Effect of the shape anisotropy on the magnetic configuration of (Ga,Mn)As and its evolution with temperature

K. Hamaya; T. Koike; T. Taniyama; Y. Yamazaki

REVIEW

Effect of the shape anisotropy on the magnetic configuration of (Ga,Mn)As and its evolution with temperature

K. Hamaya, T. Taniyama, T. Koike, Y. Yamazaki

Materials Science · Submitted 6 Mar 2006 · 12 references

Pith's verdict: Qualitative temperature-dependent shape-anisotropy effect is real and worth reporting, but the quantitative Kc/Ks split is not established because the fitted 'Ks' is roughly an order of magnitude too large for the actual wire geometry.

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arXiv IDcond-mat/0603126 (version 1)

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CitationK. Hamaya, T. Koike, T. Taniyama, Y. Yamazaki. "Effect of the shape anisotropy on the magnetic configuration of (Ga,Mn)As and its evolution with temperature." arXiv:cond-mat/0603126 (2006). https://pith.science/paper/FCOAJYN2

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Editor's note

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Hamaya and coauthors report that shape anisotropy increasingly controls the magnetic configuration of a 1.5 μm-wide (Ga,Mn)As wire as temperature rises from 10 to 25 K, because the cubic magnetocrystalline term decays faster. The qualitative observation is real and new: the MR curves change markedly in that narrow window, and at 20 K the remanent magnetization sits along the wire axis even after a perpendicular field. The temperature-dependent resistance in Fig. 4 also shows an abrupt rearrangement near 17 K. For people designing (Ga,Mn)As devices, this is a useful practical hint. The authors are transparent that the anisotropy constants are fitted, not measured.

The quantitative part does not hold up. The fitted Ks at 10 K is about 2000 erg/cm^3, which the paper says is consistent with the infinite-cylinder formula πM^2. But the wire is a 1.5 μm by 100 nm strip. Its transverse demagnetizing factor is roughly t/(w+t)=0.0625, so the magnetostatic shape-anisotropy constant is about 2πM^2 × 0.0625 ≈ 300 erg/cm^3 for M=27.5 emu/cm^3. That is seven times smaller than the fitted value. The fitted 'Ks' is absorbing cubic/uniaxial anisotropy or coherent-rotation model error. If the true shape constant is ~300 erg/cm^3, the claimed Kc/Ks crossover near 20 K is not supported. The MR data may still show an increasing shape influence, but the quantitative mechanism in the paper is not established.

A second soft spot is identifiability. Three anisotropy constants are extracted from a single demagnetizing branch of one MR loop, with no error bars or residuals. Kc and Ks likely trade off in such a fit. The paper does state the coherent-rotation assumption, which is honest, but that does not resolve the trade-off.

Who is this for? Workers in (Ga,Mn)As spintronics and magnetic anisotropy engineering. I would send it to peer review rather than desk reject, because the qualitative temperature dependence is genuinely new and could become a solid reference after the authors correct the shape-anisotropy estimate and either add fit statistics or reframe the conclusion as qualitative.

Referee report

Significance

If the quantitative extraction is reliable, the paper would provide practically useful information for designing (Ga,Mn)As spintronic devices: it identifies a temperature window in which shape anisotropy, rather than the intrinsic magnetocrystalline anisotropy, determines the magnetic easy axis, and it quantifies the crossover far below Tc. The qualitative MR data are convincing: the hysteresis loops change markedly between 10 and 20 K, and the zero-field remanent state aligns along the wire for both field directions, consistent with a growing role of shape anisotropy. The paper is also transparent about its central assumption, explicitly conditioning the analysis on coherent rotation. However, the quantitative conclusion—specifically that Kc drops faster than Ks and that the two cross near 20 K—rests entirely on a three-parameter fit of Eq. (1) to a single branch of one MR loop at each temperature, with no error bars, residual analysis, or parameter-identifiability check.

