Electronic structure and $H$-$T$ phase diagram of Eu(Fe$_{1-x}$Rh$_x$)$_2$As$_2$

TL;DR

This study explores the electronic structure and magnetic-superconducting phase diagram of Eu(Fe$_{1-x}$Rh$_x$)$_2$As$_2$, revealing how localized Eu magnetism coexists and interacts with superconductivity, using ARPES and thermodynamic measurements.

Contribution

It provides new insights into the coexistence and competition of magnetic order and superconductivity in EuFe$_2$As$_2$ family through combined experimental techniques.

Findings

Reentrant superconductivity due to magnetic interactions.

Electronic structure modifications near optimal Rh doping.

Evidence of magnetic influence on the superconducting state.

Abstract

The iron-based superconductors represent a promising platform for high-temperature superconductivity, but the interactions underpinning their pairing present a puzzle. The EuFe$_2$As$_2$ family is unique among these materials for having magnetic order which onsets within the superconducting state, just below the superconducting transition. Superconductivity and magnetic order are normally antagonistic and often vie for the same unpaired electrons, but in this family the magnetism arises from largely localized Eu moments and they coexist, with the competition between these evenly-matched opponents leading to reentrant superconducting behavior. To help elucidate the physics in this family and the interactions between the magnetic order and superconductivity, we investigate the $H$--$T$ phase diagram near optimal Rh doping through specific heat, resistivity, and magnetization measurements, and study the electronic structure by angular-resolved photoemission spectroscopy. The competition between the Eu and FeAs layers may offer a route to directly accessing the electronic structure under effective magnetic fields via ARPES, which is ordinarily a strictly zero-field technique.

Full text

I Introduction

In high-temperature superconductors, magnetism and superconductivity compete for control over the unpaired electrons, as exemplified by the competition of superconductivity with spin-density-wave and charge-density-wave order in the cupratesGhiringhelli et al. (2012); Chang et al. (2012); Blanco-Canosa et al. (2013). But the same high-temperature superconductivity may also owe its existence to fluctuations that arise as magnetic phases are suppressed — in both the cuprate and iron-based superconductors, superconductivity appears where a phase with long-range spin order is suppressed, and that spin order otherwise persists to temperatures much higher than any superconducting critical temperature $T_{\text{c}}$. More generally, the zero-field ground state of a superconductor with singlet pairing is perfectly diamagnetic, and magnetism within the material reduces the energy saved through pairing as the pair condensate is forced to adapt or compensate. Given the complex relationship between magnetism and high-temperature superconductivity, the interactions of magnetic order with these superconductors offers an important opportunity to shed light on the pairing in these systems, which remains among the greatest unsolved problems in condensed matter physics.

Doped EuFe2As2Raffius et al. (1993); Ren et al. (2008); Jeevan et al. (2008) offers a unique opportunity to study this interaction. It consists of high-temperature-superconducting FeAs layers, but the intermediate layer is a square lattice of magnetic Eu. The FeAs and Eu layers both order magnetically in the undoped parent materialRaffius et al. (1993), but their magnetism is nearly decoupledJeevan et al. (2008); Xiao et al. (2009). Superconductivity can be induced by pressureMatsubayashi et al. (2010) or by chemical substitution. The latter can occur either on the Eu site, which frustrates the magnetic order while injecting charge carriers to the FeAs planes, or within the FeAs planes, which introduces significant disorder directly into the superconducting system but leaves the magnetic sublattice largely untouched. Doped EuFe2As2 has a number of very unconventional properties, including a reentrant superconducting transition in the resistivityJiao et al. (2017a) and a reentrant spin-glass phaseBaumgartner et al. (2017), most likely as a result of the competition between superconductivity and magnetism.

Here we report the magnetic phase diagram and electronic structure of Eu(Fe1-xRhx)2As2. The superconductivity is not visible in the specific heat or ARPES data, likely as a result of the intrinsic competition between strong rare-earth magnetism in the Eu layer and high-temperature superconductivity in the FeAs layers. This may offer a route to applying zero-field techniques such as ARPES to materials in an effective magnetic field.

