Surface magnetism of Rh(001) from LDA+U calculations

M. Altarelli; N. Binggeli; N. Stojic

REVIEW

Surface magnetism of Rh(001) from LDA+U calculations

N. Stojic, N. Binggeli, M. Altarelli

Materials Science · Submitted 6 Mar 2006 · 34 references

Pith's verdict: First realistic ab initio calculation to find Rh(001) surface magnetism, but the result is contingent on the SIC double-counting choice and an uncertain Ueff, so the claim that it resolves the experiment-theory gap is not supported.

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arXiv IDcond-mat/0603127 (version 1)

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CitationM. Altarelli, N. Binggeli, N. Stojic. "Surface magnetism of Rh(001) from LDA+U calculations." arXiv:cond-mat/0603127 (2006). https://pith.science/paper/E542MP7Z

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Editor's note

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Dear X,

The thing to know: this is the first realistic ab initio calculation to find a ferromagnetic ground state for the clean Rh(001) surface, and it does so with LDA+U, a method not usually applied to weakly correlated metals. The qualitative result is new. The problem is that the paper's central physical claim—that this resolves the long-standing experiment-theory discrepancy—rests on two choices that are not independently pinned down: the value of Ueff and the double-counting correction.

What the paper does well: the execution is careful. Two independent codes (FLAPW and pseudopotential plane-wave), convergence tests, relaxation check, and a check that bulk Rh stays nonmagnetic at all Ueff used. They also applied the same method to Mo, Ru, W, and Ir surfaces and found no magnetism, which is a useful control. The layer-resolved moments and spin-density maps are plausible, and the authors are honest about the uncertainty in Ueff (they quote error bars of about 1 eV) and about the fact that the calculated moment at Ueff = 2.5 eV (1.24 μB) is an order of magnitude larger than the 0.1–0.2 μB estimated by Wu et al.

The soft spot is the double-counting dependence, and the stress-test note has it right. With the SIC correction, the ferromagnetic solution starts at Ueff ≈ 1.2 eV. With the mean-field correction—equally standard, implemented in the same code—the first magnetic solution appears only near Ueff ≈ 3 eV, with m5 = 0.10 μB and essentially degenerate energies. Since the bulk-derived Ueff is 2.8 eV, the mean-field correction gives no meaningful moment at the estimated physical value. The authors mention this in footnote 33, but then the summary says "in all cases we obtain a stable surface magnetic solution... for values of Ueff smaller than, or comparable to the calculated Ueff." That is an overstatement. The existence of the magnetic state currently depends on preferring SIC over mean-field, and no first-principles criterion is given.

So the secure result is the conditional statement: if you adopt SIC-LDA+U with Ueff ≥ 1.2 eV, the Rh(001) surface is magnetic. The broader conclusion that this explains the experiments is not secured by the data in front of you.

Who this is for: people working on surface magnetism of 4d/5d metals, and anyone interested in the reliability of LDA+U outside strongly correlated systems. It deserves a serious referee—the calculations are solid and the result is interesting enough to warrant discussion—but the referee should push for scaled-back conclusions and an explicit discussion of the double-counting ambiguity. I would not cite it as strong evidence for the experimental resolution, but I would cite it as a documented case of LDA+U's sensitivity to methodological choices.

Referee report

Significance

If robust, the result would be an important counterexample to the usual picture of Rh(001) as a nonmagnetic surface and would provide a correlation-based resolution of a long-standing discrepancy. The numerical work is careful and honest: convergence tests set the energy accuracy at 2 meV and the moment accuracy at 0.02 mu_B; two independent electronic-structure codes are used; relaxation, spin-orbit, and defect effects are checked; and several nonmagnetic control surfaces are computed. The central limitation, however, is that the physics is controlled by the input parameter Ueff and by the chosen double-counting correction: under the mean-field double-counting scheme the magnetic state is essentially absent at the estimated Ueff = 2.8 eV. The predicted moment at Ueff = 2.5 eV is also an order of magnitude larger than the 0.1-0.2 mu_B estimated experimentally. The paper is therefore better read as a well-executed demonstration that LDA+U can produce a magnetic Rh(001) solution for sufficiently large Ueff, rather than as a robust quantitative prediction of the surface moment.

