Magnetic field induced ferroelectricity and half magnetization plateau in polycrystalline R
2V
2O
7(R = Ni, Co)
R. Chen,1J. F. Wang,1,*Z. W. Ouyang,1,†Z. Z. He,2S. M. Wang,3L. Lin,3J. M. Liu,3C. L. Lu,1Y. Liu,4C. Dong,1,5 C. B. Liu,1Z. C. Xia,1A. Matsuo,5Y. Kohama,5and K. Kindo5
1Wuhan National High Magnetic Field Center and School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China
2State Key Laboratory of Structural Chemistry, Fujian Institute of Research on the Structure of Matter, Chinese Academy of Sciences, Fuzhou, Fujian 350002, China
3Laboratory of Solid State Microstructures and Innovative Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
4School of Physics and Technology, Wuhan University, Wuhan 430072, China
5The Institute for Solid State Physics (ISSP), University of Tokyo, Chiba 277-8581, Japan
(Received 20 July 2018; revised manuscript received 28 September 2018; published 5 November 2018) Low-dimensional frustrated antiferromagnet is a good model system to study exotic quantum physics. Here we report the observation of half magnetization plateau and ferroelectricity which emerge simultaneously in the bond-alternating skew-chain compoundsR2V2O7(R=Ni, Co) induced by high magnetic fields. The half plateau is stabilized in fields of 8–30 T (7–12 T) for Ni2V2O7(Co2V2O7), whereas two magnetic field induced ferroelectricities are located below and above this plateau. The remarkable high-field ferroelectricity for Ni or Co compound is about 50-60μC/m2 for the polycrystalline sample. The resulting magnetic field-temperature (H-T) phase diagrams are very complex and several distinct phase transitions are observed. The forced electric polarization by sweeping magnetic fields evidences a clear magnetoelectric coupling in Co2V2O7associated with the low-field ferroelectricity. Our magnetization data also reveal that Co2V2O7produces an effective spin-1/2 behavior at the magnetic ground state. These experimental findings improve the knowledge to multiferroics and pave the way for exploring the quantum state of frustrated antiferromagnets.
DOI:10.1103/PhysRevB.98.184404 I. INTRODUCTION
Magnetization plateau and multiferroicity are two dif- ferent emergent phenomena in frustrated antiferromagnets.
The former describes a quantum state that the magnetization (M) is magnetic field (H)-independent in a finite field range and its value is a fraction of saturation magnetization (Ms) [1–4]. The latter refers to a phase where two or more ferroic orders such as antiferromagnetism and ferroelectricity coexist [5–7]. For instance, the observed 1/3 magnetization plateau in Ba3CoSb2O9corresponds to a collinear “up-up-down” spin arrangement [2]; the spiral spin structure at a low temperature (T) or under magnetic fields accounts for the magnetically driven ferroelectricity in TbMnO3 [5]. The materials which exhibit both magnetization plateau and multiferroicity are rare because of the strict requirement of their peculiar spin configurations. This kind of material is of particular interest and usually gives rise to a complex magnetic phase diagram.
This has been studied, for instance, in the materials CuFeO2
and Ni3V2O8 [8–13]. Here we report two multiferroic ma- terialsR2V2O7 (R=Ni, Co), in which ferroelectricity and half magnetization plateau were observed simultaneously in applied magnetic fields.
