# Optical study of the antiferromagnetic ordered state in electron-overdoped
Ca0.77Nd0.23FeAs2

Run Yang  Beijing National Laboratory for Condensed Matter Physics, Institute
of Physics, Chinese Academy of Sciences, P.O. Box 603, Beijing 100190, China
Bing Xu  Center for High Pressure Science and Technology Advanced Research,
Beijing 100094, China  Yaomin Dai  Center for Integrated Nanotechnologies, Los
Alamos National Laboratory, Los Alamos, New Mexico 87545, USA  Wei Zhang
Beijing National Laboratory for Condensed Matter Physics, Institute of
Physics, Chinese Academy of Sciences, P.O. Box 603, Beijing 100190, China
College of Physics, Optoelectronics and Energy & Collaborative Innovation
Center of Suzhou Nano Science and Technology, Soochow University, Suzhou
215006, China  Jinyun Liu  Ziyang Qiu  Beijing National Laboratory for
Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences,
P.O. Box 603, Beijing 100190, China  Xianggang Qiu<EMAIL_ADDRESS>Beijing
National Laboratory for Condensed Matter Physics, Institute of Physics,
Chinese Academy of Sciences, P.O. Box 603, Beijing 100190, China
Collaborative Innovation Center of Quantum Matter, Beijing 100084, China

(August 27, 2024)

###### Abstract

In Ca1-xRExFeAs2 (RE= rare earth), an antiferromagnetic (AFM) phase as well as
a structural transition has been reported, even in the electron-overdoped
regime. Here we investigated the temperature-dependent in-plane optical
spectroscopy of overdoped Ca0.77Nd0.23FeAs2. Upon entering the AFM state, we
found an abrupt reduction of low-frequency (500-2 000$\leavevmode\nobreak\
\textrm{cm}^{-1}$) spectral weight in the optical conductivity. In sharp
contrast to the parent compounds of 122 system, where spin-density-wave gaps
have been clearly observed in the AFM state, a gap signature is absent in
Ca0.77Nd0.23FeAs2. This may be a consequence of the poor nesting condition
between hole and electron pockets. However, a spectral weight analysis shows
that the reduced spectral weight at low frequency is transferred to the high
frequency range ($\gtrsim 4\,000$$\leavevmode\nobreak\ \textrm{cm}^{-1}$),
pointing to a localization effect. These observations suggest that the AFM
order in Ca0.77Nd0.23FeAs2 is most likely to originate from a localized nature
rather than Fermi surface nesting.

###### pacs:

72.15.-v, 74.70.-b, 78.30.-j

Since unconventional superconductivity usually arises as a consequence of
suppressing an AFM order in the parent compounds by chemical substitution, its
pairing mechanism is believed to be intimately related to the magnetism Lee
_et al._ (2006). Understanding the origin of magnetism may provide important
clue to the unconventional pairing. The parent compounds of iron-based
superconductors (FeSCs), such as BaFe2As2 Richard  _et al._ (2010) and LaFeAsO
Yildirim (2008), generally feature well nested hole/electron pockets and
undergoes AFM transition at low temperature Chen  _et al._ (2014). Charge
doping can degrade the nesting condition to suppress the AFM transition, thus
inducing superconductivity at the boundary of AFM phase. Therefore, the paring
mechanism has been proposed to be associate with the scattering between hole
and electron pockets, which is induced by the nesting related spin-density-
wave- (SDW-) type fluctuations Chen  _et al._ (2014); Mazin  _et al._ (2008).
In this picture, magnetism, as well as superconductivity, may strongly depend
on the topology of the Fermi surface Yin  _et al._ (2011).

However, in FeTe the Fermi surface nesting fails in accounting for the
bicollinear AFM order Li  _et al._ (2009). Moreover, in K2Fe4Se5 Mou  _et al._
(2011) and (Li0.8Fe0.2)(OH)FeSe Zhao  _et al._ (2016), even though no hole
pockets exist at $\Gamma$ point, the superconducting gaps still open on the
Fermi surfaces. Thus, the pairing mechanism cannot be understood in terms of
Fermi surface instability, the electrons below the Fermi surface may also play
an important role Chen  _et al._ (2014). Moreover, Iimura et al. Hiraishi  _et
al._ (2014); Iimura  _et al._ (2012) has found another superconducting dome
and AFM ordered state in electron-overdoped area of REFeAsO1-xHx (RE= rare
earth), these anomalous behaviors introduce additional puzzle and could reveal
more rich physics in FeSCs. However, since the lack of large sized single
crystal, there is difficulty in carrying out detail experiments.

