Magnetic order in the chemically-substituted frustrated antiferromagnet CsCrF4

Shohei Hayashida,1, ∗ Masato Hagihala,1, 2 Maxim Avdeev,3, 4

Yoko Miura,5 Hirotaka Manaka,6 and Takatsugu Masuda1, 7

1Institute for Solid State Physics, The University of Tokyo, Kashiwa, Chiba 277-8581, Japan2Neutron Science Division, Institute of Materials Structure Science,

High Energy Accelerator Research Organization, Tsukuba, Ibaraki 305-0801, Japan3Australian Nuclear Science and Technology Organisation,New Illawarra Rd, Lucas Heights, NSW 2234, Australia

4School of Chemistry, The University of Sydney, Sydney, NSW 2006, Australia5Suzuka National College of Technology, Suzuka, Mie 510-0294, Japan

6Graduate School of Science and Engineering, Kagoshima University, Korimoto, Kagoshima 890-0065, Japan7Trans-scale Quantum Science Institute, The University of Tokyo, Tokyo 113-0033, Japan

(Dated: December 1, 2020)

The effect of chemical substitution on the ground state of the geometrically frustrated antifer-romagnet CsCrF4 has been investigated through a neutron powder diffraction experiment. Mag-netic Fe-substituted CsCr0.94Fe0.06F4 and nonmagnetic Al-substituted CsCr0.98Al0.02F4 samplesare measured, and magnetic Bragg peaks are clearly observed in both samples. Magnetic struc-ture analysis revealed a 120◦ structure having a magnetic propagation vector kmag = (0, 0, 1/2)in CsCr0.94Fe0.06F4. For CsCr0.98Al0.02F4, a quasi-120

◦ structure having kmag = (1/2, 0, 1/2) isformed. It is notable that the identified magnetic structure in CsCr0.94Fe0.06F4 belongs to a differ-ent phase of ground states from those in CsCr0.98Al0.02F4 and the parent CsCrF4. These resultssuggest that the Fe substitution strongly influences the ground state of CsCrF4.

I. INTRODUCTION

Geometrically frustrated magnets have attracted greatinterest in condensed matter physics because of theirexotic magnetic states induced by macroscopic degen-eracy of magnetic states at low temperatures [1, 2].Since the macroscopic degeneracy in the low-energy re-gion can be lifted even by small perturbations, geomet-rical frustration highlights small effects such as single-ion anisotropy [3, 4], the Dzyaloshinskii-Moriya inter-action [5, 6], magnetic dipole-dipole interaction [7, 8],exchange randomness [9–12], and site dilution [13–15].These may play key roles in determining ground statesin frustrated magnets.

The equilateral triangular spin tube antiferromagnetCsCrF4 is one of the intriguing species in geometricallyfrustrated magnets [16, 17]. It crystallizes in a hexago-nal structure with the space group P62m as illustratedin Fig. 1. The magnetic properties are due to S = 3/2Cr3+ ions. It is unique that equilateral triangles formedby CrF6 octahedra are stacked along the crystallographicc axis, forming triangular spin tubes. These tubes mag-netically couple with one another and form the kagome-triangular lattice in the ab plane [18, 19]. Magnetic sus-ceptibility measurements revealed the Curie-Weiss tem-perature θCW = −145 K and a broad maximum atT ∼ 60 K indicative of developing short-range antifer-romagnetic spin correlations [16, 17]. Due to the geo-metrical frustration and low dimensionality of the trian-gular spin tube, no clear evidence of a magnetic phase

∗ shoheih@phys.ethz.ch; Present address: Laboratory for SolidState Physics, ETH Zürich, 8093 Zürich, Switzerland

a

a

c

CrF6

Cs

J1

J2

c

J0

FIG. 1. Schematic view of the crystal structures of CsCrF4(hexagonal, space group P62m). Red lines indicate thenearest-neighbor interaction along the c axis, J0. Blue andyellow lines indicate the nearest- and second-neighbor inter-actions in the ab plane, J1 and J2.

transition was found in thermodynamic and magneticmeasurements [16, 17, 20–22].

