Possible Magnetic Chirality in Optically Chiral Magnet [Cr(CN)$_6$][Mn($S$)-pnH(H$_2$O)](H$_2$O) Probed by Muon Spin Rotation and Relaxation

A. Koda; H. Higashikawa; H. Imai; K. Inoue; K. Ohishi; R. Kadono; S. R. Saha; W. Higemoto

REVIEW

Possible Magnetic Chirality in Optically Chiral Magnet [Cr(CN)$_6$][Mn($S$)-pnH(H$_2$O)](H$_2$O) Probed by Muon Spin Rotation and Relaxation

K. Ohishi, W. Higemoto, A. Koda, S. R. Saha, R. Kadono, K. Inoue, H. Imai, H. Higashikawa

Materials Science · Submitted 1 Mar 2006 · 16 references

Pith's verdict: Solid new muSR data on both enantiomers, but the identical spectra do not establish magnetic chirality—the paper's mirror argument fails if the moments lie in the mirror plane, which the NPD structure allows.

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CitationA. Koda, H. Higashikawa, H. Imai, K. Inoue, K. Ohishi, R. Kadono, S. R. Saha, W. Higemoto. "Possible Magnetic Chirality in Optically Chiral Magnet [Cr(CN)$_6$][Mn($S$)-pnH(H$_2$O)](H$_2$O) Probed by Muon Spin Rotation and Relaxation." arXiv:cond-mat/0603012 (2006). https://pith.science/paper/MAQDUMLN

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The muSR measurements are new and the data look solid, but the paper's central claim—that the two enantiomers have mirror-image magnetic structures—is not supported by the comparison. For powder muSR, only the magnitude of the local field is measured. If the ordered moments lie in the mirror plane, which is at least consistent with the NPD structure (moments near a, no c-component shown), then a crystal-only mirror leaves |B| unchanged at every mirror-related site. The paper's argument in Fig. 5 that case (c) would give different internal fields is algebraically wrong for in-plane moments; the sign changes in the dipole tensor components that the authors mention simply do not affect the field magnitude when the moments have no component along the mirror normal. So the identical GN-(S) and GN-(R) spectra are fully compatible with an achiral magnetic structure.

What is good: this is the first muSR study of this compound, and the observation of four (possibly five) precession frequencies below T_C is a solid characterization of the local magnetic environment. The temperature dependence of the main frequency gives a sensible critical exponent and T_C. The assignment of muon sites near cyano bridges is chemically plausible, and the dipolar field calculation using the NPD structure reproduces the observed frequencies with a reasonable set of sites. That consistency is nice, but note that the muon sites are chosen to match the frequencies, so it is not an independent confirmation of the magnetic structure.

The paper also relies on an unpublished reference (Ref. 9) for prior chirality evidence, which is a weakness in the citation chain.

Who should read this: experimentalists in muSR and molecular magnetism. It is a useful data paper. But the chirality conclusion should be presented as a possibility, not a deduction. To make it stick, the authors would need either single-crystal muSR (which gives field directions), or a quantitative simulation of the alternative hypothesis, or direct evidence for an out-of-plane moment component. As is, the paper deserves peer review but the manuscript should be revised to temper the claim.

Recommendation: send it to review, not desk reject. The experimental work is honest and the data are worth publishing, but the magnetic chirality conclusion should not be the take-away.

Referee report

Major objections (2)

[Fig. 5 and text following Eq. (4)] The inference that identical ZF-muSR spectra in GN-(S) and GN-(R) prove a complete mirror-image magnetic structure is not valid for the geometry considered in Fig. 5. For the mirror r*_i = (x_i, y_i, -z_i) used in the text, the dipole field of Eq. (4) transforms under crystal-only mirroring (case c) as B*(r*) = (B_x, B_y, -B_z) when the ordered moments have no z-component. Hence |B*(r*)| = |B(r)| exactly. Since powder muSR only measures the magnitude of the local field, the precession frequencies in case (c) are identical to those of the complete mirror (case b). The NPD magnetic structure used in the paper is described only as moments 'near the a axis', with no demonstrated out-of-plane component. The statement that case (c) 'would yield different internal fields' is therefore algebraically false for the in-plane case, and the identical GN-(S)/GN-(R) spectra are fully compatible with an achiral magnetic structure.
[Final paragraph before Summary; Fig. 5 caption] The paper provides no quantitative simulation of the powder muSR spectrum for the alternative hypothesis (case c), despite claiming that this case 'would yield different internal fields'. The only cited source of non-collinearity is a hypothetical Dzyaloshinskii-Moriya interaction, and the NPD results are described as moments 'near the a axis'. To support the central conclusion, the authors should either report the full NPD moment components, including any out-of-plane (c-axis) component, or perform a numerical powder-average simulation showing that case (c) is actually distinguishable from case (b) in the measured frequencies. Without one of these, the conclusion that GN-(R) and GN-(S) are a 'complete pair of optical isomers' in the magnetic structure is not established.

