Structural and magnetic properties of the single-layer manganese oxide ${\mathrm{La}}_{1-x}{\mathrm{Sr}}_{1+x}{\mathrm{MnO}}_4$

Using x-ray and neutron scattering, we have studied the structural and magnetic properties of the single-layer manganite ${\mathrm{La}}_{1-x}{\mathrm{Sr}}_{1+x}{\mathrm{MnO}}_4(0⩽x<0.7)$. Single crystals were grown by the floating-zone method at $18\mathrm{La}∕\mathrm{Sr}$ concentrations. The low-temperature phase diagram can be understood by considering the strong coupling of the magnetic and orbital degrees of freedom, and it can be divided into three distinct regions: low $(x<0.12)$, intermediate $(0.12⩽x<0.45)$, and high $(x⩾0.45)$ doping. ${\mathrm{LaSrMnO}}_4(x=0)$ is an antiferromagnetic Mott insulator, and its spin-wave spectrum is well described by linear spin-wave theory for the spin-2 square-lattice Heisenberg Hamiltonian with Ising anisotropy. Upon doping, as the $e_g$ electron concentration $(1-x)$ decreases, both the two-dimensional antiferromagnetic spin correlations in the paramagnetic phase and the low-temperature ordered moment decrease due to an increase of frustrating interactions, and Néel order disappears above $x_c=0.115\left(10\right)$. The magnetic frustration is closely related to changes in the $e_g$ orbital occupancies and the associated Jahn-Teller distortions. In the intermediate region, there exists neither long-range magnetic nor superstructural order. Short-range-correlated structural “nanopatches” begin to form above $x\sim 0.25$. At high doping $(x⩾0.45)$, the ground state of ${\mathrm{La}}_{1-x}{\mathrm{Sr}}_{1+x}{\mathrm{MnO}}_4$ exhibits long-range superstructural order and a complex antiferromagnetic order, which differs from that at low doping. The superstructural order is thought to arise from charge and orbital ordering on the Mn sites, and for $x=0.50$ we conclude that it is of $B2mm$ symmetry. For $x>0.50$, the superstructural order becomes incommensurate with the lattice, with a modulation wave vector $ϵ$ that depends linearly on the $e_g$ electron concentration: $ϵ=2(1-x)$. On the other hand, the magnetic order remains commensurate, but loses its long-range coherence upon doping beyond $x=0.50$.

Figure 1

${\mathrm{La}}_{1-x}{\mathrm{Sr}}_{1+x}{\mathrm{MnO}}_4$ magnetic Bragg scattering intensity as a function of temperature, measured at the reciprocal space positions ${(1,0,4)}_m$ for $x=0.00,{(1,0,0)}_m$ for $x=0.05$, and ${(1,0,3)}_m$ for $x=0.07$ and 0.10. The subscript $m$ indicates the unit cell of the magnetic structure shown in the inset. The intensity is normalized by the size of the crystals, and the low-temperature value for $x=0.00$ was set to 1. The lines are fits to the form $I\sim {(1-T∕T_N)}^{2\beta }$ assuming a Gaussian distribution in Néel temperatures due to sample inhomogeneity. The values of $T_N,\beta$, and the ordered moment are listed in Table .

Figure 2

Néel temperature and ordered moment (measured at $T=10\mathrm{K}$) as function of doping for ${\mathrm{La}}_{1-x}{\mathrm{Sr}}_{1+x}{\mathrm{MnO}}_4$. The values are normalized to those of the $x=0.00$ sample. The dashed line is a guide to the eye for the doping dependence of the Néel temperature, indicating our estimate of $x_c=0.115\left(10\right)$ for the disappearance of two-dimensional long-range order.

Figure 3

$L$ scans at $T=10\mathrm{K}$ through the ${(1,0,0)}_m$ magnetic Bragg peak for $x=0$ and 0.10, normalized at the peak position. For $x=0$, the peak is resolution limited, indicating three-dimensional long-range order, while it is broader than resolution for $x=0.10$. Away from the ${(1,0,0)}_m$ peak, the diffuse scattering is two orders of magnitude higher for the $x=0.10$ sample. The extra intensity is due to a rod of two-dimensional scattering. The data were taken on the spectrometer BT7 with 13.4 meV neutrons and collimations of ${35}^{\prime }\text{−}{40}^{\prime }$-sample-${25.8}^{\prime }$-open.