In a breakthrough, recent neutron powder diffractionstudy identified long-range magnetic order of CsCrF4below 2.8 K. The magnetic moments form a quasi-120◦

structure in the ab plane [23]. The 120◦ structure propa-gates antiferromagnetically along the a and c axes with amagnetic propagation vector kmag = (1/2, 0, 1/2). Dis-cussion of ground states in the kagome-triangular lat-tice model suggested that the identified 120◦ structureoriginates from a ferromagnetic intertube coupling, theDzyaloshinskii-Moriya interaction, and a strong in-planesingle-ion anisotropy. In addition, it was found that theground state of CsCrF4 is close to the boundary on themagnetic phase diagram in the kagome-triangular latticemodel [23]. This suggests that small perturbations mayinduce various types of magnetic states in CsCrF4.

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Chemical substitution controls the magnetic statein CsCrF4 [24, 25]. Thermodynamic and magneticmeasurements for chemically substituted CsCr1−xFexF4and CsCr1−xAlxF4 showed that the magnetic stateis significantly influenced by the chemical composi-tion [25]. An antiferromagnetic transition was clearlyobserved at 4.5 K for x = 0.06 in the magnetic Fe-substituted compound, and the substituted superex-change bond Cr3+-F−-Fe3+ enhanced the in-plane mag-netic anisotropy. A glasslike transition appeared atabout 5 K for the nonmagnetic Al-substituted com-pound. In the present paper, we investigate long-range magnetic ordering in chemically substituted frus-trated antiferromagnet CsCrF4. Magnetic structures ofCsCr0.94Fe0.06F4 and CsCr0.98Al0.02F4 are identified bya combination of neutron powder diffraction experimentsand magnetic structure analysis. The most notable re-sult is that the Fe-substitution effectively turns the fer-romagnetic intertube coupling antiferromagnetic.

II. EXPERIMENTAL DETAILS

Polycrystalline samples of CsCr0.94Fe0.06F4 andCsCr0.98Al0.02F4 were prepared by a solid-state reac-tion method [16, 25]. The powder samples were loadedin vanadium-made containers, which were in turn in-stalled in a conventional liquid 4He cryostat. Neutrondiffraction measurements were performed at the highresolution powder diffractometer ECHIDNA [26, 27] in-stalled at the OPAL research reactor operated by theAustralian Nuclear Science and Technology Organisation(ANSTO). We chose a Ge(331) monochromator to ob-tain neutrons with a wavelength of 2.4395 Å, and usedthe open-open-5′ configuration. Temperatures were setat 10 K and 1.5 K. The neutron diffraction data wereanalyzed by the Rietveld method with the FULLPROFsoftware [28]. Candidates for magnetic structures com-patible with the lattice symmetry were obtained by theSARAh software [29]. We used the VESTA software [30]for drawing the crystal structures and magnetic struc-tures.

III. RESULTS AND ANALYSIS

Figures 2(a) and 2(b) show neutron powder diffrac-tion profiles at 10 K for CsCr0.94Fe0.06F4 andCsCr0.98Al0.02F4, respectively. These are reasonably fit-ted by the hexagonal structure with the space groupP62m. Obtained profile factors are Rwp = 7.33% andRe = 3.70% for CsCr0.94Fe0.06F4, and Rwp = 9.26% andRe = 5.01% for CsCr0.98Al0.02F4. The refined latticeand structural parameters (Table I) are consistent withthe previous results measured by x-ray powder diffrac-tion experiments [24, 25]. We conclude that the crystalstructures are retained at low temperatures.

Figure 3 shows neutron diffraction profiles at 1.5 and10 K, which are below and above the transition temper-

20 40 60 80 100 120 140

Inte

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arb

. un

its)

20

15

10

5

2θ (deg.)

0

(b) CsCr Al F0.98 0.02 4

Inte

nsi

ty (

arb

. un

its)

10

8

6

4

2

0

(a) CsCr Fe F0.94 0.06 4 Obs. Calc. Obs.-Calc.

