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We consider the higher order Tur\'an inequality and higher order log-concavity for sequences $\{a_n\}_{n \ge 0}$ such that \[ \frac{a_{n-1}a_{n+1}}{a_n^2} = 1 + \sum_{i=1}^m \frac{r_i(\log n)}{n^{\alpha_i}} + o\left( \frac{1}{n^{\beta}} \right), \] where $m$ is a nonnegative integer, $\alpha_i$ are real numbers, $r_i(x)$ are rational functions of $x$ and \[ 0 < \alpha_1 < \alpha_2 < \cdots < \alpha_m < \beta. \] We will give a sufficient condition on the higher order Tur\'an inequality and the $r$-log-concavity for $n$ sufficiently large. Most $P$-recursive sequences fall in this frame. At last, we will give a method to find the exact $N$ such that for any $n>N$, the higher order Tur\'an inequality holds.

In this paper, we investigate the half-metallicity of Heusler alloys Fe2Co1-xCrxSi by first principles calculations and anisotropy magnetoresistance measurements. It is found that, with the increase of Cr content x, the Fermi level of Fe2Co1-xCrxSi moves from the top of valence band to the bottom of conduction band, and a large half-metallic band gap of 0.75 eV is obtained for x=0.75. We then successfully synthesized a series Heusler Fe2Co1-xCrxSi polycrystalline ribbon samples. The results of X-ray diffraction indicate that the Fe2Co1-xCrxSi series of samples are pure phase with a high degree of order and the saturation magnetic moment follows half-metallic Slater-Pauling rule. Except for the two end members, Fe2CoSi and Fe2CrSi, the anisotropic magnetoresistance of Fe2Co1-xCrxSi (x=0.25, 0.5, 0.75) show a negative value suggesting they are stable half-metallic ferromagnets., Comment: 15 pages, 5 figures, accepted by JMMM

Abundant phenomena in CoCr2-xMnxO4 (x = 0 ~ 2) samples such as magnetic compensation, magnetostriction and exchange bias effect have been observed and investigated in this work. A structure transition from cubic to tetragonal symmetry has been found in the samples with x around 1.4. It has shown that the doped Mn3+ ions initially occupy the A (Co) sites when x < 0.2, and then mainly take the B1 (Cr) sites. This behavior results in a role conversion of magnetic contributors, and thus a magnetic compensation between two competitively magnetic sublattices at the composition near x = 0.5. Furthermore, temperature compensation has also been found in the samples with x = 0.5 and 0.6, with the compensation temperature in the range of 45 ~ 75 K. The Mn-doping also changes the frustration degree and modulates the exchange interaction in this system, and thus prevents the formation of long range conical order of spins. Therefore, the magnetoelectric transition temperature at 23 K in CoCr2O4 is shifted to lower temperature with increased dopants. The magnetostriction effect in this Cobalt spinel system has been considered for the first time. The strain has a maximum value of about 240 ppm at x = 0.2 and shows the similar tendency as the compensation behaviors. Additionally, the exchange bias effect observed in the samples with x < 0.5 shows a negative value under low cooling field for x = 0.5., Comment: 15 pages, 10 figures, 1 table, submitted for publication

Using first-principles calculations, we investigate the band structures of a series of quaternary LiMgPdSn-type Heusler compounds. Our calculation results show that five compounds CoFeMnSi, CoFeCrAl, CoMnCrSi, CoFeVSi and FeMnCrSb possess unique electronic structures characterized by a half-metallic gap in one spin direction while a zero-width gap in the other spin direction showing spin gapless semiconducting behavior. We further analysis the electronic and magnetic properties of all quaternary Heusler alloys involved, and reveal a semi-empirical general rule (total valence electrons number being 26 or 28) for indentifying spin gapless semiconductors in Heusler compounds. The influences of lattice distortion and main-group element change have also been discussed., Comment: 20 pages, 5 figures, 1 supplementary file, submitted for publication