Major objections (3)

[Table I and Footnote 33] The central claim is not robust to the choice of double-counting correction. With the SIC correction, the ferromagnetic solution appears at Ueff = 1.2 eV and is strongly stabilized at larger Ueff, but with the mean-field correction (Footnote 33) the first magnetic solution appears only near Ueff ~ 3 eV, with m5 = 0.10 mu_B and essentially zero energy gain; even at 3.5 eV, m5 = 0.18 mu_B and DeltaEsurf = -5.4 meV. Since the estimated Ueff is 2.8 eV, the mean-field correction gives no meaningful ferromagnetic stabilization at the physical value. The summary statement that "in all cases we obtain a stable surface magnetic solution ... for values of Ueff smaller than, or comparable to the calculated Ueff" is therefore not accurate. The authors should either provide a first-principles justification for preferring the SIC double-counting over the mean-field double-counting at this level of theory, or explicitly state that the predicted magnetism is contingent on the double-counting choice.
[Text near Table I] The prediction is extremely sensitive to the input parameter Ueff, and the threshold value is not safely separated from the estimated physical value. The authors state that calculated U and J values have error bars of order 1 eV; under the SIC scheme the magnetic solution disappears below Ueff = 1.2 eV, and under the mean-field scheme it disappears below about 3 eV. A surface-specific estimate of Ueff, or at least a systematic propagation of the stated 1 eV uncertainty, is needed to determine whether the physical Rh(001) surface is actually predicted to be magnetic. Without this, the conclusion that LDA+U "predicts" surface magnetism is weakened to a statement that a magnetic solution exists for sufficiently large Ueff.
[Experimental comparison paragraph] The quantitative agreement with experiment is not established. At Ueff = 2.5 eV, the calculated surface moment of 1.24 mu_B is an order of magnitude larger than the experimental estimate of 0.1-0.2 mu_B by Wu et al. The authors correctly note that temperature effects prevent a direct comparison, but this means the abstract's claim of "offering a solution to the long-standing discrepancy" should be qualified. The paper demonstrates a qualitative possibility of surface magnetism, not a quantitative resolution, and the summary should be phrased accordingly.

Minor objections (5)

[Abstract and Table I] The abstract states that the moment increases "for Ueff >= 1.2 eV," and Table I indeed shows m5 = 0.07 mu_B at 1.2 eV; however, the abstract's emphasis on the threshold would be clearer if it also noted that below 1.2 eV there is no ferromagnetic solution.
[Summary paragraph] The summary repeats that stable solutions are obtained "for values of Ueff smaller than, or comparable to the calculated Ueff," but Table I ends at 2.5 eV, below the estimated 2.8 eV. A calculation at Ueff = 2.8 eV under the SIC scheme would make this statement direct and would strengthen the paper.
[Figure 1] Figure 1 shows magnetic moments only for layers 0 through 5, but the text says the slab has 11 layers; please clarify that the layer labels refer to one half of the symmetric slab, or specify the full layer indexing.
[Figure 2 caption] The caption says the spin density map is in a (100) atomic plane perpendicular to the surface, but the text refers to the "bottom line of atoms" as the center of the slab; please specify the exact plane and the viewing direction, and clarify which line corresponds to the center.
[Throughout] The method is called "LDA+U" although the exchange-correlation functional is GGA; this is conventional but potentially confusing, and a sentence noting that "LDA+U" here means "GGA+U" would help the reader.

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The paper

The paper claims

GGA+U calculations yield a ferromagnetic Rh(001) surface for Ueff of at least 1.2 eV, with the surface moment reaching 1.24 mu_B at Ueff = 2.5 eV.

The reading

Rhodium metal is not magnetic in its bulk form, but some experiments report a weak magnetic moment on its (001) surface, and older density functional theory (DFT) calculations could not reproduce this. This paper applies DFT with an extra on-site Coulomb repulsion term, known as LDA+U, to a slab of rhodium. The extra term penalizes two electrons sitting in the same 4d orbital. The authors scan the strength of this repulsion, called Ueff, from zero to 2.5 eV. Below 1.2 eV the surface stays nonmagnetic; at 1.2 eV and above, a ferromagnetic solution appears and is lower in energy than the nonmagnetic one. The magnetic moment on the outermost atoms grows from 0.07 mu_B at 1.2 eV to 1.24 mu_B at 2.5 eV. The authors estimate Ueff for rhodium as about 2.8 eV using a simpler tight-binding method, which is inside the magnetic range. They also check that other 4d and 5d surfaces (Mo, Ru, W, Ir) remain nonmagnetic with the same scheme, so LDA+U does not trivially make every surface magnetic. The calculated moment at the physically estimated Ueff is considerably larger than the experimental estimate of 0.1 to 0.2 mu_B, and the authors note that temperature effects and the uncertainty in Ueff prevent a quantitative comparison. The core conclusion is that the missing ingredient in older calculations may be the on-site Coulomb repulsion, not some other mechanism.