Nuclear Bragg peak

Obs. Calc. Obs.-Calc.

Nuclear Bragg peak

FIG. 2. Neutron powder diffraction profiles for (a)CsCr0.94Fe0.06F4 and (b) CsCr0.98Al0.02F4 measured at 10K. Red squares and black curves show the experimental dataand simulations, respectively. Vertical bars indicate the posi-tion of the nuclear Bragg peaks. Solid curves below the barsshow the difference between the data and simulations.

TABLE I. Results of the structural refinement in space groupP62m of the neutron powder diffraction profiles measured atT = 10 K for CsCr0.94Fe0.06F4 and CsCr0.98Al0.02F4.

CsCr0.94Fe0.06F4

a (Å) 9.56402(7)

c (Å) 3.85832(3)

Cs (3g) (0.57202(12), 0, 1/2)

Cr and Fe (3f) (0.22456(23), 0, 0)

F (3f) (0.83226(14), 0, 0)

F (3g) (0.22024(15), 0, 1/2)

F (6j) (0.43914(10), 0.16142(11), 0)

CsCr0.98Al0.02F4

a (Å) 9.56886(6)

c (Å) 3.85059(3)

Cs (3g) (0.57203(17) 0, 1/2)

Cr and Al (3f) (0.22327(36), 0, 0)

F (3f) (0.83208(19), 0, 0)

F (3g) (0.22089(21), 0, 1/2)

F (6j) (0.43801(13), 0.16032(15), 0)

3

10 20 30 40 50 60

4

3

2

1

2θ (deg.)

Inte

nsi

ty (

arb

. un

its)

2

6

4

CsCr Fe F0.94 0.06 4

CsCr Al F0.98 0.02 4(b)

(a)

1.5 K10 K

1.5 K10 K

FIG. 3. Neutron powder diffraction profiles for (a)CsCr0.94Fe0.06F4 and (b) CsCr0.98Al0.02F4. Blue and redmarks are data measured at 1.5 and 10 K, respectively. Ar-rows indicate the magnetic Bragg peaks.

ature observed in the magnetic susceptibility data [25].In both samples, diffuse scattering is observed at 10 K inthe range of 20◦ ≤ 2θ ≤ 40◦, and it is suppressed belowthe transition temperature. This behavior is the sameas in CsCrF4 [23] and indicates that the short-rangespin correlations develop at 10 K. For CsCr0.94Fe0.06F4,we clearly see additional peaks at 1.5 K, indicating thelong-range magnetic order. Additional peaks are alsovisible in CsCr0.98Al0.02F4 even though their intensitiesare weak. This result suggests that the anomaly ob-served at 5 K in the magnetic susceptibility measure-ments [25] corresponds to weak long-range magnetic or-dering rather than the glasslike transition. Remarkably,the peaks for CsCr0.94Fe0.06F4 are observed at differ-ent scattering angles from those in CsCrF4, while thepeak positions in CsCr0.98Al0.02F4 are the same withCsCrF4. Indexing the observed magnetic Bragg peaksresults in the magnetic propagation vectors kmag =(0, 0, 1/2) for CsCr0.94Fe0.06F4 and kmag = (1/2, 0, 1/2)for CsCr0.98Al0.02F4.

To determine magnetic structures that are compatiblewith the space group symmetry, we performed repre-sentation analysis. We assume that a magnetic struc-ture is described by a single irreducible-representation(IR). For CsCr0.94Fe0.06F4, the representation analysiswith the space group P62m and the propagation vector

10 20 30 40 50 60

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8

6

4

2

2θ (deg.)

