A systematic study using neutron diffraction and magnetic susceptibility are reported on Mn substituted ferrimagnetic inverse spinel Ti$_{1-x}$Mn$_{x}$Co$_2$O$_4$ in the temperature interval 1.6 K $\leq$ $T$ $\leq$ 300 K. Our neutron diffraction study reveals cooperative distortions of the $T$O$_6$ octahedral for all the Jahn-Teller active ions $T$ = Mn$^{3+}$, Ti$^{3+}$ and Co$^{3+}$, which are confirmed by the X-ray photoelectron spectroscopy. Two specific compositions ($x$ = 0.2 and 0.4) have been chosen because of their unique features: noncollinear Yafet-Kittel type ordering, and weak tetragonal distortion with ${c/a}$ $<$ 1, in which the apical bond length $d_c$($T_B$-O) is longer than the equatorial $d_{ab}$($T_B$-O) due to the splitting of the $e_g$ level of Mn$^{3+}$ ions into $d_{x^2-y^2}$ and $d_{z^2}$. For $x$ = 0.4, the distortion in the $T_B$O$_6$ octahedra is stronger as compared to $x$ = 0.2 because of the higher content of trivalent Mn. Ferrimagnetic ordering in $x$ = 0.4 and $x$ = 0.2 sets in at 110.3 and 78.2 K, respectively due to the unequal magnetic moments of cations, where Ti$^{3+}$, Mn$^{3+}$, and Co$^{3+}$ occupying the octahedral, whereas, Co$^{2+}$ sits in the tetrahedral site. In addition, weak antiferromagnetic component could be observed lying perpendicular to the ferrimagnetic component. The analysis of static and dynamic magnetic susceptibilities combined with the heat-capacity data reveals a magnetic compensation phenomenon at $T_{COMP}$ = 25.4 K in $x$ = 0.2 and a reentrant spin-glass behaviour in $x$ = 0.4 with a freezing temperature $\sim$110.1 K. The compensation phenomenon is characterized by sign reversal of magnetization and bipolar exchange bias effect below $T_{COMP}$ with its magnitude depending on the direction of external magnetic field and the cooling protocol.
We have synthesized a new spinel oxide LiRh2O4 with a mixed-valent configuration of Rh3+ and Rh4+. At room temperature it is a paramagnetic metal, but on cooling, a metal-insulator transition occurs and a valence bond solid state is formed below 170 K. We argue that the formation of valence bond solid is promoted by a band Jahn-Teller transition at 230 K and the resultant confinement of t2g holes within the xy band. The band Jahn-Teller instability is also responsible for the observed enhanced thermoelectric power in the orbital disordered phase above 230 K.
We report on the epitaxial film growth and characterization of CoV$_2$O$_4$, a near-itinerant spinel vanadate, grown on (001) SrTiO$_3$. The symmetry lowering of the unit cell from cubic in the bulk to orthorhombic in the films results in dramatic differences in the magnetic anisotropy compared to bulk, as determined from structural and magnetic characterization. Bulk cubic CoV$_2$O$_4$ has been found to defy predictions by showing orbital degeneracy seemingly lasting to very low temperatures, with only small anomalies in magnetization and neutron experiments signaling a possible spin/orbital …
Motivated by recent experiments, we present a comprehensive theoretical study of the geometrically frustrated strongly correlated magnetic insulator Mn$_3$O$_4$ spinel oxide based on a microscopic Hamiltonian involving lattice, spin and orbital degrees of freedom. Possessing the physics of degenerate e$_g$ orbitals, this system shows a strong Jahn-Teller effect at high temperatures. Further, careful attention is paid to the special nature of the superexchange physics arising from the 90$^o$ Mn-O-Mn bonding angle. The Jahn-Teller and superexchange-based orbital-spin Hamiltonians are then analys…
Single crystals of electron-doped SrMnO3 with a cubic perovskite structure have been systematically investigated as the most canonical (orbital-degenerate) double-exchange system, whose ground states have been still theoretically controversial. With only 1-2% electron doping by Ce substitution for Sr, a G-type antiferromagnetic metal with a tiny spin canting in a cubic lattice shows up as the ground state, where the Jahn-Teller polarons with heavy mass are likely to form. Further electron doping above 4%, however, replaces this isotropic metal with an insulator with tetragonal lattice distorti…
