Who were the pioneers using the determinant for antisymmetrization of scalar functions?

Question

A math-history question: The function $F : \prod_{i = 1}^N \text{maps}(\mathbb{R^d}, \mathbb{R}) \to \text{maps}(\mathbb{(R^{d})}^N, \mathbb{R})$ given by $$ F(g_1,\cdots,g_N)(x_1,\cdots,x_N) = \left| \begin{matrix} g_1(x_1) & g_1(x_2) & \cdots & g_1(x_N) \\ g_2(x_1) & g_2(x_2) & \cdots & g_2(x_N) \\ \vdots & &\ddots & \vdots \\ g_N(x_1) & g_N(x_2) & \cdots & g_N(x_N) \\ \end{matrix} \right| $$ is sometimes used in formulas when the author is interested in the antisymmetrization of a collection of scalar functions. In physics it is often believed that JC Slater (1930) was the first to use a 'determinant-symbol' to denote the antisymmetrization of a collection of scalar functions. But I would not be surprised if a determinant-symbol was used for denoting the antisymmetrization of scalar functions before that time (e.g. Google said the determinant itself was introduced already in 1801 by Gauss). Do you know of the early uses of a determinant-symbol for this purpose? I will accept as an answer any really early references where the antisymmetrization of scalar functions were denoted by a determinant-symbol, as above.