II Experimental

Single crystals of several dopings of Eu(Fe1-xRhx)2As2 including undoped EuFe2As2 were grown from a (Fe,Rh)As self flux in Al2O3 crucibles as described elsewhereJiao et al. (2013, 2017a). Measurements were performed chiefly on crystals with nominal composition Eu(Fe0.88Rh0.12)2As2, which is near optimal doping. Field-cooled (FC) and zero-field cooled (ZFC) magnetization measurements were performed in a Quantum Design MPMS3 vibrating sample SQUID magnetometer, with the crystal affixed to a quartz bar sample holder using GE Varnish and Teflon or Kapton tape. Specific heat measurements were performed by the relaxation time technique in a Quantum Design Physical Properties Measurement System (PPMS), with the sample mounted using Apiezon N grease. For in-plane fields, this crystal was attached to a small copper wedge to ensure both correct alignment and good thermal contact. Several measurements were averaged for each data point, and in some temperature ranges it was necessary to discard the first measurement in each set because the sample’s temperature had not fully equilibrated. Resistivity was measured using the standard four-wire technique in a Quantum Design PPMS, with a drive current $J$ of 5 mA unless otherwise noted. The resistivity was measured for in-plane fields, which was accomplished by attaching the samples to slabs of sapphire which were then mounted upright on the sample puck. Sample stoichiometry was verified by energy-dispersive x-ray spectroscopy (EDX). Samples with nominal Rh contents of 0.09, 0.12 and 0.16 were measured to be 0.068(3), 0.095(6) and 0.101(8) and have resistive $T_{\text{c}}$s of 7.0, 18.6, and 18.8 K, respectively. Since zero resistivity was not reached, superconducting transitions were defined by a 10 % decrease from the value above $T_{\text{c}}$ to the lowest-temperature value. Optimal doping in this system corresponds to a measured Rh content of 0.09111Note that optimal doping is lower in EuFe2As2Jiang et al. (2009); Jiao et al. (2017a) than in the BaFe2As2 familyNi et al. (2009)., obtained for nominal concentrations of 0.12, so the “nearly optimal” samples investigated here are well within the uncertainty of optimal doping. This paper uses the nominal concentrations.

Angle-resolved photoemission spectroscopy (ARPES) was utilized to measure the electronic structure of the samples. Besides traditional ARPES with a helium lamp ($h\nu$ = 21.2 eV, resolution 10 meV), a laser-based ARPES system ($h\nu$ = 6.3 eV, resolution better than 5 meV) with a micrometer-scale focal spot ($<5\mu$m)Iwasawa et al. (2017) was also utilized. Since such a highly-focused beam can lead to space charge effectsZhou et al. (2005); Liu et al. (2008), it was necessary to determine the maximum laser fluence that would avoid charging, then collect data below this intensity. All ARPES measurements were performed at a base pressure better than $5\times 10^{-11}$ mbar. ARPES was performed on a separate sample from the same batch.

III Results and Discussion

The electronic structure of Eu(Fe0.88Rh0.12)2As2 measured by ARPES with a helium lamp ($h\nu$ = 21.2 eV) is displayed in Fig. 1. Figs. 1(a-d) show the Fermi surface and constant-energy contours at binding energies $E_{b}$ = 0, 20, 40, and 60 meV taken at a temperature of 15 K, just below the cricital temperature. Similar to EuFe2As2 with other dopantsThirupathaiah et al. (2011); Xia et al. (2014), there are hole pockets around the $\overline{\Gamma}$ point and electron pockets around the $\overline{M}$ points. The band dispersions centered around the $\overline{\Gamma}$ point [along cut #1 in Fig. 1(a)] and $\overline{M}$ [along cut #2 in Fig. 1(a)] at different temperatures are shown in Figs. 1(e-h) and Figs. 1(i-l), respectively. Energy distribution curves (EDCs) are shown as a function of temperature at Fermi momenta near $\overline{\Gamma}$ and $\overline{M}$ in Figs. 1(m) and 1(n), respectively. Upon increasing temperature through the critical temperature $T_{\text{c}}$ (from 15 to 50 K), no significant changes in the band structure can be observed around the $\overline{\Gamma}$ or $\overline{M}$ point, we do not observe a gap opening, and no features near the Fermi level $E_{F}$ can be unambiguously identified as coherence peaks. This is most likely a consequence of measuring too close to $T_{\text{c}}$, where the gap and coherence peaks may not have fully developed.

