S S symmetry

Article of Inorganic–Organic Hybrid (C6H5CH2CH2NH3)2MnCl4 Using Magnetic Concept

Garam Park 1, In-Hwan Oh 2,*, J. M. Sungil Park 3, Seungsoo Hahn 4 and Seong-Hun Park 5,* 1 Nuclear Chemistry Research Team, Korea Atomic Energy Research Institute, Daejeon 34057, Korea; [email protected] 2 Quantum Beam Science Division, Korea Atomic Energy Research Institute, Daejeon 34057, Korea 3 Quantum and Convergence Sciences, Korea Atomic Energy Research Institute, Daejeon 34057, Korea; [email protected] 4 Da Vinci College of General Education, Chung-Ang University, Seoul 06973, Korea; [email protected] 5 School of Electrical and Electronics Engineering, College of ICT Engineering, Chun-Aang University, Seoul 06973, Korea * Correspondence: [email protected] (I.-H.O.); [email protected] (S.-H.P.)

 Received: 29 September 2020; Accepted: 27 November 2020; Published: 30 November 2020 

Abstract: Previously, we reported that inorganic–organic hybrid (C6H5CH2CH2NH3)2MnCl4 (Mn-PEA) is antiferromagnetic below 44 K by using magnetic susceptibility and neutron diffraction measurements. Generally, when an antiferromagnetic system is investigated by the neutron diffraction method, half-integer forbidden peaks, which indicate an enlargement of the magnetic cell compared to the chemical cell, should be present. However, in the case of the title compound, integer forbidden peaks are observed, suggesting that the size of the magnetic cell is the same as that of the chemical cell. This phenomenon was until now only theoretically predicted. During our former study, using an irreducible representation method, we suggested that four spin arrangements could be possible candidates and a magnetic cell and chemical cell should coincide. Recently, a magnetic structure analysis employing a magnetic space group has been developed. To confirm our former result by the representation method, in this work we employed a magnetic space group concept, and from this analysis, we show that the magnetic cell must coincide with the nuclear cell because only the Black–White 1 group (equi-translation or same translation group) is possible.

Keywords: inorganic–organic hybrid; magnetic space group; neutron diffraction

1. Introduction Nowadays, inorganic–organic hybrid materials attract special interest because of their versatile application possibilities, including their use in solar cells, multi-ferroic properties and low-dimensional magnetism [1–4]. To understand interlayer-length effects on their magnetic behavior, many systems have been suggested. Although such trials have taken place, results have not been successful, because inorganic–organic hybrid systems generally show a high insolubility, and it is difficult to obtain a high-quality crystal suitable for a crystallographic investigation. To overcome this hurdle, we have conducted many experiments and finally we have been able to synthesize a series of layered inorganic–organic hybrid perovskite crystals using phenylethylammonium cations. Among others, the crystal structures of (C6H5CH2CH2NH3)2CoCl4 (Co-PEA), (C6H5CH2CH2NH3)2MnCl4 (Mn-PEA) and (C6H5CH2CH2NH3)2CuCl4 (Cu-PEA) have been solved by the X-ray single crystal diffraction technique [5–7]. Co-PEA crystallizes in a monoclinic space group P121/c1 (No. 14), and shows no magnetic ordering at all at low temperature. Co builds an isolated tetrahedron with Cl and between inorganic and

