Magnetization and magneto-transport staircaselike behavior in layered perovskite Sr2CoO4 at low temperature

Polycrystalline layered perovskite Sr2CoO4 sample was synthesized by high temperature and high pressure method. The staircaselike behavior has been observed in the magnetization and resistivity versus field curves of Sr2CoO4 at low temperature. The main features of the steps can be obtained from the measured results: (i) the positions of the external magnetic field at which steps occur are varying in different measurement runs, (ii) the steps only appear at low temperature and disappear with a slight increase of the temperature, (iii) the steps are dependent on the temperature and field sweep rate. Based on the features of the magnetization and magneto-transport staircaselike behavior in Sr2CoO4, the unusual phenomenon can be ascribed to an avalanche of flipping domains in terms of the random field theory.

potentials of Sr 2 CoO 4 in magnetic materials and devices. Thus, systematical experiments are urgently needed to study the exceptional phenomenon of Sr 2 CoO 4 at low temperature and explore the possibility of the staircaselike behavior for various practical applications. In this work, the magnetic and electrical properties of polycrystalline Sr 2 CoO 4 were studied below 5 K. The staircaselike behavior was observed in a series of magnetic and electrical curves, such as magnetization versus field (M-H) and resistivity versus field (ρ-H) curves. Based on the reported researches and explanations on the staircaselike behaviors observed in other materials, the mechanism of the staircaselike behavior in Sr 2 CoO 4 was discussed in detail. Figure 1 shows the powder X-ray diffraction (XRD) pattern of polycrystalline Sr 2 CoO 4 measured at room temperature. The main diffraction peaks of the sample can be fitted well with the XRD profile of Sr 2 CoO 4 and indexed using the lattice parameters for a tetragonal structure with a = 3.8372 Å and c = 12.1935 Å. A few additional peaks (marked by #) corresponding to nonmagnetic impurity SrO 2 can be observed in the pattern. However, this SrO 2 impurity phase is present in a small amount from the weak intensity of the peaks and has no effect on the magnetic properties of our sample. The inset of Fig. 1 shows the scanning electron microscope (SEM) photograph of Sr 2 CoO 4 . The grains of the sample, with the average size approximately 20 μ m, are dense and distribute uniformly.

Results
The M-H curve of Sr 2 CoO 4 measured at 1.8 K with a field sweep rate of 25 Oe/s is displayed in Fig. 2(a). The saturation magnetization is 1.02μ B /Co, and the H C is approximately 1.9 T. The large H C is caused by high anisotropy in Sr 2 CoO 4 8 . Most interestingly, unlike the general hysteresis loops, a staircaselike behavior can be observed from the M-H loop in Fig. 2(a). The steps on both sides of the hysteresis loop are central symmetry. The span (Δ M) of the four stairs on one side of the loop decreases with the increasing of the applied field (see Fig. 2(a)). The dM/dH versus field curve ( Fig. 2(b)) clearly shows that the four jumps on one side occur at − 1.84 T (1), − 2.56 T (2), − 3.20 T (3), − 3.70 T (4), respectively. Moreover, two almost invisible jumps are reflected (see the # in Fig. 2(b)). The inset of Fig. 2(a) shows the three measurement runs from the same piece of sample measured at 1.8 K with a field sweep rate of 25 Oe/s. It can be seen that the steps on these curves of the same piece of sample are obviously misaligned for different measurement runs under the same measurement condition. This result suggests the randomness of the staircaselike behavior in different measurement runs. Figure 3 shows the M-H curves of Sr 2 CoO 4 measured at different temperatures. It can be observed that with increasing of the temperature, the quantity of the steps decreases and the positions of the corresponding steps move towards the direction of high field. At 2.8 K, the staircaselike behavior disappears completely. These results suggest that the staircaselike behavior is sensitive excessively to the slight temperature variation. The inset of Fig. 3 shows the M-H curves of Sr 2 CoO 4 measured at 2 K with different magnetic field sweep rates. With the increasing of the sweep rate, the quantity of the steps increases gradually and the positions of the corresponding steps move towards the low field (see the arrow in the inset of Fig. 3). It can be deemed that the staircaselike behavior in Sr 2 CoO 4 is dependent on the magnetic field sweep rate. Figure 4 shows the ρ-H curve of Sr 2 CoO 4 measured at 2 K. The resistivity reaches a maximum at H C , which is consistent with the previous reports 1,2 . This phenomenon can be considered as tunneling MR at domain boundaries. It is attributed to the field suppression of the spin-dependent scattering at domain boundaries 8