Extended reading notes

Core claim

The paper's central claim is that 'the application of the GGA plus on-site Coulomb interaction U method predicts surface magnetism, thus offering a solution to the long-standing discrepancy between experiment and theory.' More specifically, the ferromagnetic solution becomes stable for Ueff >= 1.2 eV, with m5 = 1.24 mu_B at Ueff = 2.5 eV, and the authors conclude that corrected non-local exchange-correlation is the key ingredient for an accurate DFT description of this surface.

Load-bearing premise

The load-bearing assumption is that the effective on-site Coulomb parameter Ueff for the Rh(001) surface is at least about 1.2 eV, and that the bulk-derived estimate Ueff ~ 2.8 eV (U = 3.4 eV, J = 0.6 eV from TB-LMTO) transfers to the surface. The authors state that calculated U and J values have error bars of about 1 eV, so a surface Ueff below 1.2 eV is not excluded. If Ueff were below threshold, the LDA+U calculation would give a nonmagnetic ground state and the proposed explanation of the experimental discrepancy would fail. This assumption is separate from the execution of the DFT calculations themselves.

Original abstract

We report calculations indicating the presence of a surface magnetic moment for Rh(001), motivated by the detection of a finite moment by magnetic linear dichroism experiments. We show that, while the density functional with the local density or generalized gradient approximations (LDA and GGA) for exchange and correlation yields a non-magnetic ground state, the application of the GGA plus on-site Coulomb interaction U method predicts surface magnetism, thus offering a solution to the long-standing discrepancy between experiment and theory. The calculated moment on the outermost Rh atom increases with the strength of the effective on-site parameter Ueff=U-J, for Ueff>=1.2 eV, and is as large as 1.24 mu_B for Ueff=2.5 eV.

The compiled record

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.

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,135 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.21 · human participants 0.01 · controlled comparison 0.43 · randomized assignment 0.01 · states quantitative result 0.99 · compares with prior results 0.96 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

We report calculations indicating the presence of a surface magnetic moment for Rh(001), motivated by the detection of a finite moment by magnetic linear dichroism experiments. We show that, while the density functional with the local density or generalized gradient approximations (LDA and GGA) for exchange and correlation yields a non-magnetic ground state, the application of the GGA plus on-site Coulomb interaction U method predicts surface magnetism, thus offering a solution to the long-standing discrepancy between experiment and theory. The calculated moment on the outermost Rh atom increases with the strength of the effective on-site parameter Ueff=U-J, for Ueff>=1.2 eV, and is as large as 1.24 mu_B for Ueff=2.5 eV.

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	We report calculations indicating the presence of a surface magnetic moment for Rh(001), motivated by the detection of a finite moment by magnetic linear dichroism experiments.	result 0.51	0.89	0.44	hedged possibility 0.98
s1	We show that, while the density functional with the local density or generalized gradient approximations (LDA and GGA) for exchange and correlation yields a non-magnetic ground state, the application of the GGA plus on-site Coulomb interaction U method predicts surface magnetism, thus offering a solution to the long-standing discrepancy between experiment and theory.	result 0.51	0.90	0.80	asserted 1.00
s2	The calculated moment on the outermost Rh atom increases with the strength of the effective on-site parameter Ueff=U-J, for Ueff>=1.2 eV, and is as large as 1.24 mu_B for Ueff=2.5 eV.	result 1.00	0.94	0.23	asserted 1.00

What kind of paper the classifier reports this is: simulation study 0.99 · evidence from simulation or computation 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.** FIG. 1: (Color online) Distribution of magnetic moments per

**Figure 2.** FIG. 2: Spin density difference map (in e/

Figures reproduced from arXiv:cond-mat/0603127 by the authors.

References

Works cited (34)

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author P. Blaha , author K. Schwarz , author G. Madsen , author D. Kvasnicka , and author J. Luitz , title WIEN2k, An Augmented Plane Wave + Local Orbitals Program for Calculating Crystal Properties ( publisher Karlheinz Schwarz, Technical Universitat Wien, Austria , year 2001 )

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author A. M. Begley , author S. K. Kim , author F. Jona , and author P. M. Marcus , journal Phys. Rev. B volume 48 , pages 12326 ( year 1993 )

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author S. L. Dudarev , author G. A. Botton , author S. Y. Savrasov , author C. J. Humphreys , and author A. P. Sutton , journal Phys. Rev. B volume 57 , pages 1505 ( year 1998 )

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author O. Jepsen , author G. Krier , author A. Burkhardt , and author O. K. Andersen , title Tight-Binding LMTO Vers. 4.7 ( publisher Max-Planck-Institut f \"u r Festk \"o rperforschung, O. K. Andersen, Stuttgart, Germany , year 1994 )