0

−2

CsCr Fe F0.94 0.06 4

Obs. Calc. Obs.-Calc.Nuclear Bragg positionMagnetic Bragg position

a

a

c

c

(b) (c)

(a)

FIG. 4. (a) Neutron diffraction profile for CsCr0.94Fe0.06F4at 1.5 K. Red squares and black curves show the experimentaldata and simulations, respectively. Vertical bars and trian-gles indicate the position of the nuclear and magnetic Braggpeaks. Solid curves below the triangles show the differencebetween the data and simulations. The magnetic structureof CsCr0.94Fe0.06F4 with Γ2 (b) in the ab plane and (c) alongthe c axis.

kmag = (0, 0, 1/2) leads to five IRs. The details of theIRs and corresponding basis vectors are listed in Table II.From the Rietveld refinement, a magnetic structure de-scribed by Γ2 gives excellent agreement with the exper-imental data, as shown in Fig. 4(a). R factors for thewhole profile are Rwp = 8.67% and Re = 3.86%. Themagnetic R factor is Rmag = 7.40%. Note that smallpeaks at 2θ = 22◦ and 58◦ are likely due to nonmag-netic impurities because they are also observed at 10 K.In the identified magnetic structure, the magnetic mo-ments form a 120◦ structure in the ab plane, and theypropagate antiferromagnetically along the c axis, as dis-played in Figs. 4(b) and 4(c). The averaged magnitudeof the magnetic moment is evaluated to be 1.66(1) µB.Since an effective magnetic moment for Cr3+0.94Fe

3+0.06 is

provided by 3.12 µB(= 0.94×3 µB +0.06×5 µB), the re-fined moment size is much smaller than the effective one.This is the same result as that in the parent CsCrF4 [23].This implies that the magnetic moment strongly fluctu-ates even at 1.5 K due to the geometrical frustration andlow dimensionality.

For CsCr0.98Al0.02F4, the representation analysis withthe space group P62m and the propagation vectorkmag = (1/2, 0, 1/2) leads to splitting of the three equiv-

4

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4

2

2θ (deg.)

0

6

4

2

0

(a) Γ2

(b) Γ4

CsCr Al F0.98 0.02 4

Obs. Calc. Obs.-Calc.Nuclear Bragg peakMagnetic Bragg peak

(c) Γ2 (d) Γ4

a

a

c

ϕ

ϕ

Obs. Calc. Obs.-Calc.Nuclear Bragg peakMagnetic Bragg peak

Inte

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FIG. 5. Refined diffraction profiles for CsCr0.98Al0.02F4 at1.5 K. The IRs of the magnetic structure for the simulationsare (a) Γ2 and (b) Γ4, respectively. Red squares and blackcurves show the experimental data and simulations, respec-tively. Vertical bars and triangles indicate the position of thenuclear and magnetic Bragg peaks. Solid curves below thetriangles show the difference between the data and simula-tions. The magnetic structures of CsCr0.98Al0.02F4 with (c)Γ2 and (d) Γ4.

alent Cr sites into the two nonequivalent Cr sites; site-1(0.2233, 0, 0), (0.7767, 0.7767, 0), and site-2 (0, 0.2233, 0).Four and three IRs are associated with the site-1 andsite-2, respectively. The details of the IRs and corre-sponding basis vectors are listed in Table III. From theRietveld refinement, magnetic structures in Γ2 and Γ4give satisfactory agreement with the experimental data,as shown in Figs. 5(a) and 5(b). R factors for the wholeprofile are Rwp = 9.59% and Re = 5.05% for Γ2, andRwp = 9.65% and Re = 5.06% for Γ4. Magnetic R fac-

3+Cr 3+Cr(a) -F

Antiferromagnetic Ferromagnetic

3+Cr

3+Fe

Ferromagnetic Antiferromagnetic

-F3+Cr 3+Fe

3+Cr

3+Al

3+Cr -F

-F3+Cr

3+Cr

3+Cr 3+Cr 3+Cr

(b)

(c) (d)

FIG. 6. (a) Superexchange interactions between the Cr3+

ions in 180◦ and 90◦ bonds via the F− ion. (b) Superexchangeinteractions between the Cr3+ and Fe3+ ions in 180◦ and 90◦

bonds via the F− ion. [(c) and (d)] Spin structures with anantiferromagnetic interaction on an equilateral triangle.

