Antiferromagnetism and superconductivity: competition and microscopic coexistence

Scope

Antiferromagnetism and superconductivity can be adjacent in a phase diagram, compete within a sample, or coexist microscopically. These statements require different evidence. A nearby superconducting dome does not locate both orders in the same volume. A magnetic anomaly below a superconducting transition shows an interaction only after alternative structural, volume-fraction and instrumental explanations are considered. Static magnetic order is also distinct from the dynamic spin fluctuations proposed to mediate pairing. R1 R2 R3

Microscopic coexistence means that superconducting and magnetic order occupy overlapping regions on the length and time scales resolved by the probes. Combine local magnetic information with evidence for bulk superconductivity, report detection limits, and identify whether measurements used the same specimen, a crystal mosaic or different crystals from one batch. A resistance drop and a magnetic transition alone cannot exclude minority phases or pressure and composition gradients. R3 R4

Mathematical assumptions

A homogeneous Landau example uses $x=M^2\geq0$, $y=|\Delta|^2\geq0$ and $F=a_mx+b_mx^2+a_sy+b_sy^2+gxy$, with $b_m,b_s\gt0$. Here $g\gt0$ penalizes simultaneous amplitudes; it does not automatically exclude them. An interior minimum requires $D=4b_mb_s-g^2\gt0$ and positive solutions $x=(-2b_sa_m+ga_s)/D$, $y=(-2b_ma_s+ga_m)/D$. These coefficient definitions differ from papers that put factors of two or four in the free energy. R1

For dimensionless $a_m=a_s=-2$ and $b_m=b_s=1$, competitive coupling $g=1$ gives $x=y=2/3$ and $F=-4/3$, below either pure-order energy $-1$. At $g=3$, the interior stationary point is a saddle and the two pure minima tie. At $g=2$, a continuum $x+y=1$ is degenerate and higher-order terms can select the state. Strong negative coupling $g\lt-2\sqrt{b_mb_s}$ makes this quartic theory unbounded in the physical quadrant. Twelve constrained examples were checked against an independent dense grid; they are not material fits. R1

Inside a coexistence branch, $M^2=-a_m/(2b_m)-g|\Delta|^2/(2b_m)$. Thus positive coupling suppresses the moment relative to its continuation without superconductivity. It need not make the moment decrease as temperature falls: the bare magnetic growth can dominate. Two independent linear-temperature examples verify both cooling slopes with the same positive coupling. A decrease below $T_c$ is useful evidence, but its absence does not establish that the orders cooperate. R1

For fixed scattering geometry, an illustrative magnetic intensity scales as $I\propto f_mM^2$, where $f_m$ is magnetic volume fraction. A uniform moment reduced to $0.8$ of its reference and an unchanged moment in $0.64$ of the volume both give the same normalized intensity $0.64$. This simple nonuniqueness is why local-field distributions and amplitudes add information to diffraction. Real refinements also need magnetic structure factors, domains and instrumental corrections. R2 R3

Experimental criteria

Vaknin and colleagues' neutron result establishes magnetic order in undoped La2CuO4-y; it does not establish static antiferromagnetism inside an optimally doped superconducting sample. Huang and colleagues' BaFe2As2 diffraction study anchors the parent magnetic and structural transition. Neither parent result supplies a universal superconducting coexistence interval. Preserve family, stoichiometry and sample conditions instead of transferring a magnetic transition temperature into a superconducting $T_c$ table. R6 R7

Pratt and colleagues' final abstract reports structural and antiferromagnetic transitions near 60 K and 47 K in Ba(Fe0.953Co0.047)2As2, with superconductivity below 17 K, reduced static magnetic order and redistributed low-energy excitations. The sole author manuscript instead gives 15 K and a 4 meV gap. Its methods describe diffraction crystals grown under conditions matching the bulk-measurement specimens. Use the final abstract's 17 K as a reported transition, retain the version difference, and do not claim that every measurement used the identical crystal. The complete final methods remain unchecked. R2

Marsik and colleagues provide complementary local-probe evidence in BaFe1.89Co0.11As2. Their 21.7 K value is the midpoint of the zero-field-cooled susceptibility transition. Transverse-field muon measurements imply a magnetic volume exceeding 90 percent, with essentially unchanged signal fractions but reduced relaxation below $T_c$. A field-pinning experiment supports bulk superconductivity; infrared spectra from crystals in the same growth batch support condensate formation. The authors infer coexistence on nanometer scales, not atomic uniformity at every site. Their composition corresponds to $x=0.055$ in Ba(Fe1-xCox)2As2, not $x=0.11$. R3

Mito and colleagues report CeRhIn5 at 1.75 GPa: NQR splitting appears below $T_N=2.5$ K, while in-situ coil susceptibility has a superconducting onset near 2.0 K. The comparable diamagnetic response at higher pressures supports bulk superconductivity. Their crushed grains and estimated pressure spread of approximately 0.05 GPa are part of the evidence conditions. The retrieved author PDF includes captions but omits the actual spectra and susceptibility figures, so this review verifies the reported interpretation and methods without claiming visual confirmation of those plots. R4

Park and colleagues use pressure- and field-dependent specific heat in CeRhIn5 to infer a magnetic transition line inside the superconducting state. Their low-temperature phase diagram is an extrapolation from finite temperatures. The supplementary method measures relative ac heat capacity and calibrates pressure with a tin transition; these details matter when interpreting anomalies. Calorimetry supports thermodynamic boundaries but does not alone determine a magnetic ordering wavevector or the spatial arrangement of coexisting orders. R5

Limits and disputes

The Landau model organizes homogeneous amplitudes near transitions. It omits magnetic texture, superconducting phase coherence, disorder and gradients; a strong-coupling first-order boundary does not calculate the resulting domain structure. Fernandes and Schmalian's pairing inference additionally assumes itinerant electrons contributing to both orders and a system near particle-hole symmetry. Coexistence by itself is not a universal proof of sign-changing pairing or of a unique magnetic pairing interaction. R1

Complete scientific acceptance remains open. Selected original abstracts, author methods and available figures have been checked, alongside bounded numerical examples. Missing Mito figures, complete final-version comparisons, absolute volume calibration and experimental raw-data audits remain unresolved. Cross-probe agreement is evidence whose spatial, temporal and sample limits should remain visible, not a reason to remove those limits. R2 R3 R4 R5

Discovery implications

Record magnetic wavevector or local-field evidence, superconducting criterion, probe timescale, volume fractions, batch identity, pressure distribution and composition convention together. Compare the magnetic response above and below $T_c$ against its normal-state continuation. Separate a proposed fluctuation mechanism from evidence for static coexistence, and prefer quantitative competing explanations over a single label such as magnetic superconductor. R1 R3 R4

Related topics

Spin-fluctuation pairing, iron-based superconductors, heavy-fermion superconductors, and spin liquids and superconductivity.

Material cases

Values describe individual reports, not a ranking. Unknown means the checked source did not supply the field at this review scope.