The vanadate compounds with a formulaR2V2O7 (R = Cu, Ni, Co, Mn) show a variety of crystallographic
geometries with different magneticR2+ ions. The Cu2V2O7
compound crystallizes in at least three different polymorphs, namely,α,β,andγ phases with orthorhombic, monoclinic, and triclinic structures, respectively [14,15]. The compound Mn2V2O7 has distorted honeycomb layered structure and shows α (triclinic) and β (monoclinic) phases in low and high-temperature regions [16], while Ni2V2O7and Co2V2O7
stabilize in the ambient condition with a monoclinic structure [17,18]. Among all these materials,α-Cu2V2O7has attracted considerable attention due to its intriguing electronic and magnetic properties. This compound undergoes a canted an- tiferromagnetic ordering at TC=35 K [19]. High magnetic field study reveals successive magnetic phase transitions and a complexH-T phase diagram forH //a[20]. Interestingly, a giant electric polarization (P) as large as 0.55μC/cm2 was observed below TC [19]. Although the symmetric exchange striction, spin-dependent p-d hybridization, etc. were pro- posed [19,21,22], the mechanisms of this magnetically driven ferroelectricity have not been well understood. Moreover, α-Cu2V2O7 was regarded as the only multiferroic material among variousR2V2O7vanadate compounds [14].
Very recently, we studied Ni2V2O7 in pulsed magnetic fields up to 52 T and found that this compound also exhibits interesting magnetic phase transitions as α-Cu2V2O7 [23].
The magnetic behavior of Ni2V2O7 is dominated byS=1 Ni2+ ions. Figure 1 shows the two different Ni2+ sites in Ni2V2O7. They form bond-alternating skew chains along the c axis and are separated by nonmagnetic tetrahedrons VO4
between the chains [17]. The previous study of magnetic
R. CHENet al. PHYSICAL REVIEW B98, 184404 (2018)
FIG. 1. Crystallographic geometry of Ni2V2O7. (a) The two inequivalent Ni2+ ions (the blue and red symbols) showing the bond-alternating skew chains along thecaxis. Ni2V2O7crystallizes in a monoclinic structure with space group P21/c. (b), (c) The actual arrangements of Ni2+ions viewed along thecand theaaxis, respectively.
susceptibility and specific heat revealed magnetic transitions with a frustration ofθp/TN=4, whereθpis the Weiss constant andTNis the magnetic ordering temperature [17]. Our high- field measurements revealed that a wide half magnetization plateau is stabilized in fields of 8–30 T, accompanied by an exotic nematiclike phase transition for magnetic fields applied along three crystallographic axes [23]. In the present work, we performed magnetization and electric polarization measure- ments on Ni2V2O7 and Co2V2O7 polycrystalline samples in magnetic fields up to 60 T. Our main findings include: (1) the analog Co2V2O7 with similar skew-chain structure shows a clear half magnetization plateau in 7–12 T and behaves as a low-spin (S=1/2) state at low temperature; (2) both compounds exhibit not only half magnetization plateau but also magnetically driven ferroelectricity (50–60μC/m2); and (3) overall ferroelectric phase diagrams of the two compounds up to high magnetic fields. Therefore, Ni2V2O7and Co2V2O7
are demonstrated to be a kind of multiferroic material ex- hibiting quantum effect. The magnetic phase transitions, the H-T phase diagrams, as well as the magnetoelectric (ME) couplings of these two compounds were further investigated.
II. EXPERIMENT
A comprehensive electric polarization study on a single crystal requires various measurements with magnetic fields and electrodes applied along different crystallographic axes.
Due to the fact that the as-grown crystals are small and the crystal structure is monoclinic [23], it is difficult for us to measure electric polarization of Ni2V2O7 (or Co2V2O7) single crystals. Therefore, in this work we measured poly- crystalline samples instead of single crystals, in a similar way as reported for FeVO4 [24]. This method helps for a rapid experimental preparation and to explore the magnetoelectric property in applied magnetic fields. Ni2V2O7 and Co2V2O7
polycrystalline samples were prepared using the conventional
solid-state reaction method. The resultant powders were pressed into pellets under 15 MPa and then sintered in air at 500 °C for 48 h. The products were examined by x-ray powder diffraction (Philips X’Pert PRO). The magnetic susceptibility was measured by a commercial superconducting quantum interference device (SQUID). High-field magnetization was measured in pulsed fields using a coaxial pickup coil and cal- ibrated by a comparison with the low-field data measured by SQUID. Polycrystalline samples with dimensions of 5×5× 0.3 mm3 were used for electric polarization measurements.