To improve the energy resolution and avoid any inhomogeneity of the cleaved surface, laser-ARPES with a spot size below 5 $\mu$m was also used to measure the band structure around the $\overline{\Gamma}$ point (Fig. 2 shows data at 13 K). Despite an energy resolution better than 5 meV, there are still no significant changes with temperature and no visible gap. A superconductor with a high transition temperature would normally have a sizeable gap, but this close to the transition temperature it would be very small. The lack of observable signatures of a pairing gap may also arise from space charge effects, which we cannot completely rule out in the laser-ARPES data, or Eu acting as a magnetic impurity. The pair-breaking induced by magnetic impurities can lead to “gapless superconductivity”Abrikosov and Gor’kov (1961); Phillips (1963), a state which was discussed extensively in connection with BCS superconductors.

The band dispersion measured at 13 K in the s polarization geometry (electric field perpendicular to the plane of incidence) is shown in Fig. 2(a). This geometry will selectively detect $d_{xy}$ and $d_{yz}$ orbitals, for polarization along $y$ with $z$ being the surface normal. The difference in the Fermi wavevector $k_{F}$ between Figs. 2(a) and 1(e-h) is mostly likely due to either $k_{z}$ dispersion or differences in carrier doping at the surface — the material cleaves through the Eu charge reservoir layer. As seen more clearly in the EDCs shown in Fig. 2(b), there is a feature suggestive of a flat band near the Fermi level, reminiscent of heavy fermion physics. Such a feature can arise from a flat $4f$ band interacting with the regular electrons at low temperature (and having dipole symmetry that matches $d_{xy}$ and $d_{yz}$), or it can appear when a band top or bottom is just above the Fermi level. A parabolic fit indicates that the top of the hole pocket at $\overline{\Gamma}$ should lie $\sim$30 meV above the Fermi level, and this apparent flat band is most likely a tail from that band top, cut off by the Fermi function.

The specific heat $c_{P}$ of Eu(Fe0.88Rh0.12)2As2 is plotted as $c_{P}(T)/T$ vs. $T$ in Fig. 3a for fields along the $c$ axis, and in Fig. 3b for in-plane fields, and the susceptibility $M/H$ is plotted in Fig. 4. In the zero-field specific heat, a sharp spike around 16.5 K containing considerable entropy marks a phase transition, while a second large hump is visible around 6 K. Data taken on warming and cooling in zero field do not exhibit clear evidence of hysteresis. The considerable entropy released below 20 K would make Eu(Fe0.88Rh0.12)2As2 a heavy fermion superconductor if this were electronic entropy. However, the superconducting transition in Eu(Fe0.88Rh0.12)2As2 nearly coincides with a magnetic ordering temperature, so a significant fraction of this entropy would be expected to be magnetic. Field dependence is invaluable for disentangling these origins. The low-temperature hump gradually broadens and moves to higher temperatures with field, while the spike at the transition splits at low fields. The bulk of the entropy from the 16.5 K transition broadens and moves to higher temperatures, while a sharp jump moves rapidly to low temperature. This behavior is qualitatively the same for both field orientations, but the rates at which the transitions move differ.