Ca1-xRExFeAs2 is a newly discovered iron-pnictide family with a monotonic
structure (space group $P_{21}$) Katayama  _et al._ (2013). It consists of
alternatively stacked FeAs and (Ca,RE)As layers. Rare earth doping on Ca site
can introduce electrons into the FeAs layers and induce superconductivity with
$T_{c}=35\leavevmode\nobreak\ K(x=0.15)$ Li  _et al._ (2015). With further
electron doping, superconductivity is suppressed, however instead of the
Fermi-liquid (FL) behavior in some other iron pnictides, there is a recovery
of the AFM order, which is confirmed by recent nuclear magnetic resonance
(NMR) Kawasaki  _et al._ (2015) and neutron scattering results Jiang  _et al._
(2016a), similar to what happened in REFeAsO1-xHx Hiraishi  _et al._ (2014).
Since the AFM is intimately related to superconductivity, studying such
anomalous behavior may provide some new physics and shed new light on the
mechanism of the unconventional superconductivity in FeSCs .

In this work, we have synthesized single crystals of the electron overdoped
Ca0.77Nd0.23FeAs2 Katayama  _et al._ (2013) ($T_{N}\lesssim$73 K), and
measured its temperature dependent in-plane reflectivity before and after the
AFM phase transition. To analysis the optical conductivity, we use two Drude
components to describe the low energy ($<2\,000$$\leavevmode\nobreak\
\textrm{cm}^{-1}$) response, to account for the multiband nature of FeSCs Wu
_et al._ (2010); Dai  _et al._ (2015). Such two-Drude model reveals a narrow
temperature-dependent Drude item representing the coherent response, and a
broad temperature-independent Drude one representing the incoherent response.
Across the phase transition, we notice that the broad Drude component is
significantly suppressed. Correspondingly, the spectral weight of optical
conductivity at low frequency (50-2 000$\leavevmode\nobreak\
\textrm{cm}^{-1}$) is reduced. Unlike the parent compound of 122 system, a
lack of the signature of SDW transition in the optical conductivity indicates
the poor nesting condition. However, a spectral weight analysis shows that the
reduced spectral weight at low frequency is transferred to the high frequency
area ($\gtrsim 4\,000$$\leavevmode\nobreak\ \textrm{cm}^{-1}$), indicating a
localization effect, such as Hund’s rule coupling. We infer that the magnetism
in such electron-overdoped system may come from a localization effect and do
not rely on the topology of the Fermi surface.

High-quality single crystal of Ca1-xNdxFeAs2 were synthesized by heating a
mixture of Ca, Nd, FeAs, As powders with nominal composition of $x=0.2$
Katayama  _et al._ (2013); Kudo  _et al._ (2014), typical size was about
3$\times$3$\times$0.1 mm3. The composition determined by Inductive Coupled
Plasma Emission Spectrometer (ICP) was Ca0.77Nd0.23FeAs2. Resistivity
measurement was taken on Quantum Design Physical Property Measurement System
(PPMS). Magnetization was measured using a Quantum Design superconducting
quantum interference device (SQUID). The reflectivity from the cleaved surface
has been measured at a near-normal angle of incidence on a Fourier transform
infrared spectrometer (Bruker 80v) for light polarized in the $ab$ planes
using an $in\leavevmode\nobreak\ situ$ evaporation technique. Homes  _et al._
(1993) Data from 40 to 15 000$\leavevmode\nobreak\ \textrm{cm}^{-1}$ were
collected at 8 different temperatures from 15 to 300 K on an ARS-Helitran
cryostat. The reflectivity in visible and UV range (10 000-40
000$\leavevmode\nobreak\ \textrm{cm}^{-1}$) at room temperature was taken with
an Avaspec 2048$\times$14 optical fiber spectrometer. The optical conductivity
has been determined from a Kramers-Kronig analysis of reflectivity $R(\omega)$
over the entire frequency range. Since the measurement is made in a limited
energy range. A Hagen-Rubens relation ($R=1-A\sqrt{\omega}$) is used for low-
frequency extrapolation. Above the highest-measured frequency (40
000$\leavevmode\nobreak\ \textrm{cm}^{-1}$), $R(\omega)$ is assumed to be
constant up to 40 eV, above which a free-electron response ($\omega^{-4}$) is
used Dai  _et al._ (2013).