For the low-field dc measurement,Pwas measured by probing the zero-field pyroelectric current and isothermal polarized current via the Keithley 6514 electrometer connected with the Physical Property Measurement System (PPMS). The details can be found elsewhere [25]. For the pulsed high-field measurement, the pyroelectric current was detected by a shunt resistor (10 K) and P was derived from integrating the pyroelectric current with the time [13]. Different from the dc measurement, a bias field ofE=650 kV/m was applied before and maintained during the short pulse (∼12 ms) to fully polarize the magnetic field induced ferroelectric (FE) domains inR2V2O7.
III. RESULTS AND DISCUSSION
Figure2(a)shows the magnetic susceptibility (χ=M/H) of Ni2V2O7 measured in different magnetic fields. For H =0.1 T, two magnetic phase transitions are identified at low temperatures of T1=6.9 K and T2=5.8 K, which are in agreement with the specific-heat data reported for the
FIG. 2. (a)−(d) Temperature dependence of the magnetic sus- ceptibility χ and the electric polarization P of polycrystalline Ni2V2O7 and Co2V2O7 measured in various magnetic fields. For the Pmeasurement, the sample was cooled down in a poling field (650 kV/m) through the transition temperature. This poling field was removed at the lowest temperature and the pyroelectric current was measured while warming at a constant rate of 2 K/min. The arrows indicate the transition temperatures of the magnetic and ferroelectric phase transitions.
FIG. 3. TheM(H) curve of polycrystalline Ni2V2O7 at various temperatures. The data for each temperature were vertically offset for clarity. The red curve denotes the derivative dM/dHatT =3 K.
The arrows show the transition fields ofH1-H5.
Ni2V2O7 single crystal [23]. The transition at T1 shows a change of slope in χ indicating an antiferromagnetic or- dering below this temperature. The transition at T2 is not clearly visible in χ but is more easily noticed in the tem- perature derivative dχ/dT. AsHincreases, these two transi- tions move to the low temperature and disappear above 3 T.
Figure2(b)shows the ferroelectric polarizationPof Ni2V2O7
as a function of temperature. It is found thatPis zero when T > T1while it becomes nonzero (0.4μC/m2 at 2 K) when T < T1. As H increases, P is suppressed and preserved up to 7 T. The transition temperatures ofPare slightly smaller than those determined by the susceptibilityχ. Similar results are obtained for the polycrystalline Co2V2O7 as shown in Figs.2(c)and2(d). Differently, only one transition tempera- tureT1is visible inχ. In addition,Pis almost zero atH =0 T but it is promoted by increasingH. These experimental results suggest that the emergence of ferroelectric polarization at the low temperature should arise from the origin of magnetism in these two compounds.
Figure 3 shows the H dependence of the magnetization of Ni2V2O7 in pulsed fields up to 60 T and in various temperatures. The derivative dM/dH at 3 K is also shown for a comparison. At 1.7 K, a clear magnetization plateau is stabilized in fields of 8–30 T as reported for the single crystal [23]. It is expected that the saturation value is 2.2μB/Ni2+
withS=1 andg=2.2 [23]. Thus, the magnetization at this plateau (1.1μB/Ni2+) is exactly half of the saturation magne- tization. Above 30 T,Mincreases linearly withHup to 60 T.
Magnetic transitions ofH1-H4 are clearly recognized at 2.5, 5, 9, and 29 T in the plot of dM/dH. Interestingly, whenTis increased we observe another magnetic transition atH5(55 T at 3 K) which was not detected in our previous study [23].
This transition moves to the low fields and converges with the transition ofH4at 4.7 K, where the half magnetization plateau almost disappears.
FIG. 4. High-field magnetization of polycrystalline Co2V2O7at various temperatures. The M(H) curve was vertically offset for clarity. The red curve denotes the derivative dM/dHatT =1.4 K.
The blue curve of 1.4 K is the result corrected for Van Vleck paramagnetism evaluated from the magnetization slope above the saturation field of 28 T. The arrows show the magnetic transitions atH1-H4for dM/dH.
