Ferromagnetic cluster spin waves in molecular disks studied by inelastic neutron scattering

Nehrkorn, Joscha; Mukherjee, Shreya; Stuiber, S.; Mutka, H.; Strässle, Th.; Christou, George; Waldmann, Oliver

doi:10.1103/physrevb.86.134417

Cited by 5 publications

(16 citation statements)

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“…The representation presented in this work will hopefully establish a similarly useful tool for studying ferromagnetic molecules. Finally, FCSWT is applied to three different molecules, the Mn 10 supertetrahedron [23], a Mn 7 disk-like molecule [24], and a Mn 6 single molecule magnet [25]. These three molecules were studied previously using inelastic neutron scattering (INS), which permits direct observation of spin wave excitations and which is thus a primary tool for their experimental investigation [3,26].…”

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confidence: 99%

Ferromagnetic Cluster Spin Wave Theory: Concepts and Applications to Magnetic Molecules

Prša

Waldmann

2018

Inorganics

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Ferromagnetic cluster spin wave theory (FCSWT) provides an exact and concise description of the low-energy excitations from the ferromagnetic ground state in finite magnetic systems, such as bounded magnetic molecules. In particular, this theory is applicable to the description of experimental inelastic neutron scattering (INS) spectra at low temperatures. We provide a detailed conceptual overview of the FCSWT. Additionally, we introduce a pictorial representation of calculated wavefunctions, similar to the usual depiction of vibrational normal modes in molecules. We argue that this representation leads to a better intuitive understanding of the excitations, their symmetry properties, and has links to the energy and wavevector dependence of intensity in the neutron scattering experiments. We apply FCSWT and illustrate the results on a series of examples with available low-temperature INS data, ranging from the Mn 10 supertetrahedron, the Mn 7 disk to the Mn 6 single molecule magnet.Inorganics 2018, 6, 49 2 of 25 assumption of an ordered ground state, which in fact could be regarded as the hallmark feature of the spin wave theories.SWT is widely applied to extended magnets, in one, two, and three dimensions [12][13][14][15]. The elementary excitations correspond to waves, where the spins precess around the polarized orientation in the ground state, with phase differences between the spins described by a wave vector. Applications of SWT to magnetic clusters as small as magnetic molecules, which typically contain a dozen or so magnetic centers or less, is in contrast very scarce. This is so for a number of reasons, one is that the starting assumption of an ordered ground state is strictly never realized, and the validity of the SWT procedure is thus questionable. A notable exception is the class of magnetic molecules in which predominant ferromagnetic exchange interactions between the spins in the molecule stabilize the ferromagnetic or fully polarized ground state. Here, the theoretical methods of SWT become exact at zero temperature, for molecules of any size or composition. Luckily, this comprises quite a number of experimentally relevant magnetic molecules, such as high-spin molecules, Lanthanide containing clusters, or single molecule magnets.Few molecules with antiferromagnetic couplings were analyzed using SWT techniques [16][17][18][19][20][21][22]. The focus in this work is however on the ferromagnetically coupled clusters, for which SWT is guaranteed to work exactly for the ground state and the zero-temperature excitations. When applied to small, bounded ferromagnetic clusters, the SWT techniques and their results are similar in many respects to those in extended systems, but also notable differences exist. Therefore, in order to make the distinction apparent, and to avoid potential confusion, we use the term Ferromagnetic Cluster Spin Wave Theory (FCSWT) for the set of techniques relevant in bounded clusters.It should be mentioned that the use of the word "spin wave" in the context of bounded spin systems...

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confidence: 99%

Ferromagnetic Cluster Spin Wave Theory: Concepts and Applications to Magnetic Molecules

Prša

Waldmann

2018

Inorganics

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“…In this section the zero‐temperature INS intensities of three molecules, denoted as Mn 7 , Mn 10 , and Mn 6 , will be discussed for illustration. They were chosen because they all display a polarized ferromagnetic ground state, i.e., FCSWT applies, and were previously studied experimentally by (powder) INS at low temperatures, , . They however differ by symmetries and geometrical arrangements in space, and magnetism: The Mn 7 and Mn 10 molecules can be described by isotropic exchange‐only spin Hamiltonians whereas Mn 6 is a single‐molecule magnet (SMM) and exhibits an Ising anisotropy in addition.…”