Figure 1:  (color online) (a) Temperature dependence of normalized resistivity
of Ca0.77Nd0.23FeAs2with $I\parallel c-axis$ (blue) and $I\parallel ab-plane$
(red). (b) The temperature dependence of magnetic suseptbility of
Ca0.77Nd0.23FeAs2with $H\parallel ab$ plane at $1$ T. Inset is its derivative
with temperature. Arrows indicate the Neel temperature. Figure 2:  (color
online)Reflectivity (a) and optical conductivity (b) of Ca0.77Nd0.23FeAs2 at
various temperatures. The red arrows indicates the suppression in reflectivity
and optical conductivity.

Fig. 1(a) shows the temperature dependent resistance with $I\parallel ab$
plane and $I\parallel c$ axis, we note that above 73 K the in-plane resistance
shows a metallic behavior which decreases upon cooling, while the inter-plane
resistance shows an insulating behavior, i.e., increases with decreasing
temperature. It means that even though the CaAs layer has been reported to be
metallic, the inter-layer coupling is still weak. While at 73 K, we note a
sudden drop on both curves, and a kink could also be observed in its magnetic
susceptibility [Fig. 1(b)], these anomalies have been demonstrated to be
caused by structural and AFM phase transition Jiang  _et al._ (2016a). Below
10 K, another drop in $R(T)$ [Fig. 1(a)] may come from the filamentary
superconductivity. In addition to these observations, we also note that, in
the normal state, the in-plane resistance shows an obvious non-Fermi-liquid
(NFL) behavior(discrepancy of the $T^{2}$ behavior) Analytis  _et al._ (2014);
Dai  _et al._ (2015), but after the phase transition the system becomes much
more coherent. Such phenomenon can be understood in terms of the spin-
fluctuations scattering, i.e., in the normal state, there exists strong spin
fluctuation to scatter the carrier and results in NFL behavior, while in the
magnetic ordered state the fluctuation is greatly suppressed Dai  _et al._
(2015).

The measured in-plane reflectivity and the real part of the optical
conductivity $\sigma_{1}(\omega,\leavevmode\nobreak\ T)$ are summarized in
Fig. 2, for selected temperature above and below the AFM phase transition. The
reflectivity shows a typical metallic behavior, approaching unity at low
frequencies ($<1\,000\leavevmode\nobreak\ \textrm{cm}^{-1}$) and increasing
upon cooling. After the AFM phase transition, a suppression of
$R(\omega,\leavevmode\nobreak\ T)$ in the mid-infrared range (500-2
000$\leavevmode\nobreak\ \textrm{cm}^{-1}$) can be seen. Correspondingly,
similar behavior is also found in the optical conductivity spectra, indicating
the change of the band structure and a loss of density of states near the
Fermi level. Comparing with BaFe2As2, which also undergoes an AFM phase
transition Hu  _et al._ (2008), below 73 K, no additional gaplike feature
below 3 000$\leavevmode\nobreak\ \textrm{cm}^{-1}$ can be found, indicating no
SDW transition happened in Ca0.77Nd0.23FeAs2, the reason will be discussed
later.

To quantitatively analyze the optical data of Ca0.77Nd0.23FeAs2, we fit the
$\sigma_{1}(\omega,T)$ with a simple Drude-Lorentz mode for the dielectric
function:

$\epsilon(\omega)=\epsilon_{\infty}-\sum_{i}\frac{\Omega^{2}_{p,i}}{\omega^{2}+\frac{i\omega}{\tau_{i}}}+\sum_{j}\frac{\Omega^{2}_{j}}{\omega^{2}_{j}-\omega^{2}-\frac{i\omega}{\tau_{i}}},$
(1)

where $\epsilon_{\infty}$ is the real part of the dielectric function at high
frequencies, the second term corresponds to the Drude response characterized
by a plasma frequency $\Omega_{p,i}^{2}=4\pi ne^{2}/m^{*}$, with $n$ a carrier
concentration and $m^{*}$ an effective mass, and $1/\tau_{i}$ the scattering
rate. The third term is a sum of Lorentz oscillators characterized by a
resonance frequency $\omega_{j}$, a linewidth $\gamma_{j}$, and an oscillator
strength $\Omega_{j}$. The Drude term accounts for the itinerant carrier
(intraband) response, while the Lorentz contributions represent the localized
(interband) excitations Homes  _et al._ (2015). The complex conductivity
$\tilde{\sigma}(\omega)=\sigma_{1}+i\sigma_{2}=i\omega[\tilde{\varepsilon}(\omega)-\varepsilon_{\infty}]/60$
(in units of $\Omega^{-1}\cdot\leavevmode\nobreak\ \textrm{cm}^{-1}$). The
fitting results shown in Fig. 3(a)(b) can well reproduce the experimental
results.

Fig. 3(a)(b) summarize the fitting results, considering the multiband nature
of FeSCs, we use two Drude component(a narrow one and a broad one) and a
Lorentz components to describe the optical response below 6
000$\leavevmode\nobreak\ \textrm{cm}^{-1}$ Wu  _et al._ (2010). The narrow
Drude item has strongly temperature-dependent scattering rate at low
temperature($1/\tau_{nD}\simeq 32\leavevmode\nobreak\ \textrm{cm}^{-1}$, 10 K)
and represents the coherent response. Whereas the scattering rate of the broad
Drude item is 2 000$\leavevmode\nobreak\ \textrm{cm}^{-1}$or larger,
corresponding to a mean free path shorter than the lattice spacing and
indicating a highly incoherent character Nakajima  _et al._ (2014a, b). The
broad Drude item is much stronger than the narrow one, but it almost does not
change with the temperature, representing an incoherent background Homes  _et
al._ (2015). Across the AFM transition, in Fig. 3(c) we note the broad Drude
component is greatly suppressed. Meanwhile, the scattering rate of the
coherent response is also reduced [Fig. 3(d)]. Considering the suppressed spin
fluctuation in AFM ordered state, we infer the incoherent response may have a
relation with the AFM fluctuation. The overall plasma frequency $\Omega_{p}$
is considered to contribute from both narrow and broad Drude component with
$\Omega_{p}=(\Omega_{nD,p}^{2}+\Omega_{bD,p}^{2})^{1/2}$. In Fig. 3(c), we
note that even though the narrow Drude component is a little enhanced, the
overall frequency is suppressed across the phase transition, indicating a loss
of the itinerant carriers after the transition. So where do the lost carriers
go?

Figure 3: (color on line) (a) (b) Optical conductivity of Ca0.77Nd0.23FeAs2 at
75 K and 5 K (thick black lines), fitting with the Drude-Lorentz model (thin
red lines) and its decomposition into individual Drude and Lorentz terms. (c)
Plasma frequency for the narrow Drude(blue), broad Drude(green) and the total
weights of the narrow and broad Drude components (red) for various
temperatures. (d) $T$ dependence of the quasiparticle scattering rate
$1/\tau_{nD}$ derived from the coherent narrow Drude component.(The vertical
dashed line denotes the phase transition.)

In Fig. 4(b), we have calculated the spectral weight in different areas of
optical conductivity. From the results, one notes that the spectral weight at
high energy (4 000-15 000$\leavevmode\nobreak\ \textrm{cm}^{-1}$) varies
significantly with the temperature. Upon cooling, the spectral weight at high
frequency is continuously enhanced while the overall spectral weight keeps
constant. It means the spectral weight at low frequency is transferred from
low to high frequency area. Such a pseudogap-like behavior has been widely
attributed to the Hund’s rule coupling effect, which can localize and polarize
the itinerant electrons to enhance the electron correlation and AFM exchange
interaction Wang  _et al._ (2012). At low temperature ($\lesssim
73\leavevmode\nobreak\ K$), we observed an additional enhancement of the high-
frequency spectral weight, combined with the result of fitting analysis, we
find that the suppressed spectral weight at low frequency area (500-2
000$\leavevmode\nobreak\ \textrm{cm}^{-1}$) in the magnetic ordered state has
been moved to the high frequency area, reflecting a sudden enhanced
localization effect. Further research is needed to determine whether this
effect is caused by Hund’s rule coupling or some other effects.