Figure 4

${\mathrm{LaSrMnO}}_4$ spin waves at 10 K. The lines are fits of the spin-wave dispersion curve (assuming a Lorentzian cross section) convoluted with the resolution function of the neutron spectrometer. The data were taken on the spectrometer BT2 with 14.7 meV final energy neutrons and collimations of ${60}^{\prime }\text{−}{40}^{\prime }$-sample-${40}^{\prime }\text{−}{80}^{\prime }$.

Figure 5

${\mathrm{LaSrMnO}}_4$ spin-wave dispersion at 10 K. The line is Eq. (2) with parameters $J_1=3.4\left(3\right)\mathrm{meV},\alpha =0.044\left(6\right)$, and $J_2∕J_1=0.11\left(3\right)$.

Figure 6

Examples of energy-integrating two-axis scans of the instantaneous magnetic structure factor in the disordered phase of ${\mathrm{LaSrMnO}}_4$. Scan (a) was taken at $T=131.5\mathrm{K}$, in the temperature range just above the Néel temperature $[T_N=128.4\left(5\right)\mathrm{K}]$ where the Ising anisotropy is important. The two dashed lines are the contributions from the parallel (narrower peak) and perpendicular (broader peak) components. Scan (b) was taken at $T=160\mathrm{K}$ where the system behaves as an isotropic two-dimensional Heisenberg antiferromagnet. The horizontal bars indicate the instrumental resolution. The data were taken on the spectrometer BT7 with 13.4 meV initial energy neutrons and collimations of ${35}^{\prime }\text{−}{40}^{\prime }$-sample-${25.8}^{\prime }$-open.

Figure 7

Antiferromagnetic correlation length, in units of the tetragonal lattice constant $a_t$, as function of temperature in ${\mathrm{La}}_{1-x}{\mathrm{Sr}}_{1+x}{\mathrm{MnO}}_4$. The line is the result of a Monte Carlo simulation of the spin-2 NN square-lattice Heisenberg antiferromagnet with an exchange coupling of $J=31.8\mathrm{K}$.

Figure 8

Room-temperature lattice parameters and unit-cell volume of ${\mathrm{La}}_{1-x}{\mathrm{Sr}}_{1+x}{\mathrm{MnO}}_4$ for the tetragonal unit cell, normalized to the $x=0$ values: $a_{t0}=3.796\left(4\right)\mathrm{\AA },c_{t0}=13.18\left(2\right)\mathrm{\AA }$, and $V_{t0}=189.9\left(7\right){\mathrm{\AA }}^3$. The unit-cell volume decreases linearly with doping. The in-plane lattice parameter $a_t$ expands slightly while the out-of-plane lattice parameter $c_t$ contracts significantly with doping.

Figure 9

Comparison of ${\mathrm{La}}_{0.50}{\mathrm{Sr}}_{1.50}{\mathrm{MnO}}_4$ powder diffraction scans at room temperature and at low temperature. The scans show (a) the ${(2,2,0)}_t$ peak and (b) the ${(2,0,0)}_t$ peak. In the former case, the peak splits at low temperature, indicating an orthorhombic distortion. In the latter case, the peak width stays constant, indicating the absence of a measurable monoclinic distortion. The subscripts $t$ and $o$ denote the use of the tetragonal and orthorhombic unit cells, respectively.

Figure 10

Orthorhombicity $\delta =\mid 1-b_o∕\left(2a_o\right)\mid$ as function of temperature for ${\mathrm{La}}_{0.50}{\mathrm{Sr}}_{1.50}{\mathrm{MnO}}_4$. The structural transition occurs at $T_{\mathit{COO}}=231.5\left(5\right)\mathrm{K}$, as determined from the temperature dependence of a superstructure peak (Fig. 14). The dashed curve is a guide to the eye. Inset: Structural unit cells ($a\text{−}b$ plane) for $x=\frac{1}{2}$. The tetragonal high-temperature (orthorhombic low-temperature) unit cell is shown by dashed (continuous) lines. At low temperature, there exist two twin domains that are rotated by 90° with respect to each other. Only the manganese sites are shown.

