Magnetoelastic effects in low-dimensional magnetic systems

We consider a new realization of magnetoelastic interactions in low-dimensional magnetic systems. We show that low-dimensional spin systems are unstable with respect to the spontaneous appearance of alternating distortions of the positions of the three-dimensional nonmagnetic atoms (ligands), that s...

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Datum:	2001
Hauptverfasser:	Zvyagin, A.A., Zvyagina, G.A.
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Sprache:	English
Veröffentlicht:	Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України 2001
Schriftenreihe:	Физика низких температур
Schlagworte:	Низкотемпеpатуpная магнитостpикция магнетиков и свеpхпpоводников
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spelling	irk-123456789-1300192018-02-05T03:02:48Z Magnetoelastic effects in low-dimensional magnetic systems Zvyagin, A.A. Zvyagina, G.A. Низкотемпеpатуpная магнитостpикция магнетиков и свеpхпpоводников We consider a new realization of magnetoelastic interactions in low-dimensional magnetic systems. We show that low-dimensional spin systems are unstable with respect to the spontaneous appearance of alternating distortions of the positions of the three-dimensional nonmagnetic atoms (ligands), that surround the magnetic ions. Those distortions are supplemented by the spontaneous onset of alternating effective g factors of the magnetic ions in the phase with short-range interactions. We discuss the possibility of observing the effect in an uniform external magnetic field, which in the situation considered produces both magnetization and staggered magnetization of the magnetic subsystem. The connection of the proposed theory with recent experiments on effectively low-dimensional magnetic systems (organic spin chains, heavy-fermion compounds, rare-earth molybdates) is discussed. 2001 Article Magnetoelastic effects in low-dimensional magnetic systems / A.A. Zvyagin , G.A. Zvyagina // Физика низких температур. — 2001. — Т. 27, № 4. — С. 406-411. — Бібліогр.: 27 назв. — англ. 0132-6414 PACS: 75.10.Jm, 71.70.Fk, 71.70.Ej http://dspace.nbuv.gov.ua/handle/123456789/130019 en Физика низких температур Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
institution	Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection	DSpace DC
language	English
topic	Низкотемпеpатуpная магнитостpикция магнетиков и свеpхпpоводников Низкотемпеpатуpная магнитостpикция магнетиков и свеpхпpоводников
spellingShingle	Низкотемпеpатуpная магнитостpикция магнетиков и свеpхпpоводников Низкотемпеpатуpная магнитостpикция магнетиков и свеpхпpоводников Zvyagin, A.A. Zvyagina, G.A. Magnetoelastic effects in low-dimensional magnetic systems Физика низких температур
description	We consider a new realization of magnetoelastic interactions in low-dimensional magnetic systems. We show that low-dimensional spin systems are unstable with respect to the spontaneous appearance of alternating distortions of the positions of the three-dimensional nonmagnetic atoms (ligands), that surround the magnetic ions. Those distortions are supplemented by the spontaneous onset of alternating effective g factors of the magnetic ions in the phase with short-range interactions. We discuss the possibility of observing the effect in an uniform external magnetic field, which in the situation considered produces both magnetization and staggered magnetization of the magnetic subsystem. The connection of the proposed theory with recent experiments on effectively low-dimensional magnetic systems (organic spin chains, heavy-fermion compounds, rare-earth molybdates) is discussed.
format	Article
author	Zvyagin, A.A. Zvyagina, G.A.
author_facet	Zvyagin, A.A. Zvyagina, G.A.
author_sort	Zvyagin, A.A.
title	Magnetoelastic effects in low-dimensional magnetic systems
title_short	Magnetoelastic effects in low-dimensional magnetic systems
title_full	Magnetoelastic effects in low-dimensional magnetic systems
title_fullStr	Magnetoelastic effects in low-dimensional magnetic systems
title_full_unstemmed	Magnetoelastic effects in low-dimensional magnetic systems
title_sort	magnetoelastic effects in low-dimensional magnetic systems
publisher	Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
publishDate	2001
topic_facet	Низкотемпеpатуpная магнитостpикция магнетиков и свеpхпpоводников
url	http://dspace.nbuv.gov.ua/handle/123456789/130019
citation_txt	Magnetoelastic effects in low-dimensional magnetic systems / A.A. Zvyagin , G.A. Zvyagina // Физика низких температур. — 2001. — Т. 27, № 4. — С. 406-411. — Бібліогр.: 27 назв. — англ.