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author I. V. Solovyev , author P. H. Dederichs , and author V. I. Anisimov , journal Phys. Rev. B volume 50 , pages 16861 ( year 1994 )

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author A. M. N. Niklasson , author S. Mirbt , author H. L. Skriver , and author B. Johansson , journal Phys. Rev. B volume 56 , pages 3276 ( year 1997 )

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note We calculated a 13-layer slab and found its surface carries a magnetic moment similar to the moment at the surface of an 11-layer slab

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author S. Baroni , author A. D. Corso , author S. de Gironcoli , and author P. Giannozzi , ://www.pwscf.org

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author A. M. Rappe , author K. M. Rabe , author E. Kaxiras , and author J. D. Joannopoulos , journal Phys. Rev. B. volume 41 , pages R1227 ( year 1990 )

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[32]

note For U_ eff =2 eV, the magnetic moment on the surface Rh atom, m_5 , equals 0.44 _B and the E_ surf is -9.4 meV. For U_ eff =2.2 eV, m_5=0.62 _B and E_ surf =-15.2 meV

View on Pith
[33]

note The first magnetic solution was observed for U_ eff =3 eV, with m_5= 0.10 _B , but with virtually degenerate energies of magnetic and non magnetic solutions. For U_ eff =3.5 eV, the moment on the outermost Rh atom raised to 0.18 _B , and E_ surf =-5.4 meV

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author M. Wierzbowska , author A. Delin , and author E. Tosatti , journal Phys. Rev. B volume 72 , pages 035439 ( year 2004 )

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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]

author A. Goldoni , author A. Baraldi , author G. Comelli , author S. Lizzit , and author G. Paolucci , journal Phys. Rev. Lett. volume 82 , pages 3156 ( year 1999 )

View on Pith 1999

[2] [2]

author A. Goldoni , author A. Baraldi , author M. Barnaba , author G. Comelli , author S. Lizzit , and author G. Paolucci , journal Surf. Sci. volume 454-456 , pages 925 ( year 2000 )

View on Pith 2000

[3] [3]

author S. C. Wu , author K. Garrison , author A. M. Begley , author F. Jona , and author P. D. Johnson , journal Phys. Rev. B volume 49 , pages R14081 ( year 1994 )

View on Pith 1994

[4] [4]

note See, for example: A. Eichler and J. Hafner and J. Furthmuller and G. Kresse, Surf. Sci. 346 , 300 (1996)

View on Pith 1996

[5] [5]

author J.-H. Cho and author M. Scheffler , journal Phys. Rev. Lett. volume 78 , pages 1299 ( year 1997 )

View on Pith 1997

[6] [6]

author J.-H. Cho and author M.-H. Kang , journal Phys. Rev. B volume 52 , pages R13805 ( year 1995 )

View on Pith 1995

[7] [7]

author G. Cipriani , title International School for Advanced Studies (SISSA), Trieste, PhD thesis : Ab-initio study of oxygen adsorption on selected transition metal surfaces ( year 2000 ), ://www.sissa.it/cm/phd.php

View on Pith 2000

[8] [8]

author C. Barreteau , author R. Guirado-L\'opez , author D. Spanjaard , author M. C. Desjonqu\`eres , and author A. M. Ole\`s , journal Phys. Rev. B volume 61 , pages 7781 ( year 2000 )

View on Pith 2000

[9] [9]

author K. Wildberger , author V. S. Stepanyuk , author P. Lang , author R. Zeller , and author P. H. Dederichs , journal Phys. Rev. Lett. volume 75 , pages 509 ( year 1995 )

View on Pith 1995

[10] [10]

author B. V. Reddy , author S. N. Khanna , and author B. I. Dunlap , journal Phys. Rev. Lett. volume 70 , pages 3323 ( year 1993 )

View on Pith 1993

[11] [11]

author F. Aguilera-Granja , author J. L. Rodr\'iguez-L\'opez , author K. Michaelian , author E. O. Berlanga-Ram\'irez , and author A. Vega , journal Phys. Rev. B volume 66 , pages 224410 ( year 2002 )

View on Pith 2002

[12] [12]

author A. J. Cox , author J. G. Louderback , author S. E. Apsel , and author L. A. Bloomfield , journal Phys. Rev. B volume 49 , pages R12295 ( year 1994 )

View on Pith 1994

[13] [13]

author A. Delin and author E. Tosatti , journal J. Phys.:Condens. Matter volume 16 , pages 8061 ( year 2004 )

View on Pith 2004

[14] [14]

author O. Eriksson , author R. C. Albers , and author A. M. Boring , journal Phys. Rev. Lett. volume 66 , pages 1350 ( year 1991 )