Since the vast majority of the entropy moves to higher temperatures in field, the magnetic contribution evidently dominates. The sharp jump that moves rapidly to lower temperatures in field could in principle be either superconducting or antiferromagnetic. Susceptibility, shown in Fig. 4 shows a clear transition matching the sharp jump in the specific heat, but because full diamagnetism is not achieved, it is unable to clarify whether this is magnetic or superconducting. The rapid shift to lower temperature is inconsistent with the very gradual field dependence of the resistive superconducting transitionJiao et al. (2017a), suggesting an antiferromagnetic origin, but we note that resistive measurements may not be bulk-sensitive if superconductivity is present. In nonsuperconducting Ca-doped (Eu0.88Ca0.12)Fe2As2, an antiferromagnetic transition observed in the susceptibility at 15 K is suppressed to zero by a 1.5 T field applied along the $c$ axis, or by a 0.75 T in-plane field Tran et al. (2018). The suppression of the specific heat jump in Fig. 3 has slightly higher anisotropy and is suppressed by somewhat lower fields, but its response to field is remarkably similar. Based on the similarity to the Ca-doped material and the lack of any other sharp magnetic transition in a material which is known to magnetically order, we tentatively attribute the sharp jump to a bulk antiferromagnetic transition.

In magnetic field, the Ca-doped materialTran et al. (2018) and high-pressure-synthesized EuFe2As2Tsvyashchenko et al. (2013) exhibit a transition from the paramagnetic normal state to field-induced ferromagnetic order, which moves rapidly to higher temperature as field is applied. The broad specific heat hump that grows out of the sharp phase transition in Eu(Fe0.88Rh0.12)2As2 has a similar field dependence. As seen in Fig. 4, our susceptibility data begin to deviate at progressively higher temperatures with field, and this can be clearly identified in the magnetization as a saturation. This supports an interpretation of field-induced ferromagnetism for the higher-temperature specific heat hump in Eu(Fe0.88Rh0.12)2As2.

Our susceptibility measurements do not identify any feature that would correspond to the low-temperature hump in the specific heat. The moments have minimal entropy below this temperature, but begin to develop some above. This would indicate that the hump corresponds to stronger locking-in of moments or freezing out of their fluctuations at low temperature. In optimally-Ir-doped Eu(Fe0.88Ir0.12)2As2, tilting of the in-plane Eu spins toward the $c$ axis sets in about 2.5 K below the magnetic ordering temperatureJiao et al. (2013), but the higher susceptibility values for in-plane fields in the Rh-doped material indicate moments that already lie primarily along $c$, thus a similar reorientation is unlikely here.

Field-cooled (FC) and zero-field-cooled (ZFC) susceptibility data on Eu(Fe0.88Rh0.12)2As2 are presented in Figs. 4(g) and 4(i) for low fields along the $c$ and $a$ axes, respectively. In most doped EuFe2As2 materials, particularly in in-plane fieldsMatsubayashi et al. (2011); Jiao et al. (2013); Tsvyashchenko et al. (2013); Baumgartner et al. (2017); Tran et al. (2018), the material does not exhibit full diamagnetism in the superconducting state, only a diamagnetic shift on top of a large paramagnetic background. In general, a field-trained difference can be explained by either the freezing-in of magnetic moments or by superconductivity with vortex pinning. The difference between FC and ZFC susceptibility data is commonly used in these materials as an indication of the superconducting contribution.

A small difference between zero-field-cooled (ZFC) and field-cooled (FC) susceptibility is indeed visible in the lowest fields, with ZFC lower as expected; this difference is plotted in Figs. 4(h) and (j). For $c$-axis fields, its onset at $\sim$17 K is nearly field independent, but it becomes difficult to detect for fields above 100 mT. A similar difference persists roughly twice as high in temperature for in-plane fields, to approximately double the antiferromagnetic transition. A locking-in of spin moments in the paramagnetic state above the bulk magnetic transition is exceedingly unlikely, particularly since the Eu layer has not been directly disordered by cation substitution, so this may represent superconductivity. However, superconductivity to such a high temperature has never been observed in the EuFe2As2 system, including in resistivity measurements on similar samplesJiao et al. (2017a). The onset temperature of $\sim$32 K is approaching the maximum $T_{\text{c}}$ reported on doping the nonmagnetic analogs BaFe2As2 and SrFe2As2, so stacking faults or Eu-deficient layers may be responsible. Note that identifying this downturn with superconductivity would also imply a similar superconducting component in the undoped parent compound, where we observe similar behavior [see Figs. S8(f) and (h)], although this is nearly an order of magnitude weaker and is suppressed by much lower fields. While in-plane fields may disrupt or reorient precursor magnetic order, and our thin platelet superconductor may also benefit from the thin limit in this orientation, we consider it unlikely that this feature is representative of the bulk of the sample.