Figure 4: (color on line) (a) Enlarged optical conductivity of
Ca0.77Nd0.23FeAs2 before and after the phase transition, from which we could
clearly see the spectral weight transference indicated by the red arrow. (b)
Temperature dependence of the spectral weight,
$W^{\omega_{b}}_{\omega_{a}}\leavevmode\nobreak\ =\leavevmode\nobreak\
\int^{\omega_{b}}_{\omega_{a}}\sigma_{1}(\omega)d\omega$ between different
lower and upper cutoff frequencies. The vertical dashed line denotes the phase
transition.

Even though the spectral weight at low frequency area is greatly transferred
to high frequency area during the phase transition, we do not observe any
additional gap-like feature in the optical conductivity (Fig. 2(b)) after the
AFM phase transition (evidence given by spectral analysis is shown in Appendix
B). This is different from what happened in BaFe2As2, which undergoes an SDW
transition and has a signature of opening a gap in its optical spectrum Hu
_et al._ (2008). Comparing their Fermi surface, we note that, BaFe2As2 as a
compensate metal has equal sized electron and hole pockets, and there is a
good nesting between them along the ($\pi,\pi$) direction in the Brillouin
zone Richard  _et al._ (2011, 2010). This will lead to the instability of the
Fermi surface and SDW transition at low temperature Hancock  _et al._ (2010).
Whereas recent ARPES results on Ca0.73La0.27FeAs2 indicate electron-overdoped
FeAs layers Jiang  _et al._ (2016a), in which electron pockets is much bigger
than hole pockets and lead to poor nesting condition (comparing with the less
doped ones) so as to no SDW transition and no gap on its Fermi surface. The
AFM transition in such poorly nested system suggests the magnetism in
electron-overdoped Ca0.77Nd0.23FeAs2 does not rely on the topology of the
Fermi surface. The spectral weight transfer without a SDW gap creates a
pseudogap feature in the optical spectrum across the AFM phase transition.

Such strong magnetism in electron-overdoped Ca1-xRExFeAs2 cannot be understood
by previous theoretical model Dai  _et al._ (2012); Ikeda  _et al._ (2010), in
which the electron doping could continuously suppress the magnetic order and
low energy spin fluctuation with worsening nesting condition. Moreover, recent
NMR results point out that magnetism is rather enhanced with doping Kawasaki
_et al._ (2015), such behavior cannot be understood in terms of the Fermi
surface nesting. Thus, the mechanism for the magnetism in overdoped area
should be reconsidered.

Very recently, the XRD experiments Jiang  _et al._ (2016a) on Ca1-xLaxFeAs2
found that the height of As atom (in FeAs layer) corresponding to Fe layer in
electron-overdoped sample ($x=0.27$) is 1.422(5) Å, while it is 1.412(5) Å for
the less doped one ($x=0.195$) Katayama  _et al._ (2013), indicating the rare
earth doping could somehow increase the pnictogen height in Ca1-xLaxFeAs2.
Such behavior could enlarge the distance between Fe and As atoms and suppress
the hybridization between Fe 3d and As 4p orbitals Diehl  _et al._ (2014). As
a result, electrons on Fe atoms could be much more localized and the electron
correlation as well as the local magnetic moment are enhanced Zhang  _et al._
(2014); Diehl  _et al._ (2014). Furthermore, across the AFM phase transition
in Ca0.73La0.27FeAs2, the lattice parameters a,b,c as well as the cell volume
are found to be enlarged abruptly, such negative thermal expansion could
narrow the bandwidth and localize the electrons, which is consistent with our
observations in optical spectroscopy, thus we propose that the magnetic
transition is mostly like to have a localized origin. Even though an enhanced
localization effect accompany with the phase transition, the system is still
in a metallic state. From the fitting analysis of the optical data in Fig.
3(a)(b), we note that the AFM transition mainly affects the broad Drude item,
while the narrow one is almost unaffected. This may reflect the multiband
nature of FeSCs Si  _et al._ (2009); de Medici  _et al._ (2009), from which
the much incoherent bands (or orbitals) are selected to be localized across
the phase transition Neupane  _et al._ (2009).