In order to verify the magnetization plateau in an anal- ogous family compound, we measure the magnetization of polycrystalline Co2V2O7in pulsed fields up to 50 T as shown in Fig. 4. Indeed, the magnetization process at 1.4 K shows a clear plateau in fields of 7–12 T, which vanishes whenTis increased to 5 K. With increasingH, the magnetization nearly saturates above the critical field of 28 T. By extrapolating the M(H) curve above 28 T to a zero field, we subtract the Van Vleck paramagnetic susceptibility of the Co2+ ions.
Corrected data are shown as the blue curve. It is found that the saturation magnetization is 2.6μB/Co2+, smaller than the expected value of 3.87μB/Co2+ with S =3/2 and g=2.
This observation is reminiscent of the magnetic properties of Ba3CoM2O9 (M=Sb, Ta), in which the Co2+ ions transfer from a high-spin (S=3/2) state at high temperature to a low- spin (S=1/2) state at the magnetic ground state [2,26]. From the saturation magnetization and the relationMs=gμBS, we estimate the Landé g factor to be 5.2 with S=1/2. This large g factor implies that there exists a strong spin-orbit coupling in Co2V2O7 [18]. On the other hand, the explored plateau at 7–12 T is expectedly quantized at half of the saturation magnetization, as reported in Ni2V2O7. In addition, magnetic transitions ofH1-H4are seen at 4, 7, 12, and 18 T in the derivative dM/dH. Note that the critical fields of the plateau and the saturation field are much smaller than those of Ni2V2O7, indicating a relatively weak Co-Co exchange interaction in Co2V2O7.
We further investigate the P variations of Ni2V2O7 and Co2V2O7 in pulsed fields up to 60 and 40 T, respectively.
Figure5(a)shows the data of Ni2V2O7with magnetic fields applied parallel to the large surface of the sample, where the change ofPis defined asP =P(H)−P(H=0). At low fields belowH2=5 T,Pslightly increases and then decreases
R. CHENet al. PHYSICAL REVIEW B98, 184404 (2018)
FIG. 5. The polarizationPof polycrystalline Ni2V2O7in fields up to 60 T. (a) Pas a function of Hmeasured at 1.7 and 4.2 K, respectively. Prior to the measurements, the sample was cooled down to 1.7 K (4.2 K) with zero poling field, then measurements were performed subsequently with a bias electric field of 650 kV/m during the pulse. The arrows indicate the field-rising (-falling) sweeps. (b) Pmeasurements in various temperatures. Only the data in the falling sweeps are shown for clarity.
with a maximum atH1=2.5 T. When the magnetic field is further increased at 1.7 K,Pis retained with nearlyP =0 up to the critical fieldH4=29 T. The most striking feature of the high-field polarization is the big change ofP aboveH4, namely, magnetic field induced ferroelectricity. Remarkably, the maximum value ofPaboveH4is∼12 times larger than that belowH2. In higher fields,Pshows a sudden drop at 50 T and decreases toward zero up to 60 T. At 4.2 K, the high magnetic field can completely suppressPwithP =0. The corresponding transition field H5 is in agreement with that measured by the magnetization in Fig.3. As Tis increased, this high-field induced ferroelectricity develops well with T and finally vanishes above 5 K as shown in Fig. 5(b).
Meanwhile, the low-field ferroelectricity also disappears at a higher temperature.
The polarization behavior of Co2V2O7is shown in Fig.6.
Similar to Ni2V2O7, two differentH-induced ferroelectricities are observed in applied high magnetic fields. ThePvalue reaches 60μC/m2 at 1.7 K and 15 T. AsTis increased,P decreases gradually and disappears above 7 K. In comparison with Ni2V2O7, Co2V2O7exhibits several distinct differences in theP(H) curve: (1) the low-field ferroelectricity centered at H1 has a larger P value of about 50μC/m2; (2) the
FIG. 6. The polarizationPof polycrystalline Co2V2O7in fields up to 40 T. (a) Hvariations of Pmeasured at 1.7 K. The arrows indicate the field-rising (-falling) sweeps. We also show |P| versus H measured by a 7-T superconducting magnet for a comparison.