series	Физика низких температур
work_keys_str_mv	AT zvyaginaa magnetoelasticeffectsinlowdimensionalmagneticsystems AT zvyaginaga magnetoelasticeffectsinlowdimensionalmagneticsystems
first_indexed	2025-07-09T12:42:29Z
last_indexed	2025-07-09T12:42:29Z
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fulltext	Fizika Nizkikh Temperatur, 2001, v. 27, No. 4, p. 406–411Z vya gin A. A . and Z vya gina G. A .Ma gne toelast ic e ffec ts in low-dim ensiona l m agn etic system sZvyag in A . A. a nd Zvyag in a G. A.Mag neto elastic eff ects in low-dimen sio nal mag net ic syst ems Magnetoelastic effects in low-dimensional magnetic systems A. A. Zvyagin1,2 and G. A. Zvyagina2 1 Max Planck Institut fur Physik Komplexer Systeme, No..thnitzer Str, 38, D-01187, Dresden, Germany 2 B. Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine 47 Lenin Ave., Kharkov 61164, Ukraine Received July 25, 2000 We consider a new realization of magnetoelastic interactions in low-dimensional magnetic systems. We show that low-dimensional spin systems are unstable with respect to the spontaneous appearance of alternating distortions of the positions of the three-dimensional nonmagnetic atoms (ligands), that surround the magnetic ions. Those distortions are supplemented by the spontaneous onset of alternating effective g factors of the magnetic ions in the phase with short-range interactions. We discuss the possibility of observing the effect in an uniform external magnetic field, which in the situation considered produces both magnetization and staggered magnetization of the magnetic subsystem. The connection of the proposed theory with recent experiments on effectively low-dimensional magnetic systems (organic spin chains, heavy-fermion compounds, rare-earth molybdates) is discussed. PACS: 75.10.Jm, 71.70.Fk, 71.70.Ej Interest in electron systems with substantial coup- ling between the charge, spin, and orbital degrees of freedom of the electronic and elastic subsystems of a crystal has grown considerably during the last decade. The prime examples of the manifestation of such cooperative effects are the phenomena of col- losal magnetoresistance of manganites, non-Fermi- liquid behavior of some heavy-fermion compounds, spin-Peierls and charge ordering behaviors in inor- ganic systems and unconventional superconducti- vity [1]. The Jahn-Teller effect [2] is probably the oldest known manifestation of such a coupling. Here the degeneracy of the orbital states of a molecule is removed by the deformation of the latter. The cooperative Jahn–Teller effect reveals itself in a structural phase transition. It has been observed in a number of compounds [3]. In the spin-Peierls transition also the degeneracy of the electronic (spin, not orbital) subsystem of a one- dimensional (1D) spin chain is removed due to the coupling with a longitudinal phonon of the 3D crystal lattice. A spin gap is opened for the low- lying spin excitation. On the other hand, the corre- sponding phonon mode possesses softening (Kohn anomaly). Some of magnetic compounds with the essential coupling between spin, orbital, and elastic subsystems manifest paramagnetic spin behavior with two essentially inequivalent magnetic centers at low temperatures (which are higher, though, than the temperature of the phase transition to magnetically ordered 3D state). Often the latter has not been observed [4–9]. For higher tempera- tures the inequivalence between the two magnetic centers smears out. The presence of inequivalent magnetic centers in low-dimensional quantum spin systems is usually connected with slightly different local surrounding of two types of magnetic ions and involves either staggered g factors of the magnetic ions [4] (another case pertains to two anisotropic g tensors canted with respect to the principal axis [8] or the Dzyaloshinskii–Moriya coupling in crystals without mirror magnetic symmetry [10]. Low-lying spin excitations are gapless for these low-dimen- sional systems in the absence of an external mag- netic field. However,in an external field the low- temperature specific heat of some of those systems reveals the emergence of a spin gap induced by an external magnetic field [8,11,12]. To explain that gapped behavior a 1D spin subsystem with staggered effective g factors has been sta- died [5,13,14]. The low-temperature, low-field electron spin resonance (ESR) [4,6–9] exhibited two inequivalent magnetic centers. On the other hand, the higher-field ESR treatment reported only © A. A. Zvyagin and G. A. Zvyagina, 2001 a single magnetic center [15]. Optical (Raman and infrared) measurements [16] have revealed the tendency for softening of some lattice modes. Ultra- sonic measurements also revealed anomalous beha- viors of the sound velocities for some phonon modes