To check whether the apparent $\sim$32 K onset could be superconductivity, we measured the resistivity of a Eu(Fe0.88Rh0.12)2As2 crystal from the same batch in in-plane fields, as shown in Fig. 5. Magnetization and EDX data [$x$=0.097(6)] on this crystal are indistinguishable from those presented above. As seen in the left inset in panel (a), there is no clear feature around 32 K; the first hint of a downturn is around 22 K. As shown above, small fields suppress the magnetic transition, and this visibly reduces the low-temperature resistivity. Increasing the field beyond 0.5 T then gradually suppresses the main downturn from $\sim$19 K to $\sim$15 K at 7 T. Its gradual suppression by field and obvious competition with the magnetic order allow us to identify it as superconductivity. A second transition around 7 K which is suppressed below 1.8 K by a 6 T field is most likely due to vortex pinning, since it is not observed by any other technique. The resistivity does not approach zero, so the initial downturn is taken as indicative of the superconducting transition. Aligning the field exactly perpendicular to the field is very easy in the susceptibility measurement, but more difficult in the geometry used for our resistivity measurements, so our inability to observe any hint of a downturn at higher temperatures could be a result of inexact field alignment. However, if a misalignment of perhaps a few degrees were able reduce the onset temperature by half, that would be difficult to understand if it were bulk superconductivity. A test in which the field was rotated within the $ab$-plane found no angle dependence at low temperature, suggesting that perfect in-plane field alignment is not crucial.

We note at this point that the physical properties of these crystals differ from those with identical nominal dopings in Ref. Jiao et al., 2017a, most noticably the zero-field resistivity below $T_{\text{c}}$. The behavior below $T_{\text{c}}$ in EuFe2As2-based materials is determined by an intricate interplay between superconductity and magnetism, resulting in reentrant resistivity in most systems, which is explained in terms of flux-flow resistivity in a spontaneous vortex stateRen et al. (2009); Jiao et al. (2011, 2017a, 2017b). In this scenario, the exact shape of the resistivity reentrance is highly sensitive to the sample quality, including defects, dopant homogeneity, and pinning sites, and even to the direction along which the current is applied.

Similar to the reentrant resistivity, the difference between ZFC and FC susceptibility also shows a sharp jump back toward zero for in-plane fields, coinciding with the peak in the susceptibility. This is a result of the sample temperature lagging the thermometry — tests varying the temperature scan rate and comparing zero-field-cooled warming with field-cooled cooling and field-cooled warming measurements are shown in Fig. S7 in the Supplemental MaterialsSMr . This jump in the difference between ZFC and FC data is only seen for in-plane fields because only in-plane fields have a nonzero difference between ZFC and FC data at this temperature.

The inverse susceptibility, shown in Figs. 4c and 4f, is well fit by the Curie-Weiss law [$M/H=C/(T-\Theta_{W})$] over a wide temperature range, and indicates predominantly ferromagnetic interactions with minimal frustration. The extracted Weiss temperatures are 18.5 and 19.4 K for $c$-axis and in-plane fields, respectively, consistent with that reported earlier for the parent compoundRaffius et al. (1993). These are only marginally higher than the bulk transition in the susceptibility and specific heat, indicating minimal frustration. The respective extracted moments of 8.85 and 8.46 $\mu_{B}$ for $c$-axis and in-plane fields exceed that expected for spin-7/2 Eu2+ (7.95 $\mu_{B}$), presumably due to a contribution from Fe spins. However, the shape in $M(T)$ and field-suppression of the transition are consistent with antiferromagnetic order, and this remains true at the higher Rh doping of 0.16SMr . In Co-doped EuFe2As2, the magnetic ground state of the Eu ions evolves from an A-type antiferromagnet, to a canted antiferromagnet, and eventually to a ferromagnetJin et al. (2016) with doping, and a similar transition to ferromagnetism is observed with P or Ir dopingNowik et al. (2011); Anand et al. (2015). Our results indicate that we do not reach a high enough doping to obtain a ferromagnetic ground state.