Minor objections (5)

[Eq. (1) and Fig. 1 inset] The two-component decomposition at 294 K is described as consistent with the TF-muSR peak amplitudes, but the fitted A1/A2 values from the TF spectrum are not quoted; please give the quantitative comparison.
[Muon site assignment, Fig. 4] The coordinates or fractional occupancies of the assigned muon sites are not given; a table listing the candidate sites and the calculated dipolar fields for each observed frequency, with uncertainties, would make the assignment reproducible.
[Fig. 3 and order-parameter fit] The fit with T_C free gives beta = 0.42(13), which is not a strong constraint for the claim of 3D Heisenberg behavior; a comparison with other critical exponents or a discussion of the uncertainty would be helpful.
[Summary, last line] The phrase 'a pair of complete optical isomer' should be 'a pair of complete optical isomers'.
[Analysis with Eq. (3)] The text says n=5 above 30 K and n=4 below 30 K; please clarify why the fifth component cannot be tracked below 30 K beyond the time-resolution argument, and whether the missing asymmetry in A0 at low temperature affects the fitted amplitudes of the remaining components.

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The paper

The paper claims

Identical muon spectra in mirror-image crystals imply the magnets themselves are mirror images, giving magnetic chirality.

The reading

This paper uses muon spin rotation and relaxation (muSR) to compare local magnetic fields in two enantiomers, mirror-image crystal forms, of the molecule-based chiral magnet [Cr(CN)6][Mn(S)-pnH(H2O)](H2O) and its R counterpart. Below the magnetic ordering temperature, both compounds show four muon precession frequencies that match the internal dipolar fields computed from the average magnetic structure determined by neutron powder diffraction. The muSR spectra of the two enantiomers are virtually identical, which the authors argue means the two crystals are complete mirror images in both atomic arrangement and magnetic moment arrangement. If true, the compound's magnetic structure is itself chiral, making it a candidate for magneto-chiral dichroism and related effects.

What carries the argument

The central tool is zero-field muSR spectroscopy combined with a magnetic dipolar field calculation. The muon precession frequencies give the local internal fields at distinct muon stopping sites, and the dipole tensor formula Aαβ_dip = Σ_i (1/$r_i^{3}$)(3α_iβ_i/$r_i^{2}$ - δαβ) is used to compare those fields with predictions from the neutron-diffraction magnetic structure. The decisive argument is the mirror conversion r*_i = (x_i, y_i, -z_i): applying this to the atomic coordinates changes the signs of certain dipole tensor components, so that a crystal-only inversion would alter the internal fields, whereas a combined crystal-and-magnetic inversion leaves them unchanged. The observed identical spectra therefore point to the latter case.

Extended reading notes

Core claim

The paper reports that zero-field muSR spectra of the optically chiral magnet GN-(S) and its enantiomer GN-(R) are identical below the ferrimagnetic transition near 38 K. Four distinct muon precession frequencies appear in each, corresponding to internal fields at muon sites near the cyano bridges. The observed internal fields match the magnetic dipolar fields calculated from the average noncollinear ferrimagnetic structure suggested by neutron powder diffraction, with no local modulation of moments. Because a purely crystallographic mirror inversion without a matching inversion of magnetic moments would change the dipole tensor components at the muon sites, the identical spectra imply that both the crystal and magnetic structures invert together. Thus the two enantiomers form a complete pair of mirror images in both crystallographic and magnetic terms, supporting the presence of magnetic chirality.

Load-bearing premise

The conclusion that the two enantiomers have mirror-image magnetic structures rests on the assumption that a powder muSR measurement can tell the difference between inverting both the crystal and magnetic structures, which would give identical spectra, and inverting only the crystal structure, which the authors argue would change the internal fields at the muon sites.