in such crystals [17,18]. In this work we propose a mechanism for expla- nation of the observed anomalous behavior of the spin, orbital, and elastic subsystems of that group of magnetic low-dimensional systems. Namely, we point out that the dimerization of the effective g factors in a quantum antiferromagnetic spin chain can be caused by the coupling of the spin and orbital subsystems to the elastic subsystem, fol- lowed by a distortion of the local surrounding of the magnetic ions. In paramagnets the value of the g factor differs from 2. The difference stems from the effect of the crystalline electric field of nonmag- netic ligands due to the presence of a spin-orbit interaction. The essence of our study is following. Let the configuration of ligands, which surround two neighboring magnetic ions along the chain direction, possesses small shifts (distortions) of op- posite signs (antiferrodistortions [8]). Such distor- tions will immediately produce a change of the crystalline electric fields of the ligands. Hence, the orbital moment of the magnetic ions will be alternately affected. Then the spin–orbit interaction yields, first, two different values of the effective g factors of the magnetic ions, and second, a stag- gered Dzyaloshinskii—Moriya interaction (because of the odd magnetic symmetry with respect to the principal axis). The effect of the latter can be also transferred to the effective staggered g factor by means of an alternating rotation of spins. Hence, the staggered distortion of the nonmagnetic sur- roundings (ligands) of the magnetic ions produces two inequivalent magnetic centers for the spin sub- system. The elastic subsystem loses energy due to the alternating distortions of ligands, while the electron subsystem realizes an energy gain. The steady-state configuration of the total crystal is determined by the competition between those two processes. From the magnetic standpoint that effect is collective because the spins interact with each other. On the other hand, the inequivalence of magnetic centers can be seen only in nonzero mag- netic field, so the effect is field-induced. To fix the stage, consider the low-temperature behavior of a quasi-low-dimensional magnetic crys- tal. The spin–spin coupling along one direction of this crystal is larger than the interactions along the other crystallographic directions. Suppose this quasi-1D spin subsystem can be described by a Hamiltonian of a gapless spin-1/2 antiferromag- netic (AF) chain. The fact that the low-lying exci- tation of the 1D AF spin chain is gapless implies that the system is critical, i.e., the ground-state correlation functions decay in a power-law manner. Suppose also that for the reasons explained above, some components of the effective g factors of the spins are alternating, i.e., g1,2 = g(1 ± δ), where δ << 1 is proportional to the small alternating distortions of the local environment. The parameter δ is not fixed, but has to be determined from the conditions of the steady state. It is equivalent to the mean field approximation for phonons. It is justi- fied for the 3D elastic subsystem. The 1D spin–spin interactions will be taken into account nonper- turbatively. In the case of alternating Dzyaloshin- skii—Moriya interactions present in the spin chain the alternating effective g factors are g1,2 = g × × cos ϑ(1 ± tan ϑ), where the angle ϑ originates from, e.g., the alternating components of the crys- talline electric field of the ligands [14]. For rare- earth molybdates, where the g tensors for two cen- ters are canted with respect to the main axis, this means that g1,2 = g cos α cos θ (1 ± tan α tan θ) [8], where α and θ are the angles determining the canting of the g tensors and field direction, respec- tively. The application of a field parallel to the crystallographic axes does not change the distor- tion. For rare-earth ions (with a Kramers- or non- Kramers-doublet crystalline field ground state) for sufficiently low temperatures T compared with the crystalline-field splitting D, one can use the two lowest levels of the ion as an effective spin-1/2 with magnetically anisotropic behavior. It turns out that no change of the g factors can be produced by distortions of ligands for the ground-state doublets. They do not have orbital degrees of freedom and are therefore unaffected by distortions. However, the excited crystalline electric field states are effec- tively included. This is why a distortion of the ligands can produce a change of the g factors, through the off-diagonal matrix elements of the relevant electric-multipole operators. This means that the conditions for the applicability of our effective spin-1/2 description for rare-earth com- pounds are: (i) T << D, i.e., there is no thermal population of the