Major objections (3)

[Results and discussion (Ks calibration paragraph)] The fitted Ks at 10 K is validated by comparison with Ks = M^2/(4µ0), the value for an infinitely long circular cylinder. The measured sample is not a cylinder but a 1.5 µm-wide, 100 nm-thick strip. For a long strip the transverse demagnetizing factor is of order t/(w+t) ≈ 0.06, which gives a magnetostatic shape-anisotropy constant roughly an order of magnitude smaller than the fitted ~2000 erg/cm^3. Thus the fitted Ks is not the bare shape-anisotropy constant; it must absorb contributions from other anisotropy terms or from errors in the single-domain model. Because the central claim is the Kc/Ks crossover near 20 K in Fig. 3, this quantitative mismatch is load-bearing. The authors should replace the cylinder calibration with the actual strip-geometry estimate, or provide a micromagnetic calculation, and re-evaluate the crossover temperature.
[Results and discussion (fitting procedure and Fig. 3)] The anisotropy constants plotted in Fig. 3 are obtained from a three-parameter fit of Eq. (1) to the demagnetizing branch from +500 Oe to 0 Oe of a single MR loop at each temperature. No error bars, residuals, or sensitivity analysis are provided. With three parameters and one smooth curve, there is a real possibility of strong trade-offs between Kc and Ks, both of which affect the shape of the cos^2 φ branch. The conclusion that Kc decreases faster than Ks therefore is not robust as presented. The authors should provide confidence intervals, a fit-quality measure, or a parameter-identifiability test, for example by fixing Ks at the magnetostatic value and refitting the remaining parameters.
[Results and discussion (coherent rotation assumption)] The text states, "Provided that coherent rotation is valid for H perpendicular to the wire, the MR curves are reproduced," and the entire extraction depends on this assumption. The paper does not independently justify coherent rotation for this wire; no micromagnetic simulation, domain imaging, or complementary measurement (e.g., planar Hall effect) is shown. If the reversal involves domain nucleation or domain-wall motion, Eq. (1) is not the appropriate energy functional and the fitted constants do not represent the anisotropy energies. This conditionality is acknowledged by the authors, but it is exactly the load-bearing point for the quantitative temperature trends, and it needs to be addressed with evidence rather than assumed.

Minor objections (5)

[Figure 2 caption] The labels '90°' and '0°' in Fig. 2 are not defined in the caption; please state that they denote the angle between the applied field and the wire axis.
[Introduction and throughout] The paper uses 'magnetic domain configurations' in the title, abstract, and introduction, but the analysis is based on a single-domain coherent rotation model. Please clarify the relationship between the measured configurations and the single-domain assumption, or use more precise terminology.
[Equation (1) and reference [3]] Eq. (1) and the statement that numerical calculation using this formalism is in good agreement with experimental data are both credited to reference [3]. Because the present paper's conclusions depend on this energy functional, the authors should reproduce the essential validation or give the parameter values used for that comparison.
[Ks calibration equation] The expression Ks = M^2/(4µ0) is dimensionally ambiguous as written in the units used in the paper. Please specify the unit system or give the equivalent SI expression so that the reader can verify the numerical value.
[Figure 4 interpretation] The abrupt resistance drop near 17 K in Fig. 4 is interpreted as the onset of a significant shape-anisotropy contribution. A quantitative link between this feature and the temperature dependence of Kc and Ks in Fig. 3 would strengthen the argument; consider adding a brief discussion or a direct comparison.

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The paper

The paper claims

In a (Ga,Mn)As wire, the magnetic configuration becomes dominated by shape anisotropy as temperature rises, because the cubic magnetocrystalline anisotropy weakens faster than the shape anisotropy.

The reading

The paper asks how temperature changes the balance between a wire's shape anisotropy and the intrinsic magnetocrystalline anisotropy of the ferromagnetic semiconductor (Ga,Mn)As. Using magnetoresistance loops and a single-domain coherent-rotation energy model, it claims that the cubic magnetocrystalline term $K_c$ drops with temperature much faster than the shape term $K_s$, so the relative role of shape anisotropy grows as the sample warms. In a 1.5 $\mu$m-wide wire this means the remanent magnetization aligns along the wire axis above roughly 17–20 K, even when the magnetic field was applied perpendicular to the wire. A sympathetic reader would care because patterned (Ga,Mn)As is a candidate building block for spintronic devices, and the result identifies a temperature window in which geometry, not crystal anisotropy, sets the magnetic configuration.