We demonstrate that the onset of complex spin orders in ACr$_2$O$_4$ spinels with magnetic A$=$Co, Fe and Cu ions lowers the lattice symmetry. This is clearly indicated by the emergence of anisotropic lattice dynamics -- as evidenced by the pronounced phonon splittings -- even when experiments probing static distortions fail. We show that the crystal symmetry in the magnetic phase is reduced from tetragonal to orthorhombic for FeCr$_2$O$_4$ and CuCr$_2$O$_4$ with Jahn-Teller active A-site ions. The conical spin structure in FeCr$_2$O$_4$ is also manifested in the phonon frequencies. In contras…
Ultrasound velocity measurements of magnesium chromite spinel MgCr$_2$O$_4$ reveal elastic anomalies in the paramagnetic phase that are characterized as due to geometrical frustration. The temperature dependence of the tetragonal shear modulus $(C_{11}-C_{12})/2$ exhibits huge Curie-type softening, which should be the precursor to spin Jahn-Teller distortion in the antiferromagnetic phase. The trigonal shear modulus $C_{44}$ exhibits nonmonotonic temperature dependence with a characteristic minimum at $\sim$50 K, indicating a coupling of the lattice to dynamical molecular spin state. These res…
Dynamical properties of the lattice structure was studied by optical spectroscopy in ACr2O4 chromium spinel oxide magnetic semiconductors over a broad temperature region of T=10-335K. The systematic change of the A-site ions (A=Mn, Fe, Co, Ni and Cu) showed that the occupancy of 3d orbitals on the A-site, has strong impact on the lattice dynamics. For compounds with orbital degeneracy (FeCr2O4, NiCr2O4 and CuCr2O4), clear splitting of infrared-active phonon modes and/or activation of silent vibrational modes have been observed upon the Jahn-Teller transition and at the onset of the subsequent …
Vanadium spinels (ZnV_2O_4, MgV_2O_4, and CdV_2O_4) exhibit a sequence of structural and magnetic phase transitions, reflecting the interplay of lattice, orbital, and spin degrees of freedom. We offer a theoretical model taking into account the relativistic spin-orbit interaction, collective Jahn-Teller effect, and spin frustration. Below the structural transition, vanadium ions exhibit ferroorbital order and the magnet is best viewed as two sets of antiferromagnetic chains with a single-ion Ising anisotropy. Magnetic order, parametrized by two Ising variables, appears at a tetracritical point…
GeCu2O4 exhibits a tetragonal spinel structure due to the strong Jahn-Teller distortion associated with Cu2+ ions. We show that its magnetic structure can be described as slabs composed of a pair of layers with orthogonally oriented spin 1/2 Cu chains in the basal ab plane. The spins between the two layers within a slab are collinearly aligned while the spin directions of neighboring slabs are perpendicular to each other. Interestingly, we find that spins along each chain form an unusual up-up-down-down (UUDD) pattern, suggesting a non-negligible nearest-neighbor biquadratic exchange interacti…
We have theoretically studied successive transitions in vanadium spinel oxides with (t_2g)^2 electron configuration. These compounds show a structural transition at ~ 50K and an antiferromagnetic transition at ~ 40K. Since threefold t_2g orbitals of vanadium cations are occupied partially and vanadiums constitute a geometrically-frustrated pyrochlore lattice, the system provides a particular example to investigate the interplay among spin, orbital and lattice degrees of freedom on frustrated lattice. We examine the models with the Jahn-Teller coupling and/or the spin-orbital superexchange inte…
Ultrasound velocity measurements of cubic spinel GeCo$_2$O$_4$ in single crystal were performed for the investigation of shear and compression moduli. The shear moduli in the paramagnetic state reveal an absence of Jahn-Teller activity despite the presence of orbital degeneracy in the Co$^{2+}$ ions. Such a Jahn-Teller inactivity indicates that the intersite orbital-orbital interaction is much stronger than the Jahn-Teller coupling. The compression moduli in the paramagnetic state near the N$\acute{e}$el temperature $T_N$ reveal that the most relevant exchange path for the antiferromagnetic tr…