crystalline electric field-excited levels; (ii) off-diagonal matrix elements (between the ground-state doublet and excited levels) of the Zeeman term must be small compared with D; (iii) the matrix elements between the ground-state doublet and crystalline electric field-exited levels of the operator describing the distortion must not be too small compared to D (otherwise distortions Magnetoelastic effects in low-dimensional magnetic systems Fizika Nizkikh Temperatur, 2001, v. 27, No. 4 407 would produce a negligible change of the ground- state g factors); (iv) distortions of the ligands must not affect the exchange constant J; see below (with J << D). The Hamiltonian can be written as � sp = J ∑ j (S j S j+1 + (∆ − 1)Sj zSj+1 z ) − − µB H ∑ j (g1 S2j z + g2 S2j+1 z ) , (1) where 0 ≤ ∆ ≤ 1 is the parameter of the «easy- plane» magnetic anisotropy, H is an external mag- netic field, and µB is the Bohr magneton. It is easy to show that because of nonzero δ the application of an external field to this system yields two effects: homogeneous magnetization (mz) and staggered magnetization. The former changes the ground-state filling of the Dirac sea (H plays the role of the Fermi energy). For large enough values of the field H the spin subsystem possesses trimerization (for the Dirac sea of spinons being one-third filled), quadrimerization (for one-fourth filling), etc. For those values of the field 2nkF = π, with n being an integer and 2kF = π(1 + 2mz), i.e., we expect the series of transformations towards an inhomogeneous (incommensurate) magnetic structure due to the umklapp processes rather than the dimeriza- tion [19]. We restrict ourselves to small enough values of H here. The staggered magnetization is the relevant perturbation from the renormalization group (RG) viewpoint. It produces the gap for low-lying magnetic excitations of the system (spi- nons). We can calculate the response of our (criti- cal) spin chain to the relevant perturbation (stag- gered field). We perform such a calculation in a RG framework. Our study shows that the exponents are non-integer in general, in contrast to simple pertur- bation or mean-field theories [8,16], which of course are not legitimate for the low-dimensional quantum spin systems. An application of scaling relations provides a simple tool to understand some essential aspects of the behavior of a critical chain under a relevant perturbation. Recall that response of the free energy fcl and the correlation function ξcl of a classical critical d-dimensional system per- turbed by a relevant operator δ� ′ with RG eigen- value ν−1 > 0 is ∆fcl ∝ δdν , ξcl ∝ δ−ν . (2) A quantum critical d-dimensional system (which in our case is the spin 1D subsystem of the crystal) formally behaves in the scaling regime equivalently to a (d + z)-dimensional classical system, where z is the dynamical critical exponent. Hence, the ground- state energy and the gap of the low-lying spin excitations of the d-dimensional quantum critical system are formally proportional to the free ener- gy and to the inverse correlation function of the (d + z)-dimensional classical critical system, respec- tively. The RG eigenvalue ν−1 is related to the scaling dimension x of the particular operator by x + ν−1 = d + z. For the (conformally invariant) AF spin chain we have d = z = 1, i.e., ν = (2 − x)−1. Hence the renormalization of the ground-state ener- gy per site of the quantum critical chain and the low-lying spin excitation gap (which is equal to zero at the unperturbed point) to the staggered magnetic field are ∆Eq ∝ − (gδµ B H)2/(2−x e ), ∆ ∝ (gδµB H)1/(2−x e ) , (3) respectively, where xe is the minimal scaling expo- nent for energy—energy correlations. Here we have ignored logarithmic corrections. They are present due to the marginal operators in the RG sense and essential for the SU(2)-symmetric case. To find the scaling dimension for our critical spin chain we use the results of the conformal field theory (CFT). According to the CFT approach [20] the asymptotics of the correlation functions of pri- mary fields in the ground state are known to be 〈φ∆±(r, t)φ∆±(0, 0)〉 = exp (2iDPF r)(r − ivF t)−2∆+ × × (r + ivF t)−2∆− , where vF and PF are the Fermi velocity and the Fermi momentum, respectively [a (half-)integer D measures the momentum of the primary field in units of the Fermi momentum]. The scaling dimension and spin for each primary field are determined by xφ = ∆+ + ∆− and sφ = ∆+ − ∆−. The parameters ∆± can be calculated according to the finite-size analysis of the low-energy physics of the critical spin chain. Combining all the effects, we can write for the ground-state energy of the spin subsystem with nonzero δ Esp = − vF    gδµ B H vF    2/(2−x e ) , (4) where for our AF spin chain vF = πJ/2 × × √1 − ∆2 cos−1 ∆ is the Fermi velocity of spinons for H = 0. We point out that the scaling approach is only valid in the vicinity of the critical point, i.e., in principle the values of the magnetic field and δ are small. Note that the Fermi velocity monotonically decreases with the growth of H and becomes zero at the spin-saturation point (for A. A. Zvyagin and G. A. Zvyagina 408 Fizika Nizkikh Temperatur, 2001, v. 27, No. 4 H ≥ Hc ∼ J∆/4gµB). The exponent is equal to xe = π/2(π − cos−1 ∆) for H = 0 (it increases monot- onically with the increase of H and becomes 1 at H = Hc) [21]. Obviously Esp < 0, and hence one has an energy gain due to nonzero δ. On the other hand, in the lowest order in δ the elastic subsystem loses an energy proportional to Cδ2/2, where C is the elastic constant. Whether the ground-state steady-state configuration corresponds to zero or nonzero δ depends on the scaling exponent xe . For xe < 1 the ground-state steady-state configuration of the spin and elastic subsystems corresponds to nonzero δ, and hence, to two inequivalent spin centers (with two different g factors) and to the nonzero alternating distortions (antiferrodistor- tions) of the local environment of the magnetic ions (ligands). (Here we take into account that \|δ\| < 1.) The steady-state δ is equal to δ0 =    vF C    2−x e 2(1−x e )    gµ B H vF    1 1−x e . (5) Clearly δ0 = 0 for H = 0 and for H ≥ Hc . This is the main result of our report. For high temperatures (much higher than J), the steady-state δ is zero, naturally. Hence, there has to be a phase transition between the low-temperature phase with nonzero staggered magnetization, gapped low-lying spin ex- citations, and nonzero alternating distortions of the ligands, surrounding the magnetic ions, and the high-temperature phase in which the staggered mag- netization is zero, low-lying spin excitations are gapless and there are no distortions of the ligands. In fact we have considered the effect under a tacit assumption that the initial frequencies ω0 of the phonons which are coupled to the spin chain are small ω0 << J (adiabatic approximation). It is in principle possible to calculate the effect more pre- cisely for any ω0 [22,23]: there the conditions for the steady-state configuration of the total system correspond to the cross section of the respective phonon modes ω(q) (at q = 2kF) connected to the alternating distortions (antiferrodistortions) of li- gands with the magnetic modes [22,23]. Let us consider the interesting (RG-marginal with xe = 1) limiting case, namely ∆ = 0. That case corresponds to the XX spin-1/2 chain with alter- nating g factors. The Hamiltonian of the latter can be exactly mapped by means of the nonlocal Jor- dan—Wigner transformation on the Hamiltonian of the lattice noninteracting fermions [24]. The ground-state energy of the spin subsystem and the elastic subsystem can be written in the form Egs = Cδ2 2 − gµ B H    1 − λ c π    − − 1 π ∫ 0 λ c dλ √(δgµ B H)2 + [J cos (λ/2)]2 , (6) where λc = cos−1 [2(1 − δ2)(gµB H/J)2 − 1]. Mini- mizing the ground-state energy with respect to δ we obtain two possible solutions. The first one, δ = 0, corresponds to zero distortions. As to the second one, it satisfies the equation πC √J2 + (δgµ B H)2 (2gµ B H)2 = F    λ c 2 , k    , (7) where F(λc /2, k) is the incomplete elliptic integral of the first kind with k−1 = √1 + (δgµB H/J)2 . No- tice that for H ≥ Hc = J/gµB √1 − δ2 one has λc = π, and the integral is zero (hence for H ≥ Hc there is only one δ0 = 0 solution in the ground state, as should be the case). We emphasize again that we are studying the effect of sufficiently weak mag- netic fields, for which, on the one hand, the scaling approach is valid, and, on the other hand, we restrict consideration to the dimerization only, i.e., the field is not so strong as to produce a one-third filling of the Dirac sea, etc., or a series of trans- formations into inhomogeneous magnetic phases. Equation (7) can be re-written in the form √1 − (1 − δ2)(gµ B H/J)2 = sn (u, k) , (8) where u = πC √J2 + (δgµB H)2/(2gµB H)2 and sn (u, k) is the Jacobi elliptic sine function. This equation can be solved numerically. For k ∼ 1 (which corresponds to small δ), the asymptotic behavior of the elliptic function is known to be sn (u, k) ≈ tanh u + (1 − k2)(sinh u cosh u − u)/4 cosh2 u. (For large k one has sn (u, k) ≈ sin u − k2 × × cos u(u − sin u cos u)/4.) It is possible to write an analytical asymptotical expression for the gro- und-state steady-state nonzero δ0 as δ0 ≈ (2J/gµ B H) × ×      A tanh u0 − A2 2 − A tanh 2u0 − (Au0/cosh2 u0)      1/2 , (9) where A = √1 − (gµB H/J)2 and u0 = πCJ × × (2gµB H)−2. It is clear that nonzero δ0 can appear Magnetoelastic effects in low-dimensional magnetic systems Fizika Nizkikh