Editorial extensions

If this is right

If the two enantiomers have mirror-image magnetic structures, then the magnetic order itself is chiral, giving the compound magneto-chiral dichroism and magnetization-induced second harmonic generation responses that reflect that chirality.
The muon-site assignment and the match to the neutron-diffraction structure confirm that the average magnetic structure is realized locally without additional modulation of Cr or Mn moments.
The sharp temperature dependence of the muon precession frequency indicates three-dimensional magnetic interactions dominate, with critical exponents consistent with a 3D Heisenberg-like ferrimagnet.
The equality of the muSR spectra in the enantiomers provides a method, usable on powder samples, for recognizing when a chiral crystal also carries a chiral magnetic structure.
If the magnetic chirality is robust, it should be observable in field-polarized neutron diffraction on a single crystal, where the chiral magnetic components would break the symmetry differently in (S) and (R) forms.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

A quantitative simulation of the ZF-muSR spectrum for the 'crystal-only inversion' hypothesis of Fig. 5(c) would directly test the paper's central inference; the absence of such a simulation is the main gap.
The same muSR enantiomer-comparison strategy could be applied to other chiral molecule-based magnets, such as those in references [3]-[8], to check whether magnetic chirality is a general feature or specific to this compound.
If the magnetic structure is truly chiral, the sign of the magneto-chiral dichroism should reverse between the two enantiomers, a prediction that could be checked with the same samples used here.
The muon stopping sites near the negatively charged cyano-bridges appear to be identical in both enantiomers, so the existing dipole-field calculation could be refined with first-principles muon-site determination to increase confidence in the chirality conclusion.

Original abstract

Local magnetic fields in a molecule-based optically chiral magnet [Cr(CN)$_6$][Mn($S$)-pnH(H$_2$O)](H$_2$O) (GN-S) and its enantiomer (GN-R) are studied by means of muon spin rotation and relaxation (muSR). Detailed analysis of muon precession signals under zero field observed below T_c supports the average magnetic structure suggested by neutron powder diffraction. Moreover, comparison of muSR spectra between GN-S and GN-R suggests that they are a pair of complete optical isomers in terms of both crystallographic and magnetic structure. Possibility of magnetic chirality in such a pair is discussed.

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The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.20 · human participants 0.02 · controlled comparison 0.35 · randomized assignment 0.01 · states quantitative result 0.09 · compares with prior results 0.70 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; show every role.

Local magnetic fields in a molecule-based optically chiral magnet [Cr(CN)$_6$][Mn($S$)-pnH(H$_2$O)](H$_2$O) (GN-S) and its enantiomer (GN-R) are studied by means of muon spin rotation and relaxation (muSR). Detailed analysis of muon precession signals under zero field observed below T_c supports the average magnetic structure suggested by neutron powder diffraction. Moreover, comparison of muSR spectra between GN-S and GN-R suggests that they are a pair of complete optical isomers in terms of both crystallographic and magnetic structure. Possibility of magnetic chirality in such a pair is discussed.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	Local magnetic fields in a molecule-based optically chiral magnet [Cr(CN)$_6$][Mn($S$)-pnH(H$_2$O)](H$_2$O) (GN-S) and its enantiomer (GN-R) are studied by means of muon spin rotation and relaxation (muSR).	contribution 0.90	0.94	0.05	asserted 0.98
s1	Detailed analysis of muon precession signals under zero field observed below T_c supports the average magnetic structure suggested by neutron powder diffraction.	result 0.63	0.92	0.10	hedged possibility 0.67
s2	Moreover, comparison of muSR spectra between GN-S and GN-R suggests that they are a pair of complete optical isomers in terms of both crystallographic and magnetic structure.	result 0.62	0.92	0.67	hedged possibility 0.99
s3	Possibility of magnetic chirality in such a pair is discussed.	interpretation 0.91	0.36	0.12	hedged possibility 0.81

What kind of paper the classifier reports this is: empirical study 1.00 · evidence from observation or experiment 1.00.