Discussion
Three main characteristics of the staircaselike behavior in Sr 2 CoO 4 are concluded from the measured results: (i) the positions of the steps are varying in different measurement runs, (ii) the steps only appear at low temperature (T < 2.8 K) and disappear with a slight increase of the temperature, (iii) the steps are dependent on the temperature and field sweep rate. The possible mechanism of the staircaselike behavior will be systematically discussed below.
Resonant quantum tunneling has been applied to systems involving a large number of identical high-spin materials [14][15][16][17][18][19][20] , as in the case of Ca 3 Co 2 O 6 14,15 , and Mn 12 acetate 20 . Ca 3 Co 2 O 6 is a type of perovskite material with K 4 CdCl 6 -type structure (an infinite chain-type structure). The analogous steps can be observed from the M-H curves of Ca 3 Co 2 O 6 at low temperature 14,15 . The steps are resulted from the transformation and change of the  percentage of different magnetism in the materials caused by the applied field at different temperatures 14 . The chain-type structure is the key factor to the staircaselike behavior. The intrachain coupling is ferromagnetic and the interchain coupling is antiferromagnetic. However, Sr 2 CoO 4 is one type of two-dimensional layer structured compound. Obviously, no chain-type structure exists in Sr 2 CoO 4 . On the other hand, the most important characteristic of the staircaselike behavior in quantum-effect system is that the positions of the steps are temperature-independent below a critical temperature 17,18 . The results from the Fig. 3 of Sr 2 CoO 4 show that the steps in the six M-H curves exhibit no similar characteristic of temperature independence. This result indicates that the staircaselike behavior in Sr 2 CoO 4 is incompatible with resonant quantum tunneling.
The presence of random fields is another explanation that can lead to staircaselike behavior. Under this mechanism, a given domain is flipped by an external field, thus reversing the magnetization of the neighboring domains and finally resulting in an avalanche of flipping domains [21][22][23][24][25][26][27][28][29] considering the random field Ising model (RFIM) [31][32][33][34] . Each jump in one curve corresponds to an avalanche process where the spins (of one or more clusters in the polycrystalline Sr 2 CoO 4 ) align with the applied magnetic field 26 . The noteworthy characteristic of the steps in this theory is the randomness. The positions of the steps are varying in different measurement runs. Meanwhile, the steps can be only observed at low temperature. The ferromagnetic clusters in Sr 2 CoO 4 sample play a crucial role for this phenomenon 13,[26][27][28] . Below the critical temperature at which the steps are vanished, the ferromagnetic cluster-sizes in the sample increase, and the cluster percolation process yields an increase in the ferromagnetic correlation length with lowering the temperature 26 . The larger cluster-size can result in the bigger avalanche, which gives rise to the distinct jumps. Above the critical temperature, the thermal activation is dominating 26 , and the cluster-size is so small, which can only cause small avalanche. As a consequence, the jumps become sightless, and the hysteresis loop becomes smooth. This type of staircaselike behaviors is dependent on temperature, but independent on field sweep rate. Such an explanation has been proposed in site-diluted metamagnet Fe x Mg 1−x Cl 2 21 , single crystal antiferromagnet PrVO 3 22 , single crystalline UGe 2 23,24 , disordered systems such as the amorphous Dy-Cu 25 , polycrystalline CeNi 1−x Cu x [26][27][28][29] , and liquid quenched R 3 Co alloys 30 . All the features of the steps in Sr 2 CoO 4 are similar to the characteristics of staircaselike behaviors in PrVO 3 22 , UGe 2 23,24 , and CeNi 1−x Cu x [26][27][28][29] . The other features of the steps, except the dependence of magnetic field sweep rate, can be well explained by the random field theory. The dependence of magnetic field sweep rate may result from the magnetocaloric effect 22,35 . The positions of the corresponding steps move to higher field with the decreasing of the sweep rate. It suggests the existence of adiabaticity in Sr 2 CoO 4 . In the adiabatic state, the energy released in the spin reversal process dissipates tardily 35 . With the increasing of the sweep rate, the energy accumulates rapidly and facilitates the reversal of neighboring spins. It results in the sweep rate dependence of the steps. From this point of view, the fundamental reason of the staircaselike behavior in Sr 2 CoO 4 may be ascribed to an avalanche of flipping domains in terms of the random field theory.