Symmetry 2020, 12, 1980; doi:10.3390/sym12121980 www.mdpi.com/journal/symmetry Symmetry 2020, 12, x FOR PEER REVIEW 2 of 12 shows no magnetic ordering at all at low temperature. Co builds an isolated tetrahedron with Cl and between inorganic and organic parts various hydrogen bonds exist. Unlike Co-PEA, Mn-PEA and Symmetry 2020, 12, 1980 2 of 12 Cu-PEA show an orthorhombic space group Pbca (No.61) and magnetic ordering process occurs at TC = 10 K for Cu-PEA and at TN = 44 K for Mn-PEA. Cu-PEA and Mn-PEA belong to the 2-dimensional organiclayered partsinorganic–organic various hydrogen K2NiF bonds4 perovskite exist. Unlike type Co-PEA, of general Mn-PEA formula and Cu-PEA A2MX4 show, where an orthorhombicA = organic spacecation, group M = Pbcadivalent (No.61) metal and and magnetic X = halide. ordering Perovskite process occursis the atmineralTC = 10 name K for for Cu-PEA CaTiO and3. However, at TN = 44 in K forgeneral, Mn-PEA. ABX Cu-PEA3 or A2BX and4 type Mn-PEA compounds belong toare the known 2-dimensional as perovskite layered type. inorganic–organic The ABX3 type K 2NiFis 3-4 perovskitedimensional type and of generalA2BX4 formulais a double A2MX layered4, where type. A = organicThe K2 cation,NiF4-typeM = materialsdivalent metalare alsoand known X = halide. as PerovskiteRuddlesden–Popper-type is the mineral namecompound for CaTiOs [8].3 .Although However, both in general,of the abovementioned ABX3 or A2BX4 Cu-PEAtype compounds and Mn- arePEA known are of asa magnetically perovskite type. ordered The phase ABX3 typebelow is a 3-dimensional certain temperature, and A2 BXwe4 preferis a double Mn-PEA, layered because type. TheMn-PEA K2NiF is4-type antiferromagnetic materials are also and known an antiferromagnet as Ruddlesden–Popper-typeic system is more compounds suitable [8 ].for Although handling both with of theneutron abovementioned diffraction Cu-PEA techniques. and Mn-PEA Additionally, are of a magneticallyin general, ordered an antiferromagnetic phase below a certain system temperature, shows weforbidden prefer Mn-PEA,half-integer because peaks Mn-PEAbelow a magnetic is antiferromagnetic transition temperature. and an antiferromagnetic However, in the system case isof more Mn- suitablePEA, no for half-integer handling with forbidden neutron peaks diffraction are observed techniques. below Additionally, the Neel in temperature. general, an antiferromagnetic Instead, integer systemforbidden shows peaks forbidden that have half-integer originated peaks from below the a magn magneticetic transitionphase transition temperature. are present. However, Based in the on case a oftheoretical Mn-PEA, study no half- [9], integer if weak- forbidden peaks are observed or ferrimagnetism below the Neel by temperature. spin canting Instead, due to integer DM forbidden(Dzyaloshinsky-Moriya) peaks that have originatedinteractions from is thepresent, magnetic the phaseantiferromagnetic transition are present.cell should Based be on same a theoretical as the studychemical [9], ifcell. weak-ferromagnetism Mn-PEA shows antiferromagnetic or ferrimagnetism phas by spine transition canting dueat around to DM (Dzyaloshinsky-Moriya)44 K and, in addition, interactionsspin canting is due present, to DM the interactions antiferromagnetic causes a cell weak-ferromagnetism should be same as the or chemicalferrimagnetism cell. Mn-PEA [6]. Thus, shows this antiferromagneticcompound should phase be the transition ideal candidate at around material 44 K and, with in addition, which the spin theoretical canting due prediction to DM interactions could be causesproven. a In weak-ferromagnetism the previous study, or we ferrimagnetism reported not only [6]. Thus, X-ray this single-crystal compound shouldstructure, be thebut ideal also candidatemagnetic materialproperties with using which magnetic the theoretical susceptibility prediction and neutron could be diffraction proven. In methods the previous combined study, with we reported irreducible not onlyrepresentation X-ray single-crystal techniques. structure, However, but alsoa new magnetic approach properties using a usingmagnetic magnetic space susceptibility group has recently and neutron been diffractiondeveloped. methods To check combined and confirm with our irreducible previous representation result using atechniques. representation However, method, a new in this approach study, usingwe used a magnetic a magnetic space space group group has concept, recently and been from developed. this analysis, To check we will and show confirm that our the previous magnetic result cell usingin Mn-PEA a representation is the same method, as a chemical in this cell. study, we used a magnetic space group concept, and from this analysis, we will show that the magnetic cell in Mn-PEA is the same as a chemical cell. 2. Materials and Methods 2. Materials and Methods Before we begin, we must first understand what the magnetic moment is and the difference betweenBefore polar we vectors begin, weand must axial firstvectors. understand The magnetic what themoment magnetic of an moment atom generally is and therefers diff toerence spin betweenand is known polar as vectors an axial and vector. axial vectors.A current The loop magnetic generates moment a magnetic of an atommoment. generally Under refers a symmetry to spin andoperation, is known a current as an axialloop behaves vector. Aunlike current polar loop vectors generates such aas magnetic velocity, moment.force and Underlinear momentum. a symmetry operation,To describe a the current axial loop vector, behaves a new unlike concept polar of vectorstime reversal such asmust velocity, be introduced force and and linear denoted momentum. as 1′. ToUnder describe time thereversal, axial the vector, current a new loop concept must change of time it reversals sign and must as a be result, introduced the spin and has denoted to change as its 10. Underdirection time (see reversal, Figure 1). the current loop must change its sign and as a result, the spin has to change its direction (see Figure1).