What was examined, and what was not

sources read

arXiv listing abstract v1

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures

**Figure 1.** ZF- and LF-µSR time spectra (decay positron asymmetry), A0Pz(t), in GN-(R) at 294 K. The inset shows the fast Fourier transform of the spectrum at 260 K under a transverse field of 1 T (=135.54 MHz). 0.0 0.1 0.2 0.3 0.4 38.5 K (+0.1) 2.5 K 39.4 K (+0.15) (a) GN-(S) ZF-µSR Asymmetry 0.0 0.1 0.2 0.0 0.1 0.2 0.3 0.4 5.5 K 36.5 K (+0.1) 37.5 K (+0.2) (b) GN-(R) ZF-µSR Asymmetry Time [µs]

**Figure 2.** ZF-µSR time spectra (A0Pz(t)) in (a) GN-(S) and (b) GN-(R) at various temperatures. Note that they are shifted by an equal spacing (0.05 in GN-(S) and 0.1 in GN-(R)) for clarity, respectively. 0 10 20 30 40 0 10 20 30 40 50 GN-(S) GN-(R) ZF-µSR Frequency [MHz] Temperature [K] 0 10 20 30 40 50 60 GN-(S) f 3 f 4 f 2 f 1 ◇ ◇ ◇ ● Fourier Power [a.u.] Frequency [MHz]

**Figure 3.** Temperature dependence of the muon spin precession fr

**Figure 5.** a) A schematic illustration of atomic configurations

Showing 4 of the paper's 5 figures. See all figures in the PDF ↗ Figures reproduced from arXiv:cond-mat/0603012 by the authors.

References

Works cited (16)

[1]

011(2), A osc 2 = 0 . 021(2), A osc 3 = 0 . 002, A osc 4 = 0 . 004(1) and Anon = 0 . 059. In the case of polycrystalline sam- ples, it is predicted that Anon/A 0 is close to 1/3, corre- sponding to the probability that the direction of internal magnetic ﬁeld is parallel to the initial muon spin direc- tion. However, the observed value of Anon/A 0 is sligh...

View on Pith
[2]

G.L.J.A. Rikken and E. Raupach: Nature 390 (1997) 493

View on Pith 1997
[3]

H. Kumagai and K. Inoue: Angew. Chem. Int. Ed. 38 (1999) 1601

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[4]

G. W agniere and A. Mejer: Chem. Phys. Lett. 110 (1984) 546

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[5]

K. Inoue, K. Kikuchi, M. Ohba and H. ¯Okawa: Angew. Chem. Int. Ed. 42 (2003) 4810

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[6]

H. Imai, K. Inoue, K. Kikuchi, Y. Yoshida, M. Ito, T. Sunaha ra and S. Onaka: Angew. Chem. Int. Ed. 43 (2004) 5618

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[7]

K. Inoue, H. Imai, P.S. Ghalsasi, K. Kikuchi, M. Ohba, H. ¯Okawa and J.V. Yakhmi: Angew. Chem. Int. Ed. 40 (2001) 4242

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[8]

R. Andre´ es, M. Bissard, M. Gruselle, C. Train, J. Vaissermann, B. Mal´ ezieux, J.-P. Jamet and M. Verdaguer: Inorg. Chem.40 (2001) 4633

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[9]

K. Inoue et al ., to be published

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[10]

E. Coronado, J.R. Galan-Mascaros, C.J. G´ omez-Garcia an d J.M. Martinez-Agugo, Inorg. Chem. 40 (2001) 113

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A. Hoshikawa, T. Kamiyama, A. Purwanto, K. Ohishi, W. Higemoto, T. Ishigaki, H. Imai and K. Inoue: J. Phys. Soc. Jpn. 73 (2004) 2597

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[12]

A. Schenck: Muon Spin Rotation: Principles and Applications in Solid State Physics (Adam Hilger, Bristol, 1986)

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[13]

J. Kishine, K. Inoue and Y. Yoshida: Prog. Theor. Phys. Su ppl. 159 (2005) 82

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[16]

R. Kubo and T. Toyabe: Magnetic Resonance and Relaxation (ed. by R. Blinc, North-Holland, 1967) 134 135 136 137 TF- μSR HTF = 1 T T = 260 K Real Amplitude [a.u.] Frequency [MHz] 0 2 4 6 8 10 -0.05 0.00 0.05 0.10 0.15 0.20 0.25 HLF = 0 mT HLF = 100 mT GN-( R) T = 294 K Asymmetry Time [ μs] Fig. 1. ZF- and LF- µ SR time spectra (decay positron asymme- try),...

View on Pith 1967
[45]

94(20) MHz, f2 = 23. 89(13) MHz, f3 = 20. 39(8) MHz and f4 = 17 . 27(12) MHz, yielding the respective local magnetic ﬁeld at muon sites, B1 = 338 . 9(1) mT, B2 =

View on Pith
[176]

3(1. 0) mT, B3 = 150. 4(6) mT and B4 = 127. 4(9) mT at the lowest temperature. The comparison strongly sug- gests that all the muon sites are located near the cyano- bridges. This is also supported by the fact that the cyano- base is negatively charged and thereby reduce the elec- trostatic energy associated with the positive charge of muons. Figure 4 sho...