View on Pith 1991

[15] [15]

author S. Bl \"u gel , journal Phys. Rev. Lett. volume 68 , pages 851 ( year 1992 )

View on Pith 1992

[16] [16]

author E. H \"u ger and author K. Osuch , journal Sol. State Comm. volume 131 , pages 175 ( year 2004 )

View on Pith 2004

[17] [17]

note See, for example: P.Mohn, C. Persson, P. Blaha, K. Schwarz, P. Nov\'ak and H. Eschrig, Phys. Rev. Lett. 87 , 196401 (2001)

View on Pith 2001

[18] [18]

author V. I. Anisimov , author I. V. Solovyev , author M. A. Korotin , author M. T. Czyzyk , and author G. A. Sawatzky , journal Phys. Rev. B volume 48 , pages 16929 ( year 1993 )

View on Pith 1993

[19] [19]

author M. T. Czyzyk and author G. A. Sawatzky , journal Phys. Rev. B volume 49 , pages 14211 ( year 1994 )

View on Pith 1994

[20] [20]

author V. I. Anisimov , author J. Zaanen , and author O. K. Andersen , journal Phys. Rev. B volume 44 , pages 943 ( year 1991 )

View on Pith 1991

[21] [21]

author P. Blaha , author K. Schwarz , author G. Madsen , author D. Kvasnicka , and author J. Luitz , title WIEN2k, An Augmented Plane Wave + Local Orbitals Program for Calculating Crystal Properties ( publisher Karlheinz Schwarz, Technical Universitat Wien, Austria , year 2001 )

View on Pith 2001

[22] [22]

author A. M. Begley , author S. K. Kim , author F. Jona , and author P. M. Marcus , journal Phys. Rev. B volume 48 , pages 12326 ( year 1993 )

View on Pith 1993

[23] [23]

author J. P. Perdew , author K. Burke , and author M. Ernzerhof , journal Phys. Rev. Lett. volume 77 , pages 3865 ( year 1996 )

View on Pith 1996

[24] [24]

author H. Sawada , author Y. Morikawa , author K. Terakura , and author N. Hamada , journal Phys. Rev. B volume 56 , pages 12154 ( year 1997 )

View on Pith 1997

[25] [25]

author S. L. Dudarev , author G. A. Botton , author S. Y. Savrasov , author C. J. Humphreys , and author A. P. Sutton , journal Phys. Rev. B volume 57 , pages 1505 ( year 1998 )

View on Pith 1998

[26] [26]

author O. Jepsen , author G. Krier , author A. Burkhardt , and author O. K. Andersen , title Tight-Binding LMTO Vers. 4.7 ( publisher Max-Planck-Institut f \"u r Festk \"o rperforschung, O. K. Andersen, Stuttgart, Germany , year 1994 )

View on Pith 1994

[27] [27]

author I. V. Solovyev , author P. H. Dederichs , and author V. I. Anisimov , journal Phys. Rev. B volume 50 , pages 16861 ( year 1994 )

View on Pith 1994

[28] [28]

author A. M. N. Niklasson , author S. Mirbt , author H. L. Skriver , and author B. Johansson , journal Phys. Rev. B volume 56 , pages 3276 ( year 1997 )

View on Pith 1997

[29] [29]

note We calculated a 13-layer slab and found its surface carries a magnetic moment similar to the moment at the surface of an 11-layer slab

View on Pith

[30] [30]

author S. Baroni , author A. D. Corso , author S. de Gironcoli , and author P. Giannozzi , ://www.pwscf.org

View on Pith

[31] [31]

author A. M. Rappe , author K. M. Rabe , author E. Kaxiras , and author J. D. Joannopoulos , journal Phys. Rev. B. volume 41 , pages R1227 ( year 1990 )

View on Pith 1990

[32] [32]

note For U_ eff =2 eV, the magnetic moment on the surface Rh atom, m_5 , equals 0.44 _B and the E_ surf is -9.4 meV. For U_ eff =2.2 eV, m_5=0.62 _B and E_ surf =-15.2 meV

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[33] [33]

note The first magnetic solution was observed for U_ eff =3 eV, with m_5= 0.10 _B , but with virtually degenerate energies of magnetic and non magnetic solutions. For U_ eff =3.5 eV, the moment on the outermost Rh atom raised to 0.18 _B , and E_ surf =-5.4 meV

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[34] [34]

author M. Wierzbowska , author A. Delin , and author E. Tosatti , journal Phys. Rev. B volume 72 , pages 035439 ( year 2004 )

View on Pith 2004