Figure 1. Time reversal effect on the axial vector. The current loop changes its sense under a time- Figure 1. Time reversal effect on the axial vector. The current loop changes its sense under a time- reversal operation. reversal operation. Contrary to the axial vector, it is unnecessary to consider the loop for a polar vector. Therefore, Contrary to the axial vector, it is unnecessary to consider the loop for a polar vector. Therefore, it is relatively easy to understand the consequences due to the symmetry operation in the case of a it is relatively easy to understand the consequences due to the symmetry operation in the case of a polar vector. In Figure2, the di fferences between the two vectors under a mirror symmetry operation are shown.

Symmetry 2020, 12, x FOR PEER REVIEW 3 of 12

Symmetrypolar vector.2020, 12 In, 1980Figure 2, the differences between the two vectors under a mirror symmetry operation3 of 12 are shown.

Figure 2. DifferencesDifferences between polar and axial vectorsvectors under mirror symmetry operation.operation.

According to the previous study [[10],10], if we denotedenote a magnetic group as M andand aa conventionalconventional crystallographic groupgroup asas G,G, allall members members of of G G are are always always a a magnetic magnetic group. group. A A paramagnetic paramagnetic group group is knownis known as as a graya gray group group and and is is described described mathematically mathematically as as G G+ +G1 G10.′. ThisThis meansmeans thatthat aa paramagnetic group isis a simplea simple summation summation of a crystallographic of a crystallographic group and group a time and reversal a time applied reversal to crystallographic applied to groupcrystallographic G10. The groupgroup GG1 is′ a. colorlessThe group group. G is Each a colorless colorless group. group GEach and colorless paramagnetic group group G and or grayparamagnetic group is composedgroup or gray of 230group groups. is composed The above of 230 two groups. groups The are above trivial. two For groups the magnetic are trivial. group, For the so-calledmagnetic non-trivialgroup, the Black–White so-called non-trivial group is important.Black–White The group Black–White is important. group The can Black–White be obtained bygroup the cosetcan be decomposition obtained by technique. the coset Generally,decompositi throughon technique. the coset decompositionGenerally, through method the we coset can obtaindecomposition many subgroups, method we but can in theobtain case many of the subgroups, magnetic space but in group, the case we of can the only magnetic consider space subgroups group, ofwe index can only 2. Thisconsider relation subgroups is expressed of index as M2. Th= His relation+ (G – H)1is expressed0, where Mas isM a= magneticH + (G – H)1 group,′, where H is M a subgroupis a magnetic of index group, 2, H G is is a a subgroup conventional of index crystallographic 2, G is a conventional group and crystallographic 10 is a time reversal group operation. and 1′ is Usinga time thereversal above operation. relation, weUsing can the obtain above 1191 relation, Black–White we can groups. obtain Each1191 Black–White group can be groups. divided Each into twogroup categories can be divided based on into the two existence categories of translational based on the symmetry existence changes. of translational According symmetry to International changes. TablesAccording for Crystallography to International Tables