† Corresponding author. E-mail:
Project supported by the Science Fonds from the Ministry of Science and Technology of China (Grant Nos. 2017YFA0302903, 017YFA0303103, 2016YFA0300502, and 2015CB921302), the National Natural Science Foundation of China (Grant Nos. 11674406 and 11674372), the “Strategic Priority Research Program (B)” of the Chinese Academy of Sciences (Grant Nos. XDB07020300 and XDB07020200), and the Youth Innovation Promotion Association of the Chinese Academy of Sciences.
Nematic order and its fluctuations have been widely found in iron-based superconductors. Above the nematic order transition temperature, the resistivity shows a linear relationship with the uniaxial pressure or strain along the nematic direction and the normalized slope is thought to be associated with nematic susceptibility. Here we systematically studied the uniaxial pressure dependence of the resistivity in Sr1−xBaxFe1.97Ni0.03As2, where nonlinear behaviors are observed near the nematic transition temperature. We show that it can be well explained by the Landau theory for the second-order phase transitions considering that the external field is not zero. The effect of the coupling between the isotropic and nematic channels is shown to be negligible. Moreover, our results suggest that the nature of the magnetic and nematic transitions in Sr1 − xBaxFe2As2 is determined by the strength of the magnetic-elastic coupling.
One of the basic building blocks of iron-based superconductors is the Fe–As or Fe–Se layers, where Fe ions form a square lattice.[1] In many systems, the electronic system shows in-plane anisotropic properties that are believed to be associated with the nematic order,[2–6] which breaks the C4 rotational symmetry of the square lattice.[7] The onset of the nematic order is always coupled to a tetragonal-to-orthorhombic structural transition due to the electronic–lattice coupling,[7] i.e., the nematic transition temperature is equivalent to the structural transition temperature Ts. Therefore, from the symmetry point of view, the rotational symmetries of the nematic order and lattice are actually the same, which makes it hard to conclude whether the rotational symmetry breaking at Ts is driven by the electronic system or comes from the structural change. It is later found that the former picture should be appropriate,[8] where the nematic susceptibility is assumed to be proportional to the normalized slope of the strain dependence of elastoresistivity. This assumption has since been widely used in studying nematic susceptibility of iron-based superconductors.[9–14]
According to Ref. [8], the free energy of the nematic system under the uniaxial pressure p along the nematic direction can be written as follows:
In practice, the application of an external pressure along one lattice axis will inevitably induce strains along all directions. As pointed out in Refs. [15] and [14], the relative change of the resistivity Δρ/ρ0 to strain ε can be understood within the point group of D4h in the tetragonal notation as follows:
It has been found that the strain dependence of the elastoresistivity along the (110) direction shows a nonlinear term,[14] which is attributed to the isotropic (A1g) channel. It is argued that this is due to high-order terms as follows:[11]
However, we note that the above analysis is based on the assumption that the external field is small and the system is close to the zero-field state. In a paramagnetic system, when the magnetic field H is small, the magnetization M is proportional to H. However, when the field is large, M will show nonlinear behavior. In this work, we study the nonlinear behavior of the elastoresistivity in Sr1 − xBaxFe1.97Ni0.03As2 along the (110) direction.[13] Our results can be well described by the Landau theory for the second-order phase transition without the introduction of unusual strong coupling between the isotropic and nematic channels. Moreover, the magnetic and nematic transitions may be driven from first order to second order due to the enhancement of magneto-elastic coupling.
We first consider the effect when the external pressure is large. By minimizing the free energy of Eq. (
While the above analysis is for the uniaxial pressure dependence of the resistance, similar conclusions can be obtained for the strain dependence of the resistance since the pressure and strain are linearly coupled. The system we studied here is Sr1 − xBaxFe1.97Ni0.03As2, where the nematic and antiferromagnetic (AF) transitions change from first order to second order.[13] There is an intermediate doping range from 0.42 to 0.52, within which the nematic transition is first-order but the AF transition is second-order. All the data are obtained from Ref. [13].
Figure
Figure
Figures
As mentioned above, the nonlinear part of the resistivity may also come from the coupling between the isotropic (A1g) and nematic (B2g) channels.[14] In this case, the resistivity has a quadratic dependence on strain. However, according to Eq. (
Here we propose that the reason that a quadratic component may be wrongly obtained is because in practice, the zero-point of the pressure is hard to determine and the strain or pressure range is rather limited. In Fig.
All of the above results are consistent with those in Ref. [14], which suggests that the quadratic dependence of the resistance on the strain is wrongly obtained due to the uncertainty in determining the zero strain and the limited strain range a piezostack can achieve. While the coupling between A1g and B2g should present from the symmetry point of view, its effect is actually negligible.
We have systematically analyzed the uniaxial pressure dependence of the resistance in the Sr1 − xBaxFe1.97Ni0.03As2 system, which shows significant nonlinear behavior near the structural transition. By adopting the Landau theory for the second-order phase transition with a linear coupling between the strain and nematic order parameter, the data can be well described by considering the higher-order terms. Our results show that the coupling between the isotropic and nematic channels is negligible in iron-based superconductors. Moreover, the most significant factor in determining the nature of the magnetic and nematic transitions in Sr1 − xBaxFe1.97Ni0.03As2 may be the strength of the magneto-elastic coupling.
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