tors are Rmag = 18.8% for Γ2 and Rmag = 15.8% forΓ4. Note that it is hard to judge the optimal structurefrom these results because of the weak intensities of themagnetic Bragg peaks. The identified magnetic struc-tures with kmag = (1/2, 0, 1/2) are similar to that in theparent CsCrF4, [see Figs. 5(c) and 5(d)]. A quasi-120

◦

structure is formed in the ab plane, and it propagatesantiferromagnetically along the a and c axes. Relativeangles φ between the moments at the sites 1 and 2, asindicated in Figs. 5(c) and 5(d), are 92.4◦ for Γ2 and90.4◦ for Γ4. These angles deviate more from 120

◦ than119.5◦ (Γ2) and 108

◦ (Γ4) in CsCrF4 [23]. Refined mag-nitude of the magnetic moments is 1.04(7)µB for Γ2 and1.14(6)µB for Γ4, As well as that of Cr

3+0.94Fe

3+0.06, the re-

fined moment size of CsCr0.98Al0.02F4 is much smallerthan the effective moment 2.94 µB = (0.98 × 3 µB) forCr3+0.98Al

3+0.02. Thus, the ordered moments are strongly

suppressed by the geometrical frustration and low di-mensionality in the chemically substituted CsCrF4.

IV. DISCUSSION

In the magnetic structure analysis, the 120◦ structurehaving kmag = (0, 0, 1/2) is found for CsCr0.94Fe0.06F4.In the identified structure, the intertube spin configu-ration is different from that in the parent CsCrF4, butthe intratube structure is the same. Let us discuss Fe-substitution effect on exchange interactions. Accordingto the Goodenough-Kanamori rules [31, 32], superex-change interactions between the Cr3+ ions via the F− ionare antiferromagnetic for a 180◦ bond and ferromagnetic

5

for a 90◦ bond as displayed in Fig. 6(a). Once the Cr3+

ion is substituted by the Fe3+ ion, the superexchangeinteractions in the 180◦ and 90◦ bonds are turned intoferromagnetic and antiferromagnetic ones, respectively[Fig. 6(b)]. Since the bond angles of the nearest-neighborexchange paths along the c axis, J0, and in the ab plane,J1, (see Fig. 1) are 178

◦ and 148◦ in CsCrF4 [23], theirexchange interactions likely turn antiferromagnetic intoferromagnetic by the Fe-substitution. However, the iden-tified magnetic structure in the triangular tube retainsthe same structure as that in CsCrF4. This means thatthe bond substitution in the intratube coupling has noreal effect other than to create a small number of ferro-magnetically coupled pairs.

On the contrary, the spin configuration between thespin tubes is totally different from that in CsCrF4.In CsCr0.94Fe0.06F4, the magnetic propagation vectorin the kagome-triangular plane k2D is (0, 0). It con-trasts with k2D = (1/2, 0) in CsCrF4. This indicatesthat the substitution drastically changes the groundstate even though intertube exchange paths are com-plicated. In fact, according to the phase diagram ofmagnetic structures for the kagome-triangular latticemodel [19, 23], 120◦ structures having k2D = (0, 0) and(1/2, 0) require antiferromagnetic and ferromagnetic in-tertube couplings, respectively. We note that in thephase diagram the variation of the in-plane anisotropydescribed in Ref. [25] does not change the intertube spinconfiguration. Therefore, we conclude that in the mag-netic Fe substitution the ground state is modified dueto the evolution of the intertube coupling J2 from ferro-magnetic to antiferromagnetic.

The magnetic structure in CsCr0.98Al0.02F4 is notchanged drastically, even though the relative angle φ be-tween the spins deviates more from 120◦ than that inthe parent CsCrF4. On the basis of the classical vector-spin model, spins with the antiferromagnetic interactionform a 120◦ structure on an equilateral triangle, as dis-played in Fig. 6(c). Substituting the Cr3+ ion by theAl3+ ion creates a spin vacancy in the triangle. Thislikely induces the remaining two spins to align antiferro-magnetically [Fig. 6(d)]. Consequently, the Al substitu-tion breaks a 120◦ structure locally. However, the spinvacancy only produces a small effect on the ground stateof CsCrF4, and therefore the quasi-120

◦ structure is stillrealized globally in CsCr0.98Al0.02F4.