The ground-state properties of the spin-1 antiferromagnetic Heisenberg model on the corner-sharing tetrahedra, pyrochlore lattice, is investigated. By breaking up each spin into a pair of 1/2-spins, the problem is reduced to the equivalent one of the spin-1/2 tetrahedral network in analogy with the valence bond solid state in one dimension. The twofold degeneracy of the spin-singlets of a tetrahedron is lifted by a Jahn-Teller mechanism, leading to a cubic to tetragonal structural transition. It is proposed that the present mechanism is responsible for the phase transition observed in the spin…
We propose a scenario for the two phase transitions in $A$V$_2$O$_4$ ($A$=Zn, Mg, Cd), based on an effective spin-orbital model on the pyrochlore lattice. At high temperatures, spin correlations are strongly frustrated due to the lattice structure, and the transition at $\sim$50 [K] is an orbital order, supported by Jahn-Teller lattice distortion. This orbital order introduces spatial modulation of spin exchange couplings depending on the bond direction. This partially releases the frustration, and leads to a spin order at $\sim$40 [K]. We also study the stable spin configuration by taking acc…
The spinel FeV2O4 is known to exhibit peculiar physical properties, which is generally ascribed to the unusual presence of two cations showing a pronounced interplay between spin, orbital and lattice degrees of freedom (Fe2+ and V3+ on the tetrahedral and octahedral sites, respectively). The present work reports on an experimental re-investigation of this material based on a broad combination of techniques, including x-ray diffraction, energy dispersive and Mössbauer spectroscopies, as well as magnetization, heat capacity, dielectric and polarization measurements. Special attention was firstly…
We report the observation of an antipolar phase in cubic GaNb$_4$S$_8$ driven by an unconventional microscopic mechanism, the cooperative Jahn-Teller effect of Nb$_4$S$_4$ molecular clusters. The assignment of the antipolar nature is based on sudden changes in the crystal structure and a strong drop of the dielectric constant at $T_\mathrm{JT}=31$\,K, also indicating the first-order nature of the transition. In addition, we found that local symmetry lowering precedes long-range orbital ordering, implying the presence of a dynamic Jahn-Teller effect in the cubic phase above $T_\mathrm{JT}$. Bas…
Lacunar spinels with a chemical formula of $AM_4X_8$ form a populous family of narrow-gap semiconductors, which offer a fertile ground to explore correlation and quantum phenomena, including transition between Mott and spin-orbit insulator states, ferro/antiferroelectricity driven by cluster Jahn-Teller effect, and magnetoelectric response of magnetic skyrmions with polar dressing. The electronic and magnetic properties of lacunar spinels are determined to a large extent by their molecular-crystal-like structure. The interplay of electronic correlations with spin-orbit and vibronic couplings l…
We present our theoretical results on the mechanism of two transitions in vanadium spinel oxides $A$V$_2$O$_4$ ($A$=Zn, Mg, or Cd) in which magnetic V cations constitute a geometrically-frustrated pyrochlore structure. We have derived an effective spin-orbital-lattice coupled model in the strong correlation limit of the multiorbital Hubbard model, and applied Monte Carlo simulation to the model. The results reveal that the higher-temperature transition is a layered antiferro-type orbital ordering accompanied by tetragonal Jahn-Teller distortion, and the lower-temperature transition is an antif…