A [11], for if there Crystallography is no change A in [11], the if translational there is no change symmetry in the after translational the ,symmetry after the transition the phase istransition, known as thetranslationengleich transition is knownor tas-transition. translationengleich This means or t-transition. that the lattice This parametersmeans that arethe keptlattice after parameters the phase are transition. kept after If th theree phase is any transition. change in If thethere translational is any change symmetry, in the thistranslational corresponds symmetry, to klassengleich this correspondsor k-transition. to klassengleich This classical or k-transition. concept This is also classical valid forconcept a magnetic is also spacevalid for group, a magnetic especially space for agroup, Black–White especially group. for a If Black–White we use this concept, group. If there we areuse 674this subgroups concept, there that fulfillare 674 the subgroups equi-transition that fulfill condition. the equi-transition This group iscondition. known as This first-kind group Black–White,is known as first-kind or simply Black– BW1. TheWhite, subgroup or simply H hasBW1. the The same subgroup translation H has as the parentsame translation group G. Theas the last parent one is group a so-called G. The equi-class last one groupis a so-called or second equi-class Black–White group group, or second BW2. In Black–White this case, the group, translation BW2. symmetry In this case, is lost the but translation the crystal classsymmetry can be is kept lost [but10]. the crystal class can be kept [10].

3. Results and Discussion To analyzeanalyze the the magnetic magnetic structure structure using using a magnetic a ma spacegnetic group space concept, group weconcept, first need we information first need suchinformation as space such group, as latticespaceparameters group, lattice and theparame existenceters and of any the phase existence transitions of any including phase transitions structural andincluding magnetic. structural Mn-PEA and magnetic. has a space Mn-PEA group has Pbca a space with latticegroup parametersPbca with lattice a = 7.207 parameters Å, b = a7.301 = 7.207 Å, cÅ,= b39.413 = 7.301 Å Å,and c = Z 39.413= 4, Å and and shows Z = 4, twoand structuralshows two and structural one magnetic and one phasemagnetic transitions phase transitions at 367 K, 417at 367 K andK, 417 43 K K, and respectively 43 K, respectively [6]. The [6]. crystal The crystal structure structure is shown is shown in Figure in Figure3. The 3. The point point group group of theof the space space group group Pbca Pbca is 2 /m2is 2/m2/m2/m./m2/m. If we If look we atlook the at maximal the maximal subgroups subgroups and minimal and minimal super-groups super- ofgroups the point of the group point [group11], there [11], are there three are subgroups three subg withroups an with index an 2index of 2/ 2m2 of/ m22/m2/m2/m,/m, namely, namely, 222, mm2 222, andmm2 2 /andm. 2/m. In this In case,this case, the crystallographicthe crystallographic group group G is G mmm is mmm and and we we can can describe describe the the group group G asG G = {1, i, 2, m, 2 , 2 , m , m }, where i is inversion symmetry, 2 is a 2-fold symmetry operation along asmmm Gmmm = {1, i, 2, m,x 2x,y 2y, mx x, my y}, where i is inversion symmetry,x 2x is a 2-fold symmetry operation the x-axis and mx is a mirror-symmetry operation perpendicular to the x-axis. The possible subgroups