V. CONCLUSION

In conclusion, we have studied magnetic orders inmagnetic Fe- and nonmagnetic Al-substituted CsCrF4

through a neutron powder diffraction experiment. Mag-netic structure analysis reveals that the Fe-substitutedsample exhibits a 120◦ structure having kmag =(0, 0, 1/2), and the Al-substituted one has a quasi-120◦

structure having kmag = (1/2, 0, 1/2). Importantly,the magnetic structure in CsCr0.94Fe0.06F4 differs fromthat in the parent CsCrF4. This result suggests thatthe ground state in CsCrF4 is more sensitive to mag-netic rather than nonmagnetic substitution on the Crsite. Further studies of magnetic excitation for the Fe-substituted CsCrF4 would be important to elucidate thespin interactions.

ACKNOWLEDGMENTS

We acknowledge the support of the Australian Cen-tre for Neutron Scattering, Australian Nuclear Scienceand Technology Organisation, in providing the neu-tron research facilities used in this work. The neutrondiffraction experiments performed using ECHIDNA atANSTO, Australia were supported by the General UserProgram for Neutron Scattering Experiments, Institutefor Solid State Physics, The University of Tokyo (Pro-posals No. 18520), at JRR-3, Japan Atomic EnergyAgency, Tokai, Japan. S.H. was supported by the JapanSociety for the Promotion of Science through the Lead-ing Graduate Schools (MERIT).

TABLE II. Basis vectors for the space group P62m withkmag = (0, 0, 1/2). The atoms are defined according to Cr1:(0.2246, 0, 0), Cr2: (0, 0.2246, 0), Cr3: (0.7754, 0.7754, 0).

IRs Basis Vectors [ma mb mc]

Cr1 Cr2 Cr3

Γ2 Ψ1 [1 0 0] [0 1 0] [-1 -1 0]

Γ3 Ψ2 [0 0 1] [0 0 1] [0 0 1]

Γ4 Ψ3 [1 2 0] [-2 -1 0] [1 -1 0]

Γ5 Ψ4 [0 0 2] [0 0 -1] [0 0 -1]

Ψ5 [0 0 0] [0 0 -√

3] [0 0√

3]

Γ6 Ψ6 [2 0 0] [0 -1 0] [1 1 0]

Ψ7 [0 1 0] [1/2 1/2 0] [-1/2 0 0]

+i[√

3/2√

3/2 0] +i[√

3/2 0 0]

Ψ8 [0 0 0] [0 -√

3 0] [-√

3 -√

3 0]

Ψ9 [1/2 1/2 0] [-1/2 0 0] [0 1 0]

+i[-√

3/2 -√

3/2 0] +i[-√

3/2 0 0]

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6

TABLE III. Basis vectors for the space group P62m withkmag = (1/2, 0, 1/2). The atoms are defined according to Cr1:(0.2233, 0, 0), Cr2: (0, 0.2233, 0), Cr3: (0.7767, 0.7767, 0).

IRs Basis Vectors [ma mb mc]

Cr1 Cr2

Γ1 Ψ(1)1 [0 0 1] [0 0 1]

Γ2 Ψ(1)2 [1 0 0] [1 1 0]

Ψ(1)3 [0 1 0] [0 -1 0]

Γ3 Ψ(1)4 [0 0 1] [0 0 -1]

Γ4 Ψ(1)5 [1 0 0] [-1 -1 0]

Ψ(1)6 [0 1 0] [0 1 0]

Cr3

Γ2 Ψ(2)1 [0 -1 0]

Γ3 Ψ(2)2 [0 0 2]

Γ4 Ψ(2)3 [2 1 0]

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Magnetic order in the chemically-substituted frustrated antiferromagnet CsCrF4AbstractI IntroductionII Experimental detailsIII Results and analysisIV DiscussionV Conclusion Acknowledgments References