We have investigated the impact of covalent hybridization on martensitic structure and magnetic properties of Ni50Mn5+xGa35-xCu10 shape memory alloys. We found that the lattice distortion ((c-a)/a) of L10 martensite monotonously changes with the substitution of Mn for Ga atoms and shows a kink behavior at Ga(at.%)= 25 due to the weakened covalent effect between main-group and transition-metal atoms. Moreover, owing to the competition between covalence hybridization and magnetic ordering of introduced Mn atoms, the molecular magnetic moment and Curie temperature coincidently show maximums at Ga(at.%)=25 as well. These behaviors are closely associated with corresponding changes of the strength of covalent hybridization. The results therefore suggest that careful control of the concentration of main-group atoms in Heusler alloys can serve as an additional general tuning parameter for searching new multifunctional materials., Comment: 22 pages, 4 figures and 1 table, supplementary info, submitted for publication

The crystal structure and magnetoresponsive properties of Fe-doped MnCoGe alloys have been investigated using x-ray diffraction (XRD) and magnetic measurements. By alloying the Fe-containing isostructure compounds into MnCoGe, a magnetostructural transition from paramagnetic austenite to ferromagnetic martensite with large magnetization difference can be realized in a temperature window between the Curie temperatures of the austenite and martensite, resulting in magnetic-field-induced martensitic transformations and large magnetic-entropy changes. A structural and magnetic phase diagram of Fe-doped MnCoGe alloys has been proposed., Comment: 13 pages, 5 figures, submitted to JMMM

The structure, magnetism, magnetic compensation behavior, exchange interaction and electronic structures of Co50-xMn25Ga25+x and Co50-xMn25+xGa25 (x=0-25) alloys have been systematically investigated by both experiments and first-principles calculations. We found that all the samples exhibited body centered cubic structures with a high degree of atomic ordering. With increasing Ga content, the composition dependence of lattice parameters shows a kink point at the middle composition in Co50-xMn25Ga25+x alloys, which can be attributed to the enhanced covalent effect between the Ga and the transition metals. Furthermore, a complicated magnetic competition has been revealed in Co50-xMn25Ga25+x alloys, which causes the Curie temperature dramatically decrease and results in a magnetic moment compensation behavior. In Co50-xMn25+xGa25 alloys, however, with increasing Mn content, an additional ferrimagnetic configuration was established in the native ferromagnetic matrix, which causes the molecular moment monotonously decreases and the exchange interaction enhances gradually. The electronic structure calculations indicate that the Co50-xMn25+xGa25 alloys are likely to be in a coexistence state of the itinerant and localized magnetism. Our study will be helpful to understand the nature of magnetic ordering as well as to tune magnetic compensation and electronic properties of Heusler alloys., Comment: 41 pages, 9 figures, 3 tables, 1 supplementary file, submitted for publication

The structure and magnetic properties in doped Heusler alloys of Mn2CoGa and Mn2CoAl have been investigated by experiments and calculations. The main group elements of Ga and Al are substituted by the magnetic or non-magnetic transition metals, Co, Cu, V, and Ti in the alloy systems. Three kinds of local ferromagnetic structures, Co-Mn-Co, Mn-Co-Mn and Mn-Co-V, have been found. They embed in the native ferrimagnetic matrix and increase the magnetization with different increments. The Co-Mn-Co ferromagnetic structure shows the largest increment of 6.18{\mu}B /atom. In addition, interesting results for non-magnetic Cu increasing the magnetization and the V atom having a large ferromagnetic moment of about 1.0{\mu}B have been obtained. The exchange interaction energy can be increased by the newly added Co and depleted by supporting a ferromagnetic coupling in other substitution cases, and showing the variation of the TC. Our calculation of electronic structure verifies the strong d-d hybridization when the three ferromagnetic structures are achieved. It has also been found that the covalent effect from the Ga and Al determines the generation of the local ferromagnetic structure and the tolerance for dopant content., Comment: 18 pages, 8 figures, 1 table, submitted for publication

Tailoring the phase stability and magnetic structure by combining the antiferromagnetic MnNiGe martensite with ferromagnetic MnFeGe austenite, a magnetic-field-induced martensitic transformation has been achieved in MnNi1-xFexGe system. The doped Fe enables the isolated structural and magnetic transitions of MnNiGe to coincide at room temperature and also establishes ferromagnetic couplings in six-Mn-centering-one-Fe-atom clusters. The ferromagnetic clusters transit the antiferromagnetic state in martensite to a ferromagnetic state and the alloys are further induced to a stronger ferromagnetic state by external field, resulting in a large magnetization difference up to 50 emu/g across the transformation. The field-induced martensitic transformation thus experiences a multiple metamagnetization process., Comment: 15 pages, 5 figures and 1 table. Submitted for publication