Significantly larger fields are required to suppress the antiferromagnetic transition when the field is applied along $c$ than $a$. Since it has been previously reported that in the undoped parent compound and at low dopings for various dopants the spins lie in the plane and order ferromagnetically within each Eu planeXiao et al. (2009); Nowik et al. (2011); Jin et al. (2016), this indicates that it is relatively easy to realign the spin orientation of the Eu slabs, thereby breaking the global antiferromagnetic order.

A hump at 12-14 K in the in-plane susceptibility at low fields in P- and Ir-doped materialZapf et al. (2013); Baumgartner et al. (2017) has been attributed to a spin-glass transition below the antiferromagnetic transition in analogy to EuFe2P2. The picture here is that the $c$-axis-aligned ferromagnetic moments have a disordered $ab$-plane component driven by antiferromagnetic interlayer RKKY interactions, and this in-plane component freezes. The freezing of a perpendicular spin component has also been discussed in Ref. Jiao et al., 2017a for Rh-doped material. The remarkable agreement of our susceptibility with the Curie-Weiss law down nearly to the transition and the lack of any other sign of frustration suggest that this component is very small if it exists, but the present data do not allow us to exclude it as a possibility. This hump shifts to higher temperatures with field, but its strength in $M$ is roughly constant, making it vanish rapidly in $M/H$ as field is increased. Its strength also apparently grows with Rh dopingSMr . This behavior would be most consistent with a saturated magnetic moment associated with the dopant site. Its consistent appearance in multiple single-crystal studies by different groups using different FeAs-layer dopants supports this interpretation, but demonstrating similar doping dependence in the other systems would provide important confirmation.

As part of this work, we also measured the susceptibility of the parent compound and several Rh dopings, but found minimal differences among the doped samplesSMr . Evidently, adding enough Rh dopants to induce superconductivity significantly reduces the fields required to suppress the Eu magnetic order, and slightly reduces its onset temperature. The Eu layers are coupled through the (Fe,Rh)As layers, which also order in the undoped parent compound. Rhodium doping suppresses the Fe-site magnetic order, which may directly weaken the Eu interlayer coupling. The singlet superconducting ground state in the FeAs planes should also be less efficient at RKKY coupling. The proximity to strong rare-earth magnetism will ensure that some carriers remain unpaired, so some weak interlayer coupling remains, and the Eu moments continue to exhibit long-range order, but the reduced interlayer coupling makes it more fragile. Evidently, once there is enough Rh present to disrupt the Fe magnetism and reach a superconducting ground state, tuning this ground state has no further effect on the Eu moments.

Based on the specific heat, resistivity, and susceptibility data, it is possible to assemble an $H$–$T$ phase diagram for Eu(Fe0.88Rh0.12)2As2, shown in Fig. 6. The position of the lower-temperature hump in the specific heat was estimated based on its peak position, the antiferromagnetic transition was determined based on the midpoint of the specific heat jump, and for the high-temperature specific heat hump a midpoint was estimated. The peak position and midpoint of the jump in the susceptibility were added, and resistive transitions are based on a 10 % decrease from the value above $T_{\text{c}}$ to the lowest-temperature value and the midpoint of the jump at $T_{\text{N}}$. The phase diagram (Fig. 6) combines the results of our measurements on Eu(Fe0.88Rh0.12)2As2 for both orientations. The antiferromagnetic transition has been expanded by a factor of 5. Aside from the inclusion of superconductivity, this phase diagram bears a very close resemblance to that of nonsuperconducting Ca-doped (Eu0.88Ca0.12)Fe2As2Tran et al. (2018). Such a high degree of similarity is surprising given that the dopants in the latter case are on the Eu site, disrupting the magnetic order, while here the Rh is in the superconducting FeAs planes, weakening the competing superconductivity.