Symmetry 2020, 12, x FOR PEER REVIEW 4 of 12 along the x-axis and mx is a mirror-symmetry operation perpendicular to the x-axis. The possible subgroupsSymmetry 2020 of, 12 the, 1980 mmm point group with index 2 are 222, mm2 and 2/m, as already mentioned4 of above. 12 If we denote one subgroup as H, the first subgroup can be written for example as H1 = 222 = {1, 2, 2x, 2ofy}. theAnalogously, mmm point we group can denote with index H2 = 2mm2 are 222,= {1,mm2 mx, m andy, 2} 2 and/m, asH3 already = 2/m = mentioned {1, i, 2, m}. above. In the first If we case, thedenote magnetic one subgroup point group as H, M them’m’m’ first can subgroup be obtained can from be written {1, 2, 2 forx, 2 exampley} + {i, m, as mH1x, m=y}1222′ (see= {1, Table 2, 2x ,1). 2y }This. isAnalogously, described as we {1,can 2, 2 denotex, 2y, i’, H2m’,= m’mm2x, m’=y} {1,= 2/m’2/m’2/m’ mx, my, 2} and = H3m’m’m’= 2/m [10].= {1, This i, 2, m} magnetic. In the firstpoint case, group isthe not magnetic compatible point with group ferromagnetism, Mm’m’m’ can be because obtained if we from look{1, at 2, 2Tablex, 2y} 1,+ {i,half m, of m xthe, m spinsy}10 (see have Table the1 ).same signThis and is describedthe rest of as the{1, spins 2, 2x, have 2y, i’, an m’, opposite m’x, m’y} si=gn.2/m’2 This/m’2 means/m’ = anm’m’m’ antiferromagnetic [10]. This magnetic ordering. point Thus, ferromagneticgroup is not compatible ordering is with impossible ferromagnetism, in this magnetic because point if we group. look at This Table argument1, half of is the valid spins for have the rest ofthe magnetic same sign point and groups. the rest The of second the spins one have is {1, an 2, opposite mx, my} + sign. {i, m, This 2x, 2 meansy}1′ = {1, an 2, antiferromagnetic2′x, 2′y, i, m’, mx, my} =ordering. 2′/m2′/m2/m’ Thus, = ferromagnetic mmm’ (see orderingTable 1). is This impossible magnetic in this point magnetic group point is also group. not Thiscompatible argument with is valid for the rest of magnetic point groups. The second one is {1, 2, m , m } + {i, m, 2 , 2 }1 ferromagnetism. In the third case, the corresponding magnetic point groupx My m’m’2 can bex obtainedy 0 = {1, 2, 2 x, 2 y, i, m’, mx, my} = 2 /m2 /m2/m’ = mmm’ (see Table1). This magnetic point group from {1, 2,0 i, m}0 + {2y, my, mx, 2x}1′ (see0 Table0 1). This can be rewritten as {1, 2, i, m, 2′y, m’y, m’x, 2′x} = 2is′/m2 also′/m2/m not compatible = m’m’2. withThis ferromagnetism.point group is compatib In the thirdle with case, ferromagnetism. the corresponding The magnetic magnetic point point group M can be obtained from {1, 2, i, m} + {2 , m , m , 2 }1 (see Table1) . This can be rewritten as group m’m’2m’m’2 is similar to the previous two magny yetic xpointx 0 groups. However, if we consider the {1, 2, i, m, 2 , m’ , m’ , 2 x} = 2 /m2 /m2/m = m’m’2. This point group is compatible with ferromagnetism. magnetic moment0y y alongx 0 the c-axis,0 0 all magnetic components along the c-axis show a positive sign. The magnetic point group m’m’2 is similar to the previous two magnetic point groups. However, if we This means that the ferromagnetic ordering in this point group is only possible along the c-axis. Along consider the magnetic moment along the c-axis, all magnetic components along the c-axis show a positive another two directions, namely the a- and b-axes, antiferromagnetic ordering is possible. The above sign. This means that the ferromagnetic ordering in this point group is only possible along the c-axis. resultsAlong anotherar