In summary, we have synthesized the single crystal of Ca0.77Nd0.23FeAs2 and
investigated its optical response at temperatures before and after the phase
transition. From the optical conductivity, we find obvious spectral weight
transfer from low to high energy area without any signature of SDW gap across
the AFM phase transition. Therefore, we propose the magnetism in electron-
overdoped Ca1-xRExFeAs2 may come from the localization effect, which results
in a pseudogap feature, and do not rely on the Fermi surface nesting. Since
further electron doping by Co in Ca0.73La0.27Fe1-xCoxAs2 could induce another
superconducting dome Jiang  _et al._ (2015), more investigation on this system
may shed new lights on the mechanism of high-$T_{c}$ superconductivity in
FeSCs.

###### Acknowledgements.

We thank Kui Jin, Shiliang Li, Congcong Le and Xianxin Wu for useful
discussion. This work was supported by the NSFC (Grants No. 91121004 and 973
Projects No. 2015CB921303) and the MSTC (973 Projects No. 2011CBA00107, No.
2012CB821400, No. 2012CB921302, and No. 2009CB929102).

##  Appendix A Hall coefficient

To determine the electron concentration of Ca0.77Nd0.23FeAs2 we measured its
Hall resistance $\rho_{xy}$ and calculated the Hall coefficient at 300 K. The
Hall coefficient of Ca0.77Nd0.23FeAs2at 300 K is $-9.5\times 10^{-9}m^{3}/C$,
which is comparable with that of Ca0.73La0.27FeAs2 Jiang  _et al._ (2016b),
indicating that the Ca0.77Nd0.23FeAs2 is electron-overdoped.

Figure 5:  (color online)Hall resistance and Hall coefficient of
Ca0.77Nd0.23FeAs2 at 300 K.

##  Appendix B Detail spectral weight analysis

In Fig. 6 we calculated the ratio of the spectral weight as a function of
cutoff frequency for BaFe2As2 and Ca0.77Nd0.23FeAs2 respectively. Comparing
with BaFe2As2, we find no obvious signature characteristic of opening a gap
within the SDW scale of BaFe2As2 but an enhanced spectral weight transfer from
low to high energy area (Fig. 4(a)(b)), such behavior might be regarded as a
pseudogap behavior.

Figure 6:  (color online)Ratio of the integrated spectral weight W(T)/W(300)
as a function of cutoff frequency (wave number) in BaFe2As2 (a) and
Ca0.77Nd0.23FeAs2 (b).