What carries the argument

The central machinery is the total magnetostatic energy model, Eq. (1), which combines a [110] uniaxial term $K_u\sin^2(\phi-45^\circ)$, a $\langle100\rangle$ cubic magnetocrystalline term $(K_c/4)\sin^2 2\phi$, a shape-anisotropy term $K_s\sin^2\phi$, and a Zeeman term $-MH\cos(\phi-\theta)$. Assuming coherent rotation of a single magnetic domain, the equilibrium magnetization angle $\phi$ is obtained from $\partial E/\partial\phi=0$ with a local-minimum condition, and the longitudinal magnetoresistance is taken proportional to $\cos^2\phi$, meaning resistance is highest when magnetization lies perpendicular to the current. Fitting this model to the demagnetizing branch at each temperature lets the authors extract the temperature dependence of all three constants, and it is the mechanism by which they attribute the observed crossover to $K_c$ falling faster than $K_s$.

Extended reading notes

Core claim

The paper's central claim is that in a 1.5 $\mu$m-wide, 200 $\mu$m-long (Ga,Mn)As/GaAs(001) wire patterned along [100], the relative contribution of shape anisotropy to the magnetic configuration increases with temperature and becomes dominant above about 17 K. The evidence is that magnetoresistance curves change character between 10 and 20 K: at 10 K the remanent magnetization can lie away from the wire axis, while by 20 K it aligns along the wire axis for both $H\parallel I$ and $H\perp I$. Fitting the demagnetizing branch (from +500 Oe to 0 Oe) with the total-energy expression $E=K_u\sin^2(\phi-45^\circ)+(K_c/4)\sin^2 2\phi+K_s\sin^2\phi-MH\cos(\phi-\theta)$ yields anisotropy constants $K_u$, $K_c$, and $K_s$ as functions of temperature; the authors find that $K_c$ decreases much more steeply than $K_s$ and that the two become comparable near 20 K. They interpret this as a competition, far below the Curie temperature ($T_c\approx 60$ K), between the intrinsic cubic anisotropy of the zinc-blende lattice and the shape anisotropy of the patterned wire, with shape taking over as temperature increases even though the magnetization—and hence the absolute size of $K_s$—shrinks.

Load-bearing premise

The load-bearing premise is that the wire is a single magnetic domain that reverses by coherent rotation, because only then does fitting the demagnetizing branch of the magnetoresistance uniquely separate the cubic and shape anisotropy constants and establish the claimed temperature crossover.

Editorial extensions

If this is right

Above roughly 17–20 K in the 1.5 $\mu$m wire, the remanent magnetization follows the wire axis for both parallel and perpendicular field histories, so the patterned geometry sets the easy axis despite the crystal and growth-related anisotropies.
Because $K_c$ falls steeply while $K_s$ declines only mildly, the crossover is a sharp point at which the magnetic configuration switches character and could serve as a temperature-controlled switching threshold in a spintronic device.
The extracted 10 K value of $K_s$ is compatible with the infinite-wire estimate $M^2/(4\mu_0)$, supporting the interpretation that the enhanced remanence along the wire is genuinely shape-driven.
The same energy formalism can be applied to other wire widths and hole concentrations, meaning the temperature at which shape anisotropy dominates can be engineered through geometry and doping.

Reading between the lines

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

If the rapid drop of $K_c$ is generic for in-plane magnetized (Ga,Mn)As, the crossover temperature should vary systematically with wire width and aspect ratio; measuring a family of wires would map the shape-design phase diagram that this single-width study leaves implicit.
The paper fits only the demagnetizing branch, so a natural test is to fit the full hysteresis loop with the same constants and check whether one set reproduces both branches, which would rule out spurious parameter trade-offs.
Direct magnetic imaging across 10–25 K would decide whether the configuration change is a coherent rotation or involves nucleation of domains; the paper's energy interpretation predicts no multi-domain textures at remanence once shape dominates.
Because the anisotropy balance also depends on hole concentration, the 17–20 K crossover may be movable by electrostatic gating, which would make the shape-versus-crystal competition a tunable operating point in a semiconductor spintronic device.