Note that no bias electric field was applied during the 7-T mea- surement due to the limit of our equipment. (b)Pmeasurements in temperatures from 1.7 to 7 K. Only the data in the falling sweeps are shown for clarity.
low-field and the high-field ferroelectricities move together, and the intermediate phase withP =0 is invisible; (3) the hysteresis of theH-induced ferroelectricities becomes larger;
and (4) additional transitions can be seen in the high-field fer- roelectricity in Co2V2O7. To elucidate the low-field ferroelec- tricity and the intermediate phase around H2, we measured the P variation in dc fields up to 7 T using the PPMS. The obtained Pis small because the FE domains are not aligned under zero-bias electric field. Obviously, the evolutions ofP in both dc and pulsed fields are similar and their transition fields are the same atH1=4 T. However, the dc data drop to zero atH2where the magnetization plateau begins to appear.
This feature is consistent with the result of Ni2V2O7in Fig.5.
We speculate that in pulsed fields the nonzero P around H2 is attributed to the influence of leakage current in the Co2V2O7 sample. This may also lead to a big hysteresis for theH-decreasing sweep and a small remanentPatH =0.
TheH-T phase diagrams determined from our magnetiza- tion and electric polarization measurements are summarized in Fig.7. For Ni2V2O7 in Fig.7(a), low- and high-field FE phases are well established through the magnetic phase tran- sitions, indicating the nature of magnetically driven ferroelec- tricity. It is found that these two FE phases are separated by the half plateau and spin nematiclike phases for which the polar- ization is unchanged (P =0). In general, the magnetization
FIG. 7. High-fieldH-T phase diagrams of (a) Ni2V2O7and (b) Co2V2O7determined from the magnetization, electrical polarization, and magnetic susceptibility measurements. The blue and the green areas denote the explored low-field (LF-FE) and high-field (HF-FE) ferroelectric phases, respectively. SN phase in Fig.7(a)denotes the spin nematiclike phase. The thin solid lines are guides for the eyes. The dashed lines in Fig.7(b)separate the FE phases and the half plateau phase in Co2V2O7as proposed.
plateau has a collinear commensurate spin configuration [2], while the spin-dependent ferroelectricity is incommensurate helical (or spiral) spin ordered [6]. This scenario has already been observed in the materials CuFeO2 and Ni3V2O8 where the plateau and the FE phases are well separated [9,13].
Thus, it is reasonable that a half magnetization plateau will yield a paraelectric state (P =0) in the frustrated magnet Ni2V2O7or Co2V2O7. Based on these results, we propose the phase diagram of Co2V2O7in Fig.7(b), although our present experiment cannot give a clear phase boundary between the half plateau and the high-field FE phase (Fig.6).
Compared with Co2V2O7, the phase diagram of Ni2V2O7 looks more complex in the low-field region. A spin nemati- clike phase withP =0 is manifest before the system goes into the plateau phase, while no analogical phase is visible for Co2V2O7. One reason is that Co2V2O7 perhaps has a strong magnetic anisotropy which makes the corresponding phase boundaries and the half plateau smeared because of the polycrystalline sample. Another reason may be ascribed to the different magnetic structures of these two compounds at low temperatures. For Co2V2O7, only one magnetic transition is seen atT1 and the magnetization increases linearly in a low field (Fig.4). In contrast, Ni2V2O7undergoes two successive magnetic orderings atT1andT2. In a magnetic field, a spin- flop transition and a strong inflection take place followed by a linear increase ofMnear the plateau [23], also see Fig.3in this work. These behaviors are consistent with those features observed in LiCuVO4 which is a candidate to realize the spin nematic phase [27–29]. In this sense, it is likely that Ni2V2O7 has a more complicated spiral spin structure than that of Co2V2O7in the magnetic ground state. This may also result in a much smallerPvalue (∼5μC/m2) of the low-field FE phase than that (∼50μC/m2) of Co2V2O7. On the other hand, our experiments reveal that high magnetic fields can completely suppress the spiral spin arrangement by realization
of the half magnetization plateau. In addition, sufficient high fields can reorient the spin arrangement to spiral structure and lead to an enhanced P of the high-field FE phase. Conse- quently, two distinct ferroelectric phases exist linked by the half magnetization plateau phase for both compounds.