View on Pith

Discussion

Disagree with the review, or know something it missed? Leave a comment, highlight any passage above to comment on it, or challenge this review formally.

[1] [1]

011(2), A osc 2 = 0 . 021(2), A osc 3 = 0 . 002, A osc 4 = 0 . 004(1) and Anon = 0 . 059. In the case of polycrystalline sam- ples, it is predicted that Anon/A 0 is close to 1/3, corre- sponding to the probability that the direction of internal magnetic ﬁeld is parallel to the initial muon spin direc- tion. However, the observed value of Anon/A 0 is sligh...

View on Pith

[2] [2]

G.L.J.A. Rikken and E. Raupach: Nature 390 (1997) 493

View on Pith 1997

[3] [3]

H. Kumagai and K. Inoue: Angew. Chem. Int. Ed. 38 (1999) 1601

View on Pith 1999

[4] [4]

G. W agniere and A. Mejer: Chem. Phys. Lett. 110 (1984) 546

View on Pith 1984

[5] [5]

K. Inoue, K. Kikuchi, M. Ohba and H. ¯Okawa: Angew. Chem. Int. Ed. 42 (2003) 4810

View on Pith 2003

[6] [6]

H. Imai, K. Inoue, K. Kikuchi, Y. Yoshida, M. Ito, T. Sunaha ra and S. Onaka: Angew. Chem. Int. Ed. 43 (2004) 5618

View on Pith 2004

[7] [7]

K. Inoue, H. Imai, P.S. Ghalsasi, K. Kikuchi, M. Ohba, H. ¯Okawa and J.V. Yakhmi: Angew. Chem. Int. Ed. 40 (2001) 4242

View on Pith 2001

[8] [8]

R. Andre´ es, M. Bissard, M. Gruselle, C. Train, J. Vaissermann, B. Mal´ ezieux, J.-P. Jamet and M. Verdaguer: Inorg. Chem.40 (2001) 4633

View on Pith 2001

[9] [9]

K. Inoue et al ., to be published

View on Pith

[10] [10]

E. Coronado, J.R. Galan-Mascaros, C.J. G´ omez-Garcia an d J.M. Martinez-Agugo, Inorg. Chem. 40 (2001) 113

View on Pith 2001

[11] [11]

A. Hoshikawa, T. Kamiyama, A. Purwanto, K. Ohishi, W. Higemoto, T. Ishigaki, H. Imai and K. Inoue: J. Phys. Soc. Jpn. 73 (2004) 2597

View on Pith 2004

[12] [12]

A. Schenck: Muon Spin Rotation: Principles and Applications in Solid State Physics (Adam Hilger, Bristol, 1986)

View on Pith 1986

[13] [13]

J. Kishine, K. Inoue and Y. Yoshida: Prog. Theor. Phys. Su ppl. 159 (2005) 82

View on Pith 2005

[14] [16]

R. Kubo and T. Toyabe: Magnetic Resonance and Relaxation (ed. by R. Blinc, North-Holland, 1967) 134 135 136 137 TF- μSR HTF = 1 T T = 260 K Real Amplitude [a.u.] Frequency [MHz] 0 2 4 6 8 10 -0.05 0.00 0.05 0.10 0.15 0.20 0.25 HLF = 0 mT HLF = 100 mT GN-( R) T = 294 K Asymmetry Time [ μs] Fig. 1. ZF- and LF- µ SR time spectra (decay positron asymme- try),...

View on Pith 1967

[15] [45]

94(20) MHz, f2 = 23. 89(13) MHz, f3 = 20. 39(8) MHz and f4 = 17 . 27(12) MHz, yielding the respective local magnetic ﬁeld at muon sites, B1 = 338 . 9(1) mT, B2 =

View on Pith

[16] [176]

3(1. 0) mT, B3 = 150. 4(6) mT and B4 = 127. 4(9) mT at the lowest temperature. The comparison strongly sug- gests that all the muon sites are located near the cyano- bridges. This is also supported by the fact that the cyano- base is negatively charged and thereby reduce the elec- trostatic energy associated with the positive charge of muons. Figure 4 sho...

View on Pith