## References

  * Lee  _et al._ (2006) P. A. Lee, N. Nagaosa, and X.-G. Wen, Reviews of Modern Physics 78, 17 (2006).
  * Richard  _et al._ (2010) P. Richard, K. Nakayama, T. Sato, M. Neupane, Y.-M. Xu, J. H. Bowen, G. F. Chen, J. L. Luo, N. L. Wang, X. Dai, Z. Fang, H. Ding, and T. Takahashi, Phys. Rev. Lett. 104, 137001 (2010).
  * Yildirim (2008) T. Yildirim, Phys. Rev. Lett. 101, 057010 (2008).
  * Chen  _et al._ (2014) X. Chen, P. Dai, D. Feng, T. Xiang, and F.-C. Zhang, National Science Review 1, 371 (2014).
  * Mazin  _et al._ (2008) I. I. Mazin, D. J. Singh, M. D. Johannes, and M. H. Du, Phys. Rev. Lett. 101, 057003 (2008).
  * Yin  _et al._ (2011) Z. P. Yin, K. Haule, and G. Kotliar, Nature Materials 10, 932 (2011).
  * Li  _et al._ (2009) S. Li, C. de la Cruz, Q. Huang, Y. Chen, J. W. Lynn, J. Hu, Y.-L. Huang, F.-C. Hsu, K.-W. Yeh, M.-K. Wu, and P. Dai, Phys. Rev. B 79, 054503 (2009).
  * Mou  _et al._ (2011) D.-x. Mou, L. Zhao, and X.-j. Zhou, Frontiers of Physics 6, 410 (2011).
  * Zhao  _et al._ (2016) L. Zhao, A. Liang, D. Yuan, Y. Hu, D. Liu, J. Huang, S. He, B. Shen, Y. Xu, X. Liu, L. Yu, G. Liu, H. Zhou, Y. Huang, X. Dong, F. Zhou, K. Liu, Z. Lu, Z. Zhao, C. Chen, Z. Xu, and X. J. Zhou, Nature Communications 7, 10608 (2016).
  * Hiraishi  _et al._ (2014) M. Hiraishi, S. Iimura, K. M. Kojima, J. Yamaura, H. Hiraka, K. Ikeda, P. Miao, Y. Ishikawa, S. Torii, M. Miyazaki, I. Yamauchi, A. Koda, K. Ishii, M. Yoshida, J. Mizuki, R. Kadono, R. Kumai, T. Kamiyama, T. Otomo, Y. Murakami, S. Matsuishi, and H. Hosono, Nat. Phys. 10, 300 (2014).
  * Iimura  _et al._ (2012) S. Iimura, S. Matuishi, H. Sato, T. Hanna, Y. Muraba, S. W. Kim, J. E. Kim, M. Takata, and H. Hosono, Nature Communications 3, 943 (2012).
  * Katayama  _et al._ (2013) N. Katayama, K. Kudo, S. Onari, T. Mizukami, K. Sugawara, Y. Sugiyama, Y. Kitahama, K. Iba, K. Fujimura, N. Nishimoto, M. Nohara, and H. Sawa, J. Phys. Soc. Jpn. 82, 123702 (2013).
  * Li  _et al._ (2015) M. Y. Li, Z. T. Liu, W. Zhou, H. F. Yang, D. W. Shen, W. Li, J. Jiang, X. H. Niu, B. P. Xie, Y. Sun, C. C. Fan, Q. Yao, J. S. Liu, Z. X. Shi, and X. M. Xie, Phys. Rev. B 91, 045112 (2015).
  * Kawasaki  _et al._ (2015) S. Kawasaki, T. Mabuchi, S. Maeda, T. Adachi, T. Mizukami, K. Kudo, M. Nohara, and G.-q. Zheng, Phys. Rev. B 92, 180508 (2015).
  * Jiang  _et al._ (2016a) S. Jiang, C. Liu, H. Cao, T. Birol, J. M. Allred, W. Tian, L. Liu, K. Cho, M. J. Krogstad, J. Ma, K. M. Taddei, M. A. Tanatar, M. Hoesch, R. Prozorov, S. Rosenkranz, Y. J. Uemura, G. Kotliar, and N. Ni, Phys. Rev. B 93, 054522 (2016a).
  * Wu  _et al._ (2010) D. Wu, N. Barišić, P. Kallina, A. Faridian, B. Gorshunov, N. Drichko, L. J. Li, X. Lin, G. H. Cao, Z. A. Xu, N. L. Wang, and M. Dressel, Phys. Rev. B 81, 100512 (2010).
  * Dai  _et al._ (2015) Y. M. Dai, H. Miao, L. Y. Xing, X. C. Wang, P. S. Wang, H. Xiao, T. Qian, P. Richard, X. G. Qiu, W. Yu, C. Q. Jin, Z. Wang, P. D. Johnson, C. C. Homes, and H. Ding, Phys. Rev. X 5, 031035 (2015).