The appearance of the high-field FE phase is quite inter- esting. Especially for Ni2V2O7, the change of M above H4 is smaller than that below H2 (Fig. 3), whereas P of the high-field phase is much larger than that of the low-field one (Fig.5). Emergence of the FE phase after closing a gap (end of the plateau in this work) reminds us of the ferroelectricity in the quantum magnet TlCuCl3[30]. In this material, mixture of the singlet and triplet states causes nonzero matrix element ofSi×Sj, which results in finite electric polarization in the Bose-Einstein condensation region. It would be interesting if there exists a similar quantum state in the field-temperature region of Ni2V2O7(or Co2V2O7). Nevertheless, for Ni2V2O7, the closure of this FE phase at∼58 T is puzzling because the expected saturation field is∼80 T according to our previous study [23]. It seems that this departure of the transition field cannot be understood by the anisotropy of the H-T phase diagrams of Ni2V2O7. With respect to Co2V2O7, the saturation field corresponds to the ferroelectric-to-paraelectric phase transition. We suppose that the high-field FE phase of Ni2V2O7 is likely not a simple canted ferromagnetic phase and may collapse before reaching the saturation field, leading to a transition at ∼58 T to another spin-ordered phase like umbrella type.
Finally, the magnetoelectric responses of the above two samples were investigated. Note that this effect is associated with the low-field FE phase. For Ni2V2O7, it may exist but the smallPis out of the sensitivity limit of the instrument. For Co2V2O7, the experimental result is shown in Fig.8 due to a relatively largePwithHincreasing. It is seen that the ME response begins from the negative magnetic fields after the
R. CHENet al. PHYSICAL REVIEW B98, 184404 (2018)
FIG. 8. Time dependence of the forced electric polarization of Co2V2O7(left scale) with simultaneous magnetic field change (right scale) measured at 2 K. This measurement was performed by the PPMS with zero electric field. The oscillation of the magnetic field reaches the maximum of±7 T of the instrument.
activation of frozen FE domain wall byHsweeping [10]. The fact thatPhas a maximum (or minimum) value at±4 T and returns to zero at±7 T is in agreement with theP(H) data in Fig.6(a). Particularly, the reversal ofPwith the maximum change of about 3.4μC/m2 can be directly manipulated by the continuous sweep field up to±7 T. The frequency ofP is a double of that ofH, in agreement with that observed in FeVO4[24]. This result demonstrates the existence of a clear ME coupling between magnetic and ferroelectric orders in this material.
It should be pointed out that the present observation of half magnetization plateaus in polycrystalline samples is in- deed inconsistent with that in a honeycomb spin system Ba2CoTeO6. Ni2V2O7 shows an isotropic feature of the half plateau for H applied along all crystallographic axes [23],
while the half plateau in Ba2CoTeO6 is anisotropic and ap- pears only forHapplied along thecaxis [31]. This inconsis- tency infers that Ni2V2O7 can be described with a different spin structure of Ba2CoTeO6, and this may arise from the ME coupling that exists in this material.