Section: Resultsmentioning

confidence: 99%

“…Finally, the zero‐temperature powder INS spectrum of Mn 7 is discussed. It was experimentally measured and analyzed in much detail in ref …”

Section: Resultsmentioning

confidence: 99%

“…The low-temperature magnetic properties can be explained by a Heisenberg model with four exchange interaction constants. The exchange couplings were experimentally determined to J a = J b = 5.8 K, J 1 = -2.0 K and J 2 = 2.45 K [32] . The anisotropy of the system is zero within experimental error.…”

Section: The Mn 7 Moleculementioning

confidence: 99%

“…It was experimentally measured and analyzed in much detail in ref. [32] . In the following the focus will be on the Q dependence of the INS intensity.…”

Section: The Mn 7 Moleculementioning

confidence: 99%

See 2 more Smart Citations

Inelastic Neutron Scattering Intensities of Ferromagnetic Cluster Spin Waves

Prša

Waldmann

2019

Eur J Inorg Chem

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Inelastic neutron scattering (INS) is the key method for studying magnetic spectra. For ferromagnetic molecular nanomagnets the ferromagnetic cluster spin wave theory (FCSWT) exactly describes the low‐energy excitations from the ferromagnetic ground state. We provide a procedure starting from these molecular spin wave modes and ending with the experimentally observable INS spectra. The formulas for powder and single‐crystal spectra of isotropic and anisotropic ferromagnetic molecules are given. The INS interference pattern can be written in terms of “basis functions” fixed by the molecular geometry. We argue that this decomposition explicates the INS data when the spin wave modes are known and, vice versa, suggests a method to directly determine the quantum wavefunctions of the spin wave excitations based on the INS interference pattern. The calculation of INS observables is exemplified on three molecules: the Mn7 disc, the Mn10 supertetrahedron, and the Mn6 single molecule magnet.

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Ligand Effect on the Single-Molecule Magnetism of Tetranuclear Co(II) Cubane

Wang

Chen

et al. 2017

Inorg. Chem.

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A clear dependence on the ligand has been observed for the magnetic properties of a closely related series of Co(II) cubane structures, viz. [Co(mbm or bm)(ROH)Br] (1-MeOH, 1-EtOH, 2-MeOH, and 2-EtOH, where 1 = [Co(mbm)Br], 2 = [Co(bm)Br], bm = (1H-benzo[d]imidazol-2-yl)methanolate. and mbm = 1-Me-bm.) The [Co(OR)] cubane core consists of an octahedral Co center chelated by the alkoxide oxygen and imidazole nitrogen atoms from monoanionic bm or mbm and coordinated by methanol/alcohol and bromine. Interestingly, electrospray ionization mass spectrometry (ESI-MS) indicates that 1-MeOH and 2-MeOH are unstable in methanol and transformed to the butterfly [CoL] but that 1-EtOH and 2-EtOH are stable in ethanol. Their magnetic susceptibilities suggest ferromagnetic coupling between the nearest cobalt centers to give a theoretical S = 4 × 3/2 ground state with considerable magneto-crystalline behavior. The packing and intermolecular interactions appear to influence the geometry of the cubes and thus the anisotropy of cobalt, which leads to different blocking temperatures (T). Consequently, the compounds with mbm, 1-MeOH and 1-EtOH, exhibit T > 2 K as shown by the relaxation of magnetization in zero applied dc field where the barriers U/k are respectively 27 and 21 K and relaxation times are τ = 1.3 × 10 and 9.7 × 10 s. However, the compounds with bm, 2-MeOH and 2-EtOH, remain paramagnetic above 2 K and do not show nonlinear response of the ac susceptibilities. These findings reaffirm the subtle dependence of single-molecule magnetism on coordination geometry and intermolecular interaction.

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Ferromagnetic cluster spin waves in molecular disks studied by inelastic neutron scattering

Cited by 5 publications

References 58 publications

Ferromagnetic Cluster Spin Wave Theory: Concepts and Applications to Magnetic Molecules

Ferromagnetic Cluster Spin Wave Theory: Concepts and Applications to Magnetic Molecules

Inelastic Neutron Scattering Intensities of Ferromagnetic Cluster Spin Waves

Ligand Effect on the Single-Molecule Magnetism of Tetranuclear Co(II) Cubane

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