  * Kudo  _et al._ (2014) K. Kudo, Y. Kitahama, K. Fujimura, T. Mizukami, H. Ota, and M. Nohara, J. Phys. Soc. Jpn. 83, 093705 (2014).
  * Homes  _et al._ (1993) C. C. Homes, M. Reedyk, D. A. Cradles, and T. Timusk, Applied Optics 32, 2976 (1993).
  * Dai  _et al._ (2013) Y. M. Dai, B. Xu, B. Shen, H. Xiao, H. H. Wen, X. G. Qiu, C. C. Homes, and R. P. S. M. Lobo, Physical Review Letters 111, 117001 (2013).
  * Analytis  _et al._ (2014) J. G. Analytis, H.-H. Kuo, R. D. McDonald, M. Wartenbe, P. M. C. Rourke, N. E. Hussey, and I. R. Fisher, Nat. Phys. 10, 194 (2014).
  * Hu  _et al._ (2008) W. Z. Hu, J. Dong, G. Li, Z. Li, P. Zheng, G. F. Chen, J. L. Luo, and N. L. Wang, Phys. Rev. Lett. 101, 257005 (2008).
  * Homes  _et al._ (2015) C. C. Homes, Y. M. Dai, J. S. Wen, Z. J. Xu, and G. D. Gu, Phys. Rev. B 91, 144503 (2015).
  * Nakajima  _et al._ (2014a) M. Nakajima, S. Ishida, T. Tanaka, K. Kihou, Y. Tomioka, T. Saito, C.-H. Lee, H. Fukazawa, Y. Kohori, T. Kakeshita, A. Iyo, T. Ito, H. Eisaki, and S.-i. Uchida, J. Phys. Soc. Jpn. 83, 104703 (2014a).
  * Nakajima  _et al._ (2014b) M. Nakajima, S. Ishida, T. Tanaka, K. Kihou, Y. Tomioka, T. Saito, C. H. Lee, H. Fukazawa, Y. Kohori, T. Kakeshita, A. Iyo, T. Ito, H. Eisaki, and S. Uchida, Sci. Rep. 4 (2014b), 10.1038/srep05873.
  * Wang  _et al._ (2012) N. L. Wang, W. Z. Hu, Z. G. Chen, R. H. Yuan, G. Li, G. F. Chen, and T. Xiang, Journal of Physics: Condensed Matter 24, 294202 (2012).
  * Richard  _et al._ (2011) P. Richard, T. Sato, K. Nakayama, T. Takahashi, and H. Ding, Reports on Progress in Physics 74, 124512 (2011).
  * Hancock  _et al._ (2010) J. N. Hancock, S. I. Mirzaei, J. Gillett, S. E. Sebastian, J. Teyssier, R. Viennois, E. Giannini, and D. van der Marel, Phys. Rev. B 82, 014523 (2010).
  * Dai  _et al._ (2012) P. Dai, J. Hu, and E. Dagotto, Nat. Phys. 8, 709 (2012).
  * Ikeda  _et al._ (2010) H. Ikeda, R. Arita, and J. Kuneš, Phys. Rev. B 82, 024508 (2010).
  * Diehl  _et al._ (2014) J. Diehl, S. Backes, D. Guterding, H. O. Jeschke, and R. Valentí, Phys. Rev. B 90, 085110 (2014).
  * Zhang  _et al._ (2014) C. Zhang, L. W. Harriger, Z. Yin, W. Lv, M. Wang, G. Tan, Y. Song, D. L. Abernathy, W. Tian, T. Egami, K. Haule, G. Kotliar, and P. Dai, Physical Review Letters 112, 217202 (2014).
  * Si  _et al._ (2009) Q. Si, E. Abrahams, J. Dai, and J.-X. Zhu, New J. Phys. 11, 045001 (2009).
  * de Medici  _et al._ (2009) L. de Medici, S. R. Hassan, M. Capone, and X. Dai, Phys. Revs Lett. 102, 126401 (2009).
  * Neupane  _et al._ (2009) M. Neupane, P. Richard, Z.-H. Pan, Y.-M. Xu, R. Jin, D. Mandrus, X. Dai, Z. Fang, Z. Wang, and H. Ding, Phys. Revs Lett. 103, 097001 (2009).
  * Jiang  _et al._ (2015) S. Jiang, C. Liu, H. Cao, T. Birol, J. M. Allred, W. Tian, L. Liu, K. Cho, M. J. Krogstad, J. Ma, K. M. Taddei, M. A. Tanatar, M. Hoesch, R. Prozorov, S. Rosenkranz, Y. J. Uemura, G. Kotliar, and N. Ni,  (2015), arXiv:1505.05881 .
  * Jiang  _et al._ (2016b) S. Jiang, L. Liu, M. Schutt, A. M. Hallas, B. Shen, W. Tian, E. Emmanouilidou, A. Shi, G. M. Luke, Y. J. Uemura, R. M. Fernandes, and N. Ni,  (2016b), arXiv:1603.04899 .