Figure 11

(Top) Intensity map of the Bragg reflections in the $L=0$ plane at 100 K for ${\mathrm{La}}_{0.50}{\mathrm{Sr}}_{1.50}{\mathrm{MnO}}_4$. The gray circles represent the high-symmetry Bragg peaks of the $I4∕mmm$ structure, and the black circles represent the additional superlattice Bragg peaks of the low-temperature phase. The radius of the circles is proportional to the logarithm of the intensities. The reciprocal lattice corresponds to the low-temperature orthorhombic cell with $a_o=5.46\mathrm{\AA },b_o=10.92\mathrm{\AA }$, and $c_o=12.4\mathrm{\AA }$. The line (quarter circle) represents the maximum reachable momentum at the x-ray energy of 14 keV used in our experiment. Several reflections, for example ${(2,1,0)}_o$, could not be reached due to geometric constraints. This map should be considered qualitative since absorption and extinction are considerable in this material for 14 keV x rays. (Bottom) Two specific scans are shown, corresponding to the two regions labeled (a) and (b) on the map.

Figure 12

Low-temperature distortion of the Mn-O plane with space-group symmetry $Bbmm$. There are two manganese sites and two basal oxygen sites in this space group. The Mn1 (Mn2) sites are occupied by “${\mathrm{Mn}}^{3+}$” (“${\mathrm{Mn}}^{4+}$”) ions. The panel on the right shows the distortion around each type of Mn site. The actual $B2mm$ symmetry of ${\mathrm{La}}_{0.5}{\mathrm{Sr}}_{1.5}{\mathrm{MnO}}_4$ is lower than that indicated here, with three rather than two inequivalent manganese sites, as discussed in the text.

Figure 13

Representative $H_o,K_o$, and $L$ scans of the ${(9,0,0)}_o$ superlattice peak of ${\mathrm{La}}_{0.5}{\mathrm{Sr}}_{1.5}{\mathrm{MnO}}_4$. The upper (lower) panels show scans below (above) the Néel temperature.

Figure 14

Linear plot of the ${(4,9,0)}_o$ Bragg peak intensity in the ordered phase for $x=0.50$ as function of the temperature. The transition temperature is found to be 231.5(5) K. Inset: Integrated intensity of the ${(4,9,0)}_o$ superlattice reflection for two different levels of x-ray flux on the sample. The high flux level is $\sim 300$ times larger than the low flux. A partial melting of the ordered phase can be observed at low temperature for the data collected with the higher flux (black triangles).

Figure 15

Logarithmic plot of the correlation length of the charge/orbital order as a function of temperature for $x=0.50$. Short-range distortions associated with the low-temperature phase are still present at room temperature. The correlation length is nearly constant far above the transition temperature $[T_{\mathit{COO}}=231.5\left(5\right)\mathrm{K}]$.

Figure 16

X-ray diffraction scans of ${\mathrm{La}}_{1-x}{\mathrm{Sr}}_{1+x}{\mathrm{MnO}}_4$ in the low-temperature phase $(T=7\mathrm{K})$ along ${(4,K,0)}_o$ for (a) $x=0.475$ and (b) $x=0.65$. The vertical dashed lines indicate the commensurate positions. 1, 2, and 3 label, respectively, the first, second, and third harmonics of the low-temperature distortion. Note the logarithmic intensity scale.

Figure 17

Parameter $ϵ$ of the low-temperature modulation wave vector ${(0,ϵ,0)}_o$ as function of doping $x$ for ${\mathrm{La}}_{1-x}{\mathrm{Sr}}_{1+x}{\mathrm{MnO}}_4$, determined by synchrotron x-ray diffraction. For $x⩾0.5$, the value of $ϵ$ is directly related to the $e_g$ electron density $n_e=(1-x):ϵ=2n_e$.

Figure 18

$K_o$ scans through the ${(4,8+ϵ,0)}_o$ reflection for two samples with the same $\mathrm{La}∕\mathrm{Sr}$ content $(x=0.60)$, but different oxygen stoichiometry. The first sample is as-grown while the second sample was annealed in argon $(P_{O_2}={10}^{-5}\mathrm{bar})$ at 950 °C for 24 h.

