Quasi-two-dimensional heterostructures (K$M_{1-x}$Te)(LaTe$_{3}$) ($M$ = Mn, Zn) with charge density waves
Layered heterostructure materials with two different functional building blocks can teach us about emergent physical properties and phenomena arising from interactions between the layers. We report the intergrowth compounds KLa$M$$_{1-x}$Te$_{4}$ ($M$ = Mn, Zn; $x\approx$ 0.35) featuring two chemically distinct alternating layers [LaTe$_3$] and [K$M$$_{1-x}$Te]. Their crystal structures are incommensurate, determined by single X-ray diffraction for the Mn compound and transmission electron microscope (TEM) study for the Zn compound. KLaMn$_{1-x}$Te$_{4}$ crystallizes in the orthorhombic superspace group $Pmnm$(01/2$γ$)$s$00 with lattice parameters $a$ = 4.4815(3) Å, $b$ = 21.6649(16) Å and $c$ = 4.5220(3) Å. It exhibits charge density wave (CDW) order at room temperature with a modulation wave vector $\mathbf{q}$ = 1/2$\mathbf{b}$* + 0.3478$\mathbf{c}$* originating from electronic instability of Te-square nets in [LaTe$_{3}$] layers. The Mn analog exhibits a cluster spin glass behavior with spin freezing temperature $T_{\mathrm{f}}$ $\approx$ 5 K attributed to disordered Mn vacancies and competing magnetic interactions in the [Mn$_{1-x}$Te] layers. The Zn analog also has charge density wave order at room temperature with a similar $\mathbf{q}$-vector having the $\mathbf{c}$* component ~ 0.346 confirmed by selected-area electron diffraction (SAED). Electron transfer from [K$M_{1-x}$Te] to [LaTe$_{3}$] layers exists in KLa$M_{1-x}$Te$_{4}$, leading to an enhanced electronic specific heat coefficient. The resistivities of KLa$M_{1-x}$Te$_{4}$ ($M$ = Mn, Zn) exhibit metallic behavior at high temperatures and an upturn at low temperatures, suggesting partial localization of carriers in the [LaTe$_{3}$] layers with some degree of disorder associated with the $M$ atom vacancies in the [$M_{1-x}$Te] layers.