Temperatur, 2001, v. 27, No. 4 409 only for tanh u > A. For nonzero temperatures we calculate the free energy of our system (assuming that the Debye energy of the phonons is large, and, therefore the elastic subsystem effectively remains in the ground state) F = Cδ2 2 − T π ∑ ± ∫ 0 π dλ ln    2 cosh    ε±(λ) 2T       , (10) where ε±(λ) = gµB H ± √(δgµB H)2 + [J cos (λ/2)]2 . Then the minimization of the free energy with respect to δ yields Cδ = 1 2π ∑ ± ∫ 0 π dλ tanh ε±(λ) 2T ∂ε±(λ) ∂δ . (11) For T >> J we can replace the hyperbolic tangent by its argument, and one clearly sees that there exists only one solution to Eq. (11): δ0 = 0. The numerical analysis shows that δ0 ≠ 0 exists at low temperatures. The critical temperature Tc of the transition between the low-temperature (effectively two-center) phase and the uniform high-tempera- ture phase is obtained by setting δ0 = 0 for the second order phase transition, or the free energies of the phases with δ0 = 0 and δ0 ≠ 0 for the first-order one. The critical temperature can be estimated (with the main input to the integral given by the divergent denominator, i.e., at the van Hove singu- larities) as Tc ∼ (J − gµ B H)/ln (πCJ/2g2µ B 2 H2) . (12) The analysis shows that δ0 = 0 pertains to the mini- mum of the free energy for T > Tc and to the maximum for T < Tc . Hence the phase transition is of the second order. We again emphasize that the phase transformations studied here are magnetic field-induced; they are absent without the latter. We point out also that the order of the phase transformation in the general case is connected with the orientation of the direction of the magnetic field with respect to the crystal axes and on the mutual ratios of the exchange constant, anisotropy, mag- netic field, and elastic constant. It turns out that (alternating) distortions of the ligands, which result in the inequivalence of the effective g factors of neighboring spins in quasi-1D chains, can be supplemented in the real compounds by alternating distortions of the magnetic ions themselves (which leads to the spin-Peierls insta- bilities), as has been observed, e.g., in CuGeO3 [25]. In such a situation the two effects are additive in the formation of a spin gap for low-lying spin excitations. The values of the effects are naturally different. Although the effect studied in this work manifests itself only in some domain of values of the magnetic field, the spin-Peierls period doubling is not caused by the magnetic field. The critical temperature is determined from the condi- tion of which of the instabilities becomes mani- fested first. We suppose that the cooperative effects similar to the one studied in this paper have been observed in some rare-earth molybdates. There at low-tem- perature ESR studies that have observed two ine- quivalent magnetic centers, (see, e.g., Refs. 6–9), while for higher temperatures [7,8] or higher mag- netic fields (higher frequencies) [15] only one mag- netic center was seen. The low-temperature specific heat exhibits features at temperatures higher than the transition to the magnetically ordered phase (which were hidden, though, due to the presence of a Schottky anomaly) [8]. Ultrasonic measurements have observed anomalies in the low-temperature dependences of the velocities of sound for acous- tic [17] and optical branches [18] of the phonon spectra. Optical and magnetic investigations have observed a cooperative effect (in nonzero magnetic field), that was classified as being of the Jahn—Tel- ler type [6,16,26]. Note that the transition to the magnetically ordered state was observed at much lower temperatures (see, e.g., Ref. 8, 18, 26), hence the cooperative effect we have discussed is observed in the paramagnetic (from the magnetic viewpoint) phase. It turns out that magnetic and elastic charac- teristics of some of those systems manifested the mentioned features only for nonzero external mag- netic fields, with the order of the transition (which of the derivatives of the thermodynamic potential possesses singular behavior) being determined by the direction of the field, while for zero field for some compounds there were no observations of the Jahn—Teller-like cooperative effect [27]. Summarizing, we have studied a new realization of magnetoelastic interactions in low-dimensional magnetic systems. We have shown that low dimen- sional spin systems are unstable with respect to the spontaneous appearance of alternating distortions of the positions of the three-dimensional nonmagnetic atoms (ligands) that surround the magnetic ions. Those distortions are supplemented by the sponta- neous onset of alternating effective g factors of magnetic ions in the phase with short-range interac- tions. 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