One-dimensional magnetic order in the metal-organic framework ${\mathrm{Tb}(\mathrm{HCOO})}_{3}$

One-dimensional magnetic order in the metal-organic framework ${Tb (HCOO)}_{3}$

Daniel R. Harcombe, Philip G. Welch, Pascal Manuel, Paul J. Saines, and Andrew L. Goodwin

Phys. Rev. B 94, 174429 – Published 18 November 2016

Abstract

Variable-temperature neutron scattering measurements, reverse Monte Carlo analysis, and direct Monte Carlo simulation are used to characterize magnetic order in the metal-organic framework (MOF) $Tb {(HCOO)}_{3}$ over the temperature range 100 to $1.6 K = T_{N}$ . The magnetic transition at $T_{N}$ is shown to involve one-dimensional ferromagnetic ordering to a partially ordered state related to the triangular Ising antiferromagnet and distinct from the canonical partially disordered antiferromagnet model. In this phase, the direction of magnetization of ferromagnetic chains tends to alternate between neighboring chains but this alternation is frustrated and is not itself ordered. We suggest the existence of low-dimensional magnetic order in $Tb {(HCOO)}_{3}$ is stabilized by the contrasting strength of inter- and intrachain magnetic coupling, itself a consequence of the underlying MOF architecture. Our results demonstrate how MOFs may provide an attractive if as yet underexplored platform for the realization and investigation of low-dimensional physics.

Received 6 May 2016
Revised 10 October 2016

DOI:https://doi.org/10.1103/PhysRevB.94.174429

Physics Subject Headings (PhySH)

Frustrated magnetism

1-dimensional spin chains

Monte Carlo methods Neutron diffraction

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Daniel R. Harcombe¹, Philip G. Welch^1,2, Pascal Manuel², Paul J. Saines^3,*, and Andrew L. Goodwin¹

¹Department of Chemistry, University of Oxford, Inorganic Chemistry Laboratory, South Parks Road, Oxford OX1 3QR, United Kingdom
²ISIS Facility, Rutherford Appleton Laboratory, Harwell Science and Innovation Campus, Didcot, Oxfordshire OX11 0QX, United Kingdom
³School of Physical Sciences, University of Kent, Canterbury CT2 7NH, United Kingdom

^*P.Saines@kent.ac.uk

Article Text (Subscription Required)

Click to Expand

Supplemental Material (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 94, Iss. 17 — 1 November 2016

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
Crystal structure, key magnetic interaction pathways, and candidate magnetic structures of $Tb {(HCOO)}_{3}$ . (a) ${Tb}^{3 +}$ coordination environments (tricapped trigonal prims; polyhedra) form face-sharing columns parallel to $c$ . Columns are arranged on a triangular lattice and are connected by formate ions, shown here in stick representation. (b) Intrachain exchange pathways are ferromagnetic ( $J_{1}$ ), and the two inequivalent interchain exchange pathways $(J_{2}, J_{3}$ ) are collectively antiferromagnetic. Panels (c) and (d) represent the candidate magnetic structures proposed in Refs. [26, 35]. Circles represent Tb chains projected onto the ( $a, b$ ) plane, symbols $+$ and $-$ denote ferromagnetic chains with magnetizations along $c$ and $- c$ , respectively, and 0 denotes the absence of any ordered moment.
Reuse & Permissions
Figure 2
Temperature-dependent magnetic scattering in $Tb {(DCOO)}_{3}$ and its spinvert analysis. (a) Scattering data are shown as filled circles, with spinvert fits shown as red solid lines. Regions of the scattering pattern contaminated with nuclear scattering have been excluded. The inset shows scattering data collected at 1.6 K within the partially ordered regime together with a small-box spinvert fit. (b) Single-ion anisotropy and pairwise correlation functions at three representative temperatures spanning the paramagnetic regime studied here. The single-ion spin orientation functions are shown in stereographic projection, with colors indicating relative distribution probability $p (θ, ϕ) = ρ (θ, ϕ) / d (cos θ) d ϕ$ ; here $ρ (θ, ϕ)$ is the fraction of total spins within the angular region $d (cos θ), d ϕ$ . Spin correlation functions have been separated into intrachain (top panels) and interchain (bottom panels) terms. RMC and DMC results are shown using filled red and open blue circles, respectively; uncertainties are smaller than the symbols.
Reuse & Permissions
Figure 3
1D magnetic order in $Tb {(HCOO)}_{3}$ . (a) A fragment of the DMC spin configurations at a simulation temperature of 1.5 K is represented in red: Spins within a given chain share a common magnetization direction parallel to the chain axis, with fluctuations away from this vector reflecting the population of spin waves. Projection of these magnetization directions onto the underlying triangular lattice on which chains are arranged gives a realization of the TIA (green and blue arrows). (b) Comparison of the TIA and PDA states with Ising variables represented by green and blue spheres. In both cases every triplet of neighboring Ising states $ε = \pm 1$ obeys the sum rule $| \sum_{i} ε_{i} | = 1$ , but the PDA model contains a honeycomb sublattice (part of which is shown in white outline) with strict antiferromagnetic order. Sites not included in this sublattice adopt random Ising states; for example, of the seven contained within the highlighted region, five correspond to $ε = - 1$ (blue) and two to $ε = + 1$ (green). (c) Comparison of experimental neutron scattering data (black symbols) with neutron scattering patterns calculated for $Tb {(DCOO)}_{3}$ configurations corresponding to TIA (red line) and PDA (green line) states; the ripples are a finite-size effect [48] and are more noticeable for the PDA model because it contains 3D order. Bragg-like features appear at the regions of reciprocal space associated with maxima in the TIA diffuse scattering pattern (inset). (d) The pairwise spin correlation functions for the TIA model separated into intrachain (top) and interchain (bottom) terms. 1D order has two clear signatures in these correlation functions: The correlation length diverges for intrachain spin pairs, and the interchain correlations vanish as interchain separation increases.
Reuse & Permissions

Physical Review B

covering condensed matter and materials physics

One-dimensional magnetic order in the metal-organic framework ${Tb (HCOO)}_{3}$

Daniel R. Harcombe, Philip G. Welch, Pascal Manuel, Paul J. Saines, and Andrew L. Goodwin

Phys. Rev. B 94, 174429 – Published 18 November 2016

Abstract

Physics Subject Headings (PhySH)

Authors & Affiliations

Article Text (Subscription Required)

Supplemental Material (Subscription Required)

References (Subscription Required)

Issue

Access Options

Physical Review B

covering condensed matter and materials physics

One-dimensional magnetic order in the metal-organic framework Tb(HCOO)3

Daniel R. Harcombe, Philip G. Welch, Pascal Manuel, Paul J. Saines, and Andrew L. Goodwin

Phys. Rev. B 94, 174429 – Published 18 November 2016

Abstract

Physics Subject Headings (PhySH)

Authors & Affiliations

Article Text (Subscription Required)

Supplemental Material (Subscription Required)

References (Subscription Required)

Issue

Access Options

Authorization Required

Other Options

Download & Share

Images

Figure 1

Figure 2

Figure 3

Log In

Search

Article Lookup

Paste a citation or DOI

Enter a citation

One-dimensional magnetic order in the metal-organic framework ${Tb (HCOO)}_{3}$