconductivity. The most famous 

advance in this effort was the Nobel-prize winning discovery 

in 1986 by Bednorz and Müller of superconductivity in 

layered copper oxides. The ensuing years have revealed that 

these materials have certain common features that seem to 

be part of the ‘recipe’ for copper oxide superconductivity: 

they are layered materials containing Cu-O planes; they 

consistently possess the same number of electrons in the 

copper 3d orbitals, which are strongly polarized with holes 

in the dx

2−y2 orbitals; and they are proximal to states where 

the electron spins order antiferromagnetically. Finding similar 

superconductivity in other transition metal oxides has thus 

far proven fruitless, but are copper oxides really the only 

ones? Nickel, which sits one column to the left of copper on 

the periodic table, has long been considered a tantalizing 

alternative for achieving superconductivity in a copper-free 

transition metal oxide. Recently, trilayer nickelates with the 

chemical formula R4Ni3O8 (where R is a trivalent rare earth), 

which possess low valence nickel cations in square planar 

coordination, are particularly interesting candidate materials 

because they possess many of the same characteristics 

identified above as common to copper oxide superconductors 

[1]. Given the importance of magnetic interactions in the 

copper oxide superconductors, as well as in the iron pnictide 

superconductors, unraveling the magnetism in these trilayer 

nickelates is essential for understanding their behavior as well 

as their potential as superconductors. However, relatively few 

detailed investigations have been performed because single 

crystals have been unavailable, leading to a critical gap in our 

understanding of the magnetic behavior of these compounds.

Recently, single crystals of La4Ni3O8 (La-438) have become 

available as a result of the advent of high-pressure floating 

zone technology. La-438 crystals exhibit a semiconductorinsulator transition on cooling that is concomitant with the 

formation of charge stripes of higher and lower oxidation 

state on the nickel sites [2]. One of the major questions 

remaining is whether or not there is magnetic ordering in 

the ground-state, and if there is, how it relates to the charge 

ordering that is observed. Unfortunately, previous neutron 

powder diffraction experiments proved inconclusive. No 

magnetic Bragg reflections were observed from polycrystalline 

materials, either because the peaks were too weak to be 

detected by powder diffraction, or because the system 

did not develop long-range order. In order to resolve this 

quandary, single crystal neutron diffraction measurements 

were performed on MACS [3], which was chosen because of 

its large cold neutron flux, which is beneficial for investigating 

small single crystals with weak magnetic moments, and 

because of its spin-polarization capabilities. 

Weak satellite reflections were observed in the twodimensional plot of neutron intensity in the ground-state 

(Fig. 2A). Spin-polarized diffraction data, collected on MACS 

using the 3He polarizers and analyzers, conclusively evidenced 

a magnetic origin to the scattering – thus proving that 

La4Ni3O8 does have a magnetically-ordered ground-state (Fig. 

2B, C). Using the charge-stripe state as a starting point, an 

antiferromagnetic spin-stripe-ordering model was developed 

in which ordered spins are present on Ni1+ sites (S = 1/2) and 

absent on Ni2+ sites (S = 0), as shown in Fig. 3. The nearest 

neighboring Ni1+ sites have antiferromagnetic interactions 

within the basal plane, as well as antiferromagnetic 

interactions out of the basal plane. The data are consistent 

with a quasi-two-dimensional ordering that occurs within Ni-O 

trilayers that are uncoupled along the c-axis.

Surprisingly, several characteristics were discovered that 

distinguish La4Ni3O8 from copper oxides or single-layer 

nickelates. First, in these latter compounds, charge is the 

primary order parameter, and spin is a secondary order 

parameter that follows the charge. However, for La4Ni3O8
(b) le

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Foreword

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20 CONDENSED MATTER

2019 ACCOMPLISHMENTS AND OPPORTUNITIES 23

the strong coupling between the charge and spin leads to a 

situation in which neither order parameter appears secondary 

to the other. Second, both the polarized data as well as 

density functional theory calculations indicate that the ordered 

spins point parallel and antiparallel to the c-axis. This contrasts 

with other layered oxides, where the spin prefers to orient in 

the basal plane. 

These neutron scattering experiments have laid a foundation 

for our understanding of the magnetic correlations in La4Ni3O8, 

which possesses an electron count that matches the over-doped 

regime of the superconducting cuprates. These experiments 

have revealed how a complex interplay of the spin, charge, 

and orbitals results in coupled charge and spin stripes. The 

next challenge in this work is to modify the electron count so 

that it overlaps the optimal concentration of the copper oxide 

superconductors and then to study how the magnetic and 

charge interactions respond.

References

[1] J. Zhang, A. S. Botana, J. W. Freeland, D. Phelan, H. 

Zheng, V. Pardo, M. R. Norman, J. F. Mitchell, Nat. Phys. 

13, 864 (2017).

[2] J. Zhang, Y.-S. Chen, D. Phelan, H. Zheng, M. R. Norman, 

J. F. Mitchell, Proc. Natl. Acad. Sci. USA 113, 8945 (2016).

[3] J. Zhang, D. M. Pajerowski, A. S. Botana, L. Harriger, J. 

Rodriguez-Rivera, J. P. C. Ruff, N. J. Schreiber, B. Wang, 

Y.-S. Chen, M. R. Norman, S. Rosenkranz, J. F. Mitchell, 

D. Phelan, Phys. Rev. Lett. 122, 247201 (2019).

FIGURE 1: Structural motif of R4Ni3O8 compounds (R = La, Pr, Nd). After [1].

FIGURE 3: Spin-stripe pattern. Blue spheres refer to Ni1+ cations, and red 

spheres to Ni2+ cations. After [3].

FIGURE 2: (A) Unpolarized neutron diffraction data on a specimen of La4Ni3O8

showing weak superlattice peaks in the ground-state. (B, C) Observation of the 

peak in the Spin-Flip (SF) channel evidences magnetic ordering. After [3].