Since all features in the specific heat near the superconducting transition can be attributed to magnetism, this raises the question of why no trace of the superconductivity is visible. The specific heat jump at $T_{\text{c}}$, $\Delta c_{P}/T_{\text{c}}$, in the nonmagnetic BaFe2As2 family scales with $T_{\text{c}}$Bud’ko et al. (2009), and values in the SrFe2As2 family are quantitatively similarLeithe-Jasper et al. (2008). If the FeAs layers are assumed to behave the same in the Eu material, similar scaling should apply, which would predict a jump height of roughly 10 mJ/mol$\cdot$K2, less than 2 % of the specific heat near the transition. The uncertainty on the specific heat data near $T_{\text{c}}$ is less than 1 %, but at low fields the data at that temperature are increasing precipitously toward a phase transition. It would be difficult to detect such a small jump within that underlying background. Any broadening of the transition, which would be expected given the disorder and inhomogeneity that must accompany the replacement of Fe atoms with Rh, would make it even more challenging. At fields on the order of 0.5 T, the magnetic specific heat is far less singular, but there is still no superconducting transition visible. This is a small change in field for the superconductivity, so the superconducting transition should only be very slightly weaker and broader. In fact, the lower resistivity around this field suggests that we might even expect a stronger, sharper superconducting transition with the magnetism suppressed. It should be visible, and it is not.

The key may lie in the competition with strong rare earth magnetism. The magnetic fields impinging upon the FeAs layer even in zero external field will induce a vortices and shielding currentsJiao et al. (2017b), reducing the entropy saved in the superconducting state. The specific heat of a Type-II superconductor in field has a reduced jump height, which may push it beyond our detection limit even in low or zero field in doped EuFe2As2. We note that no specific heat jump at $T_{\text{c}}$ has been observed in Ir-doped and P-doped Eu-122 eitherParamanik et al. (2014); Nandi et al. (2014), likely for the same reasons. Unfortunately, this makes it difficult to confirm that the observed superconductivity is an intrinsic, bulk property. If the material is effectively in high field even at zero applied field, that could offer another alternative explanation for the absence of a pairing gap in ARPES. Under high (effective) fields in a Type-II superconductor, the gap is not only reduced but also spatially inhomogeneous on a lengthscale well below that of even our $\mu$-ARPES spot size. This would broaden and fill in the gap, making it impossible to observe.

Since the superconductivity is forced to coexist with strong rare-earth magnetic moments even in their paramagnetic state, the superconducting phase exists in an intrinsic vortex state even at low fieldsJiao et al. (2017b). This will reduce not only the entropy savings, but also the diamagnetic shielding, making the superconductivity largely invisible to both specific heat and magnetization. Indeed, no unambiguous signatures of superconductivity are immediately obvious in our data for any doping or field orientation.

We now return to the problem of the susceptibility glitch at 32-34 K in in-plane fields, suggestive of superconductivity. This was not observed in the resistivity, for which several explanations are possible. One possibility would be that the material is in a regime of free flux flow, so that the drive current for the resistivity measurement moves the vortices perpendicular to the current, causing resistive losses. Reducing the drive current by a factor of 25 [Fig. 5(a) inset] had no significant effect, but this could still be too large for very weak pinning. Another explanation could be that this higher-temperature superconducting contribution may be destroyed by a small misorientation of the field. A 45∘ rotation of the field within the $ab$ plane had no effect on the data (not shown), implying that any such misorientation would need to introduce a $c$-axis component; however, a rotation of the field about the $c$-axis, which should produce perfect in-plane alignment at some angle, found no angle-dependence. Superconductivity ocurring only in low in-plane fields could suggest that disrupting the antiferromagnetic Eu order greatly enhances superconductivity, but it could also be consistent with thin superconducting slabs, perhaps at the surface or at stacking faults, which are more readily observed under in-plane fields thanks to thin-limit effects. The weak nature of this downturn and its appearance at the same temperature irrespective of doping, but only for one field orientation, suggest an extrinsic origin. Nonetheless, the data are suggestive of superconductivity at roughly double the highest known $T_{\text{c}}$ in doped EuFe2As2, and this clearly warrants further investigation.