Figure 19

Neutron diffraction scans along ${(1,0,L)}_o$ for $x=0.475$ and $x=0.50$. The measurements were taken at 13 K and 7 K, respectively, on the spectrometer BT7 with 13.4 meV neutrons and collimations of ${35}^{\prime }\text{−}{40}^{\prime }$-sample-${25.8}^{\prime }$-open.

Figure 20

Magnetic order parameter curves of the antiferromagnetic phase for samples with doping $x=0.475$ and $x=0.50$, as described in the text.

Figure 21

Energy-integrating scans of the magnetic fluctuations in the disordered phase for $x=0.475$ (two-axis neutron scattering mode) in the paramagnetic phase. The lines are fits to a two-dimensional isotropic Lorentzian cross section convoluted with the instrument resolution. The data were taken on the spectrometer BT7 with 13.4 meV initial energy neutrons and collimations of ${35}^{\prime }\text{−}{40}^{\prime }$-sample-${25.8}^{\prime }$-open.

Figure 22

Instantaneous antiferromagnetic correlation length as function of temperature for $x=0$ and $x=0.475$. The downward arrows indicate the onset of long-range magnetic order.

Figure 23

Triple-axis scans of the short-range magnetic correlations in a $x=0.60$ sample at low temperature $(T=9\mathrm{K})$. The dashed line in the left panel represents the instrument resolution. The magnetic correlations are short-range and essentially two-dimensional. The correlation length, as estimated from these triple-axis scans, is about 3.5 Å along ${\left[001\right]}_o$ and 29(1) Å along ${\left[100\right]}_o$. The data were taken on the spectrometer BT7 with 13.4 meV neutrons and collimations of ${35}^{\prime }\text{−}{40}^{\prime }$-sample-${25.8}^{\prime }$-open.

Figure 24

Temperature dependence of the antiferromagnetic short-range peak intensity in samples with doping $x=0.60$ and 0.65.

Figure 25

Scans along ${(H,8-H,0)}_t$ for $x=0.40,x=0.33$, and $x=0.25$ revealing diffuse peaks indicative of short-range order. At lower doping $(x=0.15)$, however, no peak is observable. Small secondary-phase peaks were found at $H=4.07$ ($x=0.15$ and $x=0.25$) and at $H=4.12(x=0.40)$, but are not included in the figure.

Figure 26

(a) Integrated intensity and (b) correlation length along ${\left[100\right]}_o$ of the structural short-range order peaks as function of temperature for two samples with intermediate doping: $x=0.33$ and $x=0.40$.

Figure 27

Logarithmic contour plot of the scattering intensity around the ${(4,4,0)}_t$ peak in a $x=0.33$ sample. The diffuse scattering is composed of thermal diffuse scattering (TDS) and Huang-like scattering due to Jahn-Teller distortions.

Figure 28

(a) Linear plot of the diffuse scattering intensity around the ${(4,4,0)}_t$ peak as function of the temperature (for $x=0.33$). The straight line is an estimate of the thermal diffuse scattering. (b) The Jahn-Teller component of the diffuse scattering near ${(4,4,0)}_t$ scales linearly with the intensity of the broad peak at position ${(4.26,3.74,0)}_t$ shown in Fig. 26a.

Figure 29

Magnetic and structural phase diagram of ${\mathrm{La}}_{1-x}{\mathrm{Sr}}_{1+x}{\mathrm{MnO}}_4$. The data come from x-ray structural scattering (●), neutron scattering [◆ (this work) and ◇ (Ref. 37)], magnetometry (◻, Ref. 4) and muon spin rotation (▷, Ref. 36) measurements. The abbreviations are $G$-AF, $G$-type antiferromagnet; CE-AF, CE-type antiferromagnet; SG, spin glass; COO, charge/orbital order phase; SRO, short-range charge and orbital order. The dotted vertical line at $x=0.25$ indicates the extent to which SRO is visible. The dashed line at $x=0.70$ indicates the approximate solubility limit of ${\mathrm{La}}_{1-x}{\mathrm{Sr}}_{1+x}{\mathrm{MnO}}_4$.