IV. CONCLUSION
The magnetic and dielectric properties of polycrystalline R2V2O7 (R=Ni, Co) have been investigated in high mag- netic fields up to 60 T. Half magnetization plateau and mag- netic field induced ferroelectricities were observed simulta- neously in both compounds. The resulting high-field phase diagrams are very complex in which the half plateau phases and the ferroelectric phases are well separated. In addition, an intriguing magnetoelectric coupling has been demonstrated for Co2V2O7 with the low magnetic field driven ferroelec- tricity. The high magnetic field driven ferroelectricity for Ni or Co compound is about 50–60μC/m2. It is worth men- tioning that our polarization measurements were performed on the polycrystalline samples. Detailed investigations based on large-sized single crystals are desirable in order to clarify the mechanisms of the magnetically driven ferroelectricities and the quantized magnetization plateau in these fascinating materials.
ACKNOWLEDGMENTS
J.F.W. would like to thank M. Tokunaga for useful com- ments about the high-field electric polarization results. This work was supported by the National Natural Science Foun- dation of China (Grants No. 11574098, No. U1832214, No.
11474110, and No. 51571152) and the National Key R&D Program of China (Grant No. 2016YFA0401704). J.M.L. ac- knowledges support from The National Key Research Project of China (Grant No. 2016YFA0300101) and NSFC (Grant No. 51721001).
[1] M. Oshikawa, M. Yamanaka, and I. Affleck,Phys. Rev. Lett.
78,1984(1997).
[2] Y. Shirata, H. Tanaka, A. Matsuo, and K. Kindo,Phys. Rev.
Lett.108,057205(2012).
[3] M. Jaime, R. Daou, S. A. Crooker, F. Weickert, A. Uchida, A. E.
Feiguin, C. D. Batista, H. A. Dabkowska, and B. D. Gaulin, Proc. Natl. Acad. Sci. USA109,12404(2012).
[4] H. Ishikawa, M. Yoshida, K. Nawa, M. Jeong, S. Kramer, M.
Horvatic, C. Berthier, M. Takigawa, M. Akaki, A. Miyake, M.
Tokunaga, K. Kindo, J. Yamaura, Y. Okamoto, and Z. Hiroi, Phys. Rev. Lett.114,227202(2015).
[5] T. Kimura, T. Goto, H. Shintani, K. Ishizaka, T. Arima, and Y.
Tokura,Nature (London)426,55(2003).
[6] T. Yoshinori, S. Shinichiro, and N. Naoto,Rep. Prog. Phys.77, 076501(2014).
[7] S. Dong, J.-M. Liu, S.-W. Cheong, and Z. Ren,Adv. Phys.64, 519(2015).
[8] N. Terada, Y. Narumi, K. Katsumata, T. Yamamoto, U.
Staub, K. Kindo, M. Hagiwara, Y. Tanaka, A. Kikkawa, H.
Toyokawa, T. Fukui, R. Kanmuri, T. Ishikawa, and H. Kitamura,
Phys. Rev. B 74, 180404 (2006); N. Terada, Y. Narumi, Y.
Sawai, K. Katsumata, U. Staub, Y. Tanaka, A. Kikkawa, T.
Fukui, K. Kindo, T. Yamamoto, R. Kanmuri, M. Hagiwara, H. Toyokawa, T. Ishikawa, and H. Kitamura,ibid.75,224411 (2007).
[9] T. Kimura, J. C. Lashley, and A. P. Ramirez,Phys. Rev. B73, 220401(2006).
[10] H. Tamatsukuri, S. Mitsuda, T. Nakajima, K. Shibata, C.
Kaneko, K. Takehana, Y. Imanaka, N. Terada, H. Kitazawa, K. Prokes, S. Matas, K. Kiefer, S. Paeckel, A. Sokolowski, B. Klemke, and S. Gerischer, Phys. Rev. B 93, 174101 (2016); J. Beilsten-Edmands, S. J. Magorrian, F. R. Foronda, D. Prabhakaran, P. G. Radaelli, and R. D. Johnson, ibid.94, 144411(2016).
[11] G. Lawes, A. B. Harris, T. Kimura, N. Rogado, R. J. Cava, A. Aharony, O. Entin-Wohlman, T. Yildirim, M. Kenzelmann, C. Broholm, and A. P. Ramirez,Phys. Rev. Lett. 95, 087205 (2005).