IV Conclusion

The antagonistic relationship between the Eu and FeAs layers in EuFe2As2 disrupts both the long-range magnetic order and bulk superconductivity. The consequence for the magnetism is that the ground state can be tuned by doping the FeAs layers, likely disrupting the interlayer coupling, and our work indicates that the magnetism’s $H$–$T$ phase diagram can be traversed with laboratory magnets. The superconductivity may also be tunable — our data indicate that the FeAs layers feel a strong field even under zero applied field. The upper critical fields in the iron-based superconductors are normally very high and difficult to access, but the EuFe2As2 family may make the high-field region far more accessible. In particular, ARPES is a strictly zero-field technique due to the immediate destruction of momentum information by any applied magnetic field, so field-dependent ARPES is ordinarily completely impossible. Our results suggest that in the EuFe2As2 system, ARPES can be performed at a higher effective magnetic field. Tuning the magnetic layers, for instance by Ca or Sr doping, should return the system to lower effective field, allowing an effective-magnetic-field-dependent ARPES study and directly accessing the electronic structure under conditions that are ordinarily inaccessible to ARPES.

Acknowledgements.

The authors thank M.L. Zhu, X.M. Wang, and the group of J. Zhao at Fudan University for measurement assistance. This work was supported by the National Natural Science Foundation of China (Grant No. 11674367) and the Zhejiang Provincial Natural Science Foundation (Grant No. LZ18A040002). DCP is supported by the Chinese Academy of Sciences through 2018PM0036. The ARPES beamtime at the Hiroshima Synchrotron Radiation Center was granted under Proposal 17AG004.

Supplemental Material: Additional Susceptibility Results

Figure S7 shows the results of the sweep rate and direction on the difference between zero-field-cooled and field-cooled susceptibility data. As seen in Fig. S7(b), a slower sweep rate results in a smaller spike at the bulk transition, suggesting that this feature is an artifact due to the sample temperature lagging the thermometry. Comparing field-cooled sweep directions in Fig. S7(c), this spike exists when cooling and warming are subtracted, but not when zero-field-cooled and field-cooled warming scans are subtracted, again confirming its extrinsic origin. The glitch at 34 K, however, exists independent of sweep rate or direction, and only when ZFC and FC runs are subtracted. This indicates that it is a real effect, although not necessarily an intrinsic bulk property of the material.

It is useful to check the effect of Rh doping on the transition. The physics in Eu(Fe1-xRhx)2As2 is dominated by a competition between strong rare-earth magnetism in the Eu layer and high-temperature superconductivity in the FeAs layer. Doping with Rh is expected to have a strong effect on the superconductivity, while any impact on the magnetic layer will be mainly through changes in the interlayer coupling. Magnetization measurements as a function of doping are presented in Fig. S8. Adding Rh to the undoped parent compound changes the behavior somewhat, but further Rh doping only leads to nearly-imperceptible further changes. The zero-field transition appears to shift to slightly higher temperature with doping, with a corresponding slight increase in the field required to suppress it, and the spin-glass hump around 13 K appears to grow with doping. In the parent compound, while a sharper peak is seen at the transition which looks similar and appears at slightly higher temperature than in the doped samples. This survives to significantly higher fields in the parent compound. The parent compound is not believed to superconduct at ambient pressure. This doping dependence provides additional evidence to suggest that the main transition here is antiferromagnetic ordering of the Eu moments, not superconductivity.