This review summarizes more than 100 years of research on spinel compounds, mainly focusing on the progress in understanding their magnetic, electronic, and polar properties during the last two decades. Many spinel compounds are magnetic insulators or semiconductors; however, a number of spinel-type metals exists including superconductors and some rare examples of d-derived heavy-fermion compounds. In the early days, they gained importance as ferrimagnetic or even ferromagnetic insulators with relatively high saturation magnetization and high ordering temperatures, with magnetite being the fir…
We review the mechanism of spin-lattice coupling in relieving the geometrical frustration of pyrochlore antiferromagnets, in particular spinel oxides. The tetrahedral unit, which is the building block of the pyrochlore lattice, undergoes a spin-driven Jahn-Teller instability when lattice degrees of freedom are coupled to the antiferromagnetism. By restricting our considerations to distortions which preserve the translational symmetries of the lattice, we present a general theory of the collective spin-Jahn-Teller effect in the pyrochlore lattice. One of the predicted lattice distortions breaks…
The lacunar spinel GeV4S8 undergoes orbital and ferroelectric ordering at the Jahn-Teller transition around 30 K and exhibits antiferromagnetic order below about 14 K. In addition to this orbitally driven ferroelectricity, lacunar spinels are an interesting material class, as the vanadium ions form V4 clusters representing stable molecular entities with a common electron distribution and a well-defined level scheme of molecular states resulting in a unique spin state per V4 molecule. Here we report detailed x-ray, magnetic susceptibility, electrical resistivity, heat capacity, thermal expansio…
Possible routes to superconductivity in the surface layers of V-doped Mg$_{1-δ}$Ti$_2$O$_4$ through multiple charge transfers and suppression of Jahn-Teller activity
We report on optical spectroscopy on the lacunar spinels GaV$_4$S$_8$ and GeV$_4$S$_8$ in the spectral range from 100 to 23000 cm$^{-1}$ and for temperatures from 5 to 300 K. These multiferroic spinel systems reveal Jahn-Teller driven ferroelectricity and complex magnetic order at low temperatures. We study the infrared-active phonon modes and the low-lying electronic excitations in the cubic high-temperature phase, as well as in the orbitally and in the magnetically ordered low-temperature phases. We compare the phonon modes in these two compounds, which undergo different symmetry-lowering Ja…
The canting angles and fluctuation of the magnetic ion spins of spinel oxide MnCr${}_2$O${}_4$ were studied by nuclear magnetic resonance (NMR) at low temperatures, which has a collinear ferrimagnetic order below $T_C$ and a ferrimagnetic spiral order below $T_s < T_C$. Contrary to previous reports, only one spin canting angle of Cr ions was observed. The spin canting angles of Mn and Cr ions in the ferrimagnetic spiral obtained at a liquid-He temperature were $43\,^{\circ}$ and $110\,^{\circ}$, respectively. The nuclear spin-spin relaxation was determined by the Suhl-Nakamura interaction at l…
Polar lacunar spinels, such as GaV$_4$S$_8$ and GaV$_4$Se$_8$, were proposed to host skyrmion phases under magnetic field. In this work, we put forward, as a candidate for Néel-type skyrmion lattice, the isostructural GaMo$_4$S$_8$, here systematically studied via both first-principles calculations and Monte Carlo simulations of model Hamiltonian. Electric polarization, driven by Jahn-Teller distortion, is predicted to arise in GaMo$_4$S$_8$, showing a comparable size but an opposite sign with respect to that evaluated in V-based counterparts and explained in terms of different electron counti…
Crystal structure, magnetic susceptibility, and specific heat were measured in the normal cubic spinel compounds MnSc_2S_4 and FeSc_2S_4. Down to the lowest temperatures, both compounds remain cubic and reveal strong magnetic frustration. Specifically the Fe compound is characterized by a Curie-Weiss temperature Θ_{CW}= -45 K and does not show any indications of order down to 50 mK. In addition, the Jahn-Teller ion Fe^{2+} is orbitally frustrated. Hence, FeSc_2S_4 belongs to the rare class of spin-orbital liquids. MnSc_2S_4 is a spin liquid for temperatures T > T_N \approx 2 K.