The intrinsic pinning of magnetic domain walls is compatible with the magnetization jumps observed in alloy samples [36][37][38] . The domain walls motioning inside the ferromagnetic domains depend on the pinning effect introduced by foreign elements and the local crystal fields. The pinning effect can result in the creation of energetic barriers, which influence the magnetization process at low temperature 36 . In the case of EuBaCo 1.92 M 0.08 O 5.5−δ (M = Zn, Cu) 37 , Zn 2+ and Cu 2+ are the origin of the pinning of the narrow domain walls. When the magnetic field becomes high enough to overcome the pinning effect, the domain walls tend to disappear and the spins of the ferromagnetic domains are all aligned. This type of the staircaselike behaviors strongly depends on the external magnetic field sweep rate. When the magnetic field changes slowly enough, the M-H curve becomes normal with no jump 38 . This phenomenon was similar to the result from the inset of Fig. 3 in Sr 2 CoO 4 . In the perfect Sr 2 CoO 4 crystals, no substituted defect results in the effective pinning. However, here, the saturated moment of the Sr 2 CoO 4 sample (1.02μ B /Co) is lower than the calculated value (1.97 μ B /Co) 2 . Meanwhile, the μ eff of Co ion (4.11 μ B /Co) in Sr 2 CoO 4 is also different from the spin only moments of LS Co 4+ (1.73 μ B /Co), IS Co 4+ (3.87 μ B /Co), and HS Co 4+ (5.92 μ B /Co) 1,4 . These results suggest that multiple spin states may exist in our Sr 2 CoO 4 sample. The interactions between the neighboring IS or HS Co ions (Co(IS or HS)-O-Co(IS or HS)) are antiferromagnetic 39,40 , though the ground state of Sr 2 CoO 4 is ferromagnetic 6 . It means that antiferromagnetism and ferromagnetism are coexistent in Sr 2 CoO 4 , which can lead to multiple magnetic phases. The multiple magnetic phases may result in the intrinsic pinning of magnetic domain walls 36,41,42 , and further contribute to the magnetization and magneto-transport staircaselike behavior in the Sr 2 CoO 4 .
In summary, layered perovskite compound Sr 2 CoO 4 polycrystalline sample was synthesized by high temperature and high pressure method. The magnetic and magneto-transport properties of Sr 2 CoO 4 were studied at low temperature. A staircaselike behavior on M-H and ρ-H curves was observed in polycrystalline Sr 2 CoO 4 below 2.8 K. The steps appear with a certain degree of randomness in different measurement runs. The staircaselike behavior is dependent on the temperature and the magnetic field sweep rate. The fundamental reason of the staircaselike behavior can be considered as the presence of random fields, leading to an avalanche of flipping domains. The multiple magnetic phases which can result in the intrinsic pinning of magnetic domain walls, may contribute to the magnetization and magneto-transport staircaselike behavior in the Sr 2 CoO 4 .

Methods
Polycrystalline sample of composition Sr 2 CoO 4 was synthesized under high pressure at high temperature. Starting materials of SrO 2 and Co were well mixed in a molar ratio of SrO 2 : Co = 2 : 1. The mixture was sealed into a gold capsule. The capsule was first compressed at 6 GPa in a high pressure apparatus (flat-belt-type-high-pressure apparatus, 1500 ton), then heated to 1200 °C for 30 minutes and finally quenched to room temperature followed by releasing of pressure. The crystal structure of the polycrystalline sample was identified by the powder X-ray diffraction (XRD, Rigaku Smartlab3), using Cu-Kα radiation (λ = 1.54184 Å). The morphology of the sample was observed using a scanning electron microscope (SEM). The dc magnetic measurements were investigated using a vibrating sample magnetometer (VSM) integrated in a physical property measurement system (PPMS-9, Quantum Design). The electrical resistivity of the sample was measured with a Quantum Design PPMS-9 system using the standard four-probe ac method.