Original abstract

We study the effect of the shape anisotropy on the magnetic domain configurations of a ferromagnetic semiconductor (Ga,Mn)As/GaAs(001) epitaxial wire as a function of temperature. Using magnetoresistance measurements, we deduce the magnetic configurations and estimate the relative strength of the shape anisotropy compared with the intrinsic anisotropies. Since the intrinsic anisotropy is found to show a stronger temperature dependence than the shape anisotropy, the effect of the shape anisotropy on the magnetic domain configuration is relatively enhanced with increasing temperature. This information about the shape anisotropy provides a practical means of designing nanostructured spin electronic devices using (Ga,Mn)As.

The compiled record

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What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.08 · human participants 0.02 · controlled comparison 0.07 · randomized assignment 0.01 · states quantitative result 0.06 · compares with prior results 0.11 · 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 study the effect of the shape anisotropy on the magnetic domain configurations of a ferromagnetic semiconductor (Ga,Mn)As/GaAs(001) epitaxial wire as a function of temperature. Using magnetoresistance measurements, we deduce the magnetic configurations and estimate the relative strength of the shape anisotropy compared with the intrinsic anisotropies. Since the intrinsic anisotropy is found to show a stronger temperature dependence than the shape anisotropy, the effect of the shape anisotropy on the magnetic domain configuration is relatively enhanced with increasing temperature. This information about the shape anisotropy provides a practical means of designing nanostructured spin electronic devices using (Ga,Mn)As.

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 study the effect of the shape anisotropy on the magnetic domain configurations of a ferromagnetic semiconductor (Ga,Mn)As/GaAs(001) epitaxial wire as a function of temperature.	contribution 1.00	0.95	0.05	asserted 0.64
s1	Using magnetoresistance measurements, we deduce the magnetic configurations and estimate the relative strength of the shape anisotropy compared with the intrinsic anisotropies.	method 1.00	0.97	0.05	asserted 0.99
s2	Since the intrinsic anisotropy is found to show a stronger temperature dependence than the shape anisotropy, the effect of the shape anisotropy on the magnetic domain configuration is relatively enhanced with increasing temperature.	interpretation 0.53	0.94	0.76	asserted 1.00
s3	This information about the shape anisotropy provides a practical means of designing nanostructured spin electronic devices using (Ga,Mn)As.	interpretation 0.93	0.24	0.12	asserted 0.93

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

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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: Normalized MR curves obtained by numerical calcu

**Figure 4.** FIG. 4: Temperature dependent resistance of a wire sample

Showing 2 of the paper's 4 figures. See all figures in the PDF ↗ Figures reproduced from arXiv:cond-mat/0603126 by the authors.

References

Works cited (12)

[1]

C. R¨ uster, T. Borzenko, C. Gould, G. Schmidt, L. W. Molenkamp, X. Liu, T. Wojtowicz, J. K. Furdyna, Z. G. Yu, and M. E. Flatte, Phys. Rev. Lett. 91, 216602 (2003)

View on Pith 2003
[2]

K. F. Eid, B. L. Sheu, O. Maksimov, M. B. Stone, P. Schiﬀer, and N. Samarth, Appl. Phys. Lett. 86, 152505 (2005)

View on Pith 2005
[3]

K. Hamaya, R. Moriya, A. Oiwa, T. Taniyama, Y. Ki- tamoto, Y. Yamazaki, and H. Munekata, Jpn. J. Appl. Phys. 43, L306 (2004)

View on Pith 2004
[4]

U. Welp, V. K. Vlasko-Vlasov, X. Liu, J. K. Furdyna, and T. Wojtowicz, Phys. Rev. Lett. 90, 167206 (2003)

View on Pith 2003
[5]

K. Hamaya, T. Taniyama, Y. Kitamoto, R. Moriya, and H. Munekata, J. Appl. Phys. 94, 7657 (2003)

View on Pith 2003
[6]

M. Sawicki, F. Matsukura, A. Idziaszek, T. Dietl, G. M. Schott, C. Ruester, C. Gould, G. Karczewski, G. Schmidt, and L. W. Molenkamp, Phys. Rev. B 70, 245325 (2004)

View on Pith 2004
[7]

K. Hamaya, R. Moriya, A. Oiwa, T. Taniyama, Y. Ki- tamoto, and H. Munekata, IEEE Trans. Magn. 39, 2785 (2003)

View on Pith 2003
[8]