We present our theoretical and numerical results on thermodynamic properties and the microscopic mechanism of two successive transitions in vanadium spinel oxides $A$V$_2$O$_4$ ($A$=Zn, Mg, or Cd) obtained by Monte Carlo calculations of an effective spin-orbital-lattice model in the strong correlation limit. Geometrical frustration in the pyrochlore lattice structure of V cations suppresses development of spin and orbital correlations, however, we find that the model exhibits two transitions at low temperatures. First, a discontinuous transition occurs with an orbital ordering assisted by the …
We present the results of broadband dielectric spectroscopy of GaMo$_4$S$_8$, a lacunar spinel system that recently was shown to exhibit non-canonical, orbitally-driven ferroelectricity. Our study reveals complex relaxation dynamics of this multiferroic material, both above and below its Jahn-Teller transition at T$_{\textrm{JT}}=47$ K. Above T$_{\textrm{JT}}$, two types of coupled dipolar-orbital dynamics seem to compete: relaxations within cluster-like regions with short-range polar order like in relaxor ferroelectrics and critical fluctuations of only weakly interacting dipoles, the latter …
We use density-functional band-structure calculations to explore the origin of the up-up-down-down (UUDD) magnetic order in Cu$_2$GeO$_4$ with the frustrated $J_1-J_2$ spin chains coupled into layers within the spinel-like crystal structure. In contrast to earlier studies, we find that the nearest-neighbor coupling $J_1$ may be negligibly small, owing to a nearly perfect compensation of the ferromagnetic direct exchange and antiferromagnetic superexchange. Under this condition, weak symmetric anisotropy of the exchange couplings gives rise to the UUDD order observed experimentally and also elu…
Magnetic spinels (with chemical formula $AX_{2}$O$_{4}$, with $X$ a 3$d$ transition metal ion) that also have an orbital degeneracy are Jahn-Teller active and hence possess a coupling between spin and lattice degrees of freedom. At high temperatures, MgV$_{2}$O$_{4}$ is a cubic spinel based on V$^{3+}$ ions with a spin $S$=1 and a triply degenerate orbital ground state. A structural transition occurs at T$_{OO}$=63 K to an orbitally ordered phase with a tetragonal unit cell followed by an antiferromagnetic transition of T$_{N}$=42 K on cooling. We apply neutron spectroscopy in single crystals …
We report on structural, magnetic, electrical, and thermodynamic properties of Gd-doped LaMnO3 single crystals for Gd doping levels 0 <= x <= 1. At room temperature, for all doping levels the orthorhombic O' phase is indicative for a strong Jahn-Teller distortion. All compositions are insulating. The magnetism of La$_{1-x}$Gd$_x$MnO$_3$ is dominated by the relatively strong Mn-Mn exchange. The weakening of the antiferromagnetic interactions due to the significant decrease f the Mn-O-Mn bond angles leads to the continuous suppression of the magnetic phase-transition temperatures into the antife…
CuAl2O4 is a normal spinel oxide having quantum spin, S=1/2 for Cu2+. It is a rather unique feature that the Cu2+ ions of CuAl2O4 sit at a tetrahedral position, not like the usual octahedral position for many oxides. At low temperatures, it exhibits all the thermodynamic evidence of a quantum spin glass. For example, the polycrystalline CuAl2O4 shows a cusp centered at ~2 K in the low-field dc magnetization data and a clear frequency dependence in the ac magnetic susceptibility while it displays logarithmic relaxation behavior in a time dependence of the magnetization. At the same time, there …
Low-temperature heat-capacity investigations on the spinel FeCr2S4 with ferrimagnetic spin order and orbitally degenerated Jahn-Teller active Fe2+ ions in a tetrahedral crystal field, provide experimental evidence of an orbital liquid state above 10 K. We demonstrate that the low-temperature transition at 10 K arises from orbital order and is very sensitive to fine tuning of the stoichiometry in polycrystals. In single crystals the orbital order is fully suppressed resulting in an orbital glass state with the heat capacity following a strict T^2 dependence as temperature approaches zero.