[12] J. F. Wang, M. Tokunaga, Z. Z. He, J. I. Yamaura, A. Matsuo, and K. Kindo,Phys. Rev. B84,220407(2011).
[13] Y. J. Liu, J. F. Wang, Z. Z. He, C. L. Lu, Z. C. Xia, Z. W.
Ouyang, C. B. Liu, R. Chen, A. Matsuo, Y. Kohama, K. Kindo, and M. Tokunaga,Phys. Rev. B97,174429(2018).
[14] S. Bhowal, J. Sannigrahi, S. Majumdar, and I. Dasgupta,Phys.
Rev. B95,075110(2017).
[15] Z. Z. He and Y. Ueda,Phys. Rev. B77,052402(2008).
[16] Z. Z. He and Y. Ueda,J. Cryst. Growth310,171(2008);J. Solid State Chem.181,235(2008); Z. Z. He, Y. Ueda, and M. Itoh, Solid State Commun.147,138(2008).
[17] Z. Z. He, J. I. Yamaura, Y. Ueda, and W. Cheng,Phys. Rev. B 79,092404(2009).
[18] Z. Z. He, J. I. Yamaura, Y. Ueda, and W. Cheng,J. Solid State Chem.182,2526(2009).
[19] J. Sannigrahi, S. Bhowal, S. Giri, S. Majumdar, and I. Dasgupta, Phys. Rev. B91,220407(2015).
[20] G. Gitgeatpong, M. Suewattana, S. Zhang, A. Miyake, M. Tokunaga, P. Chanlert, N. Kurita, H. Tanaka, T. J.
Sato, Y. Zhao, and K. Matan, Phys. Rev. B 95, 245119 (2017).
[21] Y. W. Lee, T. H. Jang, S. E. Dissanayake, L. Seunghun, and H. J.
Yoon,Europhys. Lett.113,27007(2016).
[22] J. T. Zhang, J. L. Wang, C. Ji, B. X. Guo, W. S. Xia, X. M. Lu, and J. S. Zhu,Phys. Rev. B96,165132(2017).
[23] Z. W. Ouyang, Y. C. Sun, J. F. Wang, X. Y. Yue, R. Chen, Z. X.
Wang, Z. Z. He, Z. C. Xia, Y. Liu, and G. H. Rao,Phys. Rev. B 97,144406(2018).
[24] B. Kundys, C. Martin, and C. Simon,Phys. Rev. B80,172103 (2009).
[25] M. F. Liu, H. M. Zhang, X. huang, C. Y. Ma, S. Dong, and J. M.
Liu,Inorg. Chem.55,2709(2016).
[26] K. M. Ranjith, K. Brinda, U. Arjun, N. G. Hegde, and R. Nath, J. Phys.: Condens. Matter29,115804(2017).
[27] L. E. Svistov, T. Fujita, H. Yamaguchi, S. Kimura, K. Omura, A. Prokofiev, A. I. Smirnov, Z. Honda, and M. Hagiwara,JETP Lett.93,21(2011).
[28] N. Buttgen, K. Nawa, T. Fujita, M. Hagiwara, P. Kuhns, A.
Prokofiev, A. P. Reyes, L. E. Svistov, K. Yoshimura, and M.
Takigawa,Phys. Rev. B90,134401(2014).
[29] A. Orlova, E. L. Green, J. M. Law, D. I. Gorbunov, G. Chanda, S. Krämer, M. Horvatic, R. K. Kremer, J. Wosnitza, and G. L.
J. A. Rikken,Phys. Rev. Lett.118,247201(2017).
[30] S. Kimura, K. Kakihata, Y. Sawada, K. Watanabe, M. Matsumoto, M. Hagiwara, and H. Tanaka,Nat. Commun.7, 12822(2016).
[31] P. Chanlert, N. Kurita, H. Tanaka, D. Goto, A. Matsuo, and K. Kindo,Phys. Rev. B93,094420(2016).