H. X. Tang, R. K. Kawakami, D. D. Awschalom, and M. L. Roukes, Phys. Rev. Lett. 90, 107201 (2003)

View on Pith 2003
[9]

S. T. B. Goennenwein, S. Russo, A. F. Morpurgo, T. M. Klapwijk, W. Van Roy, and J. De Boeck, Phys. Rev. B 71, 193306 (2005)

View on Pith 2005
[10]

X. Liu, Y. Sasaki, and J. K. Furdyna, Phys. Rev. B 67, 205204 (2003)

View on Pith 2003
[11]

U. Welp, V. K. Vlasko-Vlasov, A. Menzel, H. D. You, X. Liu, J. K. Furdyna, and T. Wojtowicz, Appl. Phys. Lett. 85, 260 (2004)

View on Pith 2004
[12]

K. Hamaya, T. Taniyama, Y. Kitamoto, T. Fujii, and Y. Yamazaki, Phys. Rev. Lett. 94, 147203 (2005); K. Hamaya, T. Koike, T. Taniyama, T. Fujii, Y. Kitamoto, and Y. Yamazaki, cond-mat/0511392 (to be published in Phys. Rev. B)

View on Pith Pith review arXiv 2005

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]

C. R¨ uster, T. Borzenko, C. Gould, G. Schmidt, L. W. Molenkamp, X. Liu, T. Wojtowicz, J. K. Furdyna, Z. G. Yu, and M. E. Flatte, Phys. Rev. Lett. 91, 216602 (2003)

View on Pith 2003

[2] [2]

K. F. Eid, B. L. Sheu, O. Maksimov, M. B. Stone, P. Schiﬀer, and N. Samarth, Appl. Phys. Lett. 86, 152505 (2005)

View on Pith 2005

[3] [3]

K. Hamaya, R. Moriya, A. Oiwa, T. Taniyama, Y. Ki- tamoto, Y. Yamazaki, and H. Munekata, Jpn. J. Appl. Phys. 43, L306 (2004)

View on Pith 2004

[4] [4]

U. Welp, V. K. Vlasko-Vlasov, X. Liu, J. K. Furdyna, and T. Wojtowicz, Phys. Rev. Lett. 90, 167206 (2003)

View on Pith 2003

[5] [5]

K. Hamaya, T. Taniyama, Y. Kitamoto, R. Moriya, and H. Munekata, J. Appl. Phys. 94, 7657 (2003)

View on Pith 2003

[6] [6]

M. Sawicki, F. Matsukura, A. Idziaszek, T. Dietl, G. M. Schott, C. Ruester, C. Gould, G. Karczewski, G. Schmidt, and L. W. Molenkamp, Phys. Rev. B 70, 245325 (2004)

View on Pith 2004

[7] [7]

K. Hamaya, R. Moriya, A. Oiwa, T. Taniyama, Y. Ki- tamoto, and H. Munekata, IEEE Trans. Magn. 39, 2785 (2003)

View on Pith 2003

[8] [8]

H. X. Tang, R. K. Kawakami, D. D. Awschalom, and M. L. Roukes, Phys. Rev. Lett. 90, 107201 (2003)

View on Pith 2003

[9] [9]

S. T. B. Goennenwein, S. Russo, A. F. Morpurgo, T. M. Klapwijk, W. Van Roy, and J. De Boeck, Phys. Rev. B 71, 193306 (2005)

View on Pith 2005

[10] [10]

X. Liu, Y. Sasaki, and J. K. Furdyna, Phys. Rev. B 67, 205204 (2003)

View on Pith 2003

[11] [11]

U. Welp, V. K. Vlasko-Vlasov, A. Menzel, H. D. You, X. Liu, J. K. Furdyna, and T. Wojtowicz, Appl. Phys. Lett. 85, 260 (2004)

View on Pith 2004

[12] [12]

K. Hamaya, T. Taniyama, Y. Kitamoto, T. Fujii, and Y. Yamazaki, Phys. Rev. Lett. 94, 147203 (2005); K. Hamaya, T. Koike, T. Taniyama, T. Fujii, Y. Kitamoto, and Y. Yamazaki, cond-mat/0511392 (to be published in Phys. Rev. B)

View on Pith Pith review arXiv 2005