Using density-functional theory calculations and experimental investigations on structural, magnetic and dielectric properties, we have elucidated a unique tetragonal ground state for MnTi2O4, a Ti^{3+} (3d^1)-ion containing spinel-oxide. With lowering of temperature around 164 K, cubic MnTi2O4 undergoes a structural transition into a polar P4_1 tetragonal structure and at further lower temperatures, around 45 K, the system undergoes a paramagnetic to ferrimagnetic transition. Magnetic superexchange interactions involving Mn and Ti spins and minimization of strain energy associated with co-ope…
In view of recent controversy regarding the orbital order in the frustrated spinel ZnV2O4, we analyze the orbital and magnetic groundstate of this system within an ab initio density functional theory approach. While LDA+U calculations in the presence of a cooperative Jahn-Teller distortion stabilize an A-type staggered orbital order, the consideration of relativistic spin-orbit effects unquenches the orbital moment and leads to a uniform orbital order with a net magnetic moment close to the experimental one. Our results show that ab initio calculations are able to resolve the existing discrepa…
The ferrimagnetic spinel $\mathrm{CoV_2O_4}$ has been a topic of intense recent interest, both as a frustrated insulator with unquenched orbital degeneracy and as a near-itinerant magnet which can be driven metallic with moderate applied pressure. Here, we report on our recent neutron diffraction and inelastic scattering measurements on powders with minimal cation site disorder. Our main new result is the identification of a weak ($\frac{Δa}{a} \sim 10^{-4}$), first order structural phase transition at $T^*$ = 90 K, the same temperature where spin canting was seen in recent single crystal meas…
We report on a systematic optical investigation of wüstite. In addition, the sample under consideration, Fe0.93O, has been characterized in detail by electrical transport, dielectric, magnetic and thermodynamic measurements. From infrared reflectivity experiments, phonon properties, Drude-like conductivity contributions and electronic transitions have been systematically investigated. The phonon modes reveal a clear splitting below the antiferromagnetic ordering temperature, similar to observations in other transition-metal monoxides and in spinel compounds which have been explained in terms o…
Cubic to tetragonal distortion in spinel compounds have been a contentious issue for last two decades. Different groups have proposed different mechanisms to understand such a distortion in these spinels, which are: (i) spin lattice coupling mechanism known as the spin driven Jahn-Teller (JT) effect, (ii) the strong relativistic spin-orbit coupling, a moderate JT distortion and weak V-V interactions and (iii) the JT effect. Now, in order to know the possible cause for such a distortion, we have avoided these complexities (various interactions among spin, electronic, orbital and lattice degrees…
Comprehensive neutron-powder diffraction and Rietveld analyses were carried out to clarify the relation between the crystal and magnetic structures of La2-2xSr1+2xMn2O7 (0.30 =< x =< 0.50). The Jahn-Teller (JT) distortion of Mn-O6 octahedra, i.e., the ratio of the averaged apical Mn-O bond length to the equatorial Mn-O bond length, is Delta_JT=1.042(5) at x=0.30, where the magnetic easy-axis at low temperature is parallel to the c axis. As the JT distortion becomes suppressed with increasing x, a planar ferromagnetic structure appears at x =< 0.32, which is followed by a canted antiferromagnet…
The lacunar spinel GaV4S8 exhibits orbital ordering at 44 K and shows a complex magnetic phase diagram below 12.7 K, which includes ferromagnetic and cycloidal spin order. At low but finite external magnetic fields, Néel-type skyrmions are formed in this material. Skyrmions are whirl-like spin vortices that have received great theoretical interest because of their non-trivial spin topology and that are also considered as basic entities for new data-storage technologies. Interestingly, we found that the orbitally ordered phase shows sizable ferroelectric polarization and that excess spin-driven…
